interfacial photochemistry of retinal proteins - wayne state

Interfacial photochemistry of retinal proteinsp

Felix T. Hong

Department of Physiology, Wayne State University School of Medicine, Detroit, MI 48201, USA

Abstract

Retinal proteins are membrane-bound protein pigments that contain vitamin A aldehyde(retinal) as the chromophore. They include the visual pigment rhodopsin and fouradditional ones in the plasma membrane of Halobacterium salinarium (formerly

Halobacterium halobium ). These proteins maintain a ®xed and asymmetric orientation inthe membranes, and respond to a light stimulus by generating vectorial charge movement,which can be detected as an electric potential across the membrane or an electric currentthrough the membrane. These phenomena are collectively called the photoelectric e�ects,

which defy a rigorous quantitative treatment by means of either conventional (solutionphase) photochemistry or conventional electrophysiology. As an alternative to themainstream approach, we utilize the analytic tools of electrochemical surface science and

electrophysiology to analyze two molecular models of light-induced charge separation andrecombination. Being tutorial in nature, this article demands no prior knowledge about thesubject. A parsimonious equivalent circuit model is developed. Data obtained from

reconstituted bacteriorhodopsin membranes are used to validate the theoretical model andthe analytical approach. Data generated and used by critics to refute our approach isshown to actually support it. The present analysis is su�ciently general to be applicable toother pigment-containing membranes, such as the visual photoreceptor membrane and the

chlorophyll-based photosynthetic membranes. It provides a coherent description of a widerange of light-induced phenomena associated with various pigment-containing membranes.In contrast, the mainstream approach has been plagued with self-contradictions and

paradoxes. Last, but not least, the alternative bioelectrochemical approach also exhibits apredictive power that has hitherto been generally lacking. Comparison of the photoelectrice�ects is made with regard to bacteriorhodopsin, rhodopsin, and the chlorophyll-based

photosynthetic apparatus Ð in the spirit of reverse engineering (biomimetic science). Thetechnological applications of bacteriorhodopsin as an advanced material for the

0079-6816/99/$ - see front matter # 1999 Published by Elsevier Science Ltd. All rights reserved.

PII: S0079 -6816 (99)00014 -3

Progress in Surface Science 62 (1999) 1±237

www.elsevier.com/locate/progsurf

pDedicated to the memory of the late Professor Alexander Mauro of The Rockefeller University.

E-mail address: [email protected] (F.T. Hong)

construction of molecular devices and the implication of the photoelectric behavior ofbacteriorhodopsin for solar energy conversion are also discussed. # 1999 Published by

Elsevier Science Ltd. All rights reserved.

Nomenclature

ADP/ATP adenosine 5 '-diphosphate/adenosine 5 '-triphosphateBChl/BPh bacteriochlorophyll/bacteriopheophytinBLM/sBLM bilayer (black) lipid membrane/supported bilayer lipid

membranebR/hR/sR bacteriorhodopsin/halorhodopsin/sensory rhodopsinCCCP carbonyl cyanide-m-chlorophenylhydrazoneCID charge-injection devicesDIDS 4-acetamido-4 '-isothiocyano-2,2 '-stilbenesulfonateEDTA ethylenediamine-N,N,N ',N '-tetraacetic acidEGTA ethylene glycol-bis(b-aminoethyl ether)-N,N,N ',N '-

tetraacetic acidERP early receptor potentialFCCP carbonyl cyanide-p-tri¯uoromethoxyphenylhydrazoneFET ®eld e�ect transistorGDP/GTP guanosine 5 '-diphosphate/guanosine 5 '-triphosphatec-GMP guanosine 3 ',5 '-cyclic monophosphateIPT interfacial proton transferISFET ion-sensitive ®eld e�ect transistorITO indium tin oxideLB Langmuir±BlodgettLED light-emitting diodeLRP late receptor potentialML multi-layeredNAD+/NADH nicotinamide adenine dinucleotide (oxidized form/

reduced form)NADP+/NADPH nicotinamide adenine dinucleotide phosphate (oxidized

form/reduced form)OD oriented dipolePDE phosphodiesteraseSITS 4,4 '-diisocyano-2,2 '-stilbenesulfonateTEMED N,N,N ',N '-tetramethylethylenediamineTM Trissl±MontalTPBÿ tetraphenyl borateTPP+ tetraphenyl phosphonium

F.T. Hong / Progress in Surface Science 62 (1999) 1±2372

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. Morphology of retinal protein-containing membranes . . . . . . . . . . . . . . . . . . . . . 92.1. Purple membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2. Visual photoreceptor membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3. Structures of retinal proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4. Photochemical reactions of retinal proteins . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.1. Rhodopsin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2. Bacteriorhodopsin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5. Photoelectric e�ects in pigment-containing membranes . . . . . . . . . . . . . . . . . . . . 185.1. Light-induced rapid charge displacement . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2. De®nition of photoelectric e�ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205.3. Fast photoelectric signal in reconstituted bR membranes . . . . . . . . . . . . . 215.4. pH dependence of early receptor potential: apparent paradox? . . . . . . . . . 23

5.5. Mainstream approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.6. Necessity for alternative approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6. Methods of membrane reconstitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6.1. Black lipid membranes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326.2. Phospholipid vesicles (liposomes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356.3. Nucleopore-supported ®lms or Collodion ®lms . . . . . . . . . . . . . . . . . . . . 35

6.4. Immobilized gel technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366.5. Langmuir±Blodgett technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366.6. Takagi±Montal method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

6.7. Trissl±Montal method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386.8. Multi-layered thin ®lm method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

7. Electrical measurements of AC photoelectric signals. . . . . . . . . . . . . . . . . . . . . . 407.1. Open-circuit measurement (current clamp method). . . . . . . . . . . . . . . . . . 407.2. Short-circuit measurement (voltage clamp method) . . . . . . . . . . . . . . . . . 417.3. Tunable voltage clamp method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

8. Mechanisms of AC photoelectric e�ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438.1. Gouy±Chapman analysis of interfacial proton transfer mechanism . . . . . . 43

8.1.1. Electrostatic calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478.1.2. Kinetic calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

8.2. Gouy±Chapman analysis of oriented dipole mechanism . . . . . . . . . . . . . . 53

8.3. Concept of chemical capacitance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558.4. More re®ned molecular models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

9. Equivalent circuit analysis of AC photoelectric signals . . . . . . . . . . . . . . . . . . . . 56

9.1. Strictly short-circuit measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579.2. Measurements under conditions in between short-circuit and open-circuit . 619.3. Open-circuit measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

9.4. Optimizing measurement by tuning access impedance . . . . . . . . . . . . . . . . 66

F.T. Hong / Progress in Surface Science 62 (1999) 1±237 3

10. Analysis of AC photoelectric signal from bacteriorhodopsin . . . . . . . . . . . . . . . . 6610.1. Search for method to separate B1 and B2 . . . . . . . . . . . . . . . . . . . . . . . . 66

10.2. Method for isolating pure B1 signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6710.3. E�ect of varying access impedance and thickness of Te¯on thin ®lm . . . . . 6910.4. Temperature e�ect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

10.5. E�ect of varying aqueous pH and proton±deuterium exchange . . . . . . . . . 7510.6. E�ect of chemical modi®cation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7810.7. E�ect of point mutation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

10.8. Chloride ion e�ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8210.9. Divalent cation e�ect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8610.10. Assignment of molecular mechanisms to B1 and B2 components. . . . . . . . 89

10.11. Q-tip experiment: rationale behind ML method . . . . . . . . . . . . . . . . . . . . 9210.12. Method for isolating B2 component . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9610.13. Evidence of hypothetical B2 ' component . . . . . . . . . . . . . . . . . . . . . . . . . 101

10.13.1. Coupled interfacial proton-transfer reactions . . . . . . . . . . . . . . . . 102

10.13.2. Concept of local reaction conditions . . . . . . . . . . . . . . . . . . . . . . 10410.13.3. `Di�erential' experiment: evidence for existence of B2 ' . . . . . . . . . 10410.13.4. Interpretation of pH dependence of B2 and B2 '. . . . . . . . . . . . . . 106

11. Why is chemical capacitance physically distinct from membrane capacitance?. . . . 10811.1. Experimental evidence in support of existence of series capacitance . . . . . . 110

11.2. Relationship between photovoltage and photocurrent. . . . . . . . . . . . . . . . 11411.2.1. Condition 1 (open-circuit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11511.2.2. Condition 2 (short-circuit) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

11.2.3. Interpretation of Trissl's ®rst-derivative relationship. . . . . . . . . . . 11611.3. Additional evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11711.4. Reconciling data reported by other laboratories . . . . . . . . . . . . . . . . . . . . 120

12. Analysis of DC photoelectric signal from bacteriorhodopsin . . . . . . . . . . . . . . . . 12112.1. Equivalent circuit for DC photoelectric e�ect . . . . . . . . . . . . . . . . . . . . . 12312.2. Null current method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

12.3. Null-current analysis of DC photoelectric data . . . . . . . . . . . . . . . . . . . . 12912.4. Interpretation of DC photoelectric data . . . . . . . . . . . . . . . . . . . . . . . . . 133

12.4.1. Step-function photoswitching of proton-translocating channel. . . . 133

12.4.2. Interpretation of voltage dependence of photocurrent. . . . . . . . . . 13412.4.3. Interpretation of spike-like waveform of photocurrent . . . . . . . . . 135

12.5. I±V analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13612.6. E�ect of ionophores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

12.7. Evaluation of membrane reconstitution methods . . . . . . . . . . . . . . . . . . . 14012.7.1. Orientation of bR molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . 14412.7.2. Is bR completely incorporated in a reconstituted membrane? . . . . 144

12.8. Mechanism of ionophore action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

13. AC photoelectric signal from other pigments . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

13.1. Early receptor potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15213.1.1. Direct measurement of ERP in reconstituted membranes . . . . . . . 15213.1.2. Direct assay of protonation and deprotonation . . . . . . . . . . . . . . 154

13.2. AC photoelectric signal from halorhodopsin . . . . . . . . . . . . . . . . . . . . . . 15613.3. AC photoelectric signals from photosynthetic reaction centers. . . . . . . . . . 157


14. Comparison of bacteriorhodopsin and photosynthetic reaction centers. . . . . . . . . 15914.1. Photosynthetic reaction center of Rhodopseudomonas viridis . . . . . . . . . . . 161

14.2. Structurally di�erent systems with similar functional design . . . . . . . . . . . 162

15. Comparison of bacteriorhodopsin and rhodopsin. . . . . . . . . . . . . . . . . . . . . . . . 166

15.1. Molecular processes of visual transduction . . . . . . . . . . . . . . . . . . . . . . . 16615.2. Why is ERP not necessarily an epiphenomenon? . . . . . . . . . . . . . . . . . . . 16815.3. E�ect of surface potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

15.4. Trigger mechanism of visual transduction . . . . . . . . . . . . . . . . . . . . . . . . 17215.5. Visual photoreceptor membrane as ®eld-e�ect transistor. . . . . . . . . . . . . . 172

16. Comparison of bacteriorhodopsin and halorhodopsin. . . . . . . . . . . . . . . . . . . . . 175

17. Correlation between electrical and optical responses . . . . . . . . . . . . . . . . . . . . . . 179

18. Retinal protein research and arti®cial solar-energy conversion. . . . . . . . . . . . . . . 184

19. Retinal protein research and molecular electronics . . . . . . . . . . . . . . . . . . . . . . . 187

19.1. Bacteriorhodopsin as advanced material . . . . . . . . . . . . . . . . . . . . . . . . . 18819.2. Concept of intelligent materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18819.3. Molecular devices based on photoelectric e�ect of bR . . . . . . . . . . . . . . . 191

19.4. Reverse engineering and biomimetic science. . . . . . . . . . . . . . . . . . . . . . . 195

20. Philosophical digression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

20.1. Experimental data, mathematical models and physical models. . . . . . . . . . 19820.2. Critique on concept of chemical capacitance . . . . . . . . . . . . . . . . . . . . . . 20120.3. Tentative nature of physical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20420.4. Ockham's razor and Bayesian analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 205

20.5. Postdiction, prediction and parsimony . . . . . . . . . . . . . . . . . . . . . . . . . . 207

21. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

Appendix A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

1. Introduction

Retinal proteins are protein pigments, which contain retinal (vitamin Aaldehyde) as the chromophore, and are invariably bound to biological membranes.The ®rst known retinal protein was the visual pigment rhodopsin, which exists inthe rod photoreceptor membranes of the vertebrate eyes. Invertebrates also utilizeretinal proteins as the visual pigment. However, retinal proteins are not unique tothe animal kingdom. In the 1970s, Oesterhelt and Stoeckenius [1] discovered anew retinal protein in Halobacterium salinarium (formerly Halobacterium


halobium ), which was named bacteriorhodopsin. Subsequently, three additionalretinal proteins were found in the same organism. Since then, many investigatorshave become more attracted to these retinal proteins of bacterial origin than torhodopsin.

Halobacterium salinarium is an archibacterium whose natural habit is a salt ¯at[1±4]. Its plasma membrane consists of a mosaic of purple and red membranepatches. Residing in these membrane patches are four structurally related retinalproteins. Bacteriorhodopsin, the most abundant of the four, is the only proteincomponent in the purple membrane and is a light-driven proton pump [5]. Theremaining three retinal proteins, halorhodopsin [6], sensory rhodopsin I (or simply,sensory rhodopsin) and sensory rhodopsin II (or phoborhodopsin) [7], are found inthe red membrane. The red membrane also contains the electron transport chaincomponents, and the F0±F1 complex of ATP synthetase/ATPase. Halorhodopsin(hR) is a light-driven chloride ion pump, whereas sensory rhodopsin I and II aresensory pigments, which serve phototaxis functions.

Bacteriorhodopsin (bR) and rhodopsin share many structural and chemicalsimilarities. However, bR is functionally analogous to photosynthetic reactioncenters of green plants, cyanobacteria and purple phototrophic bacteria. Both bRand reaction centers convert absorbed light energy to a transmembrane protongradient. The energy so stored is then utilized to power the ATP synthetase, whichconverts ADP and inorganic phosphate into ATP [8], in accordance withchemiosmotic theory [9±11]. Bacteriorhodopsin is essentially a stripped-downversion of photosynthetic apparatus; protons are pumped by a single moleculeinstead of a chlorophyll-protein supramolecular complex. In brief, Halobacteriautilize a `visual' pigment to perform photosynthesis.

The most intriguing similarity between bR and rhodopsin is the appearance of aspecial kind of electric signal when the membrane, to which the retinal protein isbound, is stimulated by a brief light pulse. Unlike many bioelectric signalscommonly encountered in neural phenomena, this type of electric signal ischaracterized by an ultrafast risetime. It is not generated by ionic di�usion but,instead, by light-induced rapid charge displacements. These electric signals aresimilar to the gating current in the squid axon and are known as fastphotovoltages, fast photopotentials, or displacement photocurrents. Thephenomena are collectively known as the fast photoelectric e�ect. A well-knownexample is the early receptor potential (ERP), which was ®rst discovered in theretina of Cymolgus monkey by Brown and Murakami [12,13] more than threedecades ago. Subsequently, similar signals were discovered in chloroplasts, in thepigmented epithelia of the eyes, as well as in reconstituted bR membranes. As weshall demonstrate, these photosignals are manifestations of interfacialphotochemistry of membrane-bound pigment proteins. Additional insight into thefunction of retinal proteins can be gained by analysis and comparison ofdisplacement photocurrents from various retinal proteins.

The fast photoelectric e�ect was a controversial subject, even before thediscovery of the ERP-like photosignal in reconstituted bR membranes.Investigators are divided in their opinions, though not equally, with regard to how


to measure a fast photoelectric signal and how to interpret the measured data.The conventional approach routinely decomposes the measured transientphotoelectric signal into as many exponential components as possible, andinterprets the resulting time constants as the photochemical relaxation timeconstants directly. As will be shown in the present review, this popular approachis problematic and, for lack of better terminology, will be referred to as themainstream approach in this article. The alternative approach, to be described andexplained here, will be referred to as the bioelectrochemical approach, for brevity.

In the bioelectrochemical approach, the starting point is two simple molecularmodels of light-induced vectorial charge separation and recombination. Equivalentcircuits are derived from these models by applying: (a) the Gouy±Chapman di�usedouble layer theory, and (b) standard chemical kinetic analysis (Section 8). Thesetwo equivalent circuits will be referred to as microscopic models. An additionalequivalent circuit, which was originally constructed to describe the experimentallymeasured data, will be referred to as the macroscopic model. It will be shown thatboth microscopic models can be reduced to this same macroscopic model. Anelectrochemical concept of chemical capacitance, unique to pigment-containingmembranes, is developed. On the basis of correspondence of the macroscopic andthe microscopic models, it will be shown that chemical capacitance has its originin the interfacial processes during light-induced vectorial charge separation andrecombination.

An electrical measurement method called tunable voltage clamp is used tomeasure and analyze fast photoelectric signals in the conceptual framework ofchemical capacitance (Section 7). It will be shown that the experimentallymeasured time constants in a fast photoelectric signal are not the intrinsicphotoelectric relaxation time constants, under most measurement conditions inpractice. Deconvolution by means of equivalent circuit analysis is required toextract the intrinsic photoelectric relaxation time constants (Section 9).Experimental tests of the validity of the equivalent circuit analysis are primarilybased on reconstituted bR membranes (Section 10). Both data generated in ourown laboratory and data reported by other laboratories will be used to validatethe bioelectrochemical approach. Curiously, data used by others to validate themainstream approach can also be used to debunk the mainstream approach(Section 11). The main ¯aw of the mainstream approach is its contradiction of abasic tenet of the fast photoelectric e�ect: a fast photoelectric signal is acapacitative electric signal. Thus, the mainstream approach is not a viablealternative to the bioelectrochemical one. In this article, insight into why the ¯awof the mainstream approach has so far escaped detection by many of itspractitioners will be provided.

In addition to the fast photoelectric response, the steady-state photoelectricresponse of a reconstituted bR membrane to continuous light illumination isanalyzed by a null current method (Section 12), and the result is compared withthat from the conventional I±V curve analysis. The analysis of the steady-stateand the fast photoresponses requires di�erent methodologies. For reasons madeclear in the analysis presented in Sections 8 and 9, the fast and steady-state


photosignals correspond to AC and DC electric signals, respectively. These termswill be de®ned rigorously in Section 5.2.

Fast photoelectric signals from other photobiological membranes will also beexamined (Section 13). Comparisons will be made between rhodopsin andbacteriorhodopsin, in light of the new understanding of ERP and its analogoussignal in reconstituted bR membranes (Section 15). The conventional wisdom hasconcluded that ERP plays no role in visual transduction. We shall argue that thisconclusion may be premature, and that ERP may be the mechanistic trigger forthe initiation of the visual transduction process.

We shall also compare bR and the photosynthetic reaction center ofRhodopseudomonas viridis, and examine Nature's strategy for designing an e�cientsolar-energy converter (Section 14). Additional evidence will be provided toindicate that bR does not operate like a photodiode but, by virtue of a di�erentmechanism, it functions just as e�cient as a photodiode (Section 18). Thequestion as to whether Nature utilized a common design for a visualphotoreceptor and a photosynthetic apparatus will be considered. Nature's designprinciples may be extracted by reverse engineering. The possible applications ofthese design principles in molecular electronics will also be discussed (biomimeticscience). Prototype examples in which bR is used as an advanced functionalmaterial for device construction will also be given (Section 19). In addition, acomparison is made with two closely related ion pumps, bR and hR (Section 16).

Light-induced transient absorbance changes (optical responses) are key dataused in deciphering mechanisms of bR and hR functions. The conformations ofthese ion pumps are sensitive to local electric ®elds, which are generated byphotoelectric responses under open-circuit conditions. The resulting conformationchanges may a�ect kinetics of both electrical and optical responses. A comparisonof optical and electrical responses suggests such a feedback e�ect, which maycontribute to the kinetic complexities encountered in optical measurements(Section 17).

Most likely, readers familiar with the literature of the fast photoelectricphenomena will have noticed that our present (bioelectrochemical) approachconstitutes a major departure from the mainstream one. Presently, bothapproaches coexist in the bR literature. However, the two approaches are notmerely two equivalent ways of analyzing the fast photoelectric e�ect; they areutterly incompatible with each other. A philosophical digression on mathematical(numerical) and physical (molecular) modeling is intended to clarify someconceptual issues (Section 20). While this review presents evidence and argumentsto indicate why the mainstream approach is ¯awed, the readers are advised toconsult several existing treatises for the contrasting view [14±28].

The topic of photoelectric e�ects, in general, has been reviewed in the broadcontext of biomembranes and with a pertinent historical perspective by Tien [29].Review articles of similar nature, written by the present author, but ofconsiderably shorter length, are available [30±45].

The retinal proteins have been a fertile proving ground for many scienti®capproaches, both experimental and theoretical. For example, investigations of the


bathochromic shift of the absorption spectrum of the chromophore, in terms ofinteraction between the chromophore and the apo-protein portion of bR(bacterio-opsin), stimulated the development of theoretical tools for predicting andinterpreting the absorption spectra of retinal proteins [46±49]. Other examples areresonance Raman and femtosecond spectroscopies [50]. The advances made inthese techniques were, at least in part, motivated by bR research. E�orts infunctional reconstitution of bR also stimulated the development of a number ofmembrane reconstitution techniques (Section 6). As a testimonial from the presentarticle, novel features of the fast photoelectric signals motivated us to develop amethodology that combines electrophysiology and electrochemical surface science(i.e., the bioelectrochemical approach ). We shall also demonstrate that thismethodology is generally applicable to pigment-containing membranes andorganic thin ®lms.

Our aim is to present a comprehensive, self-contained and somewhatpedagogical exposition. Pertinent concepts and analysis are developed in a step-by-step logical fashion. No prior knowledge of the author's work is required. Adual presentation will be adopted with regard to the analysis of the equivalentcircuit model. First, derivation of mathematical models will be presented insu�cient detail, so that veri®cation by interested readers is feasible withoutconsulting previously published work. Second, additional verbal and intuitivereasoning will also be provided, so that readers may gain su�cient insight toenable independent judgment on the validity of the model, without attending todetailed mathematical analysis. No attempts will be made for exhaustiveness withregard to the cited literature. Background information will be presented only inabbreviated forms and only in su�cient detail for the comprehension of theinterfacial electrical phenomena (Sections 2±6). For more details aboutHalobacterium salinarium, authoritative reviews should be consulted [50±65].

2. Morphology of retinal protein-containing membranes

2.1. Purple membrane

Halobacterium salinarium is a unicellular organism (0.5 mm in diameter and 4±10 mm in length). The plasma membrane consists of a mosaic of purple and redmembranes. The purple membrane is essentially a two-dimensional protein crystal(Fig. 1). The crystal lattice is hexagonal with a unit cell size of 63 AÊ [66,67]. It isformed by packing of bR in a trimeric structure. The functional integrity of themembrane depends on an asymmetric orientation of bR. In its native form, lightenergy absorbed by bR is utilized to translocate protons from the cytoplasmic sideto the extracellular side (vectorial proton transport ). Thus, illumination of H.salinarium in culture acidi®es the culture medium. The fact that this protongradient is linked to the production of ATP was vividly demonstrated by anexperiment performed by Racker and Stoeckenius [68] many years ago. Theyreconstituted purple membrane into phospholipid vesicles together with the


oligomycin-sensitive ATPase/ATP synthetase from beef heart. Upon illumination,the medium was alkalinized and ATP production could be detected in themedium. The apparent reversal of the gradient, as compared to the in vivosituation, can be explained by the observation that the orientation of bR in thereconstituted vesicles is inside-out. The orientation of ATP synthetase is alsoinside-out; its F1 stalk sticks out towards the medium. That is why the synthesizedATP was released into the medium rather than into the cytosol.

2.2. Visual photoreceptor membranes

Two kinds of photoreceptor cells are found in vertebrates. The rods areelongated cylindrical cells specialized in dim light and colorless vision, whereas thecones are cone-shaped cells specialized in bright light and color vision. Both cellsconsist of inner and outer segments. The former contains a nucleus andmitochondria, while the latter consists exclusively of folded membranes, to whichvisual pigment molecules are bound (rhodopsin for rods and three kinds of visualpigments for cones). The dense stacking of folded membranes is accomplished bya process of folding of the plasma membrane that starts from the basal part in thevicinity of the inner segment (Fig. 2). Near the apical part, the folded membranesbecome detached from the plasma membrane and form free-¯oating discs insidethe outer segment. In the case of cones, the folded membranes remain attached tothe plasma membranes. It is important to realize that the disc membrane of therod outer segment is actually an inside-out vesicle when compared with theregular plasma membrane. For a concise account of the visual photoreceptorstructure, see Ref. [70].

Fig. 1. Electron density map of bacteriorhodopsin, viewed in direction perpendicular to membrane

surface, at 6 AÊ resolution. Irregular concentric rings represent a-helices. Contour of bR trimers is

evident. (Reproduced from Ref. [67])


3. Structures of retinal proteins

Retinal proteins are single polypeptide chains [71±77]. The chromophore retinal(vitamin A aldehyde) is attached to the e-amino group of the lysine (residue 216 inbR and residue 296 in rhodopsin). These single-chained polypeptides fold intoseven transmembrane a-helical loops, with the C-terminus facing the cytosol andthe N-terminus facing the extracellular space (in the case of bR [55,78] and conepigments [79,80]) or disc lumens (in the case of rhodopsin [77]) (Figs. 3 and 4). Itis of interest to note that the theme of seven transmembrane a-helical is shared by

Fig. 2. Diagrams showing rod (A) and cone (B) outer segments. Lamellar membrane structure of rod

outer segment consists of stack of ¯attened vesicles, which are detached from plasma membrane of rod

cell, except near base, where folded membranes remain attached to plasma membrane. Folded

membranes in cone cell are all attached to plasma membrane. (Reproduced from Ref. [69])


a large class of membrane-bound proteins known as the G protein-coupled receptorsuperfamily [81].

The retinal proteins contain a large fraction of hydrophobic amino acids. Asexpected, the intramembrane portions of the seven a-helical loops are mostlyhydrophobic and the interloop regions at either aqueous phase are morehydrophilic. The segregation of hydrophobic and hydrophilic amino acids makesretinal proteins amphiphilic (amphipathic ), and thus, helps anchor the protein inthe membrane. In addition, there are some hydrophilic amino acids in thepredominantly hydrophobic regions, especially near the chromophore binding site.Some of these charged residues are thought to be important proton-binding siteswhich are distributed along the transmembrane proton-translocating path of bR[55,82].

The three-dimensional structure of bR has not been determined to the level ofatomic resolution. Henderson and co-workers [55,78] applied Fourier analysis toelectron di�raction patterns of purple membranes at reduced temperature, andreported a three-dimensional map of bR with a resolution of 3.5 AÊ in a directionparallel to the membrane plane, but lower in the perpendicular direction. Fig. 3(B)shows the proton-translocating path across the purple membrane, thechromophore and its binding site, lysine residue 216 (K216), and a number of keyamino acid residues. The residues aspartate 96 (D96) and 85 (D85) are theprimary proton donor to the Schi�-base proton-binding site [83] and the primaryproton acceptor of the Schi�-base proton [55,58], respectively. A recently re®nedbR structure at 2.3 AÊ resolution reveals that D85 is connected to the Schi� basethrough a hydrogen-bonded water molecule, and forms a second hydrogen bondwith another water molecule [84]. Initially, the residue glutamate 204 (E204) wasregarded as the terminal proton release group at the extracellular surface [85].Subsequently, additional evidence indicated that another residue glutamate 194(E194) accepts protons from E204 [86]. Thus, the terminal proton release group isE194 instead. However, since the distance between D96 and the Schi� base is 12AÊ , proton transfer between the two binding sites is unlikely to be accomplished ina single step. A hydrogen-bonded chain formed by several additional residues hasbeen suggested and bound water has also been implicated [58]. Using benzamidinecrystals as a nucleation surface, Schertler et al. [87] obtained orthorhombiccrystals of bR, which di�ract to a resolution of 3.6 AÊ along the a- and b-directions and to 4.2 AÊ in the c-direction.

Fig. 3. Structure of bacteriorhodopsin. (A) Diagram shows secondary structure and amino-acid

sequence of bacteriorhodopsin (bR), halorhodopsin (hR) and sensory rhodopsin (sR). Amino acids are

represented by standard single-letter code. Triplet codes stand for amino-acid residues for sR, bR and

hR, in that order. Conserved residues, which line retinal-binding pocket, are shown as diamonds, but

less conserved residues in proton-translocating path are shown as circles. C-terminus is located

intracellularly and is shown at top of diagram. (B) Partial 3D structure of bR shows key amino-acid

residues in proton-translocating path. Protonated Schi� base is primary proton donor, whereas residues

Asp85 and Asp96 are primary proton acceptor and secondary proton donor, respectively. (Reproduced

from Ref. [55])


Fig. 4. Structure of bovine rhodopsin. (A) Secondary structure and amino-acid sequence are shown

with seven a-helices I±VII. Amino acids are represented by standard single-letter code. Helix-connecting

loops i1±i4 and C-terminus are located on cytoplasmic surface. N-terminus and loops e1±e3 are facing

intradiscal space. Forks, attached to asparagine residues 2 and 15 (N2 and N15), depict oligosaccharide

chains. Disul®de bridge links cysteine residues 110 (C110) and 187 (C187). Cysteine residues 322 (C322)

and 323 (C323) are palmitoylated. Retinal is linked to lysine residue 296 (K296). (B) Helical bundle

model for 3D conformation is shown with hydrophobic pocket containing 11-cis retinal. (Reproduced

from Ref. [77])


Using a similar approach, some progress has been made in elucidating therhodopsin structure [88,89]. Low-resolution three-dimensional structures wereobtained for cattle [90], frog [91], and squid [92] rhodopsin. Rhodopsin alsocontains seven transmembrane a-helices. But the helix orientation with respect tothe membrane plane is di�erent from that of bR. An a-carbon template for thetransmembrane helices in the rhodopsin family was constructed [93].

Using a similar technique, Havelka et al. [94] determined the three-dimensionalstructure of hR, the chloride-transporting retinal protein, to 7 AÊ . Like bR, hRalso has an arrangement of seven transmembrane a-helices.

4. Photochemical reactions of retinal proteins

4.1. Rhodopsin

Earlier e�orts in elucidating the photochemistry of rhodopsin were mostlyaccomplished by means of ¯ash photolysis [95]. Basically, the primaryphotoreaction of rhodopsin is an isomerization. The chromophore retinal in dark-adapted rhodopsin has a cis-con®guration at position 11 of the conjugated chain(11-cis retinal) (absorption maximum 498 nm). Illumination causes an ultrafastphotoreaction in which the bond rotation leads to an all-trans con®guration. Theensuing reactions are thermal in nature, and are described as a sequence ofphotoreactions, known as the photobleaching sequence (Fig. 5(A)). The end resultis hydrolysis of rhodopsin, forming a colorless product opsin and free all-transretinal (absorption maximum 380 nm). Reattachment of retinal to opsin, so as toform the dark-adapted rhodopsin, requires the intervention of an enzyme, retinalisomerase, which catalyzes the conversion of all-trans to 11-cis retinal. The retinal,so converted, is then spontaneously bound to opsin. The photointermediates ofrhodopsin bleaching sequence are given names, such as photorhodopsin,hypsorhodopsin, bathorhodopsin, lumirhodopsin, metarhodopsin I and II. Each ofthem are characterized by an absorption maximum, a lifetime, and a temperatureat which further reactions can be arrested.

The metarhodopsin I to metarhodopsin II transition constitutes a majorconformational change of rhodopsin [97]. Metarhodopsin II is a crucialintermediate that is directly linked to visual excitation via another sequence ofchemical reactions known as the cyclic GMP cascade [98]. Conversion ofrhodopsin to metarhodopsin II causes it to bind a peripheral protein transducin (aG protein, or GTP-binding protein), thus initiating a GDP±GTP exchange of thelatter and activating it [99,100]. Once activated, transducin binds and activatesanother peripheral protein, a precursor of phosphodiesterase (PDE). Activatedphosphodiesterase initiates hydrolysis of cyclic GMP [101±103]. Cyclic GMP (c-GMP) is a water-soluble molecule that keeps the Na+ channels on the plasmamembrane open [104]. These Na+ channels are predominantly open in the dark,and they allow a massive ionic current to enter the cytoplasm at the outer segment[105]. Massive hydrolysis of cyclic GMP causes this ionic current to diminish,


Fig. 5. Photochemistry of rhodopsin. (A) Diagram shows photobleaching sequence, together with cyclic

GMP cascade. Absorption maxima and lifetimes of various photointermediates are explicitly indicated.

Also shown are temperatures, below which further ensuing reactions are arrested. PDE stands for

phosphodiesterase, cGMP for guanosine 3 ',5 '-cyclic monophosphate, GDP for guanosine diphosphate,

and GTP for guanosine triphosphate. (B) Sequence of deactivation of photo-excited rhodopsin is

shown as cycle. R�activates transducin (T ). R

�becomes phosphorylated at as many as seven sites

�R��Pi �7� by rhodopsin kinase. Photophosphorylation allows it to be inactivated by arrestin. Complex

�R��Pi �7 � Arrestin� loses all-trans retinal and arrestin, thus forming phosphorylated opsin [O�Pi �7],which is subsequently dephosphorylated by protein phosphatase 2A (PrP2A). (Reproduced from Refs.

[96] (A) and [77] (B))


resulting in hyperpolarization of the photoreceptor membrane, which signi®es thesensing of photon ¯uxes [106,107]. The light-induced reduction of the Na+ currentis manifest as the late receptor potential (LRP) (see Section 5.1).

In comparing the secondary structures of bR and rhodopsin (Figs. 3(A) and4(A)), it is worth noting that there are numerous serine or threonine residues atthe cytoplasmic domain of rhodopsin, which are conspicuously absent in bR.These are sites of photophosphorylation (seven sites on an average up to amaximum of nine sites) [108]. Photophosphorylation of rhodopsin initiates asequence of events leading to termination of the c-GMP cascade. Two proteins areinvolved in this process: rhodopsin kinase and arrestin [109,110]. First, rhodopsinkinase is activated by its binding to the surface of photo-excited rhodopsin(metarhodopsin II) [111,112]. Activated rhodopsin kinase then phosphorylatesphoto-excited (illuminated) rhodopsin, but not unilluminated rhodopsin [113].Photophosphorylation of rhodopsin is a prerequisite to subsequent binding ofarrestin, which is a regulatory protein (Fig. 5(B)). Binding of arrestin to thecytoplasmic surface of phosphorylated excited rhodopsin results in the inhibitionof rhodopsin's ability to continue to activate transducin. Binding of arrestin israther speci®c. Arrestin binds strongly to phosphorylated excited rhodopsin, butnot to unphosphorylated excited rhodopsin or phosphorylated unilluminated (andregenerated) rhodopsin [114]. These speci®c requirements ensure that photo-excited rhodopsin will not be prematurely inactivated until the c-GMP cascade iswell on its way. With the intervention of these processes, photo-excited rhodopsinis deactivated much sooner than would be possible with the bleaching ofrhodopsin and the release of free all-trans retinal. For further details, severalauthoritative reviews on various aspects of vision are available[77,96,98,106,107,115±125].

4.2. Bacteriorhodopsin

The photochemistry of bR is similar to that of rhodopsin. The absorptionspectrum of bR depends on its state of light adaptation. Fully dark-adapted bRcontains a mixture of 13-cis retinal and all-trans retinal, and its absorptionmaximum is 568 nm. When it is light-adapted the absorption maximum is 570 nmand the chromophore is in the all-trans con®guration. Again, a large part of ourknowledge about bR was derived from ¯ash photolysis. Upon pulsed illumination,bR undergoes a sequence of chemical reactions, during which the absorptionmaximum shifts continuously. Historically, these photointermediates in a cyclicreaction scheme are designated with letters, such as J, K, L, M, N, and O, and thereaction scheme is known as the bR photocycle [126] (Fig. 6). Each of theseintermediates is characterized by an absorption maximum and a characteristiclifetime. The striking similarity between these photointermediates and those of therhodopsin photobleaching sequence is apparent. A major di�erence appears at thelast step; the chromophore of bR is not hydrolyzed and the pigment is cycledback to bR. While regeneration of rhodopsin requires the intervention of retinalisomerase, regeneration of bR is spontaneous and cyclic. Earlier models of the


photocycle are characterized by a one-way cyclic reaction sequence and a single Mstate. An improved photocycle has been proposed by VaÂ roÂ and Lanyi [128±132],in which two M states, M1 and M2, are present. In addition, they discovered thatmany of the steps in the photocycle are reversible with almost equal rates for theforward and reverse reactions. The conversion from M1 to M2 incurs a majorconformational change (deprotonation/reprotonation switch ). Proton pumping isdriven by light via deprotonation of the Schi� base. One proton is released to theextracellular side during the L4M reaction, and taken up again from theintracellular side during the decay of N. The M14M2 reaction allows the Schi�base to switch from the extracellular orientation to the intracellular orientation inorder to be reprotonated from the intracellular side. This reaction conversion canbe conveniently viewed as the analogous reaction of the metarhodopsin I tometarhodopsin II reaction. For further details, the readers are referred to severalreviews [50±52,56±58,65,133,134].

As we shall demoersible charge transfers are the key processes responsible forthe fast photoelectric e�ect. In fact, our previous analysis of the fast photoelectrice�ect leads to the prediction of many such reversible processes [135].

5. Photoelectric e�ects in pigment-containing membranes

5.1. Light-induced rapid charge displacement

At the time of its discovery, ERP was thought to be a new type of bioelectric

Fig. 6. Photocycle of bacteriorhodopsin. Bacteriorhodopsin exists in dark-adapted form D548 and light-

adapted form B570. Subscripts indicate absorption maximum of intermediates. Blue light illumination

drives M states back to B570. (Reproduced from Ref. [127])


phenomenon for the following reasons [13,136±142] (Fig. 7). ERP appears withouta detectable latency upon stimulation (less than 1 ms at that time) [12]. In contrast,the late receptor potential (LRP), which is ionic di�usion in nature, has a latency of1.7 ms (Fig. 7(A) and (B)). While LRP can be abolished by anoxia, or by othertreatments that disrupt the supply of metabolic energy, ERP persists under theserough treatments. ERP consists of two separate signal components, known as R1and R2. The fast component, R1, has a cornea-positive polarity, whereas the slowcomponent, R2, has the opposite polarity. R2 can be reversibly inhibited by lowtemperature, but R1 persists even at ÿ358C [143,144] (Fig. 7(C)±(E)). ERP fromcone photoreceptors is similar: it consists of a brief depolarizing phase (R1)followed by a hyperpolarizing (R2) phase [145±147].

The generating mechanism of ERP is di�erent from that of LRP and manyother bioelectric signals commonly encountered in the investigation of the nervoussystem, such as action potentials. The latter events occur in the millisecond timescale and are the results of ionic di�usion. ERP was thought to be generated bycharge displacements. A commonly envisioned picture is the shifting of chargedgroups in the amino-acid side chains as a result of conformational changes. Thismechanism is usually referred to as the dipole mechanism (see Sections 5.4 and8.2), and was widely accepted by investigators in bR research. Other possiblemechanisms were not seriously considered until the advent of techniques for

Fig. 7. Early receptor potential from retina of Cynmolgus monkey (A and B), and from albino rat (C,

D and E). In Records A and B, stimulus was 20-ms ¯ash. ERP appeared without appreciable delay,

after light stimulus, and later merged into late receptor potential (also known as a wave of

electroretinogram). Late receptor potential can be abolished by anoxia, leaving ERP intact, as shown

by dotted line in Record A. Records C, D, and E were taken at 358C, 258C and 08C, respectively.(Reproduced from Refs. [116] (A and B) and [144] (C, D, E))


forming arti®cial membranes and for reconstituting membrane-bound proteins inan arti®cial membrane.

In 1968, Tien [148] reported the direct observation of a light-induced electricalsignal in an arti®cial bilayer lipid membrane (BLM) that contained a chloroplastextract. Subsequently, fast photovoltages were reported in many arti®cialmembranes that contain various kinds of dyes or pigments [29,30]. Most recentstudies of ERP and ERP-like fast photovoltages were based on BLM or othervariant types of reconstituted membranes. As will become apparent later,membrane reconstitution turned out to be crucial in the elucidation of the fastphotoelectric e�ect.

Because of the small size and the ubiquitous presence of ERP, the conventionalwisdom has assigned no physiological signi®cance to it and has regarded it as anepiphenomenon Ð an evolutionary vestige serving no known physiologicalfunction. In the literature of bR, however, the fast photovoltage has convenientlybeen used as an indicator of proton movement within the molecule. Investigatorsroutinely made attempts to correlate the components of the fast photovoltage withthe photointermediate products of ¯ash photolysis, and molecular interpretationwas usually based on indirect inferences (see Section 17).

In photosynthetic and purple membranes, light-induced charge separation is themain electrical event. The fast photovoltages or the displacement photocurrentsare the macroscopic manifestation of such charge movements. They aremacroscopically observable, because the pigment and other accessory componentsare spatially oriented with respect to the membrane and the resulting chargemovement is thus vectorial in nature. It is apparent that the relaxation of the fastphotoelectric signal directly re¯ects the chemical relaxation of charge movement atthe microscopic scale. The striking similarity between ERP and the fastphotoelectric signal associated with bR suggests that there might be some earlycommon steps in the primary light-induced event in both photosynthesis andvision (Sections 14 and 15).

5.2. De®nition of photoelectric e�ects

In the literature of light-induced electric phenomena in biomembranes, the termphotoelectric e�ect encompasses electrical phenomena in which the photochemicalreactions of the membrane-bound dye or pigment are the source of electricity.This de®nition excludes the LRP mentioned in Section 5.1. LRP is a generatorpotential, i.e., a localized membrane potential change when a sensory receptor cellis stimulated. It is generated by the Na+ conductance change of the plasmamembrane, which is caused indirectly by the photochemical reaction of rhodopsin,i.e., there are many intervening steps between the two events (cf. the c-GMPcascade, Section 4.1).

For the purpose of mathematical modeling and experimental analysis, it isconvenient to di�erentiate between a fast photoelectric signal, induced by a brieflight pulse, and a steady-state photoelectric signal, in response to continuousillumination. A more rigorous way to di�erentiate these two types of signals is to


examine whether a net charge transport across the membrane has beenaccomplished or not [30]. If there is no net charge transport, the electric signal ispurely capacitative, and the phenomenon can be described as the AC photoelectrice�ect. If there is a net charge transport, the electric current contains a DCcomponent and the corresponding phenomenon can be described as the DCphotoelectric e�ect. As will be explained later, a pulsed-light stimulation is moree�ective in generating an AC photoelectric signal, whereas a continuous (steady)light stimulation is often required to make a DC photoelectric signal observable(see Section 9.1).

Biophysical studies of the photoelectric e�ects used to be di�cult, because ofthe complex geometry of membrane structures inherent in the rod or conephotoreceptors and in the chloroplasts. More recently, Sullivan and co-workers[149,150] succeeded in cloning rhodopsin and its mutants in cultured cells andwere able to measure ERP by means of the patch-clamp technique, thusalleviating the complication arising from complex geometry. However, it was theadvent of the technique of forming arti®cial BLMs that made it possible to studythe photoelectric e�ect under rigorously controlled experimental conditions.Reconstituted membranes were introduced to the study of photoelectric e�ects in1968 [148]. The majority of investigations of ERP were done prior to 1968,whereas the ®rst report on the photoelectric e�ects of bR was published in 1974[151]. It is important for the readers to have this historical perspective in mind,while comparing the rhodopsin and bR literatures.

5.3. Fast photoelectric signal in reconstituted bR membranes

The ®rst demonstration of the photoelectric e�ect in bR was performed byDrachev et al. [151,152]. These authors succeeded in incorporating oriented purplemembrane fragments into a planar BLM and demonstrated an electric potentialacross the membrane during continuous illumination (Fig. 8(A)). Thephotovoltage is sustained as long as the illumination continues. However, whenthe proton ionophore CCCP was added to the membrane, or when the circuitrywas shunted with an external resistor, the monotonic waveform was transformedinto a spike-like signal (Fig. 8(B)), which is often referred to collectively asdi�erential responsivity (Sections 11.1 and 19.3). Based on the analysis of thiswaveform, we suggested that an ERP-like signal, in addition to a DC photosignal,might be present in the reconstituted bR membrane [153].

The direct experimental demonstration of an ERP-like photoelectric signal inreconstituted bR membranes was reported by Trissl and Montal in 1977 [154],using a millisecond light ¯ash as the light source and using a di�erent method ofreconstitution: oriented purple membrane sheets were deposited on a thin Te¯on®lm (see Section 6.7 for details). Using a similar approach, Darszon et al. [155]observed the early receptor potential in vitro. Trissl and Montal pointed out thesimilarity between the observed signal and the early receptor potential in visualmembranes.


An additional component of the fast photosignal was subsequently observed byHong and Montal [156]. This additional component has a submicrosecondrisetime and is resistant to temperature changes. It is, therefore, analogous to theR1 component of ERP (see Section 5.1). In contrast, the slow componentresembles R2, because it has a polarity opposite to B1, and can be reversiblyinhibited by low temperature. These two components were therefore named B1and B2, respectively (Fig. 9). The contrasting di�erence in temperature sensitivitysuggests that the R1 and R2 components are generated by two separate chemicalreactions, so are the B1 and B2 components.

Fig. 8. Electrical response of reconstituted bR membrane to long square-wave light pulse. Open-circuit

photovoltages, measured before (Record A) and after (Record B) addition of 0.2 mM of CCCP, are

shown. Shunting with external resistor has similar e�ect. (Reproduced from Ref. [152])


5.4. pH dependence of early receptor potential: apparent paradox?

As mentioned in Section 5.1, the generally accepted molecular mechanism forERP generation is known as the dipole mechanism (or oriented dipole mechanism).It is known that rhodopsin maintains a ®xed orientation in the photoreceptormembrane, with its C-terminus facing the cytosolic side and the N-terminus facingthe interior of the disc membrane of the rod outer segment (lumenal side). It thuspresents no conceptual di�culty to comprehend the notion of light-induced chargeseparation in association with photobleaching of rhodopsin, since it undergoes asequence of light-induced conformational changes, which are expected to causemovements of bound charges.

However, light-induced intramolecular charge separation is not the whole story.In 1967, Hagins and McGaughy [157] demonstrated that the photocurrentassociated with ERP satis®es the zero time-integral condition, from which theyinferred that ERP is a capacitative process, i.e., ERP is an AC photoelectricsignal. This view was shared by Murakami and Pak, who performed intracellular

Fig. 9. Variation of relaxation time course of fast photoelectric signal from reconstituted bR

membrane, under di�erent measurement conditions. Membrane was reconstituted by means of TM

method. Record A shows photoresponse measured under open-circuit condition. Records B and C are

photoresponses measured under same near-short-circuit condition but displayed at di�erent time scales.

Signals were taken from same preparation. Light source was dye-laser pulse, which is shown at bottom

of Record B. Initial positive and negative spikes, in Record A, and negative spike, in Record B, are

stimulus artifacts. B1 and B2 components have positive and negative polarities, respectively.

(Reproduced from Ref. [156])


recording of ERP from vertebrate photoreceptors [158]. The capacitative nature ofERP implies that there is no net charge transport across the membrane during theERP transient. Thus, the molecular process responsible for the generation of ERPmust involve both charge separation and charge recombination. The idea ofreversible charge displacement is supported by Cone's [159] ®nding of thephotoreversal potential (Fig. 10): the visual membrane, which has been ®rstenriched with predominantly the metarhodopsin photointermediate from priorillumination, responds to a second light ¯ash with a signal that resembles ERP inwaveform, but has a reversed polarity. Thus, the dipole mechanism must beamended to include charge recombination, so that it is consistent with theobservation of Hagins and McGaughy. But is the oriented dipole mechanism theonly possible way to generate the ERP signal?

By comparing the relaxation of ERP with that of the photointermediates ofrhodopsin ¯ash photolysis, Cone [160] showed that the R2 component of ERP hasthe same time course as the metarhodopsin I to metarhodopsin II transition (Fig.11). Ostroy and co-workers [161] further demonstrated that the amplitude of theR2 component varies linearly with the amount of metarhodopsin II produced.This metarhodopsin I to metarhodopsin II transition constitutes a majorconformational change of rhodopsin; a proton is bound, and several sulfhydrylgroups are exposed [97]. Cone [159] proposed proton binding (interfacial protontransfer) as a possible generation mechanism of the R2 component. Ostroy [142]also considered the same possibility. Ostroy and co-workers further noticed thatthe time course of the R2 component is comparable to the time course of theabsorbance change passed through a high-pass resistance±capacitance (RC) ®lter[161] Ð an interesting observation that is consistent with an equivalent circuit tobe presented in Section 9 (see also discussion in Section 11.1).

That an interfacial proton transfer mechanism is theoretically sound is supportedby the study of interfacial electron transfer in a model membrane system, whichwe carried out in the early 1970s [162,163]. Our model system consisted of a BLMwhich contained a lipid-soluble magnesium porphyrin (either Mg mesoporphyrinIX ester or Mg octaethylporphyrin). The aqueous phases contained electrolytesand potassium ferricyanide, as the electron acceptor, and potassium ferrocyanide,as the electron donor, so that a redox gradient was imposed across the membrane.Pulsed-light illumination caused electrons to be transferred from the photo-excitedmagnesium porphyrin molecules in the membrane to the electron acceptorferricyanide ions in the aqueous phase (vectorial electron transfer ). We observed atransient photoelectric signal which possesses all major characteristics of ERP (seeTable 1). We demonstrated that the photosignal is generated by interfacialelectron transfer and its subsequent reverse reaction [163].

Thus, in principle, an interfacial proton transfer during the metarhodopsin I tometarhodopsin II reaction is capable of generating an AC photoelectric signal Ðthe R2 component. When a proton is transferred from the aqueous phase to thehydrophilic domain of rhodopsin, its counterion must be left behind in theadjacent di�use double layer. This process constitutes another kind of chargeseparation Ð charge separation across a membrane±water interface. The


subsequent reverse reaction, in which metarhodopsin II is converted back tometarhodopsin I with a concurrent proton release, constitutes the chargerecombination.

Why then was the proton binding (interfacial proton transfer) mechanism forthe R2 generation eventually abandoned by its proponents? The main reason wasthe failure to demonstrate experimentally a signi®cant pH dependence of the R2signal [164,165]. As shown in Fig. 12(A), the R2 amplitude is essentially constantin the range of pH 5±8 [166]. A more signi®cant pH dependence would beexpected for R2 if it was caused by a proton-binding reaction. Since themetarhodopsin I to metarhodopsin II transition is an acid±base reaction, theproton participates in the reaction as one of the reactants. By virtue of the law ofmass action, the R2 signal should vary with pH in a stoichiometrical fashion.Lindau and RuÈ ppel [167] investigated photoreceptor membranes oriented oncellulose ®lters with the speci®c objective to di�erentiate between the oriented

Fig. 10. Photoreversal potential. Photosignals were measured from excised eye of albino rat at 278C.Three test ¯ashes contained long-wavelengths which are primarily absorbed by rhodopsin. Blue

photoregenerating ¯ash contained wavelengths which are absorbed by longer-lived intermediates.

Control trace was obtained from second eye, subjected to same bleaching exposure and test ¯ashes, but

without blue ¯ash. (Reproduced from Ref. [159])


dipole and interfacial proton transfer mechanisms. Again, they failed to observethe pH and ionic strength dependence expected of the interfacial proton transfermodel. The apparent lack of a signi®cant pH dependence of the R2 component isthus instrumental to the refutation of the proton binding mechanism. But theabsence of the expected pH dependence of the R2 component constitutes anapparent paradox.

A similar apparent paradox also exists with regard to the B2 component of thecorresponding bR signal [168] (Fig. 12(B)). At the time of its discovery, no pHdependence could be demonstrated for the B2 signal [154]. Yet interfacial protonbinding (and release) is an obligatory process for proton translocation. Accordingto our analysis (Section 8.1), an AC photosignal ought to be observable.

The key to the explanation of the above-mentioned apparent paradox lies in theunderstanding of interfacial photochemistry of retinal proteins and the related

Fig. 11. Comparison of time course of R2 component of ERP and formation of metarhodopsin II.

Latter was monitored by absorbance change at 400 nm. Flash duration was 0.1 ms. (Reproduced from

Ref. [160])

Table 1

Major characteristics of ERP (reproduced from Ref. [163])

1. No detectable latency

2. Independent of membrane ionic mechanism

3. Of membrane origin

4. Action spectra same as the absorption spectra of membrane-bound pigments

5. Linearly dependent on pigment photoreaction

6. Manifestation as a displacement current


membrane phenomena, which exhibits peculiar characteristics that are absent insolution phase photochemistry, as well as in classical electrophysiology. Solutionphase photochemistry does not deal with heterogeneous reactions between twophases of anisotropic media: the membrane and aqueous phases. Therefore, theconventional approach of chemical kinetic analysis in the solution phase isinadequate. On the other hand, the membrane phenomena associated with retinalproteins also have no counterpart in conventional electrophysiology. Whileconventional electrophysiology primarily treats the physical phenomena of passiveion transport driven by an externally imposed transmembrane electrochemical

Fig. 12. pH dependence of amplitudes of fast photovoltages from rhodopsin (A) and bacteriorhodopsin

(B), measured under open-circuit conditions. ERP was decomposed into R1 and R2. Analogous bR

signal was decomposed into Components I, II and III. (Reproduced from Refs. [166] (A) and [168] (B))


gradient, the electrophysiology of retinal-protein-containing membranes treatslight-induced electric currents driven by an internal source: the photoemfassociated photochemical reactions. A direct transplant of existingelectrophysiological methodology o�ers little help. The solution to the problem, aswell as the elucidation of ERP and the ERP-like signal in bR membranes, requiresa combined electrochemical and electrophysiological approach. In order toappreciate the necessity of such a combined approach, we shall ®rst highlight themainstream approach and point out the unresolved problem before prescribing asolution.

5.5. Mainstream approach

In solution phase photochemistry, it is a common practice to decompose apulsed-light-generated chemical relaxation signal into as many exponentialcomponents as the curve ®tting process permits. This approach has been widelyused in the analysis of pulsed-light-induced (fast) photoelectric signals recordedfrom membranes that contain oriented bR. Once this analysis is done, the nextstep is to attempt to correlate each signal component with a corresponding signalcomponent in the spectral relaxation of the photocycle. This approach, referred toas the mainstream approach for brevity, was adopted in the majority of reportsappearing in the literature about photoelectric e�ects. Such an approach, however,is problematic.

As we shall discuss in detail, the mainstream approach often led toinconsistencies in the same reconstituted membrane system under di�erentconditions and in similar systems under similar conditions in di�erentlaboratories. The data variability cannot be satisfactorily explained by theconventional wisdom, but is fully expected from our alternative analysis. Thediscrepancies appear to be a consequence of some uncontrolled hiddenparameters, the inclusion of which forms the basis of our alternative analysis (seeSection 11.4).

5.6. Necessity for alternative approach

Our main objection to the mainstream approach, described in Section 5.5, is itsviolation of the zero time-integral condition established by Hagins and McGaughy[157]; the photocurrent associated with ERP must satisfy the following condition:�1

0

I�t� dt � 0, �5:1�

where I�t� is the time course of the photocurrent. This condition means that thephotocurrent I�t� must change its polarity during its transient time course, so thatthe area enclosed by the curve above the baseline can be equal to the areaenclosed by the curve below the baseline. In other words, the total amount ofcharges moving forward initially (the area above the baseline) must be equal to


the total amount of charges moving backward subsequently during the relaxationprocess (the area below the baseline). This condition is thus a characteristic of acapacitative (AC) electric signal.

A signal component in the form of a single exponential decay obviously cannotpossibly satisfy this condition (

�10 exp�ÿt=ti � dt 6� 0, where ti is the decay time

constant). This can be made clear by examining Fig. 13, which was intended toillustrate the generation of a capacitative signal by a single step of charge shiftinside the membrane [169]. The charge shift during the transition from state Ei tostate Ei�1 is shown to be represented by an impulsive rise of the photocurrentwhich decays with a characteristic time constant ti. Time-integration of thephotocurrent thus yields the amount of charges which shift in the directionperpendicular to the membrane surface as a function of time. It is apparent thatthe result shows that the charges that are separated during this transition neverrecombine (Fig. 13(C)). The latter conclusion directly contradicts the notion ofcapacitative current; it does not satisfy the condition described in Eq. (5.1).

Common sense in electronics engineering leads to a second objection. Themembrane that is capable of generating an ERP-like capacitative currentresembles an electronic device in which the current (or voltage) generator isembedded in a thin ®lm matrix. It is therefore inconceivable that the photosignalrelaxation can be analyzed and interpreted without, at the same time, consideringthe interaction between the active current generator and the passive RC network.Here the RC network is formed by the inert supporting substrate Ð thephospholipid bilayer membrane. Thus, the presumed hidden parameters,mentioned in Section 5.5, could be related to the interaction of various RCelements. Hagins and RuÈ ppel [141], and Govardovskii [170] proposed equivalentcircuit models (cable models with RC networks) for an intact rod cell, andattempted to account for the waveform of ERP. Hochstrate and co-workers [171]recognized the shaping e�ect of the RC property of the photoreceptor membraneand proposed a two-capacitor model to account for the ERP waveform. However,they associated the second (series) capacitor with the capacitor of the non-pigmented portion of plasma membrane. As we shall see, this second capacitor,which we named chemical capacitance, indeed exists, but also persists inreconstituted systems where the distorting e�ect of non-pigmented plasmamembrane is absent. The e�ect of the RC network formed by the photoreceptormembrane (essentially a linear RC ®lter) on the time course of the observed ERPwas also recognized by Brindley and Gardner-Medwin [164], but was apparentlyignored or neglected by most other investigators working on ERP and the ERP-like signal from bR.

It is of interest to note that Hodgkin and O'Bryan [145] proposed the followingequation to describe the waveform of R1 and R2 as measured intracellularly fromturtle cones:

j�t� � ÿNKd0�t� � BNKa3exp� ÿ a3t�, �5:2�

where d0�t� is the unit impulse (d-function at t � 0), B, K and a3 are constants, N


is the number of excited molecules, and j�t� is the outward current representing

the ERP (called early receptor current). Had the parameter B been set to unity,

the waveform de®ned by Eq. (5.2) would have satis®ed the zero time-integral

condition (5.1). Further discussion will be given in Section 9.1.

As we shall demonstrate in Section 9, the time course of an AC photosignal,

measured under conditions other than a strictly short-circuit condition, is

inevitably distorted by the membrane RC relaxation process. In the extreme

condition, namely open-circuit, the directly measured relaxation time constants are

virtually artifacts (see Eq. (9.25) in Section 9.3). Thus, Lindau and RuÈ ppel's [167]

failure to observe the expected pH and ionic strength dependence of R2 was most

likely caused by the distortion of signal time course inherent in open-circuit

measurements. An additional e�ect caused by partial overlap of the two signal

components further contributes to masking of the pH e�ect (see Section 10.5 for

details).

From the point of view of chemical kinetics, the photochemical reactions of bR

Fig. 13. Principle of capacitative coupling, according to mainstream approach. (A) Membrane is

represented by dielectric layer, which is interposed between two plates of parallel-plate capacitor.

Under short-circuit conditions, ¯ash excitation creates initial unstable state Ei, which relaxes to stable

product state Ei�1 with time constant ti. (B) Process leads to measurable transient photocurrent I,

which decays to zero with same time constant as that of transition Ei4Ei�1. (C) Time-integration of

photocurrent generates curve that represents accumulation of separated charges Q as function of time.

According to this interpretation, capacitance is charged with rising exponential time course to steady

level but is never discharged. Thus, charges are separated but never recombined Ð description

contradicting notion of capacitative coupling. (Reproduced and modi®ed from Ref. [169])


take place in a heterogeneous system involving a membrane phase and twoaqueous phases. The vectorial nature of proton movement also makes thechemical reactions anisotropic. From the point of view of electrophysiology, thephotoelectric e�ect is unique in the localization of the current (or, equivalently,voltage) source; it resides either at the membrane±water interface or within themembrane phase. In contrast, the current source encountered in classicalphysiology always resides outside of the membrane or, more precisely, outside ofthe di�use double layers Ð thin layers of solution at the vicinity of a membranesurface where net excess charges accumulate. Thus, the analytical handling of thephoto-electromotive force (photoemf) has no precedents in classicalelectrophysiology. Classical electrophysiology is required to deal with only threemacroscopic electrical parameters: emf (or voltage), current, and resistance. Bycontrolling one of the three parameters and by measuring a second one, Ohm'slaw allows the third parameter to be determined by computation. With themeasurement of photoelectric signals, however, it is not possible to get all themacroscopic electrical parameters with only a single act of measurement, becauseof the existence of the photoemf, which must be distinguished from the externallyapplied transmembrane voltage (cf. Section 12).

Our alternative approach seeks to decompose the AC photoelectric signal byphysical means, namely, by utilizing di�erent membrane reconstitution methods.Our signal decomposition protocol is therefore model-independent. Being model-independent is crucial, if the measured signals are to be used to check theconsistency of our proposed equivalent circuit models, otherwise the practice isreduced to circular reasoning. Thus, our equivalent circuit model makes a sharpprediction about the experimental data; no free parameters are available to rescuea poor ®t (see Sections 9.2, 20.1 and 20.4).

In contrast, the `model' of signal decomposition used in the mainstreamapproach is not subject to the same constraint as those in our bioelectrochemicalapproach. In fact, it is subject to no constraints; exponential decomposition isvirtually guaranteed by the mathematical manipulation. In other words, the`model' proposed by the mainstream approach is so `amorphous' that it cannot beproved wrong by comparing the model with the very data used for modelconstruction. Of course, it can be shown to be problematic by virtue of theinconsistencies mentioned above (see also Section 11.4).

6. Methods of membrane reconstitution

The development of techniques of forming arti®cial model membranes and forreconstituting membrane-bound proteins is a crucial breakthrough in membranebiophysics research. Without these techniques, serious mathematical modeling ofthe photoelectric e�ects would be virtually impossible. Investigations on thephotoelectric e�ects of bR were mostly carried out on reconstituted membranes.In the following survey, the advantages and shortcomings of each method will bebrie¯y discussed.


6.1. Black lipid membranes

The original method of forming black lipid membrane (or bilayer lipidmembrane, BLM) was developed by Mueller et al. in 1962 [172,173] (Fig. 14). Theprocedure requires the use of a mixture of chloroform and methanol as thesolvent in which phospholipid molecules are dissolved or dispersed (membrane-forming solution). The BLM is formed in a chamber with two compartments,which are separated from each other with a Te¯on plate. The Te¯on partition hasa small aperture (hole of 1±2 mm2), on which the BLM is to be formed. Theaperture is immersed in an electrolyte solution. A drop of the membrane-formingsolution is then transferred to the aperture, either by means of an artist's brush ora syringe with a plastic tubing attached to the needle tip. The membrane-formingsolution is initially spread on the aperture as a thick layer of liquid, and a colorfulrainbow-like interference pattern can be observed under a dissecting microscope.If the preparation of the membrane-forming solution has the `correct' compositionand properties (it is still more art than science), thin regions which are bimolecularin thickness will appear as tiny colorless dots (dubbed `black holes'), which have atendency to expand at the expense of thicker regions and to coalesce with oneanother. Eventually, a thin black lipid membrane is formed and the excess lipidmaterial accumulates at the edge of the aperture, forming the Plateau±Gibbs

Fig. 14. Experimental arrangement and diagrammatic representation of molecular organization of

BLM. (A) BLM is formed in aperture (hole) of Te¯on partition, which separates two aqueous phases.

(B) Enlarged aperture area shows thin bilayer and thick Plateau±Gibbs border. (C) Detailed molecular

structure of BLM is shown to contain membrane-bound protein, amphiphilic pigment and carotenoid.



border. Phospholipids are amphiphilic. Therefore, in a thin lipid bilayer, thehydrophilic polar head groups are facing the aqueous phases whereas thehydrophobic nonpolar hydrocarbon tails are buried inside the bilayer, with a tail-to-tail orientation.

An electrical measurement can be made with a pair of electrodes inserted in thetwo aqueous phases across the Te¯on partition. The compositions of the twoaqueous phases can be modi®ed independently by the addition of chemicals or bythe replacement of the bathing solution.

The advantage of this method is its simplicity and versatility; the experimentalconditions are easily controlled. The major disadvantage is the instability of theBLM. There are many treatments to improve the mechanical stability of themembrane. The extreme is to use photopolymerizable lipids in the membrane-forming solution [175]. Cross-linking is established after the membrane is formed.This method has been used in the fabrication of a biosensor [176]. Thedisadvantage of the latter method is that it eliminates one important andpotentially useful feature of the membrane, namely, membrane ¯uidity. Someimportant membrane functions depend on interactions of integral proteins vialateral di�usion, which would not be possible without membrane ¯uidity (seediscussion in Ref. [177]).

Another variant method that solves the stability problem has been developed byTien and co-workers (supported BLM or sBLM) [178]. By dipping a platinumwire with a freshly cut surface in a phospholipid±water mixture, a BLM formsspontaneously on the fresh surface. This method has been used in fabrication ofmolecular sensors [179], and may be suitable for studying the AC photoelectrice�ect of bR. It is, however, not suitable for studying the DC photoelectric e�ect,because of the lack of a suitable electrodic reaction that can convert a protoncurrent to an electron current (see Section 19.4). Subsequently, Tien and co-workers [180] succeeded in depositing BLM on the surface of an agar gel, thuscircumventing the latter problem, because a pair of reversible electrodes can thenbe used with the aid of KCl agar bridges.

The solvent chloroform±methanol used in the original recipe of Mueller et al. isdetrimental to many proteins and is not suitable for membrane proteinreconstitution. By substituting n-decane for chloroform±methanol, this problem isalleviated. We routinely used this latter membrane forming solution toreconstitute bR, following a procedure modi®ed by DancshaÂ zy and Karvaly [181].The study of this type of membranes for the DC photoelectric e�ect will bepresented in Section 12.

The DancshaÂ zy±Karvaly method is described as follows. The membrane-forming solutions consists of phospholipid (azolectin) in n-decane, which has beenpreviously saturated with n-octadecyl amine (with a positively charged quaternaryammonium group). A planar BLM with positive surface charges is ®rst formedaround a hole in a Te¯on partition described above. An aliquot of purplemembrane suspension in water is then added to one of the two compartments.Purple membrane sheets will then fuse to the planar bilayer. Enhancement of thefusion process can be achieved by the addition of a multivalent cation, such as


Ca2+. The overwhelming majority of the membranes reconstituted by means ofthis method show a preferential orientation of the purple membrane in such a waythat the extracellular surface of the purple membrane sheet is attached to theplanar bilayer. That is, the cis side, where the purple membrane suspension wasadded, corresponds to the cytoplasmic side. This orientation is deduced from theDC photoelectric e�ect which indicates a steady-state photocurrent ¯owing fromthe cis side to the trans side. To the best of the author's knowledge, there is noreliable reconstitution method that ascertains the degree of orientation. But theexistence of a DC photocurrent indicates that there is a preferential orientation.

In using the DancshaÂ zy±Karvaly method, some authors considered the fusion ofpurple membrane fragments to be incomplete; the purple membrane sheets areattached to the BLM like a sandwich (the `sandwich' model) [182] (Fig. 15(A)).We shall dispute this interpretation by experimental evidence from the DCphotoelectric data of bR [183] (see Section 12.7).

An alternative method of bR reconstitution makes use of phospholipid vesicles,which are free-¯oating spherical lipid bilayers without a solid support [151].Bacteriorhodopsin is ®rst reconstituted into phospholipid vesicles (see Section 6.2).The vesicles are then added to the aqueous phase and allowed to fuse with aplanar BLM, which contains no bR initially. This method was developed and ®rstused by Drachev et al. [151] to demonstrate the photoelectric e�ect of bR. Theseauthors contended that the fusion of vesicles with the planar bilayer wasincomplete, forming button-like structures on the planar BLM (the `button'model) [184] (Fig. 15(B) and (C)). However, we found this interpretation

Fig. 15. Schematic diagrams showing `sandwich' model of Bamberg et al. (A) and `button' model of

Drachev et al. (B and C). (A) Patch of purple membrane is attached to planar lipid bilayer without

complete fusion. Proton-translocating path is interrupted by non-conducting plain bilayer. Addition of

CCCP or gramicidin creates proton-di�usion path through plain bilayer. (B) Fusion of bR-containing

vesicles with planar bilayer is incomplete, forming button-like structures. (C) Localization of bR and

proton-transocating and proton-di�usion paths are shown. (Reproduced from Refs. [182] (A) and [185]

(B, C))


questionable and suggested that the fusion may be complete [183]. The detailedanalysis will be given in Section 11.1.

6.2. Phospholipid vesicles (liposomes)

Phospholipid vesicles (liposomes) are formed by sonication of a mixture ofphospholipid and electrolyte solution. Since no organic solvent is used, this is apreferred method of membrane protein reconstitution. Indeed, it is usedextensively in bioenergetic research [186]. It is possible to assay the rate of chargetransport across the vesicle membrane. The detection method includes the use ofradioactive tracers, and voltage sensing dyes with computer imaging techniques.This method is useful for measurements of steady-state proton transport andmeasurements of the DC photoelectric response, but is inadequate for the ACphotoelectric e�ect, because of the slow response time of the detection methods.Dye-mediated sensing has a better time resolution, but may still su�er fromdi�usion-limited processes. This problem is partially alleviated by conjugating dyemolecules to bR, forming an in situ reporter group [187].

6.3. Nucleopore-supported ®lms or Collodion ®lms

These methods were developed for the purpose of increasing the mechanicalstability. The Nucleopore-supported ®lms are formed by spreading membrane-forming solution on a Nucleopore ®lm directly [188]. Alternatively, a Collodion®lm can be formed by spreading the ®lm on an air±water interface with a dilutedCollodion solution (USP) in amyl acetate [189]. The ®lm, after it is dried, mustthen be impregnated with phospholipid membrane-forming solution. Both theNucleopore ®lm and the Collodion ®lm are porous. When membrane-formingsolution is spread on these ®lms, numerous tiny lipid membranes are formed.Apparently, the stability is attained at the expense of the size of individual lipidmembranes.

The disadvantage is that the individual tiny membrane cannot be readily viewedand it is uncertain as to whether the individual membranes are of bimolecularthickness. In fact, Drachev, who originally developed the Collodion ®lm, thoughtthe membranes were thick and not bimolecular layers. But again, we dispute thisview and we think at least some of the membranes are actually bilayer thin [183](Section 10.13). In contrast, Mountz and Tien [188], who developed theNucleopore ®lm, thought the majority of the individual tiny membranes were thin.

Korenbrot and Hwang [190,191] developed a similar technique, using theLangmuir±Blodgett (LB) technique to orient purple membranes on an air±waterinterface (see Section 6.5) and using a nitrocellulose ®lm support to deposit abilayer of purple membranes. The orientation of bR is greatly enhanced by theuse of the LB technique.


6.4. Immobilized gel technique

DeÂ r et al. [192] developed a technique of forming a slab of gel with immobilizedpurple membranes trapped in it. The purple membrane fragments are mixed with30% acrylamide and 0.8% N,N '-methylene bis-acrylamide, and oriented under thein¯uence of an applied DC electric ®eld of 15 V/cm. The oriented purplemembrane fragments are then immobilized by polymerization of the acrylamidegel, initiated by 0.3% TEMED (N,N,N ',N '-tetramethylethylenediamine) and 1.5%ammonium persulfate. The orientation of bR is maintained in the absence of theelectric ®eld due to immobilization of the solidi®ed gel.

Improved orientation of purple membranes can be achieved by the combinede�ect of both electric and magnetic ®elds [193]. The orientation e�ect of anapplied DC electric ®eld is based on the presence of a permanent electric dipolemoment in bR and the purple membrane [194]. On the other hand, orientation byan applied DC magnetic ®eld is based on diamagnetic anisotropy [195,196]. Theapplication of a magnetic ®eld alone will produce a purple membrane sample ofmixed orientations, because the magnetic dipole moment is induced rather thanpermanent. A combined application of electric and magnetic ®elds will achieve agreater degree of orientation e�ect, because the magnetic ®eld reinforces theorientation e�ect, of which the polarity (directionality) is primarily dictated by theelectric ®eld.

The main advantage of the immobilized gel technique is the possibility ofmaking simultaneous measurements of the AC photoelectric signal and thespectral relaxation signal. In addition, measurements at low temperature arefeasible. The disadvantage is the impossibility of maintaining di�erent electrolytecompositions of the two aqueous phases, because the gel ®lm is permeable tosmall ions (cf. Section 10.13.3).

6.5. Langmuir±Blodgett technique

The LB technique, developed in the 1930s [197,198], is a popular method fordepositing organic thin ®lms on a solid substrate and is widely used in biosensorfabrication. It essentially exploits the amphiphilic properties of certain molecules,such as phospholipids and fatty acids. A monomolecular layer of phospholipidcan be spread at the air±water interface in a trough (Langmuir trough), ®lled withwater or an electrolyte solution. When the ®lm is compressed by a barrier, thephospholipid molecules will be compacted, so that the hydrophilic polar headgroups will be immersed in water (the subphase), while the hydrophobic nonpolarhydrocarbon chains will be pointing upward into the air. The ®lm quality can bemonitored by the surface pressure±area dependence curve (isotherm). The surfacepressure of the ®lm increases as the area is reduced by compression.

The ®lm can be transferred to a solid support, such as a glass substrate coatedwith a thin and transparent layer of metal, which becomes one of the twoelectrodes. The second electrode can also be evaporated onto the LB ®lm. Multi-layered LB ®lms can be engineered with various orientations (Fig. 16).


Fig. 16. LB technique of forming multiple orientated layers of organic thin ®lms on glass substrate. (A)

Dye stu�, dissolved in chloroform and mixed with fatty acid, is spread on air±water interface on

Langmuir trough. Mechanical compression forms compact monolayer. (B) Double-layered thin ®lms of

various orientations are formed by dipping glass substrate into aqueous subphase, and then pushing it

in or pulling it out in pre-planned sequence. (Reproduced from Ref. [199])

Photoelectric responses from LB ®lms of bR have been reported [200,201]. Someinvestigators observed that no DC photocurrent can be observed, which is indeedexpected in the absence of a molecular mechanism for proton-current-to-electron-current conversion (see Section 19.4).

6.6. Takagi±Montal method

The Takagi±Montal method is an ingenious technique for making a BLM andcan be considered an extension of the LB technique. The method was originallydeveloped by Takagi et al. [202] (Fig. 17). They spread two phospholipidmonolayers on the water surfaces of two adjacent Langmuir troughs. The twotroughs are separated by a moving partition with an aperture similar to thatcommonly used in the BLM technique. When this partition is pushed downvertically, two monolayers will attach to the two sides of the partition and willmeet at the aperture to form a bona ®de BLM. This method was subsequentlymodi®ed, enhanced and popularized by Montal and Mueller [203], who used a®xed partition, but formed the bilayer by raising the water level instead.

Unlike the original BLM technique, the Takagi±Montal method does not utilizeorganic solvents. It is a method suitable for reconstituting membrane-boundproteins. There is another distinct advantage. By apposing two separatemonolayers, the Takagi±Montal method a�ords the possibility of forming anasymmetrical BLM (by fusing two monolayers, which are comprised of di�erent

Fig. 17. Takagi±Montal method of forming BLM. In original method of Takagi et al., amphiphilic

molecules of phospholipid are spread and compressed at air±water interface on Langmuir trough.

Te¯on partition with hole is then dipped into trough, and two monolayers are pulled into water, as

shown. Two monolayers meet at hole to form BLM. In modi®cation of Montal and Mueller, partition

remains stationary, but (two) water levels are raised by infusing electrolyte solution into aqueous

subphases. (Reproduced from Ref. [202])


types of phospholipid) and for incorporating membrane proteins with a ®xed andasymmetrical orientation. Takagi et al. [202] used this method to reconstituterhodopsin into the BLM. Subsequently, the method modi®ed by Montal andMueller was used to demonstrate the presence of the early receptor potential froma reconstituted rhodopsin membrane [155,204].

The disadvantage of the Takagi±Montal method is its technical di�culty andthe instability of the formed membranes. Consequently, there is a limit to themembrane size. Furthermore, the membrane may have an excessively lowresistance, and the amplitude of the photovoltage may be substantially diminishedby shunting owing to a leaky membrane. However, we must point out here thatshunting, due to low membrane resistance, may not be a serious problem if thephotocurrent is measured instead of the photovoltage (see Sections 8.3 and 9.1).

6.7. Trissl±Montal method

The Trissl±Montal (TM) method [154] is a variant of the Takagi±Montalmethod. It was intended to combat the problem of low resistance in a Takagi±Montal membrane. Essentially, an oriented monolayer of phospholipid or anoriented layer of purple membrane is spread in only one of the two aqueouscompartments, and there is no aperture in the partition (Fig. 18). This methodallows an oriented layer of purple membranes to be attached to a thin (6.35 mm)Te¯on ®lm. In view of the high resistance of the Te¯on substrate, a TM ®lm isnot leaky, but it also does not exhibit the DC photoelectric e�ect. However, this

Fig. 18. TM method of reconstituting bR membranes. Method is similar to Montal and Mueller's

version of Takagi±Montal method, except that Te¯on partition (thickness 6.35 mm) has no hole in it,

and only one monolayer is made. In our applications, purple membrane sheets (not really monolayers)

are ®rst oriented in air±water interface, and then plated onto Te¯on ®lm. (Reproduced from Ref. [156])


method turns out to be quite useful for studying the AC photoelectric e�ect ofbR. The mechanical stability is extremely high and the photosignal so obtainedremains reproducible and essentially constant in amplitude for many days. Thesignal-to-noise ratio of data obtained by means of the TM method is su�cientlygood for mathematical modeling, and is a function of ®lm thickness, ®lm area,and the intensity of illumination. The thinner the Te¯on ®lm the larger the signalamplitude. The signal amplitude is a linear function of the light intensity untilsaturation. Therefore, if the laser light power is not a limiting factor, the largerthe ®lm area, the greater the signal amplitude that can be observed.

6.8. Multi-layered thin ®lm method

The TM method was subsequently modi®ed by Okajima to deposit multiplelayers of oriented purple membrane sheets on a thin Te¯on ®lm [205]. We shallrefer to this method as the multi-layered (ML) thin ®lm method. A drop ofaqueous suspension of purple membrane fragments is placed on a sheet of thinTe¯on ®lm (thickness 6.35 mm), which has been previously coated with a thinlayer of phospholipid/octadecylamine in n-decane. A thick ML ®lm is thus formedon the Te¯on substrate. The preparation is allowed to air-dry for at least fourdays before it is mounted in a chamber and rehydrated. The necessity ofprolonged drying will be explained in Section 10.11.

7. Electrical measurements of AC photoelectric signals

Earlier reports on the AC photoelectric signals, elicited from arti®cial BLMs,adopted the conventional methodology of classical electrophysiology. Themethods include the current-clamp (open-circuit) measurement and the voltage-clamp (short-circuit) measurement. Reports of AC photoelectric signals measuredwith the open-circuit method outnumbers those measured with the voltage clampmethod. We further introduced a method named tunable voltage clamp, underconditions which are neither open-circuit nor short-circuit, but somewhere inbetween [162,206].

7.1. Open-circuit measurement (current clamp method)

The open circuit method is synonymous with the galvanostatic method inelectrochemistry. The essence of an open-circuit measurement is that the inputimpedance of the measuring device must be much higher (at least two or threeorders of magnitude) than the source impedance of the voltage (or current) sourcein the membrane. If this condition is ful®lled, the amount of current ¯owing intothe measuring device will be negligible and the membrane will be in exactly thesame condition electrically as when no measuring device is connected. Failure tomeet this condition will cause a signi®cant fraction of current to be diverted to themeasuring device. This fraction will not reach the membrane to charge the


membrane capacitor. As a result, the measured transmembrane voltage will besigni®cantly less than its physiological value, i.e., the value when the measuringdevice is disconnected. The open-circuit condition can be accomplished by usingan electrometer which has an input impedance of 1016 O (Fig. 19(A)). In addition,a constant current can be applied under open-circuit conditions, and themembrane is said to be current-clamped. All the applied current then goesthrough the membrane, because of the high input impedance of the electrometer.An open-circuit voltage is thus measured with current-clamping at zero current.

7.2. Short-circuit measurement (voltage clamp method)

The voltage clamp method is synonymous with the potentiostatic method inelectrochemistry. This method is widely used in classical electrophysiology and isthe single most important method that allowed Hodgkin and Huxley [207] todecipher the mechanism of the action potential. It is often described in a textbookas the method, in which an appropriate amount of current is injected through themembrane, so as to keep the membrane at a prescribed ®xed transmembranepotential. Such a description, while technically correct, does not address thecentral criterion that must be met in order to successfully clamp the membranepotential.

The essence of a voltage-clamp measurement is to maintain a short-circuitcondition at all times. Thus, the same potential as an externally applied voltage (Ein Fig. 19(B)), but with an opposite polarity, will be re¯ected across themembrane as a result of imposing a short-circuit condition across the virtualground (VG ) and the ground (G ). The active clamping current injected by theampli®er can thus be regarded as the current ¯ow resulting from short-circuiting.A special case arises when the voltage source is set to zero or when no externalvoltage source is connected; short-circuiting makes the two sides of the membraneequipotential, i.e., voltage-clamped at zero. A short-circuit condition requires thatthe access impedance be much smaller than the source impedance. In the setupshown in Fig. 19(B), the access impedance includes the input impedance of thecurrent ampli®er, the electrode impedance, and the impedance of electrolyteinterposed between the electrodes and the membrane.

7.3. Tunable voltage clamp method

For reasons described later, a short-circuit condition is sometimes di�cult toachieve or maintain (Section 9.2). A commonly encountered situation inmeasuring the AC photoelectric signal is an unintentional measurement of a(short-circuit) current under condition that is neither short-circuit nor open-circuit, i.e., the access impedance is neither zero nor in®nity. This situation mayarise without warning, especially when the nature of the photocurrent source isuncertain. An unsuspicious investigator may fall victim to this pitfall withoutknowing it. However, once the pitfall is recognized, the situation can readily be


Fig. 19. Methods of electrical measurements. (A) Open-circuit measurement (switch S open) and

current-clamp measurement (switch S closed) are shown. Transmembrane potential is monitored by

electrometer (V ), con®gured in voltage mode (with high input impedance). Its two input leads

terminate at two electrodes. High-impedance current source is made of battery, in series with resistance

that is much greater than membrane impedance (e.g., 1011 O). (B) Voltage-clamp circuit is shown,

consisting of operational ampli®er (A ), con®gured in inverted mode. Negative feedback loop,

comprising of RC network (with variable resistor Rf and capacitor Cf ), serves as gain control as well as

low-pass ®lter for noise control. Essentially, it is current-to-voltage converter (with low input

impedance). E is command voltage source, which sets desired clamping potential. Summing point VG is

held at virtual ground, and can be considered to be equipotential to ground G. Membrane potential,

which has amplitude equal to E but with opposite polarity, thus appears across membrane.



remedied by including the non-zero access impedance in an equivalent circuitanalysis.

Because the photocurrent source in a photo-active membrane often contains acapacitative reactance, the membrane source impedance may be higher than theaccess impedance at the low-frequency range and at steady state (DC), but mayplummet precipitously to a signi®cantly lower value at the high-frequency range.It is therefore of paramount importance to include the access impedance in theequivalent circuit analysis whenever in doubt. We further take advantage of thee�ect of varying the access impedance by tuning the access impedance to optimizethe measurement. This is the essence of the tunable voltage clamp method[162,163,206]. For a full explanation see Section 9.

In using an operational ampli®er in the inverted mode, the signal gain iscontrolled by the resistor (Rf) in the feedback loop. The greater the Rf is thegreater the output signal amplitude is. However, the feedback loop alsoconstitutes a low-pass RC ®lter. The greater the Rf is the slower the instrumentalresponse time is. These two features constitute the well-known e�ect of gain-bandwidth tradeo�. We are thus forced to use the ampli®er as an attenuatorinstead of an ampli®er in order to preserve the required bandwidth. This problemcan be readily circumvented by cascading the ®rst ampli®er with another or moreoperational ampli®ers in the inverted mode. In this way, the ®rst ampli®er servesmerely as the current-to-voltage converter and the second and the subsequentstages are then the true ampli®ers.

8. Mechanisms of AC photoelectric e�ect

We shall analyze the two molecular mechanisms mentioned in Section 5.4 byinvoking the Gouy±Chapman di�use double layer theory [208]. The objective is toderive two separate equivalent circuits, one for each model. Hence, we canestablish an unequivocal connection between the measured macroscopic electricalparameters and the underlying molecular kinetic parameters [163,209]. Anadditional objective is to devise an experimental strategy to di�erentiate betweenthe two possible molecular mechanisms. Methodology for electrical measurements,as outlined in Section 7, will also be evaluated in light of new insight gained fromthe analysis.

8.1. Gouy±Chapman analysis of interfacial proton transfer mechanism

The light-induced physical events at the two membrane surfaces are similar:proton uptake at the cytoplasmic surface and proton release at the extracellularsurface. Here, we shall analyze the event at the cytoplasmic surface in detail.Analysis of the event at the opposite surface can be adapted with appropriatemodi®cations.

A simpli®ed scheme of interfacial proton transfer is shown in the left-hand halfof Fig. 20. Illumination of bR causes a proton to be bound to its hydrophilic


cytoplasmic domain. The proton binding site is assumed to be on a mathematicalplane with an in®nitesimal thickness that de®nes the cytoplasmic membrane±waterinterface. Proton binding thus generates a sheet of surface charges at thecytoplasmic surface. These surface charges are continuously and uniformlydistributed on the mathematical plane (smeared charge assumption ). This latterassumption is a prerequisite for the use of the Gouy±Chapman theory. We furtherassume that there is a discontinuity at the membrane±water interface with regardto the dielectric constant and a discontinuity in the charge density as well as therate of ionic cloud relaxation (see below). The dielectric constant in the membranephase is treated as if it were homogeneous, so are those in the two aqueousphases.

In order to make the mathematical analysis manageable and to obtain explicitsolutions, it is necessary to impose restrictive conditions in the form ofapproximations and assumptions. These conditions are listed as follows:

. Condition 1 (Fixed and smeared surface charge assumption ): Photogeneratedsurface charges (P+) form a continuous sheet of ®xed surface charges with anin®nitesimal thickness (designated PH+ in Fig. 20). This means that the plane,where the positive charge is located, does not move away from the surface andinto the membrane interior during the course of charge separation andrecombination. The intramembrane charge movement (in the forward direction)following proton binding occurs on a slower time scale than charge binding. Noproton transport would take place, if intramolecular charge movement werecompletely absent.

. Condition 2 (Condition of a ®xed proton-acceptor concentration ): The reverseproton transfer is a bimolecular reaction involving PH+ and the protonacceptor, H2O. Condition 2 is guaranteed because of the natural abundance ofwater in the aqueous phase. The condition of a ®xed proton acceptorconcentration allows the relaxation process to be reduced from a second-orderprocess to a pseudo-®rst-order one. In order for the corresponding condition,condition of a ®xed proton-donor concentration, to be valid for the interfacialprocess at the extracellular surface, the aqueous pH must be bu�ered.

. Condition 3 (Constant ®eld assumption ): Space charge inside the membrane issu�ciently low so that the electric ®eld inside the membrane is constant.

. Condition 4 (Assumption of a linearly light-dependent photoresponse ): Theamplitudes of the two components of the ERP have been shown to be linearlydependent on the light intensity except at saturating light intensities [210] (Fig.21(A)). A similar property has been observed with the analogous bR signals[211] (Fig. 21(B)). Here, the derivation is restricted to the range of linear lightdependence, and we assume that the rate of production of P+ is a linearfunction of the light intensity.

. Condition 5 (Assumption of a linear dependence of the forward proton-transferrate on the pigment concentration ): The rate of forward proton transfer isassumed to be proportional to the (surface) concentration of pigment in thedark state. This assumption is justi®ed on the basis of the ®nding that the R1


and the R2 amplitudes of the ERP are proportional to the amount ofrhodopsin bleached [144,210] and also to the total rhodopsin concentration[212].

The discontinuity of both the dielectric constant and the charge density at themembrane surface have an important consequence on the kinetics of chargemovements. The relaxation of the ionic cloud (ionic atmosphere) in the aqueousphases is much faster than the relaxation of the photoelectric event. This can beshown by the following simple calculation. The ionic cloud relaxation of an ionic

Fig. 20. Interfacial proton transfer (IPT) mechanism and oriented dipole (OD) mechanism. IPT

mechanism describes transfer of proton from adjacent aqueous phase to membrane phase, while leaving

counterion behind in aqueous phase. Ground-state pigment is designated as P. Excited pigment that

binds proton from aqueous phase is designated as P�. Charge-density pro®le is also shown, along with

equivalent circuit. OD mechanism describes light-induced generation of transient array of oriented

electric dipoles, inside membrane. Diagram is self-explanatory. Two circuits can be further reduced to

common irreducible one (bottom of diagram). (Reproduced from Ref. [209])


system is characterized by the time tr required for the ions to di�use over adistance of the Debye length L:

tr � L2

2D, �8:1�

where D is the di�usion constant of the ionic species in question, and L is theDebye length (3.1 AÊ for 1 M KCl; 9.7 AÊ for 0.1 M KCl). For a typical di�usionconstant of 10ÿ5 cm2/s of small ions, the relaxation time constant tr is 0.05 ns for1 M KCl, and 0.5 ns for 0.1 M KCl. Inside the lipid bilayer, the ionicconcentration is estimated to be lower than 10ÿ9 M which corresponds to a Debyelength of 3� 104 AÊ (more than two orders of magnitude larger than themembrane thickness!). The ionic cloud relaxation time constant would then be ofthe order of seconds. Thus, the space charge density inside the membrane is solow and their (average) mobility so slow that practically no charge screening takesplace inside the membrane within the time range of interest (0.1 ms to 1 ms). Incontrast, the ionic cloud relaxation in the aqueous phase is so fast that it readjustsalmost instantaneously to the build-up and decay of P+ in the time range ofinterest.

Thus, there is wide separation in the time domain of three events: (a) the ioniccloud relaxation in the aqueous phase, (b) the light-induced charge separation andrecombination under investigation, and (c) the ionic cloud relaxation inside themembrane. This peculiarity of non-overlapping time domains greatly simpli®es thecalculation. Thus, the electrical calculation can be performed independently of thekinetic calculation. In other words, during each and every moment throughout thetime course of charge separation and recombination, the electrostatic condition

Fig. 21. Light-intensity dependence of AC photoelectric signals. (A) Amplitude of R2 component of

ERP is shown as function of ¯ash energy. (B) Amplitude of transient photocurrent spike from LB ®lm

of bR, in response to step illumination, is similarly shown as function of light power of continuous

illumination. Slope of 458 slope indicates initial linear light dependence. Deviation from linearity

indicates subsequent saturation (not shown in B). See Section 19.3 for detailed discussion of transient

spikes (di�erential responsivity). (Reproduced from Refs. [210] (A) and [211] (B))


prevails in the aqueous phases, because the space-charge distribution there isalways in (quasi-)equilibrium, but it never reaches equilibrium in the membranephase. As a consequence, the space-charge pro®le in the aqueous phases can beanalyzed by classical electrostatics, whereas there is no space charge inside themembrane. Thus, the Poisson±Boltzmann equation is applicable in the aqueousphases, whereas the constant ®eld condition is applicable in the membrane phase.The space-charge pro®le shown in Fig. 22(A) thus represents a snapshot taken ata typical moment during time course of the photochemical kinetic process.

8.1.1. Electrostatic calculationLet us consider an ideal short-circuit condition, in which the bulk regions of the

two aqueous phases are maintained at equipotential (voltage-clamped to zeropotential). Let us also take the bulk region potential as the reference level. ThePoisson±Boltzmann equations for the cytoplasmic side of the aqueous phase(ÿ1<xR0 in Fig. 22(A)), and for the extracellular aqueous phase (dRx<�1 inFig. 22(A)) are set up according to standard procedures [208]. For a symmetricaluni-univalent salt solution such as KCl (ignoring the contributions of other ionsto the ionic strength, for the sake of simplicity), the Poisson±Boltzmann equation,which is valid for both aqueous phases, can be written as follows:

d2Cdx2� ÿ4pFC0

E

�exp

�ÿ FC�x�

RT

�ÿ exp

�FC�x�RT

��

� 8pFC0

Esinh

�FC�x�RT

�, �8:2�

for both ÿ1<xR0 and dRx<�1, where C�x� is the electric potential atcoordinate x, C0 is the bulk salt concentration, E is the dielectric constant ofwater, F is the Faraday constant, R is the universal gas constant, and T is theabsolute temperature. Eq. (8.2) can be rewritten as

F

RT

d2C�x�dx2

� 1

L2sinh

�FC�x�RT

�, �8:3�

with the Debye length

L ��ERT

8pF 2G

r, �8:4�

where G is the ionic strength of the aqueous solution.The boundary conditions at the remote bulk aqueous phases are as follows:

C� ÿ1� ��

dCdx

�ÿ1� C� �1� �

�dCdx

��1� 0: �8:5�

Integration of Eq. (8.3) gives


F

RT

dC�x�dx

�22

Lsinh

�FC�x�2RT

�, �8:6�

where the positive sign is taken for ÿ1<xR0, and the negative sign is taken fordRx<�1. Since the photogenerated P+ is regarded as a sheet of surface chargeat the cytoplasmic interface (with a surface concentration [P+]), application ofGauss' theorem of electrostatics to both interfaces gives two additional boundaryconditions:

Fig. 22. Schematic diagram showing how equivalent circuit is derived from solving Poisson±Boltzmann

equation. (A) Potential pro®le C�x� and charge-density pro®le r�x� are shown across membrane, which

spans from x � 0 to x � d. (B) Pro®les are re-interpreted, in terms of charging of three discrete

capacitances: geometric capacitance (Cg) and two double-layer capacitances (Cd). Photoemf E 0p�t�injects current at left interface. C�0� and C�d � represent potential at left and right membrane±water

interfaces, respectively. Charges on each capacitances, qd, qg and qp, are indicated. Potential pro®le of

equivalent circuit is shown at bottom part. See text for details. (Reproduced from Ref. [163])


E

�dCdx

�0ÿ� Em

�dCdx

�0��4pF�P��, �8:7�

E

�dCdx

�d�� Em

�dCdx

�dÿ, �8:8�

where Em is the dielectric constant of the membrane. The subscripts 0ÿ and 0+

denote that the derivatives are evaluated at x � 0 with the limit approaching fromthe left and from the right, respectively. Similar meanings hold for dÿ and d�.

The remaining boundary condition is provided by the constant ®eld condition:�dCdx

�0��

dCdx

�dÿ� C�d� ÿC�0�

d: �8:9�

Evaluation of Eq. (8.6) at the two membrane±water interfaces gives the followingexpressions:�

dCdx

�0ÿ� 2RT

FLsinh

�FC�0�2RT

�, �8:10�

�dCdx

�d�� ÿ2RT

FLsinh

�FC�d�2RT

�: �8:11�

Substitution of Eqs. (8.9)±(8.11) into Eqs. (8.7) and (8.8) gives the followingequations:

Em

d

�C�d� ÿC�0�

�� 4pF�P�� 2RTE

FLsinh

�FC�0�2RT

�, �8:12�

Em

d

�C�d� ÿC�0�

�� ÿ2RTE

FLsinh

�FC�d�2RT

�: �8:13�

For C�0�, C�d � � 2RT=F (51.2 mV at room temperature), we further makeapproximations such as:

sinh

�FC�0�2RT

�1FC�0�

2RT: �8:14�

After rearranging, we obtain the following relation:

Em

4pd

�C�0� ÿC�d�

�� F�P�� ÿ E

4pLC�0� � E

4pLC�d�: �8:15�

Inspection of Eq. (8.15) leads to the following identi®cation for the expression ofthe geometric capacitance Cg (per unit area) and the double-layer capacitance Cd

(per unit area) in the limit of small surface potentials:


Cg � Em

4pd, �8:16�

Cd � E4pL

: �8:17�

Note that F�P�� is the amount of photogenerated charge qp (per unit area). Eq.(8.15) can therefore be rewritten as follows:

Cg

�C�0� ÿC�d�

�� qp ÿ CdC�0� � CdC�d�: �8:18�

Let us divide qp into two fractions qg and qd according to the following relations:

qd � CdC�0�, �8:19�

qg � qp ÿ qd � Cg

�C�0� ÿC�d�

�, �8:20�

qg � CdC�d�: �8:21�Eqs. (8.19)±(8.21) can be used to de®ne a charge distribution on three discretecapacitances and the corresponding electric potential across each capacitance, asshown schematically in Fig. 22(B). The potential pro®le is highly schematized byconcentrating the excess charges in the double layer into a sheet of unde®nedthickness at a distance L from the interface. A more realistic picture of thepotential pro®le and charge distribution, which can be obtained by integrating Eq.(8.6), is given in Fig. 22(A).

By inspecting Fig. 22(A), it is apparent that the photogenerated surface chargesP+ polarize both the adjacent aqueous solution and the opposite aqueoussolution. Only a fraction of charges qd have been compensated for by the excesscounterions in the double layer of the cytoplasmic side. The remaining fraction ofcharges, qg, are not screened by the ionic cloud inside the membrane and,therefore, they extend their polarizing e�ect, beyond the membrane, into theextracellular aqueous phase, only to be compensated for by the excess counterionsin the double layer on that side.

The equivalent circuit would not be complete without a photoemf (photo-electromotive force) which accounts for the `driving force' (or rather, drivingpotential) of the photocurrent, i.e., the voltage or current source of thephotoelectric signal. Since the photocurrent is driven by an interfacial proton-transfer reaction, one expects the photoemf to be associated with the cytoplasmicinterface, such as is shown in Fig. 22(B). The localization of the photoemf acrossthe interface is indeed consistent with the physical picture, and would give rise tothe appropriate charge distribution (see Section 11.3 for a unique pattern ofcharge distribution on the three capacitances) Ð the photoemf drives thephotocurrent in such a way that positive charges are building up at thecytoplasmic surface and (net) negative charges are building up in the two doublelayers. It is obvious that the only sensible way to connect the photoemf to the


system is to put it in parallel with the double-layer capacitance of the adjacentinterface and in series with the geometric capacitance and the double-layercapacitance of the other interface.

Now we can combine Cg and the Cd on the extracellular side to form a singlecapacitance C 0p according to the following relation:

1

C 0p� 1

Cg

� 1

Cd

: �8:22�

Thus, the following relation can be written:

qd

Cd

� qg

C 0p� qp

C 0p � Cd

: �8:23�

Analysis of the equivalent circuit in Fig. 22(B) gives the following expression ofcharge at the interface:

qp�t� ��t0

E 0p�u�Rp

exp

�uÿ t

t 0p

�du, �8:24�

where

t 0p � Rp

ÿC 0p � Cd

�: �8:25�

Note that, when the charges (qp) recombine, the ¯ow of current splits into twofractions. One fraction proceeds to discharge C 0p and is externally measurable (asimilar splitting appears during charge separation):

I�t� � _qg�t� �C 0p

C 0p � Cd

_qp�t�

� C 0pC 0p � Cd

"E 0p�t�Rp

ÿ 1

t 0p

�t0

E 0p�u�Rp

exp

�uÿ t

t 0p

�du

#:

�8:26�

The other fraction proceeds to discharge the adjacent Cd and is externallyimmeasurable:

i�t� � _qd�t� �Cd

C 0p � Cd

_qp�t�

� Cd

C 0p � Cd

"E 0p�u�Rp

ÿ 1

t 0p

�t0

E 0p�u�Rp

exp

�uÿ t

t 0p

�du

#:

�8:27�

The latter process is tantamount to internal short-circuiting in the AC sense, andit reduces the e�ectiveness of E 0p�t� for generating an externally measurablephotocurrent, by an attenuation factor, C 0p=�C 0p � Cd�. The same externalphotocurrent, I(t ), could be generated if the equivalent circuit were replaced with


another circuit, in which a photoemf Ep�t� is connected in series with Rp and Cp

provided that the values of Ep�t� and Cp are de®ned by the following relations(designated as the irreducible equivalent circuit in Fig. 20):

Cp � C 0p � Cd, �8:28�

Ep�t� � C 0pC 0p � Cd

E 0p�t�: �8:29�

Eq. (8.25) can thus be rewritten as follows:

t 0p � RpCp: �8:30�

This reduced equivalent circuit cannot be further reduced, and is indistinguishablefrom the microscopic equivalent circuit on the sole basis of an externalphotocurrent measurement. It is a simple linear high-pass RC ®lter circuit with atime constant t 0p. The parameter Cp in the reduced equivalent circuit is a parallelcombination of C 0p and the left-hand side Cd. C

0p, in turn, is a series combination

of Cg and the right-hand side Cd.In contrast, the membrane capacitance Cm is a series combination of Cd, Cg, and

Cd:

1

Cm

� 1

Cd

� 1

Cg

� 1

Cd

: �8:31�

The di�erence between the physical origin of Cp and that of Cm is apparent.

8.1.2. Kinetic calculationIn the above electrostatic calculation, only Conditions 1±3 are required.

Conditions 4 and 5 are, however, also required for the kinetic calculation. Theyare essential for the validity of the linear light dependence of ERP and its lack oflatency. If Conditions 4 and 5 are not valid, then the kinetic interpretation of theelectric parameters may become less than straightforward. The equivalent circuitmay still be valid, but the quantitative agreement may not be expected.

Let us now consider the process of interfacial proton binding occurring at thecytoplasmic interface. The case of interfacial proton release at the extracellularinterface can be treated in a similar manner. The proton acceptor A (i.e., H2O) isneutral and has a ®xed concentration whether the pH is bu�ered or not. Theproton donor A+ (i.e., H3O

+) bears a positive charge, and has a ®xedconcentration when the pH is bu�ered. The kinetic equation describing theproduction rate of charge separation can be written as

d�P��dt� l�P� ~I�t� ÿ k�A��P��, �8:32�

where [P+] and [P ] are the surface concentrations of P+ and P, respectively, [A ]


is the ®xed proton acceptor concentration at the intracellular side, ~I �t� is the lightintensity per unit area, l is the proportionality constant which includes thequantum yield and the absorption cross section, and k is the second-order rateconstant of the reverse interfacial proton-transfer reaction. At low light intensity,we have �P�� P �. Therefore, [P ] can be replaced by its initial value [P ]0, thetotal pigment surface concentration. Eq. (8.32) can be solved for [P+]:

�P��t� � l�P�0�t0

~I �u�exp�k�A��uÿ t� du: �8:33�

The physical meaning of t 0p and E 0p�t� can be deduced by a comparison of theresult of the kinetic calculation with the equivalent circuit analysis. By identifyingqp with F[P+], Eq. (8.33) can be rewritten as follows:�t

0

E 0p�u�Rp

exp

�uÿ t

t 0p

�du � lF�P�0

�t0

~I�u�exp�k�A��uÿ t� du: �8:34�

Finally, the following identi®cations can be made:

1

t 0p� k�A�, �8:35�

lF�P�0 ~I �t� � E 0p�t�Rp

: �8:36�

Thus, the parameter 1=t 0p is the pseudo-®rst-order rate constant of the reverseinterfacial proton transfer. Eq. (8.36) indicates that the photoemf is proportionalto the surface concentration of the membrane-bound pigment and is a linearfunction of the illuminating light, whereas the resistance Rp is inverselyproportional to the forward charge-transfer rate.

The validity of Eq. (8.32) depends on the validity of Conditions 4 and 5.However, the restriction imposed by these conditions can be relaxed. For example,if the forward reaction (i.e., formation of P+ from its precursor) is independentof [P+], a relation similar to (8.32) can be obtained and, therefore, Eq. (8.35)remains valid. As for Eq. (8.36), it may or may not remain valid. It will remainvalid if the formation of the precursor of P+ has a linear light dependence.Otherwise, the function ~I�t� can be implicitly de®ned, and essentially describes thetime dependence of the formation rate of the precursor of P+. Therefore, theagreement of the time course of the photoemf with that of the stimulating lightintensity is equivalent to the condition of the lack of latency. The latter conditionis the hallmark of ERP-like signals.

8.2. Gouy±Chapman analysis of oriented dipole mechanism

A Gouy±Chapman analysis of the oriented dipole mechanism is similar to that


of the interfacial proton transfer mechanism. Here, the di�erences will behighlighted.

Again for simplicity, let us consider a prototype case in which the separatedcharges span the entire thickness of the membrane. In real life, the extent ofcharge separation in bR and rhodopsin is not exactly known, but it is likely to beonly a fraction of the entire membrane thickness. However, this simpli®cationdoes not detract from the essential physical picture.

While the interfacial proton transfer generates a sheet of surface charge at theinterface where the transfer takes place, two sheets of surface charges of equalmagnitude but opposite polarity are generated, forming an array of orientedelectric dipoles. With appropriate and minor modi®cations, all the conditionslisted in Section 8.1, except Condition 2 (i.e., the condition of ®xed protonacceptor concentration), remain in e�ect. Instead, we may replace Condition 2with the following assumption: the recombination of the oriented dipoles is a ®rst-order process.

The Poisson±Boltzmann equation for the two aqueous phases is set up in asimilar fashion. The boundary conditions (8.7) and (8.8) are now replaced by

E

�dCdx

�0ÿ� Em

�dCdx

�0�ÿ4pF�Pÿ�, �8:37�

E

�dCdx

�d�� Em

�dCdx

�dÿÿ4pF�P��, �8:38�

where [P+] and [Pÿ] are the surface charge concentration at the two interfaces,respectively, due to the formation of transient oriented dipoles. Note that�P�� Pÿ�.

Eqs. (8.12) and (8.13) are now replaced by the following pair of equations:

Em

d

�C�d� ÿC�0�

�ÿ 4pF�Pÿ� � 2RTE

FLsinh

�FC�0�2RT

�, �8:39�

Em

d

�C�d� ÿC�0�

�ÿ 4pF�P�� ÿ2RTE

FLsinh

�FC�d�2RT

�: �8:40�

As a consequence, the expressions relating the potentials of the three capacitancesand the amount of charges on each of them become the following:

Cg

�C�d� ÿC�0�

�� F�Pÿ� � CdC�0� � F�P�� ÿ CdC�d�: �8:41�

Reinterpretation of these expressions as charge-potential relationships in terms ofthe three fundamental capacitances describes how events at the two interfacesinteract. Again, the negative surface charges on the left-hand side are split intotwo fractions. One fraction is exactly equal to the charges in the adjacent doublelayers, but with opposite polarity, CdC�0�. This fraction is considered to be stored


on the left-hand side Cd. The other fraction is considered to be stored on Cg.Similarly, the surface charges on the right interface are split into two fractions.One fraction is stored on Cd, and the other fraction is on Cg. Thus, the doublelayers merely screen part of the surface charges. The unscreened portions ofsurface charges are stabilized by pairing with each other, and they constitute thecharges being stored in Cg. These stored charges on Cg are responsible for thepresence of the light-induced electric ®eld inside the membrane.

Eq. (8.41) can be interpreted as a description of the amount of charges and thepotential across three individual capacitances, as shown schematically in Fig. 20.Again, an inspection of the charge on the three capacitances makes it clear thatthe only sensible way to place a photoemf is to put it across the geometriccapacitance, i.e., across the full extent of charge separation. In the case of chargeseparation that does not span the entire thickness of the membrane, the photoemfwill ride across the two sheets of charges that represent the transient array ofelectric dipoles, which are completely buried inside the membrane. Since therelaxation of charge recombination is probably not in®nitely fast, a series resistorRp is inserted, so that the ®rst-order rate constant of charge recombination equals1=RpCp, where Cp is given by

Cp � Cg � Cd

2, �8:42�

which indicates that the photoemf is in series with the two double-layercapacitances, but is in parallel with the geometric capacitance.

Following the same procedure, it can be shown that the microscopic equivalentcircuit can be further reduced to the same irreducible equivalent circuit, derived inthe previous section.

The time constant t 0p must now be interpreted as the inverse of the (true) ®rst-order time constant of charge recombination.

8.3. Concept of chemical capacitance

The most salient feature of the irreducible equivalent circuit is that thephotovoltage (or photocurrent) source is AC-coupled to the external world via thecapacitance Cp. We named the parameter Cp the chemical capacitance [162,163].As we shall demonstrate in Section 11.3, the chemical capacitance is physicallydistinct from the ordinary membrane capacitance. The network formed by Rp andCp is identi®ed to be a linear high-pass RC ®lter circuit with the cut-o� frequencyfp, which is related to the time constant t 0p by the following relationship:

fp � 1

2pt 0p: �8:43�

If Ep were connected to a pure resistor, a photocurrent proportional to Ep wouldgo through that resistor. This current, which carries net charges across theresistor, is a DC photocurrent. Now Ep is connected to a linear high-pass RC


®lter, and therefore no DC photocurrent can go through. In the Fourier sense, theAC components of the photocurrent with a frequency below fp will be attenuated.The displacement photocurrent is therefore an AC (capacitative) photocurrent.This is why faster photosignal components have a greater amplitude than slowerones, given the same amount of charge displacement. Of course, faster signalshave a shorter duration. This is also part of the reason why a leaky Takagi±Montal ®lm has little e�ect on the measurement of AC photocurrent; the leakingcurrent is a DC current (see also Section 9.1).

8.4. More re®ned molecular models

The IPT and the OD models represent two distinct types of prototype molecularmechanisms. As pointed out in the analysis, the sheet of light-induced surfacecharges in the IPT model may not be exactly located at the membrane surface, butrather in the membrane interior of some distance from the surface. In the ODmodel, the pair of separated charges may not span the entire thickness of themembrane. These re®nements can be readily incorporated into the models. Theequivalent circuit will appear similar macroscopically. The capacitances, such as Cd

and Cg in the diagram, may now become composite ones, with more than one kindof dielectric material sandwiched together, as illustrated in Fig. 8 in Ref. [31].

An additional re®nement may be carried out by including the dipole potentiallocated near the membrane surface. The inclusion of the dipole potential, which isusually static and light-independent, does not alter the overall physical picturepresented above, because of the principle of linear superposition.

The derivation here would be adequate for the purpose of conceptually linkingthe macroscopic equivalent circuit to the microscopic molecular picture. All thesere®nements would be required if one is interested in ®tting the microscopic modelswith molecular parameters. In this regard, inclusion of these re®nements may stillnot be adequate in view of the crude agreement of the Gouy±Chapman theory interms of measurable molecular parameters (see Section 20.2).

9. Equivalent circuit analysis of AC photoelectric signals

The equivalent circuit derived in the preceding section represents thephotochemical event. A complete equivalent circuit must also include the RCrelaxation event of the inert supporting structure Ð the lipid bilayer, consisting ofthe ordinary membrane resistance (Rm) and membrane capacitance (Cm). Such acomplete equivalent circuit is shown in Fig. 23. The circuit contains two separateRC networks placed in parallel with each other. The photochemical branch alsocontains an additional element Rs, which is placed in parallel with Cp. Rs

represents the resistance encountered by the DC photocurrent. The parallelconnection is an appropriate one, because of the following consideration. The ACphotocurrent that ¯ows through Cp represents the fraction of separated chargesthat does recombine (undergoing reverse charge transfer), whereas the DC


photocurrent that ¯ows through Rs represents the remaining fraction that doesnot recombine (undergoing further forward charge transfer). Thus, the AC andthe DC photocurrents represent two di�erent options of the disposition of theseparated charges, and, therefore, must ¯ow through two circuit paths that areconnected in parallel instead of in series. The equivalent circuit also includes theaccess impedance (or access resistance, Re).

The photocurrent I(t ), as detected by the external measuring device, has ananalytical solution in terms of the parameters in the equivalent circuit (AppendixA.1.1). The results are summarized here.

9.1. Strictly short-circuit measurement

Consider a measurement under a strictly short-circuit condition, i.e., Re � 0.The analytical solution of the photocurrent is independent of Rm and Cm, and isgiven by

I�t� � Ep�t�Rp

ÿ�1

tp

ÿ 1

RsCp

��t0

Ep�u�Rp

exp

�uÿ t

tp

�du, �9:1�

where

1

tp

� 1

RpCp

� 1

RsCp

: �9:2�

Fig. 23. Universal equivalent circuit for photoelectric e�ect. Photochemical event is represented by RC

network including: (a) photoemf Ep�t�, (b) internal resistance Rp of Ep�t�, (c) chemical capacitance Cp,

and (d) transmembrane resistance Rs. With exception of strictly short-circuit measurement, time course

of photoelectric signal is further shaped via interaction with another RC network, formed by: (a)

membrane resistance Rm, (b) membrane capacitance Cm, and (c) access resistance Re. The charges on

Cm and Cp are qm and qp, respectively. Also shown are currents through various parts of the network.

See text for further explanation. (Reproduced from Ref. [30])


Note that the time constant tp as de®ned by Eq. (9.2) di�ers slightly from t 0p asde®ned by Eq. (8.30). This is because charge draining by a DC photocurrentmakes the relaxation slightly faster; the discharging path Rs can be regarded asbeing in parallel with the path Rp. In chemical terminology, the continuation ofthe forward proton transfer from the cytoplasmic surface towards the membrane(or rather protein) interior contributes to the decline of [P+], as does the reverseproton transfer (see Section 12).

Let us consider now the use of a stimulating light pulse, which has a durationmuch shorter than the time constant of charge recombination. The photoemf canbe regarded as being proportional to the d-function: Ep�t� � E0 � d�t�, where E0 isa constant scale factor depending on the light intensity, wavelength, and geometryof the thin ®lm, etc. As de®ned mathematically, d�t� has an in®nite amplitude andan in®nitesimal duration, but a ®nite area of unity under the curve of its graphicrepresentation. Thus, at time zero, charges separate instantaneously, and aninstantaneous surge of photocurrent goes through the chemical capacitance as wellas the external measuring device. Since Re � 0, all photocurrent goes through Re,and no photocurrent charges the membrane capacitor Cm or leaks through Rm.Therefore, no photovoltage will build up across the membrane, i.e., the membraneis short-circuited. Just as fast as the photoemf has been turned on, it is turned o�upon cessation of illumination and the chemical capacitance begins discharging.As shown in Fig. 24, the photocurrent appears as a d-function-like spike and theninstantaneously reverses its direction Ð the reverse phase of the photocurrent isthe dark current that discharges Cp. The reversed photocurrent subsides along anexponential time course with the time constant tp.

The analytical solution for the photocurrent with a d-function-like photoemf isgiven by

I�t� � E0

Rp

"d�t� ÿ

�1

tp

ÿ 1

RsCp

�exp

�ÿ t

tp

�#: �9:3�

The photocurrent consists of a fast rising positive spike with an in®nitely narrowwidth and an in®nite amplitude but a ®nite area under the curve, and a negativeexponential component which decays with the time constant of tp. Thephotocurrent shown in Eq. (9.3) can be decomposed into an AC component,Iac�t�, and a DC component, Idc�t�:

Iac�t� � E0

Rp

"d�t� ÿ 1

tp

exp

�ÿ t

tp

�#, �9:4�

Idc�t� � E0

Rp

� 1

RsCp

exp

�ÿ t

tp

�: �9:5�

Note that the positive spike of the AC component encloses an area of E0=Rp

above the base line, whereas the negative exponential peak encloses an equal area


below the baseline. Therefore, Iac�t� satis®es the zero time-integral condition (5.1).Note that the waveform (5.2), proposed by Hodgkin and O'Bryan [145], has therudimentary form required to satisfy Eq. (5.1), if only the parameter B is set tounity. However, the free parameter B is required to ®t the spike to R1 and theexponential term to R2. Thus, our interpretation imposes a subtle di�erence: bothterms of Eq. (9.4) ®ts either R1 or R2, but not both, with a single set ofparameters.

The DC component consists of a single positive exponential term with the sametime constant, but with a much smaller amplitude. In fact, the amplitude of thelatter is smaller by a factor of tp=RsCp, or roughly Rp=Rs. Thus, the DCcomponent is virtually undetectable when the AC component is being measured.However, it is possible to observe the DC component of the photosignal, if thephotosignal is subjected to the action of a low-pass ®lter that preferentiallysuppresses the AC component (see Section 12). Note that Idc�t� does not satisfythe zero time-integral condition.

As mentioned in Section 5.6, LaÈ uger's [169] graphic depiction of thecapacitative photocurrent is actually the DC photocurrent. This can be madeapparent by an inspection of Fig. 13 and a reference to Eq. (9.5), which againillustrates the fallacy of the model described in Fig. 13. It is not possible to

Fig. 24. Photosignal relaxation time courses as calculated in accordance with equivalent circuit shown

in Fig. 23. Two types of illumination are considered: brief d-function-like light pulse and long square-

wave light pulse. Note that relaxation time course varies with change of discharging time constant, tm,

as de®ned by Eq. (9.11). Under open-circuit conditions (i.e., Re � 1), photosignal relaxes with two

exponential time constants, ts and tl, of which longer one, tl, approaches membrane RC relaxation

time constant, RmCm. Under short-circuit or near-short-circuit conditions, photosignal in response to

long square-wave light pulse exhibits `on' spike and `o�' spike, as expected in linear high-pass RC ®lter.

This characteristic waveform may disappear, if tm exceeds critical value, tmc. (Reproduced from Ref.

[30])


represent an AC photocurrent component with a single exponential term; anadditional d-function-like spike must be included in order to satisfy the zero time-integral condition.

A long square-wave light pulse (with a step function-like waveform) is oftenused in the measurement of DC photovoltages (e.g., see Fig. 8). However, a sharprise and fall of the pulse often generates a transient photoresponse in addition to aDC photovoltage (see also Section 12). It is of interest to see how the transientresponse is described by the equivalent circuit. By taking Ep�t� to be a stepfunction, which is zero at time t � 0 and rises to a ®xed value E0 with no latency,the on-response of the photocurrent is

I�t� � E0

Rp

� tp

RsCp

� E0

Rp

�1ÿ tp

RsCp

�� exp

�ÿ t

tp

�

1E0

Rs� E0

Rp� exp

�ÿ t

tp

�:

�9:6�

Similarly, the o�-response is

I�t� � ÿE0

Rp

�1ÿ tp

RsCp

�� exp

�ÿ t

tp

�1ÿ E0

Rp

� exp

�ÿ t

tp

�, �9:7�

where t � 0 is taken as the moment of light-o�.This means the photocurrent will rise instantaneously to a peak magnitude of

E0�1=Rs � 1=Rp� and then decay exponentially with a time constant tp, not tothe baseline, but to a ®xed steady state DC photocurrent of the magnitudeE0=Rs. The o�-response shows an instantaneous decline of the photocurrent to alevel about E0=Rp below the baseline, which is then followed by an exponentialdecay back to the baseline. Had Rs been set to in®nity, the on-response wouldhave decayed to the baseline eventually. The steady-state level when Rs is ®nitethus represents the DC photocurrent. The on-overshoot (positive spike) and theo�-overshoot (negative spike) re¯ect the presence of the AC photocurrent; theexponential term in the on-response is exactly canceled by that in the o�-response.

The relative ease in observing the AC component at high frequency can bereadily understood by examining the equivalent circuit. The AC component isthe photocurrent passing through the series capacitance Cp, whereas the DCcomponent is the photocurrent passing through Rs. Thus, at a su�ciently highfrequency, the impedance due to Cp can be neglected. As a result, the ACcomponent has a source impedance of the value of Rp, whereas the DCcomponent has a source impedance of the value Rp � Rs, or simply Rs. Thus,the amplitude of the AC photocurrent far exceeds that of the DCphotocurrent.

Since the source impedance declines from its DC value of Rs to the value ofRp at su�ciently high frequencies (i.e., megahertz), a short-circuit condition,which is met at the steady-state measurement, may not be adequate for the


measurement of the AC photoelectric signal. The short-circuit condition requiresthat the access impedance Re be much less than Rp. A lack of appreciation ofthis `tricky' feature has contributed to misinterpretation of some photoelectricdata (see Sections 11).

9.2. Measurements under conditions in between short-circuit and open-circuit

If, however, the access impedance Re is neither zero nor in®nite as comparedwith the source impedance, the measurement will be neither strictly open-circuitnor strictly short-circuit. The photocurrent splits into two fractions, which arepartitioned between the path to the external circuit and the path to themembrane RmCm circuit. As a result, the photocurrent relaxation will begoverned by the interaction of two RC circuits. A second-order ordinarydi�erential equation can be set up to describe the situation (Appendix A.1.1).The resulting photocurrent going through the external circuit contains twoexponential convolution terms instead of just a single one, as in Eq. (9.1):

I�t� �ÿ1=ts ÿ 1=RsCp

�ReCm�1=ts ÿ 1=tl �

�t0

Ep�u�Rp

exp

�uÿ t

ts

�du

ÿÿ1=tl ÿ 1=RsCp

�ReCm�1=ts ÿ 1=tl �

�t0

Ep�u�Rp

exp

�uÿ t

tl

�du,

�9:8�

where ts and tl are de®ned by the following equations:

1

ts

� 1

2

24� 1

RpCm

� 1

tp

� 1

tm

�

��

1

RpCm

� 1

tp

� 1

tm

�2

ÿ4�

1

RpCmRsCp

� 1

tptm

�s 35, �9:9�

1

tl

� 1

2

24� 1

RpCm

� 1

tp

� 1

tm

�

ÿ��

1

RpCm

� 1

tp

� 1

tm

�2

ÿ4�

1

RpCmRsCp

� 1

tptm

�s 35: �9:10�

The parameter tp is de®ned in Eq. (9.2), and the parameter tm is de®ned by thefollowing equation:

1

tm

� 1

ReCm

� 1

RmCm

: �9:11�


Note that tm is the time constant for discharging Cm, and can be reduced bymeans of either external short-circuiting (a voltage-clamp measurement) orinternal short-circuiting (action of an ionophore which reduces Rm).

By setting Rs to in®nity, the DC component is ignored. Again, given a d-function-like impulse of illumination, the observed AC photocurrent will decay intwo time constants, ts and tl:

Iac�t� � E0

RpReCm�1=ts ÿ 1=tl ��1

ts

exp

�ÿ t

ts

�ÿ 1

tl

exp

�ÿ t

tl

��: �9:12�

Note that Eq. (9.12) consists of two exponential terms of opposite polarity. Thetwo time constants, ts and tl, are neither tp nor tm but rather a mixture of anumber of RC constants including tp and tm. However, the intrinsic relaxationtime constant tp can be recovered by deconvolution. In fact, the pair ofsimultaneous Eqs. (9.9) and (9.10) can be solved for Rp and Cp in terms of theremaining parameters. These remaining parameters are all experimentallymeasurable. It can be shown that unique solutions for Rp and Cp do exist(Appendix A.1.2). Thus, the equivalent circuit is completely de®ned byexperimental measurements, and there are no freely adjustable parameters. Thescale factor E0 can be determined by normalization of the computed waveformagainst the measured one.

An intuitive way to explain why our equivalent circuit analysis leaves no roomfor freely adjustable parameters is to rewrite Eq. (9.12) as follows:

I�t� � Asexp

�ÿ t

ts

�ÿ Alexp

�ÿ t

tl

�, �9:13�

where the two exponential time constants, ts and tl, are de®ned by Eqs. (9.9) and(9.10), whereas the two amplitudes, As and Al, are related to the circuitparameters by the following relations:

As � E0

Rp

� 1

ReCmts�1=ts ÿ 1=tl � , �9:14�

Al � E0

Rp

� 1

ReCmtl�1=ts ÿ 1=tl � : �9:15�

Note that the two amplitudes are related to the two time constants by thefollowing simple inverse proportionality relation:

As

Al

� tl

ts

: �9:16�

In general, a bi-exponential decay curve is determined by four independentparameters: two for the time constants and two for the amplitudes. The twoamplitude factors can be replaced with the ratio As=Al and a scale factor for peak


normalization. Thus, the two exponential time constants and the scale factor canbe determined experimentally. This leaves the amplitude ratio as the lastparameter to be determined, but the inverse proportionality relation (9.16) ®xesthe last parameter. Therefore, there are no free parameters in our model. Thus,the experimental test of the equivalent circuit model boils down to the veri®cationof the inverse proportionality relation between the amplitudes and the timeconstants (9.16). If our model is indeed correct, Eq. (9.16) can be used as acriterion for a pure AC photoelectric signal component. Eq. (9.16) also impliesthat the photocurrent satis®es the zero time-integral, since the area under anexponential curve is equal to the product of the peak amplitude and the decaytime constant (Asts � Altl).

The time course of the photocurrent in response to a long square-wave lightpulse is given as follows. For the on-response,

I�t� � E0

Re

� 1

1� ÿRs � Rp

��1=Re � 1=Rm �

ÿ E0

Rp

�ÿRsCp ÿ ts

�exp� ÿ t=ts � ÿ

ÿRsCp ÿ tl

�exp� ÿ t=tl �

ReCmRsCp�1=ts ÿ 1=tl � :

�9:17�

For the o�-response,

I�t� � E0

Rp

�ÿRsCp ÿ ts


ÿRsCp ÿ tl


ReCmRsCp�1=ts ÿ 1=tl � : �9:18�

9.3. Open-circuit measurement

It is instructive to see what happens when Re approaches in®nity, i.e., open-circuit condition. The above equations shown in Section 9.2 still hold, but nowthe measurement must be reported in terms of electric potential, V�t� � I�t� � Re.Here, Re is very large and I(t ) is very small but their product is ®nite. Also,tm1RmCm. T. Thus,

V�t� �ÿ1=ts ÿ 1=RsCp

�Cm�1=ts ÿ 1=tl �

�t0

Ep�u�Rp

exp

�uÿ t

ts

�du

ÿÿ1=tl ÿ 1=RsCp

�Cm�1=ts ÿ 1=tl �

�t0

Ep�u�Rp

exp

�uÿ t

tl

�du:

�9:19�

In principle, an open-circuit measurement provides equivalent information to whatis provided by a short-circuit measurement. In practice, this is hardly feasible. Thefollowing analysis will explain why.

From Eqs. (9.9) and (9.10), it follows that


1

tstl

� 1

tptm

� 1

RpCmRsCp

, �9:20�

1

ts� 1

tl� 1

tp� 1

tm� 1

RpCm: �9:21�

To a crude approximation, Cp1Cm, and Rs1Rm. Thus, tp � RpCp1RpCm, andtm � RmCm1RsCm. Therefore, we have

1

tstl

1 2

tptm

, �9:22�

1

ts

� 1

tl

1 2

tp

� 1

tm

, �9:23�

of which the solutions are

ts1tp

2, �9:24�

tl1tm: �9:25�

The faster exponential component contains the information about thephotochemical relaxation, but the slower component contains information that isexclusively the passive relaxation of the membrane RC network. This is the caseof excessive interaction between the photochemical event and the membrane RCevent. In principle, the open-circuit data contains as much information as the datamade under near-short-circuit conditions using the tunable voltage clamp method.In practice, it is di�cult to obtain an accurate value of tp by deconvolution.

Furthermore, the slower component is so much smaller than the fastercomponent that a high-gain ampli®er must be used to measure it. Because of theconcurrent ampli®cation of noises, a low-pass ®lter is often needed to suppress thenoises and thus, inadvertently, also suppresses the faster component that containscrucial photokinetic information.

The corresponding result, when a long square-wave light pulse is used, is givenas follows. For the on-response,

V�t� � E0Rm

Rm � Rs � Rp

ÿ E0 �ÿRsCp ÿ ts


ÿRsCp ÿ tl


RpCmRsCp�1=ts ÿ 1=tl � :

�9:26�

For the o�-response,


V�t� � E0 �ÿRsCp ÿ ts


ÿRsCp ÿ tl


RpCmRsCp�1=ts ÿ 1=tl � : �9:27�

Note that the constant term in the on-response, E0Rm=�Rm � Rs � Rp�, is the DCphotovoltage. It contains only a fraction of E0, because the voltage is dividedamong Rm, Rs, and Rp, as can be readily seen from applying the principle ofvoltage dividers in electronics.

The two exponential terms both in the on-response and in the o�-responseconstitute the AC photovoltage. The waveform may appear as a monotonic riseupon illumination and a monotonic decay upon cessation of illumination, or mayappear with an on-overshoot or o�-overshoot (Fig. 24). Usually, RsCp is greaterthan ts, but it may be greater or smaller than tl. If RsCp is smaller than tl, thenthe two exponential terms will have the same polarity, both negative in the on-response and both positive in the o�-response, and the photovoltage will risemonotonically towards its DC value and decay monotonically towards thebaseline, not with a single exponential time course but with two exponential timeconstants, ts and tl. The shorter time constant will almost certainly be overlooked.

If, however, RsCp is greater than tl, then the two exponential terms will haveopposite polarities and there will be a positive and a negative spike (on- and o�-overshoot). The positive spike rises with ts and decays with tl, and the negativespike is similar.

The same remarks apply to the photocurrent measured with a ®nite but non-zero access impedance (see Eqs. (9.17) and (9.18)). Note that the strictly short-circuit photocurrent always has a positive and a negative spike.

Consider now the case of a monotonic open-circuit photovoltage. As the timeconstant tm is diminished either by decreasing Re or by decreasing Rm, themonotonic waveform will be transformed into a spiky waveform at a criticalstage. This is because a reduction of tm leads to a decrease of the parameter tl.The critical time constant at which this transition takes place is designated as tmc

in Fig. 24 [30]. This peculiar e�ect was demonstrated in the data of Drachev et al.[152], as shown in Fig. 8, but these latter authors proposed a di�erentinterpretation.

The spike-like waveform shown in Fig. 8(B) is often referred to as di�erentialresponsivity. Thus, according to our interpretation, di�erential responsivity is amanifestation of the AC photoelectric e�ect. Alternative interpretations will bediscussed and refuted in Sections 11.1 and 19.3.

9.4. Optimizing measurement by tuning access impedance

The tunable voltage clamp method [162,206], which tunes the access impedance,enables us to optimize the measurement by bringing the two exponentialcomponents into a range feasible for accurate measurements as well as a rangewhere the computed parameters are sensitive to the variations of measuredparameters. Obviously, open-circuit conditions are the worst condition for thispurpose. We found that the optimal tuning of the access impedance is such that


tm1tp, �9:28�

or

Re1Rp: �9:29�

In the terminology of electronics, this is called impedance matching. The presenceof a non-zero access impedance is an asset rather than a nuisance.

10. Analysis of AC photoelectric signal from bacteriorhodopsin

10.1. Search for method to separate B1 and B2

The equivalent circuit analysis, described in Section 9, applies only to ACphotosignals generated by a single step of charge separation and recombinationwith either a ®rst-order or a pseudo-®rst-order kinetics [163]. Thus, for a singlechemical relaxation process, there are no freely adjustable parameters in theequivalent circuit, because all input parameters for a computation based on theequivalent circuit can be determined experimentally. If, however, there are two ormore chemical processes in the photosignals, such as those from reconstitutedrhodopsin or bR membranes, two or more separate sets of parameters must beused: one set for each process. The parameters can no longer be uniquelydetermined by experiments, and curve ®tting by trial and error is thus required.This latter requirement is deemed less satisfactory, because it is tantamount to theintroduction of one or more free parameters, which determine how these signalcomponents are to be decomposed. An agreement between the equivalent circuitand the measured (composite) signal would be less compelling evidence for itsvalidity. On the other hand, the mainstream approach commonly found in theliterature decomposes the photosignal into as many exponential terms as possible.The experimental data thus impose no constraints on the individual parameters Ðthe mainstream approach enlists twice as many free parameters as the exponentialterms: one for the decay time constant and another for the amplitude of eachexponential terms. The mainstream approach thus guarantees an agreementbetween the model and the data under any circumstance. But its validity can bequestioned by experimental inconsistencies (see Sections 11.4 and 20).

The prerequisite for testing the equivalent circuit is to ®nd a physical methodthat allows for a pure component to be isolated. We initially turned to theliterature of the ERP for inspiration. The only known method for separating R1from R2 was by lowering the temperature. For semi-quantitative analysis, thismethod is adequate. In view of the similar temperature dependence of the ERP-like signal from bR, we attempted to isolate the pure B1 signal by lowering thetemperature. The attempt was unsuccessful, presumably, because the temperaturewas not low enough to completely suppress the B2 component. Subsequently, wefound that the B2 component can be selectively inhibited by treating the


membrane with ¯uorescamine [32,213]. Unfortunately, the inhibition of B2 wasagain incomplete.

Apparently, a di�erent approach was required. The approach was to search fora new method of reconstitution that enables us to form a bR membrane thatexhibits only the B1 component. Since a pure B1 component is expected to ®t theequivalent circuit, and since there is no freely adjustable parameters that can forcea signal to ®t the equivalent circuit, the titration end point of the search for theunknown method could be taken as the ®nding of a reconstitution method thatmakes it possible for a photosignal to consistently ®t the equivalent circuit. Inother words, the agreement with the equivalent circuit is the criterion of the`purity' of a photosignal component.

10.2. Method for isolating pure B1 signal

We succeeded in isolating the B1 component by means of the ML method asdescribed in Section 6.8. When an ML thin ®lm reconstituted from puri®ed purplemembranes is illuminated with a pulsed laser light, a photoelectric signal, which is®ve to ten times larger in amplitude than that found in a Trissl±Montal ®lm, canbe observed. This signal consistently agrees with the prediction of the equivalentcircuit, and consistently satis®es Eq. (9.16).

A typical photosignal obtained by means of the ML method at 258C and pH 2is shown in Fig. 25 (noisy curves). A computed theoretical curve based on theequivalent circuit of Fig. 23 is superimposed (smooth curves). All the inputparameters for the computation listed in the legend are determined experimentally.For each computation, the input parameters must be the matching set. Uses ofparameters determined for a ®lm other than the one with which the theoreticalcurve was to be compared invariably led to poor ®t. In the case in which the valueof Re mismatched, deviation of the theoretical curve from the measured one wasconsiderable.

The negative feedback loop of the operational ampli®er in the measuring devicealso serves as a linear low-pass RC ®lter, and its e�ect on the measured signalshould be included in the computation, i.e., the low-pass ®lter RC time constantof this feedback loop is taken as the instrumental time constant tf (� RfCf , asshown in Fig. 19(B)). This was implemented by subjecting the photocurrentdescribed by Eq. (9.8) to a process of convolution with a low-pass ®lter timeconstant of tf � 0:355 ms, which was determined experimentally rather thancalculated (Cf includes stray capacitance). The light pulse was not strictly a d-function. It was approximately a triangular function (Fig. 25(B)). In thecomputation, Ep�t� is assumed to have the same time course of the power of thelight pulse, and is taken to be a triangular function with a half-width duration of0.8 ms.

Computation, based on the experimentally derived input parameters, essentiallydetermines the entire time course of the photocurrent except for a scale factor.Since the photocurrent is a linear function of the photoemf, the scale factor canbe determined by normalization of the (positive) peak of the signal. The


Fig. 25. Equivalent circuit analysis of B1 component. ML method was used for reconstitution.

Aqueous solution contained 0.1 M KCl and 10 mM L-histidine, bu�ered at pH 2. Measurement was

made, at 258C, with access impedance of 39.2 kO and instrumental time constant of 0.355 ms. Lightsource was pulsed dye laser (590 nm). Light pulse was simulated with triangular waveform, with half-

height duration of 0.8 ms. Experimentally determined input parameters are: ts � 3:4 ms, tl � 24:0 ms,tm � 6:42 ms, and Rm � Rs � 1. These parameters, together with Re, provide su�cient information to

compute remaining parameters: Rp � 60:3 kO, Cp � 211 pF, and tp � 12:7 ms. Computed curves

(smooth traces) are superimposed on measured curves (noisy traces), after normalization with respect to

positive peak. Normalization yields peak photoemf of 155 mV. Same data are shown in two di�erent

scales (A and B). Measured laser pulse is also shown (bottom trace in Record B). (Reproduced from

Ref. [205])


normalization process yields a peak photoemf of 155 mV. The corresponding ®rst-order relaxation time constant tp, obtained by deconvolution, is 12.7 ms(Rp � 60:3 kO, Cp � 211 pF). The error incurred in computing tp is less than 6%,although the errors for Rp and Cp are greater. Note that the root-mean-squaredeviation of the theoretical curve from the experimental curve was found to be 2.2nA, which is comparable to the noise level of 1.6 nA (root-mean-square value) inthe measured signal; the ®t was as good as can be expected, considering thesignal-to-noise ratio of the data.

The same set of data is shown on an expanded time scale along with thewaveform of the stimulus laser pulse in Fig. 25(B). Note that the e�ect ofconvolution of the nonzero pulse width with the low-pass ®lter time constant (tf)was included in the computation. In view of the excellent agreement of thecomputed rise phase and the measured one, we conclude that the assumption thatthe photoemf has the same time course as the light pulse is valid, i.e., there is nodetectable latency (of the B1 component) at a time resolution of 0.335 ms.1

Statistical analysis of data collected from separate membranes at pH 2 gives thevalues of tp of 12:320:7 ms [205].

10.3. E�ect of varying access impedance and thickness of Te¯on thin ®lm

The inclusion of the access impedance in equivalent circuit analysis is crucial tothe implementation of the tunable voltage-clamp measurement. The use of Te¯on-supported thin ®lms is crucial to ensure su�ciently good data quality (in terms ofsignal-to-noise ratio). An obvious question to ask is: might the agreement betweenthe theoretical curve and the measured photosignal, shown in Fig. 25, befortuitous because of the choice of a particular value of the access impedance and/or the presence of the Te¯on ®lm?

Two separate measurements were made with the same ML ®lm preparation,under the same conditions, except for two di�erent values of the access impedance(20 and 40 kO) [205] (Fig. 26). Two separate sets of input parameters wereobtained from measurements. The experimental curve obtained at Re � 20 kO wascompared with a theoretical curve, which was computed by using a procedureslightly di�erent from that used in Fig. 25: the input parameters used in thecomputation for the condition Re � 20 kO were the values of circuit parameters(except Re) obtained from the analysis of the experimental curve measured atRe � 40 kO. Normalization yielded a peak photoemf of 120 mV. The role of thetwo experimental curves was then reversed so that the experimental curve at Re �40 kO was compared with the computed curve based on parameters obtained atRe � 20 kO. In this latter computation, the photoemf turned out to be 122 mV.The agreement of the time course as well as the determined values of peak

1 The shortest risetime of the AC photoelectric signal from a reconstituted bR membrane was

reported by Simmeth and Ray®eld, using an open-circuit method [214]. The risetime was about 5 ps,

which is limited by the instrumental time constant.


photoemf indicate that a cross-prediction can be made entirely from ameasurement previously made at a di�erent value of the access impedance. Inother words, the two separate measurements with di�erent Re values re¯ect thesame kinetic process, though the two experimental curves exhibit signi®cantlydi�erent (apparent) relaxation time courses. In fact, we found that tp measured atRe � 20 kO is not statistically di�erent (at the 5% level of signi®cance) from thatmeasured at Re � 40 kO (the two sets of data were pooled in the compilation ofTable 2). Thus, the relaxation time course of the photocurrent can be modulatedby varying the access impedance. In other words, the relaxation time course isin¯uenced by external loading. In view of the dependence of the apparentrelaxation time course on the measurement condition, an attempt to interpret theapparent relaxation time constant without a detailed analysis could lead tomisleading conclusions.

Fig. 26. E�ect of varying access impedance on measured B1 time course. Two separate measurements

were made, at 258C, on same membrane preparation, under almost identical conditions except for

values of access impedance: 20 and 40 kO. Aqueous solution contained 3 M KCl and 50 mM L-

histidine, bu�ered at pH 2. Equivalent circuit analysis of data, measured at 40 kO, generated complete

set of circuit parameters, which were then used to compute predicted time course expected at 20 kO(smooth curve). Similarly, data analysis at 20 kO cross-predicts theoretical curve for time course at 40

kO. Experimental (noisy) and theoretical (smooth) curves are superimposed for comparison. Although

time courses are di�erent for two measurements, deconvolution yields nearly identical intrinsic

relaxation data: Rp � 61:0 kO, Cp � 207 pF, and tp � 12:6 ms for measurement at Re � 20 kO;Rp � 65:3 kO, Cp � 192 pF, and tp � 12:5 ms for measurement at Re � 40 kO. See text for details.


Table 2

E�ect of varying Te¯on ®lm thickness (compiled from Ref. [205])

Kinetic parameter 6.35 mma 12.7 mma

tp at 258C (ms) 12:320:7 (n � 8) 12:920:6 (n � 6)

a No di�erence at the 5% level of signi®cance.


In the equivalent circuit analysis described above, the Te¯on ®lm was treated asa part of the membrane dielectric. Clearly, it is the thickness and the area of theTe¯on ®lm that mainly determine the values of Cm. Therefore, the thickness of theTe¯on ®lm has a major in¯uence on the apparent relaxation time through itse�ect on the value of the charging time constant tm. In order to ascertain thee�ect of the Te¯on ®lm, we determine tp values in an ML membrane made ofTe¯on ®lm of 12.7 mm in thickness, under otherwise identical conditions (pH 2,258C) (see Table 2) [215]. The value of tp was found to be 12:920:6 ms (n � 6).The corresponding value obtained from an ML membrane made of Te¯on ®lm of6.35 mm in thickness is 12:320:7 ms (n � 8). There is no di�erence between thetwo values at the 5% level of statistical signi®cance. Again, the time course of thephotosignal measured at thickness 12.7 mm can be cross-predicted from themeasurement made at thickness 6.35 mm (Fig. 27).

Thus, the waveform of B1 can be modulated by varying electrical parameters ofthe inert supporting structure such as Rm and Cm. A dramatic example is providedby the measured signal from a thin-®lm metal electrode assembly shown in Fig.28. Oriented purple membranes were deposited on a glass substrate, which waspreviously coated with a transparent metal electrode and a layer of dielectric of a

Fig. 27. E�ect of varying thickness of Te¯on ®lm on measured B1 time course. Photosignals were

obtained, at 24218C, from three separate ML membranes of bR, made of Te¯on ®lms of 6.35, 12.7,

and 25.4 mm in thickness, respectively. Aqueous solution contained 0.1 M KCl and 10 mM L-histidine,

bu�ered at pH 2. Access impedance was 40 kO and instrumental time constant was 0.4 ms.Experimental data are shown as noisy curves. Smooth curves are predictions, based on input

parameters which were determined by deconvolution of photosignal from ML membrane with Te¯on

thickness of 6.35 mm. (Reproduced from Ref. [215])


thickness of about 800 AÊ [215]. A signi®cant lengthening of the apparentrelaxation time course (in the range of about half a second) is evident.

In summary, the photosignal obtained by means of the ML method appears tobehave predictably in accordance with the equivalent circuit shown in Fig. 23.Until the ML method was developed, we had never succeeded in ®tting a bRphotosignal with the equivalent circuit, using a TM ®lm or a bR-containing BLM.Presumably, it is because all these photosignals contained both B1 and B2. Wewere thus led to a tentative conclusion that the signal obtained by means of theML method contains a single component Ð pure B1 signal. With additionalinsight, we have subsequently been able to ®t a signal obtained by means of theTM method to the equivalent circuit at a special condition under which the B2component is completely abolished (see Section 10.12).

10.4. Temperature e�ect

As shown in Fig. 29(A), in which both B1 and B2 are present, the temperature

Fig. 28. AC photocurrent generated from bR thin ®lm assembly, supported on solid transparent metal

electrode. (A) Glass plate was coated with transparent metal electrode, which was partially overlaid

with thin dielectric layer (0800 AÊ in thickness). Oriented layer of purple membrane (not bR monolayer)

was deposited onto the metal/dielectric ®lm assembly. (B) Photocurrent was measured, at 268C, withaccess impedance of 80 O and instrumental time constant of 0.4 ms. Aqueous solution contained 3 M

KCl and 50 mM L-histidine, bu�ered at pH 3. Note that relaxation stretched into time range of about

half a second. (Reproduced from Ref. [215])


e�ect is quite prominent. As the temperature is lowered, the negative peakdecreases and the positive peak increases. In contrast, the temperature e�ect onthe isolated B1 component is much less remarkable, but is not completely absent[32] (Fig. 29(B)). Therefore, the temperature e�ect observed in Fig. 29(A) must beattributed predominantly to B2.

The small di�erence of the time course of B1 between 58C and 458C is not due

Fig. 29. Temperature dependence of B1 and B2. Data in Record A were from TM ®lm (B1 + B2), and

data in Record B were from ML ®lm (pure B1). Aqueous solution contained 3 M KCl and 50 mM L-

histidine, bu�ered at pH 7. Access impedance was 40 kO and instrumental time constant was 35 ms in

A, and 0.355 ms in B. Also D2O replaced water in Record B in order to further suppress any remnant

of B2 Ð maneuver deemed unnecessary from hindsight (see Section 10.11). Temperature e�ect is

reversible. (Reproduced from Ref. [32])

Table 3

Kinetic parameters of B1 (compiled from Ref. [205])

Parameters H2Oa D2O

a

tp at 258C (ms) 12:320:7 (n � 8) 12:621:4 (n � 6)

Activation energy (kcal/mol) 2:5420:24 (n � 20) 2:4520:9 (n � 16)



to experimental error but is experimentally reproducible. Furthermore, theagreement of the isolated B1 component with the equivalent circuit is maintainedat all temperatures in the range being tested (5±458C). Deconvolution allows us tocalculate tp at various temperatures and to construct an Arrhenius' plot (Fig. 30).The activation energy is approximately 2.5 kcal/mol (Table 3).

Now let us examine Fig. 7(C)±(E) and compare the temperature dependence ofERP with that of the bR signals. Although the waveforms are di�erent, thetemperature-induced changes are qualitatively similar. As the temperaturedecreases, the R2 peak diminishes in amplitude, but the amplitude of the R1 peakincreases instead. An uncritical interpretation would have led to the conclusionthat low temperature inhibits the R2 component, but enhances the R1 component.It was remarkably correct that, in the ERP literature, R1 was described as

Fig. 30. Activation energy of B1. Relaxation rate constant (kp � 1=tp) of B1 was determined as

function of temperature, from 5 to 458C. Arrhenius's plot is shown. Slope yields activation energy of

2:5420:24 kcal/mol. (Reproduced from Ref. [205])


temperature-resistant. R1 can be isolated by lowering the temperature to 58C[137,144]. But no small temperature dependence of R1 was reported in theliterature. Without the help of membrane reconstitution methodology, it wassimply not technically feasible to demonstrate unequivocally the possible smalltemperature dependence of R1 at the time of the discovery of ERP.

10.5. E�ect of varying aqueous pH and proton±deuterium exchange

The apparent lack of pH dependence of ERP has led to the rejection of theinterfacial proton transfer model as a viable mechanism for the ERP generation(Section 5.4). The ERP-like signal from bR was initially reported to be pH-

Fig. 31. Proton's role in generation of B2. Data illustrate e�ects of varying pH (A) and D2O±H2O

exchange (B) on AC photosignal from TM ®lms of bR, at 258C. Access impedance was 40 kO and

instrumental time constant was 33 ms. Aqueous solution contained 3 M KCl and 50 mM L-histidine,

titrated to various pH values, in Record A, or bu�ered at pH 7, in Record B. Aqueous solution was

exchanged with D2O solution of comparable electrolyte composition, in Record B. E�ect of D2O±H2O

exchange is reversible. pH e�ect is also reversible except above pH 11. (Reproduced from Ref. [205])


independent [154]. However, those data were obtained under open-circuitconditions. The data measured under near-short-circuit conditions werecompletely di�erent [205]. As shown in Fig. 31(A) for a TM ®lm reconstitutedfrom bR, the pH e�ect is evident throughout the range of pH from 0 to 11.Apparently, B2 is inhibited by low pH, because the signal waveform approachesthat of the B1 component at low pH.

The fact that the proton appears to participate in the generation of B2 ratherthan merely modulate B2 generation is evident in the e�ect of proton±deuteriumexchange (Fig. 31(B)). At neutral pH, B2 is signi®cantly subdued by the D2Oreplacement, whereas the kinetic isotope e�ect is less prominent at pH 2. That thepH dependence and the kinetic isotope e�ect on the photosignal from a TM ®lmmust be solely attributed to the B2 component can be made clear by comparingthese e�ects on the pure B1 component as seen in an ML ®lm.

Fig. 32. pH dependence of B1. Aqueous solution contained 3 M KCl and 50 mM L-histidine in D2O,

titrated with NaOD or DCl to various pH values. (A) Data from two ML ®lms, measured at 258C,with slightly di�erent membrane capacitances, were normalized to (positive) peak amplitudes (158 pF

in membrane #1 and 205 pF in membrane #2). Access impedance was 40 kO and instrumental time

constants were 0.355 ms in membrane #1, and 0.457 ms in membrane #2. Note that pH 7 data appear in

both membranes. Therefore, if measurements were made from same preparation, all signals would be

superimposable after normalization. (B) Amplitude of signals from membrane #2, measured at various

pH values, were adjusted for pH-dependent absorbance changes (rather than normalized to peak

amplitudes). (Reproduced from Ref. [205])


As shown in Fig. 32(A), the B1 signal from two separate membranes are shownover the pH range from 2 to 10. The photosignals measured at various pH valuessuperimpose after normalization. The slight di�erence between the two sets ofsignals from two di�erent membranes re¯ects the slight variation of tm. The B1amplitude varies slightly as pH varies. Fig. 32(B) shows the pH dependence of theB1 amplitude after correction of pH-dependent absorbance changes. Thus, B1appears to be completely independent of pH with regard to both the amplitude andthe relaxation time course. The e�ect of overnight replacement of water with D2Oalso shows no e�ect on the kinetic parameters of the B1 component (Table 3).

Thus, the pH dependence of B2 seems to be consistent with the interfacialproton transfer mechanism. On the other hand, we are inclined to attribute B1 toan intramolecular charge separation (oriented dipole mechanism). However, thedisplaced charge in B1 is unlikely to be the proton, because of a lack of thekinetic isotope e�ect. Speci®cally, the displaced charge is not the Schi�-baseproton, in view of the report of Ehrenberg et al. [216]. Using rapid mixingtechniques and resonance Raman spectroscopy, these investigators found that the1H=2H exchange time for the Schi�-base proton is 4.7 ms.

Thus, our interpretation of pH dependence disagrees with that of Drachev et al.(Fig. 12(B)). Here, Component I of Drachev et al. corresponds to the B1component (both of them have a polarity opposite to that of physiological protontransport). Components II and III correspond to the rise and decay phases of theB2 component, respectively. According to the interpretation of Drachev et al.,

Fig. 33. Schematic diagram showing decomposition of AC photosignal, according to equivalent circuit

analysis. Each component decays with two exponential time constants, and each satis®es zero time-

integral condition (5.1). Time interval, between onset of photosignal and polarity reversal, is designated

as tr. Amplitude ratio of two (positive and negative) peaks, p�=pÿ, is designated as B1/B2.

(Reproduced and modi®ed from Ref. [156])


Component I is not prominent except in the range of pH below 2, whereasComponents II and III are essentially pH-independent in the medium pH range.At pH below 2, Components II and III decline precipitously to zero, while theamplitude of Component I becomes more than doubled. This phenomenon isduplicated in reconstituted rhodopsin membranes reported by Trissl (Fig. 12(A)).In fact, Trissl even assigned pK values to the transition zones at which R1 seemsto grow at the expense of R2 [166].

Here, we must point out that the graphs in Fig. 12 show plots of the amplitudeof signal components vs. pH. We have suggested that the signal amplitude is not agood indicator of the underlying kinetic processes, especially when the relaxationtime courses are not invariant. The changes of relative amplitudes of the twosignal components at pH below 2, shown in Fig. 12(A) and (B), can be readilyexplained as follows.

Consider the schematic in Fig. 33, which was originally constructed for theinterpretation of our bR data under a near-short-circuit condition, in accordancewith the equivalent circuit shown in Fig. 23. It can also be used for open-circuitdata (see Section 9.3). Each component is shown to decay with two exponentialterms, but B1 and B2 have opposite polarities. A typical signal from a TM ®lm atroom temperature and neutral pH is shown as the algebraic sum of B1 and B2.Because of the partial overlap of the B1 decay phase and the B2 rise phase,inhibition of B2 alone leads to an apparent increase of the B1 peak. Thus,Drachev et al. [168] inadvertently attributed the pH dependence of B2 to B1 in therange of pH 0 to 2. Presumably, the same explanation applies to the rhodopsindata shown in Fig. 12(A), and the accompanying pK values thus have dubiousmeaning. Our interpretation of the pH e�ect on ERP is supported by anobservation on isolated retina [165]; low pH substantially enhances and prolongsR1 but depresses R2. The reported waveform of ERP did show the overlap of theR1 decay and the R2 rise.

The same deceptive e�ect of apparent peak enhancement, due to removal of theopposing peak, can also be seen in the temperature e�ect of both rhodopsin [144]and bacteriorhodopsin (Figs. 7(C)±(E) and 29(A)), as well as in the pH e�ect onERP [165]. Pak and Cone [144] must have recognized this pitfall. Otherwise, theywould have concluded that low temperature inhibits R2, but enhances R1.

10.6. E�ect of chemical modi®cation

The pH e�ect on the ERP-like signal of bR is consistent with the notion thatB2 originates from the membrane surface, whereas B1 originates from the deep-seated hydrophobic region. An additional test of this idea is to use a chemicallabel that does not penetrate the membrane and, therefore, can only a�ect theexposed hydrophilic domains of bR at the membrane surface. The role of such areagent can be ®lled by ¯uorescamine [32,213]. Fluorescamine is a chemical labelwhich binds to primary amines, but hydrolyzes, in seconds, in an aqueous solutionat alkaline pH. Therefore, it does not reach the hydrophobic region of bR.

Fig. 34 shows the e�ect of in situ ¯uorescamine treatment of a TM ®lm (A) and


Fig. 34.


an ML ®lm (B). A stock solution of ¯uorescamine in acetonitrile was added to theaqueous phase, after the control photosignal had been recorded. Partial inhibitionof the B2 component is evident. The amplitude of B1 is slightly diminished, but itsrelaxation time course is unchanged. The amplitude change of B1 is due to thee�ect of solvent (acetonitrile) used to prepare the ¯uorescamine stock solution[213].

The lack of e�ect of ¯uorescamine on B1 may be due to the inability of¯uorescamine to penetrate the multiple purple membrane layers. The incompleteinhibition of B2 may be due to the limited extent of in situ chemical modi®cation.In order to check this possibility, additional experiments with a modi®edexperimental protocol were performed. A sample of puri®ed purple membrane wastreated with ¯uorescamine ®rst while still in an aqueous suspension. Thechemically treated sample was then washed and used for reconstitution (Fig.34(C)). These experiments con®rmed that the lack of e�ect on B1 was not due toinaccessibility of deep-seated layers in an ML ®lm. Furthermore, the B2component is nearly completely inhibited, whereas B1 remains intact. Theremaining photosignals is almost pH-independent and the time course is close tothat of B1.

10.7. E�ect of point mutation

Chemical modi®cation with ¯uorescamine fails to completely abolish B2. Wethus turned to site-directed mutagenesis for the possibility of complete inhibitionof the B2 component. The rationale is as follows. The di�erence in the spatialorigin of B1 and B2 suggests that it may be possible to eliminate B2, but leave B1intact, by a point mutation of a strategically important amino-acid residue. This isaccomplished by site-directed mutagenesis using a bR-de®cient mutantHalobacterium salinarium as the expression system [217]. Our objective ofselectively suppressing B2 is met by a point mutation of bR at residue 212, where

Fig. 34. E�ect of chemical modi®cation with ¯uorescamine. (A) Photosignals from TM ®lm of bR,

taken at 258C before and after treatment with ¯uorescamine (in acetonitrile as solvent), are shown.

Aqueous solution contained 0.1 M KCl and 5 mM sodium borate, at pH 7. Access impedance was 40

kO and instrumental time constant was 35 ms. Control experiment, with only acetonitrile added, shows

amplitude reduction by 17%, without change of time course. Signal after ¯uorescamine treatment has

been adjusted for solvent-induced decline of amplitude. (B) Photosignals from ML ®lm of bR, before

and after treatment with ¯uorescamine, are shown. Conditions were similar to those of Record A,

except that instrumental time constant was 0.457 ms. Signals, taken before and after treatment, were

normalized to positive peak and shown superimposable. Normalization factor 22% is equivalent to

¯uorescamine-induced amplitude reduction. Adding acetonitrile alone caused amplitude to decrease by

same degree. (C) Photosignals from TM ®lm, reconstituted from bR that had been pre-treated in vitro

with ¯uorescamine, were recorded at four di�erent pH values at 268C. In vitro ¯uorescamine treatment

of bR allows for greater extent of completion of chemical modi®cation. Photosignals are normalized to

positive peak. Aqueous solution contained 1 M KCl and 10 mM L-histidine, bu�ered at various pH

values. Access impedance was 40 kO and instrumental time constant was 1.5 ms. (Reproduced from

Ref. [213])


Fig.35.AC

photoelectric

signalfrom

TM

andML

®lm

sofD212N.Allsignals

weretaken

withaccessim

pedance

of40kO.Photosignals

inRecordsA,B,

andC

weretaken

from

TM

®lm

sat23.58C

,238C

and258C

,respectively,whereasRecord

Dwasfrom

ML

®lm

at268C

.(A

)pH

dependence

ofsignals

is

shownforTM

®lm

,bathed

inaqueoussolutionwhichcontained

4M

NaCland50mM

phosphate

bu�er.Signals,measuredatpH

6.1,8.1

and9.4,were

norm

alizedto

positivepeakandshownsuperim

posable

(inset).(B)Data

weretaken

under

similarconditionsexceptthataqueousphase

contained

0.1

M

KCland

10mM

citrate

bu�er.Signals,measured

atpH

3.7,6.0,7.6,and

11.0,werenorm

alized

topositivepeak

and

shown

superim

posable

(inset).

Superpositionis

less

satisfactory

forpH

11.0.(C

)Typicalphotosignals

from

TM

®lm

ofwild-typebR

isshownforcomparison.(D

)Pure

B1wastaken

from

ML

®lm

ofD212N

under

comparable

conditions.

Photosignals,from

Record

AatpH

6.1,8.1

and9.4,andfrom

Record

BatpH

3.7,6.0

and7.6,

werenorm

alizedto

positivepeakofB1,andare

shownsuperim

posable

ininset.(R

eproducedfrom

Ref.[219])


the naturally occurring amino acid, aspartic acid, is replaced with asparagine(mutant D212N ) [218,219].

The pH dependence of a D212N membrane, formed by means of the TMmethod, is shown in Figs. 35(A) and (B) at two salt concentrations. Thephotosignals from a TM ®lm of wild-type bR under identical experimentalconditions is shown in Fig. 35(C) for comparison. Note that there is no pHdependence between pH 6 and 11, at high salt concentration, and between 4 and11, at low salt concentration. This observation suggests that D212N is naturallydevoid of the B2 component under those conditions. At low pH, the TM ®lm ofD212N does exhibit a pH dependence. This pH dependence indicates that the B2component at low pH has a polarity opposite to its polarity at neutral and highpH. That is, the remnant B2 component exhibits a polarity reversal as the pH isprogressively lowered. Furthermore, this remnant B2 component is stronglyin¯uenced by the electrolyte composition (see Section 10.8).

In order to unequivocally demonstrate the absence of B2 in the medium to highpH range in a TM ®lm of D212N, the corresponding photosignal obtained bymeans of the ML method is shown in Fig. 35(D). This latter signal, whichcontains the B1 component exclusively, can be shown to superimpose, afternormalization, with those signals from the corresponding TM ®lm in the range ofpH from 6 to 11 (Fig. 35(D) inset). Thus, we conclude that the photosignals froma TM ®lm of D212N consist solely of the B1 component in the medium to highpH range.

The e�ect of point mutation in D212N again lends additional credence to ourprotocol of signal decomposition. Presumably, Nature had also chosen todecompose the composite signal along the same demarcation, which we arrived atonly after a series of tortuous attempts had been made and a lengthy analysis hadbeen performed.

As for the search of speci®c amino acids serving speci®c functions, it isprobably wishful thinking on our part. An examination of the bR structure, asrevealed by Henderson et al. [55], indicates that residue 212 is buried in thehydrophobic portion of bR and is actually closer to the extracellular side than thecytoplasmic side. Therefore, residue 212 could not be the cytoplasmic protonbinding side. But then, how does the point mutation at residue 212 manage tosuppress B2? In the absence of a de®nite answer, one can only say that di�erentfunctional groups in bR are conformationally coupled together. It is therefore notsurprising that a structural change at a remote location in the hydrophobic regioncould a�ect a speci®c function at the cytoplasmic hydrophilic domain (cf. charge-conformation interactions, Section 10.13.4).

10.8. Chloride ion e�ect

The salt e�ect on the B2 component at low pH in reconstituted TM ®lms ofD212N is intriguing, because it is not a simple ionic strength e�ect, but rather achloride ion e�ect, as can be shown by the following experiment [219].

Control experiments were ®rst performed on a TM ®lm of D212N in a Clÿ-free


electrolyte solution (100 mM of Na2SO4). The pH was adjusted by titration withconcentrated NaOH or H2SO4, thus maintaining a Clÿ-free composition.Photosignals were measured at room temperature (23±258C). As shown in Fig. 36,the B2 component is virtually pH-independent in the absence of chloride ions.Addition of a minute amount of NaCl progressively increases the amplitude of theB2 component. Since the presence of divalent anion SO2ÿ

4 practically ®xes theionic strength at a constant value, the salt e�ect cannot be attributed to ionicstrength. The e�ect is primarily due to changes of Clÿ concentration.

The chloride ion e�ect is not unique to D212N mutant. In fact, a similar e�ectalso exists in wild-type bR [220] (Fig. 37). Furthermore, the Clÿ-dependent B2

Fig. 36. E�ect of Clÿ on AC photoelectric signal from TM ®lm of D212N. (A) TM was reconstituted

from D212N in Clÿ-free medium. Measurement condition was same as that in Fig. 35(A), except that

aqueous solution contained 0.1 M Na2SO4 and 50 mM phosphate bu�er (Clÿ-free medium), and

temperature was 258C. Normalized data are shown in inset. (B) Another ®lm was formed in same Clÿ-free medium. pH was ®rst lowered to 1.3. Aliquot of concentrated NaCl solution was then added

repeatedly, and progressive changes of photosignal were recorded after each addition. Actual NaCl

concentrations are indicated. (Reproduced from Ref. [219])


signal can be inhibited by DIDS (Fig. 38(A)) and SITS (data not shown). DIDS(4-acetamido-4 '-isothiocyano-2,2 '-stilbenesulfonate) and SITS (4,4 '-diisocyano-2,2 '-stilbenesulfonate) are known chloride ion transport blockers. Controlexperiments, using an ML ®lm reconstituted from wild-type bR (pure B1component), show that neither the addition of Clÿ at low pH nor the subsequent

Fig. 37. E�ect of Clÿ at low pH on AC photosignal of wild-type bR. (A) TM ®lm was initially

immersed in solution, which contained 1 M Na2SO4 and 10 mM sodium citrate, at pH 1.2. Small

amounts of concentrated NaCl stock solution were then added to bring Clÿ concentration from 0 to

768 mM. All signals were recorded from same ®lm. (B) For comparison, MgSO4 was added to Clÿ-freemedium (1 M Na2SO4 and 10 mM L-histidine, at pH 0.8). Two signals, which were recorded in

following order, correspond to: (a) Clÿ-free medium, and (b) subsequent addition of 800 mM MgSO4

(shown superimposable without normalization). (Reproduced from Ref. [220])


addition of DIDS has any e�ects on B1 (Fig. 38(B)). Other halides, such as Brÿ

and Iÿ, were also tested. A similar e�ect was observed with Brÿ but not with Iÿ

(data not shown). The addition of Iÿ causes a slight decrease of the signalamplitude. The Brÿ-dependent e�ect is less conspicuous at pH 1.8 than at pH 0.8.The reason for this pH-modulation e�ect is not known.

Fig. 38. E�ect of Clÿ and DIDS at low pH on AC photosignal of wild-type bR. (A) TM ®lm was initially

immersed in solution, which contained 1 M Na2SO4 and 10 mM L-histidine, at pH 1.4. Signals a, b, and

c, recorded in that order, correspond, respectively, to: (a) Clÿ-free medium, (b) subsequent addition of

667 mM NaCl, and (c) further addition of 125 mM DIDS. (B) Signals from ML thin ®lm are shown for

comparison. Initial solution contained 1 M Na2SO4 and 10 mM L-histidine, at pH 1.1. Three

photosignals were sequentially recorded in following order, and correspond to: (a) Clÿ-free medium, (b)

subsequent addition of 800 mM NaCl, and (c) further addition of 167 mM DIDS. All three signals are

shown superimposable without normalization. Also superimposed is normalized photosignal (d) from

TM ®lm, in Clÿ-free medium (same as signal a in Record A). (Reproduced from Ref. [220])


It is evident that ionic strength is not the factor leading to the appearance ofthe low-pH B2 signal but the presence of Clÿ or Brÿ is (cf. Fig. 37(B)).

10.9. Divalent cation e�ect

The Clÿ e�ect, described in the previous section, is manifest only at low pH. In

Fig. 39. E�ect of divalent cations at high pH on AC photosignal of wild-type bR. (A) TM ®lm was

initially immersed in solution, which contained 1 M Na2SO4 and 10 mM sodium phosphate bu�er, at

pH 9. Starting with solution free of Ca2+ and Clÿ, concentration of CaCl2 was gradually increased

from 0 to 250 mM. (B) Control experiment, in which 750 mM NaCl was added instead, shows no

signi®cant change of photosignal. Solution initially contained 1 M Na2SO4 and 10 mM L-histidine, at

pH 9.0. (Reproduced from Ref. [220])


the range from neutral to high pH, its e�ect is rather inconspicuous and isprobably due to nonspeci®c reasons, such as the ion strength e�ect (see later). Inthe same pH range, there is, however, a signi®cant e�ect of divalent cations on theB2 signal [220]. Shown in Fig. 39(A) is the response of a TM ®lm at pH 9 to

Fig. 40. E�ect of divalent cation and chelator at high pH on AC photoelectric signal of wild-type bR.

(A) TM ®lm was initially immersed in solution, which contained 0.1 M Na2SO4 and 10 mM sodium

phosphate bu�er, at pH 8.4. Signals a, b, and c, recorded in that order, correspond, respectively, to: (a)

Ca2+- and Clÿ-free solution, (b) subsequent addition of 290 mM CaCl2, and (c) further addition of 250

mM EGTA. (B) Photosignals from ML ®lm are shown for comparison. Initial solution contained 1 M

Na2SO4 and 10 mM L-histidine bu�ered, at pH 8.1. Photosignals, recorded in following order,

correspond to: (a) Mg2+- and Clÿ-free medium, (b) subsequent addition of 250 mM MgCl2, and (c)

further addition of 250 mM EDTA (shown superimposable without normalization). (Reproduced from

Ref. [220])


increasing concentrations of CaCl2. The e�ect so observed is due speci®cally toCa2+, but not to Clÿ, since addition of a comparable amount of NaCl has littlee�ect (Fig. 39(B)). Mg2+ ion has a similar e�ect. In contrast to the Clÿ e�ect, thedivalent cation e�ect is manifest only in the medium to high pH range (cf. Fig.37(B)).

The divalent cation e�ect can be partially inhibited by chelators such as EGTAand EDTA, as is evident in Fig. 40(A). The divalent cation e�ect is restored afterthe replacement of fresh aqueous solution without chelators. The addition ofchelators alone has no e�ect. The inhibitory e�ect of EGTA and EDTA isapparently caused by their ability to chelate Ca2+.

Control experiments using an ML ®lm shows that neither the addition ofdivalent cations nor the subsequent addition of divalent cation chelators has anye�ects on B1 (Fig. 40(B)). Thus, the e�ect is speci®cally on the B2 component.Photosignals shown in Figs. 39 and 40 were all taken at room temperature (23±258C).

Again, the enhancement e�ect is not caused by the increase of ionic strength,since the electrolyte solution has already contained divalent anion SO2ÿ

4 and,therefore, has substantial ionic strength before the addition of divalent cations.

The B2 component is not entirely insensitive to ionic strength, however [32]. Asmall e�ect is discernible when the concentration of KCl is changed from 100 mMto 1 M, and the e�ect is reversible (Fig. 41). In contrast, the signal from an ML®lm (i.e., pure B1) shows no such changes. The B1 relaxation time constant is nota�ected by the change of KCl concentration (Table 4).

The lack of sensitivity to changes of ionic strength has also been cited to rejectthe interfacial proton transfer mechanism for ERP and the ERP-like signal inreconstituted bR membranes [154]. Again, the absence of such an e�ect isprobably due to the open circuit method used to measure the signal (see Sections9.3 and 9.4).

Fig. 41. E�ect of varying KCl concentration. Photosignals were taken from a TM ®lm of bR at 258C.Aqueous solution contained either 0.1 M or 3 M KCl (both bu�ered with 50 mM L-histidine at pH 7).

E�ect of changing KCl concentration is reversible. (Reproduced from Ref. [32])


10.10. Assignment of molecular mechanisms to B1 and B2 components

From the experimental analysis presented in several preceding sections, acontrasting pattern of the behavior of B1 and B2 emerges, with regard to thee�ects of temperature, pH, halides, divalent cations, ionic strength, and H2O/D2Oexchange, as well as the vulnerability to a water-soluble chemical label and topoint mutation at residue 212. With the exception of temperature, thedemonstrated e�ects are exclusively limited to B2. It is apparent that the B1 andB2 components, as de®ned by our protocol of signal decomposition, represent atleast two distinct molecular processes. The B2 component is likely to be generatedat or near the (cytoplasmic) membrane surface. On the other hand, the B1component is likely to be generated in the hydrophobic domain buried inside themolecule. This is supported by the observation that B1 is generally insensitive tochanges of the aqueous composition and inaccessible for the water-soluble reagent¯uorescamine. That water is not required for the B1 generation is demonstratedby the B1-like photosignal from a TM ®lm of bR sandwiched between two Te¯on®lms, recalling that a TM ®lm normally exhibits a large negative peak re¯ectingthe presence of B2 (Fig. 42). Although the possibility that some water might bepresent between the two Te¯on ®lms cannot be excluded, the near total absence ofB2 peak suggests that the remnant water, if present, was not su�cient to generatea B2 signal.

In light of the analysis of the OD and IPT mechanisms presented in Section 8,the pH and the kinetic isotope e�ects strongly suggest that the B2 component isgenerated by the interfacial proton transfer mechanism, and the B1 component ismost likely generated by the oriented dipole mechanism.

The lack of a detectable latency of the B1 component suggests that it may begenerated by the early event after photon absorption, possibly thephotoisomerization. It has been suggested that the B1 component may begenerated by proton movement associated with the deprotonation of the Schi�base [17]. If so, then the initial movement of protons is in the direction oppositeto the direction of physiological proton transport. For this reason, Keszthelyi hasproposed a `sling-shot' model. According to this model, deprotonation of theSchi�-base proton leads to proton movement in the direction opposite to thephysiological direction of proton transport. This step stores potential energy,which is subsequently utilized to move protons in the forward direction. However,the model does not square well with the demonstrated absence of kinetic isotope

Table 4

E�ect of varying KCl concentration (reproduced from Ref. [32])

Kinetic parameter 0.1 M KCla 3.0 M KCla

tp at 258C (ms) 12:820:7 (n � 6) 12:420:7 (n � 8)



e�ect of the B1 component (Section 10.5). The model is not consistent with ourobservations on several bR mutants either.

The pH dependence of fast photosignals generated by four bR mutants isshown in Fig. 43 [39]. At a ®rst glance, each record shows a unique pattern of pHdependence, almost like a ®nger print. While we are far from being able to drawintelligent conclusions with regard to structure-function relationship, the dataserve to refute the interpretation that B1 re¯ects the molecular process ofdeprotonation of the Schi� base. Since the aspartate group at residue 85 isgenerally considered to be the immediate acceptor of the Schi�-base proton, thelatter interpretation would predict total absence or, at least, diminution of B1 inthe mutant D85N, in which the proton-binding carboxylic group of aspartate iseliminated by a substitution with asparagine.

We are thus inclined to interpret the B1 component as light-induced non-protoncharge separation and recombination, presumably associated with thephotoisomerization of the chromophore. Molecular dynamics calculationsperformed by Birge and co-workers [133,134,221] further indicate thatdeprotonation of the Schi�-base proton is probably not fast enough to accountfor the B1 signal. Instead, they attribute B1 to charge shifting in conjunction withphotoisomerization of the bR chromophore. Based on quantum mechanicalcalculations, Kuhn and Kuhn [222] proposed a proton-pumping mechanism thatlinks the shift of negative charge away from the Schi�-base nitrogen, followingphotoisomerization, as the cause of the reduction in the pKa of the Schi�-baseproton-binding site.

We have initially associated B2 with the interfacial proton uptake at the

Fig. 42. AC photosignal from oriented purple membranes, sandwiched between two thin Te¯on ®lms.

Bacteriorhodopsin membrane was ®rst reconstituted by means of TM method. Another Te¯on ®lm was

then overlaid onto it. Purple membrane has no direct contact with aqueous solution on either side of

assembly. Vaseline was applied to space in between two Te¯on ®lms (6.35 mm). Possibility that water

was trapped in space between two Te¯on ®lms cannot be excluded. Photosignal, taken at 228C, hassame polarity as that of B1, as compared to signal from ML ®lm. Aqueous solution contained 3 M

KCl and 50 mM L-histidine, at neutral pH. Access impedance was 57 kO and instrumental time

constant was 0.4 ms. (Reproduced from Ref. [215])


Fig.43.pH

dependence

ofphotosignals

from

TM

®lm

s,reconstituted

from

variousbR

mutants:(A

)D212N;(B)D115N;(C

)D96N;(D

)D85N.

Measurementconditionswereslightlydi�erentin

each

mutant.However,di�erence

isnotcrucialhere.

(Reproducedfrom

Ref.[39])


cytoplasmic interface, mainly because of the pH and deuterium±hydrogenexchange e�ects. Proton transport is such a prominent function of bR that protonuptake at the cytoplasmic interface and proton release at the extracellular surfaceare obligatory processes. The manifestation of proton uptake as an ACphotosignal that is sensitive to the change of aqueous phase composition isexpected. However, in view of the data shown in Sections 10.8 and 10.9, the B2component at low pH may be more complex. Recall that the generation of B2 atlow pH requires the presence of halide ions; protons alone are insu�cient. Alsorecall that the signal induced by halide ions can be inhibited by DIDS or SITS.Thus, the low pH B2 component is likely to be generated by an interfacial Clÿ

transfer mechanism. Apparently, the process is modulated by pH. The alternativepossibility that the low pH B2 is generated by an interfacial proton transfer (inthe opposite direction), which is modulated by Clÿ, is considered less likely, butcannot be completely ruled out. The physiological signi®cance of the chloride ione�ect is discussed in greater detail in Section 16.

The contrasting characteristics of the B2 component at low pH and at mediumto high pH suggest that B2 itself may be a composite signal, consisting of a lowpH component (tentatively called B2-a component) and a high pH component(tentatively called B2-c component).

Do our present results indicate that the B2-c component may be generated byinterfacial Ca2+ or Mg2+ transfer? We have no de®nite answer to this question.However, since the B2-c component does not vanish completely in the absence ofdivalent cations and that the B2 component is sensitive to the D2O/H2O exchange[205], at least part of the B2-c component is generated by interfacial protontransfer. Yet it is possible that there may be additional contribution, from othercations, to the B2 component. Marinetti and Mauzerall [223] demonstrated, byconductimetry, the release and uptake of ions other than protons at pH 8. Theidentity of the suspected ion or ions was not established. It could well be Ca2+ orMg2+. More recently, ToÂ th-BoconaÂ di et al. [224] reported that the conductivityincrease due to non-proton ion release in the bR membrane can be abolished byimmobilizing bR in gel. They proposed an alternate interpretation in terms of apolarizability change of the membrane.

The most intriguing aspect of the Ca2+ e�ect on B2-c is its implication to themolecular mechanisms of the blue transition, induced either by acidi®cation or bydeionization. This implication will be discussed in Section 17.

10.11. Q-tip experiment: rationale behind ML method

The characteristics of the B1 and B2 components, as de®ned by theaforementioned decomposition protocol, strongly suggest that B1 and B2 arenatural entities and re¯ect separate steps of chemical reactions. But a lingeringquestion remains: why does the ML method successfully eliminate the B2component? The answer is provided by the following experiment, which wenicknamed `Q-tip' experiment, because a Q-tip (cotton swab) can be used totransform an ML ®lm into a TM ®lm [225,226].


The working hypothesis of the Q-tip experiment is shown in Fig. 44. Theobservation that the ML ®lm gives rise to signals with larger amplitudes suggeststhat an ML ®lm contains multiple layers of highly oriented purple membranesheets. The B1 signal is therefore magni®ed by virtue of signal additivity. The B2signal stays the same, because its generation requires direct access of aqueousprotons; only the top layer has such an access. Thus, the amplitude of the MLsignal is expected to increase roughly in proportion to the number of layers ofpurple membranes, and the relative contribution of the B2 signal will bediminished accordingly.

The overlap of the B1 decay and the B2 rise mentioned in Section 10.5 has animportant bearing on the interpretation of data from the Q-tip experiment;diminution of B2 can be misinterpreted as enhancement of B1. Therefore, thechanges of the apparent amplitudes of the two peaks cannot be used directly toassess the di�erent characteristics of the two components under variousexperimental conditions. Instead, we monitor two numerical indicators. One is theratio of the amplitudes of the two peaks (B1/B2), which is equal to the ratio p+/pÿ shown in Fig. 33; the other is the time interval between the onset and thereversal of the photocurrent (tr). As the true amplitude of B2 decreases, both theratio B1/B2 and the time interval tr increase progressively.

Here, we must point out that these parameters are convenient visual aids, butare not fundamental molecular constants. In fact, these parameters change withthe change of the access impedance of the measurement. These parameters arealso a�ected by the instrumental time constant (i.e., the low-pass ®lter timeconstant) as well as the duration (time course) of the light pulse. Nevertheless, themodulation e�ect (on the relaxation time course) of the waveform of thestimulating light pulse, of the access impedance, and of the instrumental timeconstant are completely predictable by means of the equivalent circuit analysis.Therefore, if all these modulation factors are kept ®xed, the parameters B1/B2and tr are convenient indicators of the relative changes of the B1 and the B2components. It is important to realize that the ratio B1/B2 does not become

Fig. 44. Schematic showing di�erence of TM ®lm (A) and ML ®lm (B). See text for further

explanation. (Reproduced from Ref. [42])


in®nite when B2 vanishes, but rather it assumes a ®nite value that is characteristicof the B1 component (cf. Eq. (9.16)). Recall that the B1 component has a biphasicwaveform (with a positive and a negative peak), because it must satisfy the zerotime-integral condition, whereas a monophasic signal never satis®es Eq. (5.1) (seeFig. 13).

Since the photocurrent is a linear function of the light intensity, the amplitudeof the photocurrent usually varies with the light intensity, unless the illuminatinglight is su�ciently intense to saturate the photoresponse. On the other hand, sincethe time course of the photocurrent is independent of the illuminating lightintensity, the parameters B1/B2 and tr are not a�ected by ¯uctuation of the laser-light intensity. These parameters are therefore experimentally more reproduciblethan the amplitudes of the two peaks.

Thus, for typical photoresponses from a TM membrane, B1/B2 and tr appearsto be 1.5 and 7 ms, respectively, at 248C and pH 7.6 (Fig. 45(A)). Lowering thetemperature to 6.48C increases these parameters to 3 and 9 ms, respectively.Lowering the pH to 2 causes even greater increases.

In Fig. 45(B), photoresponses from a freshly made ML ®lm is shown. Thesignal amplitude is considerably greater than a TM ®lm, suggesting the presenceof multiple oriented layers of purple membranes. The values of B1/B2 and tr atneutral pH and room temperature are considerably greater that those of a TM®lm, and are actually close to those of a TM ®lm at neutral pH and reducedtemperature (6.48C and pH 7.6 in Fig. 45(A)). This indicates that the relativecontribution of B2 is diminished. But B2 is not completely absent, because thephotosignal still exhibits a slight pH dependence.

An attempt to remove the multiple layers was then made by stripping theselayers with a cotton swab. Such a maneuver, however, failed to eliminate thephotosignal completely (Fig. 45(C)). A remnant signal was left, which shows acharacteristic pH dependence almost indistinguishable from that of a TM ®lm(cf. Figs. 45(A) and (C)). The prominent pH sensitivity, expected of the B2component in a TM ®lm, had been restored.

This is of course not the complete story, because the ML ®lm did not exhibit apure B1 signal as expected. The key factor is the duration of drying the thin ®lmin air; prolonged drying is required to eliminate B2. Thus, the same experimentwas then repeated with an ML ®lm, which had been air-dried for more than fourdays. The photosignal from such a preparation shows no trace of pH dependenceover a broad pH range (Fig. 45(D)). Stripping with a cotton swab againdiminished the amplitude, but failed to restore the pH dependence; the values ofB1/B2 and tr remained virtually unchanged (Fig. 45(E)). In fact, the diminutivephotosignal has exactly the same relaxation time course as that in the ML ®lm, asthey can be made to superimpose after normalization of the peak amplitude (Fig.45(F)).

The ML ®lm that has been dried for more than four days clearly loses its abilityto generate a B2 signal, but its B1 generating mechanism is apparently intact. Theexact reason is not known, but the observation is consistent with our molecularinterpretation of the two components. Apparently, the B2 mechanism, which is


implemented at the cytoplasmic surface, is permanently impaired, presumably,because of (localized) denaturation by drying. The B1 mechanism, beingimplemented in the buried chromophore binding region, is better protected andthus remains unimpaired.

Previously, we did not realize the importance of prolonged drying. Traceamounts of pH dependence did show up in some of our earlier data. In fact, wehad to combine the ML method together with D2O replacement, in order toeliminate the pH dependence of a TM ®lm (e.g., Fig. 32). With the bene®t of

Fig. 45. Q-tip experiments. Photosignals from wild-type bR, measured at various pH values and/or

temperatures, are shown for: (A) typical TM ®lm, (B) fresh ML ®lm before stripping with cotton swab,

(C) fresh ML ®lm after stripping, (D) aged ML ®lm before stripping, and (E) aged ML ®lm after

stripping. Aqueous solution contained either 0.1 M KCl (A, B, C) or 1 M KCl (D, E), and 10 mM L-

histidine bu�er. Access impedance was 40 kO and instrumental time constant ranged from 1.33 to 1.77

ms. Indicators B1/B2 and tr are also shown. (F) In aged ML ®lm, photosignals after stripping (from

Record E) is shown to superoimpose with photosignal before stripping (pH 6.1 in Record D), if they

were normalized to positive peak of latter signal. (Reproduced from Ref. [226])


hindsight, D2O replacement would not be necessary, had the TM ®lms beenallowed to dry for a longer period.

The revelation of how the ML method works casts a shadow on the aboveinterpretation of D212N. Could the absence of B2 in the neutral to high pH rangebe caused by partial denaturation as a result of handling? This is a distinctpossibility, because D212N in aqueous suspensions appears to be less stable thanthe wild-type. For example, D212N suspended in an electrolyte solution bu�eredat pH 3 will denature within three days, whereas the wild-type lasts severalmonths under the same conditions.

An answer to the above question will not be immediately available, until themissing B2 signal re-appears, when the sample is handled di�erently. For example,if the B2 signal appears in neutral pH in vivo by means of a patch-clampexperiment, then one can conclude that the absence of B2 is an artifact ratherthan inherent of the point mutation. Even so, the vulnerability of the B2mechanism suggests the spatial segregation of the sites of B1 and B2 generation.Unfortunately, a negative result of such a patch-clamp experiment mustnecessarily be treated as inconclusive.

10.12. Method for isolating B2 component

Since a typical TM ®lm exhibits both the B1 and B2 components and, since theB1 component can be isolated in pure form by means of the ML method,isolation of the pure B2 component appears to be a simple matter of signalsubtraction. However, since the ML method yields thin ®lms with augmented B1contribution according to the actual number of purple membrane layers, and sincethe number of layers varies from ®lm to ®lm, the correction (scale) factor to beused in the subtraction must be experimentally determined. The determination ofthis scale factor can be implemented by a method to be described below [227]. Thedescription will be facilitated if the parameters B1/B2 and tr, de®ned in Section10.13, are used.

Theoretically speaking, when B2 vanishes, both B1/B2 and tr should becomeequal to the corresponding parameters of the pure B1 signal, obtained by meansof the ML method (B1=B2 � 6, tr � 12 ms; see Fig. 45(D)), if our decompositionprotocol is indeed correct. The B2 component in a composite signal, obtained bymeans of the TM method, may be abolished by titrating the pH or lowering thetemperature until the value of either B1/B2 or tr coincides with the correspondingparameter of a standard B1 signal (from an ML thin ®lm). Since we have alsoshown that lowering the temperature has a small, but measurable, e�ect on the B1component, whereas the B1 component has no measurable pH e�ect (see Sections10.4 and 10.5), we choose to titrate the pH instead of the temperature. The endpoint of titration can be either the coincidence of B1/B2 or tr with thecorresponding parameter of a standard pure B1 signal.

Recalling the analysis presented in Section 9.2, the time course of the compositesignal is expected to agree with Eqs. (9.13) and (9.16), when the B2 component isabolished. Therefore, instead of the individual parameters B1/B2 and tr, we may


choose the superposition of the titrated photosignal, after normalization, with thestandard B1 signal to be the end point of titration. As we shall see later, the latterend point is more reliable than the mere coincidence of either B1/B2 or tr. Thesuperposition automatically ensures that the two signals have identical values ofB1/B2 and tr. In addition, the superposition allows for the determination of theunknown scale factor needed for the isolation of the pure B2 signal.

That the B2 component does not simply vanish at low pH, but ratherundergoes a polarity reversal, is suggested by the D212N data at low pH (Fig. 36).A closer inspection suggests that the polarity reversal of the B2 component inD212N thin ®lm may also be present in wild-type bR thin ®lm. It is evident inFig. 45(A) that the values of B1/B2 and tr corresponding to a TM ®lm at pH 2.0and 248C far exceeds the values corresponding to a pure B1 signal. On the otherhand, lowering the temperature to 6.48C, while maintaining the pH at 7.6, causesthese parameters to approach, but not exceed, those of B1. These observationssuggest the following. Lowering the temperature to 6.48C inhibits the B2component, but does not completely abolish it, whereas lowering the pH to 2.0, atroom temperature, apparently overshoots the titration end point and reverses itspolarity. Thus, if there is a polarity reversal of the B2 component in wild-type bR,it takes place at a pH value greater than 2, but less than 7.6, i.e., the titration endpoint is between pH 7.6 and pH 2.0.

The pH titration experiment was carried out on a TM ®lm, which allows forboth B1 and B2 to be observed. The photosignals were shown in Fig. 46 for each

Fig. 46. pH dependence of composite signal (B1 + B2), measured from TM ®lm of wild-type bR.

Photosignals were measured at various pH values, ranging from 1.7 to 6.0, and at 268C. Access

impedance was 40 kO and instrumental time constants was 1.3 ms. Aqueous solution contained 10 mM

KCl and 10 mM potassium citrate. pH titration was carried out with HCl or KOH. Signals are plotted

without normalization. (Reproduced from Ref. [227])


pH in the range from 6.0 to 1.7 without normalization. The pH dependence of theparameters B1/B2 and tr, extracted from these data, are shown in Fig. 47(A) and(B), respectively. Note that the error bars in Fig. 47(A) and (B) are not standarderrors in the conventional sense. Instead, they are estimated errors generated bynoise and uncertainty of the base line in each signal trace. Likewise, the means arenot true mean values obtained in a statistical sense. Instead, they are valuesdetermined from each signal trace by using a time-averaged baseline for eachindividual signal in Fig. 46. As the pH is varied from 6.0 to 1.7, the parametersB1/B2 and tr increase from 2.7 to approximately 15 and from 6 ms toapproximately 20 ms, respectively. The monotonic nature of these variations isevident.

The standard B1 signal (Fig. 48) was taken from a photosignal generated in anaged ML ®lm, also shown as part of Fig. 45(D). It was measured under the sameconditions (Re � 40 kO; instrumental time constant 1.3 ms) as in Fig. 46.

Each of the composite signals shown in Fig. 46 was normalized to the peak ofthe standard B1 signal and then the possible superposition was checked. With theexception of the signal measured at pH 2.7, none of these signals superimposessatisfactorily with the standard B1 signal. Thus, the end point of titration wasfound to be pH 2.7. The photosignal at pH 2.7 is shown normalized to thestandard B1 signal in Fig. 48(A). For comparison, the superposition of thenormalized photosignals at pH 2.5 and at 3.0 with the standard B1 signal isshown in Fig. 48(B). Note that the superposition of the normalized photosignals

Fig. 47. pH dependence of B1/B2 (A) and tr (B). These parameters were extracted from data that are

shown in Fig. 46. Error bars are not standard errors in conventional sense, but are estimated dispersion

(variance) of data, resulting from noise and uncertainty of baseline in each trace. Means (®lled circles)

are not ensemble-averages, but are single values, determined from each signal trace with time-averaged

baseline. Time-average of signal trace, preceding onset of photosignal, was regarded as best-estimated

baseline. Presence of noise makes determination of baseline uncertain. In addition, noise also makes

determination of time interval tr erratic. (Reproduced from Ref. [227])


as pH 2.5 and at pH 3.0 is rather unsatisfactory, although their correspondingvalues of the parameters B1/B2 and tr are actually quite close to those of thestandard B1 component.

In view of the nearly perfect superposition at pH 2.7, but rather poorsuperpositions at pH 2.5 and 3.0, we conclude that the composite signal at pH 2.7

Fig. 48. Superposition of standard B1 signal (from ML ®lm) with normalized composite signals,

measured at pH 2.7 (A), and at pH 2.5 and 3.0 (B). Standard B1 signal was taken from Fig. 45(D)

(268C; pH 6.1). (A) Also shown is composite signal from TM ®lm at pH 2.7 (labeled pH 2.7 in Fig.

46), which was normalized to positive peak of standard B1 signal, by using scale factor of 10. Two

signals superimpose almost perfectly. Deviation, during time interval between time marks 25 and 40 ms,was due to non-recurring noise, which was inadvertently recorded together with signal. (B)

Superpositions of composite signal at pH 2.5 and 3.0, normalized to positive peak of standard B1

signal, are rather unsatisfactory, even though values of their parameters B1/B2 and tr are not too far

o� from corresponding values of standard B1 signal. (Reproduced from Ref. [227])


shares the same values of B1/B2 and tr with the standard B1 signal. The scalefactor was found to be 10 (=65 nA/6.5 nA).

Once the scale factor is determined, the pure B2 component at various pHvalues can then be obtained by subtracting the normalized B1 signal from eachsignal trace shown in Fig. 46, if the amplitude of B1 is pH-independent. However,from Section 10.5, it is known that the amplitude of the B1 component is slightlypH-dependent, although its time course is not. Thus, the amplitude of thestandard B1 signal must be adjusted for this pH dependence in addition to thenormalization factor determined at pH 2.7, before the subtraction is carried out toobtain pure B2 signals at various pH values. This additional factor can thus beempirically determined. The results so obtained are shown in Fig. 49. It is evidentthat the isolated B2 signal exhibits a polarity reversal at pH 2.7. If we ignore theslight pH dependence of the B1 amplitude, the result of isolated B2 would be stillbe similar, and the polarity reversal remains at pH 2.7 (data not shown).

The titration data shown above indicates that the pH dependence of B2 is well-behaved (monotonic); both the parameters B1/B2 and tr increase monotonicallywith decreasing pH. This behavior guarantees that it is always possible to ®nd apH value, where the B1/B2 ratio of the composite signal coincides with that of thestandard B1 signal measurement, under comparable conditions. Similarly, it isalways possible to ®nd a pH value where the tr interval is identical with that ofthe standard B1 signal. However, there is no guarantee that the pH valuesobtained in either way will be identical. Thus, theoretically speaking, if ouranalysis is correct, the two pH values, using either B1/B2 or tr as the titration endpoint, should be identical. However, the errors of both parameters increase as thepH is lowered, rendering the end-point determination inaccurate.

Fig. 49. pH dependence of isolated B2. Standard B1 signal from Fig. 48 was normalized to positive

peak of the composite photosignal at pH 2.7, by means of multiplication factor F1, which is 0.1, as

determined in Fig. 48(A), and then was subtracted from each of composite signals, shown in Fig. 46.

Polarity reversal at pH 2.7 is evident. (Reproduced from Ref. [227])


The ratio B1/B2 can be accurately determined, if it is close to unity (at highpH). As the pH is lowered, the error increases, because the parameter B1/B2 mustbe obtained by dividing a progressively increasing positive peak by a progressivelydecreasing negative peak (Fig. 47(A)). Likewise, the accuracy of the time intervaltr is better at high pH when it is shorter. As the pH is lowered, the errorincreases, because the decay curve intersects the baseline at a more and moreshallow angle, rendering it more sensitive to the uncertainty of the baseline (Fig.47(B)). Near the end point, the error of either parameter becomes substantial.Thus, the determined end point based on the ratio B1/B2 or the interval tr isunreliable, and it may be inconclusive as to whether the end points determined bythe two parameters are actually identical. This is why we chose to use thesuperposition of the signal time course as the titration end point instead; theagreement or the lack of it is now judged by the entire relaxation time course. It ismuch less a�ected by noise or superimposed artifacts. On the other hand,deviation from a perfect ®t is also easier to detect. Furthermore, a nearly perfectsuperposition is also an assurance that the two end points, determined by meansof B1/B2 and tr, respectively, are identical. Thus, by requiring that the end pointof titration be a superposition of the photosignal with the standard B1 signal(after normalization), we actually subjected our component analysis to a stringenttest.

Recall that compliance with Eqs. (9.13) and (9.16) are expected for a pure ACphotosignal component but not for a composite signal consisting of more thanone component. They are obeyed by the photoelectric generated from interfacialelectron transfer reaction at the membrane±water interface [163], and is also bythe B1 component (from an aged ML ®lm). Now this relationship is also obeyedby a TM signal at pH 2.7, but not at other pH values. Thus, we can con®dentlyconclude that B2 is completely abolished at pH 2.7, but the B1 componentremains intact. The agreement is possible only if the signal from the TM ®lm atpH 2.7, shown in Fig. 46, and the standard B1 signal, shown in Fig. 48, satisfytwo conditions: (a) both signals decay with the same two time constants, ts and tl,and (b) the ratio of the amplitude of the two exponential terms, in each signal, isequal to the inverse ratio of the above two time constants, in accordance with Eq.(9.16). In view of this constraint and the stringent requirement of overlap of theentire signal time course, an accidental agreement is extremely unlikely. Thesimple and unambiguous result of our titration experiment is a testimony that ourdecomposition protocol is indeed the correct one.

10.13. Evidence of hypothetical B2 ' component

If our interpretation of the B2 component is correct, a symmetry considerationof the interfacial proton transfer mechanism suggests that an interfacial protontransfer (release) at the extracellular surface ought to generate a B2-likephotosignal that is also pH-sensitive. We shall name this hypothetical componentthe B2 ' component.

The detection of the B2 ' component is potentially problematic, because it is


supposed to have the same polarity (from the intracellular side to the extracellularside) as the B2 component, and is also expected to be pH-dependent. Thisproblem can be solved by the help of the following kinetic consideration.

10.13.1. Coupled interfacial proton-transfer reactionsAlthough the detailed mechanism of proton translocation in the purple

membrane is not known, a very general model which summarizes the consensus ofmany investigators can be constructed. Most investigators entertain the idea of atransmembrane proton-conduction channel across the span of the membrane. Thischannel or proton-translocating path is formed by multiple proton-binding sitesattached to side chains of the polypeptide. Otto et al. [83] demonstrated that thecarboxylic group at the residue 96-aspartate (D96) is the immediate proton donorto the Schi�-base proton-binding site, whereas the residue 85-aspartate (D85) isthe proton acceptor of the Schi�-base proton [58]. Nagle and Morowitz [228,229]proposed a mechanism of proton conduction, which is similar to that in the icecrystal (hydrogen-bonded chain). The original idea was usually credited toOnsager. Honig [230] proposed a four-state model of proton conduction, whichessentially treats bR like an enzyme.

The model shown in Fig. 50 links these ideas together and facilitates anelectrochemical analysis [35]. The model is reminiscent of the electron transportchain except that it is a proton being transported instead of an electron (seeSection 14). The existence of such a proton transport chain was supported byrecent evidence obtained by Dioumaev et al. [86] in a bR mutant. They proposedGlu-194 (E194) as the proton release group, which corresponds to A5 in Fig. 50.This model, together with the electron transport chain in mitochondria and in thephotosynthetic reaction center, can be regarded as a scheme of coupled consecutivecharge-transfer reactions. Thus, several sequential chemical reactions are chained

Fig. 50. Coupled consecutive proton-transfer reactions across purple membrane of Halobacterium

salinarium. Actual number of binding sites is not known. For simplicity, only ®ve binding sites (A1

through A5) are shown. Site A3 is proton-binding site at Schi�-base linkage. Two adjacent sites, A2 and

A4, are Asp96 and Asp85, respectively. Additional sites exist between sites A4 and A5, and also possibly

between A1 and A2. It is understood that Schi� base is neutral when unprotonated, and is positively

charged when protonated. Reverse reactions are not shown. (Reproduced from Ref. [35])


together, in such a way that the products of a particular reaction become thereactants of the subsequent reaction in the downstream of the chain, whereasthe reaction gets its reactants from the products of the preceding reaction in theupstream of the chain. Aqueous protons in the cytosol are fed into thischain by an interfacial proton-transfer reaction. The proton is released at the endof the chain into the extracellular space by another interfacial proton-transferreaction.

An important element of this model is the presence of a reverse proton-transferreaction in each reaction in the chain, including two interfacial proton-transferreactions. Some investigators thought that one of the proton-transfer steps mustbe one-way in order for the proton pump to work. But a simple theoreticalconsideration quickly shows that such a one-way reaction, while desirable, is notnecessary for the pump to work. This proton translocation is not a consequenceof reaching an equilibrium. Energy input from absorbed photons is required forthe pump to work. Despite the presence of reverse proton transfers, light energyinput will ensure the net one-way (vectorial) proton transport. Of course, thepresence of a highly irreversible step will make the proton pump even moree�cient, and experimental evidence indicates that a deprotonation/reprotonationswitch does exist [231,232,233] (see Section 18).

It is generally agreed upon that the immediate `driving force' of the proton ¯owis the light-induced decrease of the pKa (or rather, increase of the pKb) of theSchi�-base proton-binding site (A3) [234]. In the schematic, this pKa change drivesthe forward proton transfer to the immediate proton acceptor A4. By virtue of thelaw of mass action, as applied to these coupled consecutive reactions, theequilibration of the reactions in the downstream direction of the chain will beshifted to the right (i.e., extracellular side). On the other hand, deprotonation ofthe Schi�-base proton-binding site A3 creates a vacancy, which is similar to thehole (e.g., oxidized `special pair') in the primary electron-donor site in thephotosynthetic reaction center except with an opposite sign. Again, by virtue ofthe law of mass action, equilibration of the reactions upstream to the Schi�-baseproton-binding site will result in deprotonation of A2 and reprotonation of theSchi� base. Eventually, the shift of equilibrium will be back-propagated all theway to the cytoplasmic side, and again the equilibrium of these reactions will bedriven to the right.

The actual number of proton-binding sites is not known. It is possible thatadditional sites appear between A1 and A2 as well as between A4 and A5. Thus,the minimum requirement for such a proton pump to work is that one of thesesteps must be light-driven. Protons will be pumped unidirectionally from thecytoplasmic side to the extracellular side regardless of proton transfer in thewrong direction, caused by the back reactions. Of course, more than one of thesesteps can be light-driven, as has been suggested by Honig in his four-state model[230], but the minimum of one is required. Fig. 50 is thus a minimalist model.

10.13.2. Concept of local reaction conditionsIn principle, each and every step of the consecutive proton transfers, together


with the corresponding reverse reaction, can generate a component ofdisplacement photocurrent. Our equivalent circuit analysis, however, shows thatthe faster the relaxation is the larger the amplitude is of the photocurrentcomponent (Sections 8.3 and 9.1). Thus, our present measurement reveals onlythose components with a relaxation time constant in the microsecond range.

A pertinent question to ask is: which of those proton-transfer reactions in theproton transport chain is/are rate-limiting? Apparently, neither of the twointerfacial proton-transfer reactions are rate-limiting. This can be inferred fromthe following consideration. As indicated in Section 9.1, the observation that theamplitude of the DC photocurrent is several orders of magnitude smaller thanthat of the AC photocurrent strongly suggests that the transmembrane protontranslocation is considerably slower than the two interfacial proton-transferreactions. It follows that the two interfacial proton-transfer reactions must bechemically decoupled in the microsecond time scale. In other words, a shift ofequilibrium of the interfacial proton transfer at the cytoplasmic side, induced by alight pulse, will not have time to propagate along the proton transport chain allthe way to the extracellular side, and vice versa. In other words, there is no timeto reach a steady state. Experimental evidence for this assertion can be found in arecent report by Cao et al. [235]. These investigators used bR with the covalentlylinked pH indicator dye, ¯uorescein, to monitor the surface-potential changeduring extracellular proton release, and found that the proton release is notcorrelated to the transfer of proton from the Schi� base to D85. Thus, at least aslow step interposes between Schi�-base deprotonation and proton release to theextracellular space.

For all practical purposes, the two interfacial proton-transfer reactions can beregarded as two independent chemical reactions, although the same bR moleculehappens to be one of the reactants for both reactions. Under this condition, theinterfacial proton uptake at the cytoplasmic side will depend on the protonconcentration at this side (cytosolic pH), but not on that of the extracellular side,and vice versa. This peculiar situation is enunciated as the concept of localreaction conditions [135]. A similar situation exists for the interfacial electrontransfer in the model Mg-porphyrin-containing BLM. We suspect that thissituation may be fairly general in photobiological membranes.

10.13.3. `Di�erential' experiment: evidence for existence of B2 'The concept of local reactions thus forms the basis of an experiment, which was

designed to di�erentiate between the B2 and the B2 ' components on the basis oftheir dependence of the pH of the adjacent aqueous phase. The result of such anexperiment is shown in Fig. 51.

Bacteriorhodopsin was reconstituted into a Collodion-supported membraneoriginally developed by Drachev et al. (Section 6.3). Plain lipid membranes were®rst formed on the Collodion support. An aliquot of purple membrane aqueoussuspension was then added to one side (referred to as the cis side). We were ableto elicit both DC and AC photoelectric responses from such a preparation. TheDC photocurrent ¯ows from the cis side to the trans side, as does the slower


component of the AC photoelectric response. On the other hand, the faster ACcomponent has a polarity opposite to that of the DC component and the slowerAC component. In addition, the slower component can be reversibly inhibited bylowering the pH at the cis side. Therefore, the fast component can be identi®ed asthe B1 component, and the slow component as the B2 component.

The `di�erential' experiment then proceeded as follows [32,135]. First, the pH atthe cis side was lowered to suppress the B2 component (the negative peak). Whilethe pH at the cis side was being kept low, the pH at the trans side was alsolowered. The latter maneuver resulted in the reappearance of the negative peak.However, this negative peak has a di�erent time course: it decays faster than theregular B2 does. Its appearance, in the presence of low pH, suggests that there is asignal originating from the trans side (extracellular side). Furthermore, thisphotosignal has a pH dependence opposite to that of the regular B2 component,as appearing in a TM ®lm Ð low pH enhances it rather than suppresses it. Wetherefore attribute this signal to the hypothetical B2 ' component.

Recently, Misra [236] analyzed the pH dependence of B2, and associated thiscomponent with proton release. Here, we must point out that Misra reconstitutedbR in a gel membrane by means of a method developed by DeÂ r et al. [192] (seeSection 6.4). Since both surfaces of the membrane were exposed to the sameelectrolyte composition, it is di�cult to distinguish B2 from B2 '. Thus, their B2may correspond to B2 ' in our present terminology.

10.13.4. Interpretation of pH dependence of B2 and B2 'We were led to the di�erential experiment by the assumption that the B2 and

Fig. 51. `Di�erential' experiment showing existence of two separate components of photosignals,

corresponding to proton uptake and release, respectively, at two membrane±water interfaces. See text

for explanation. (Reproduced from Ref. [32])


the B2 ' components will respond to the (local) pH changes, because the rate ofphotosignal relaxation will be strongly in¯uenced by the (local) pH, i.e., the localconcentration of one of the reactants, proton. Thus, in accordance with LeChaÃ telier's principle, increasing cytoplasmic pH favors deprotonation of thecytoplasmic binding site of bR, whereas decreasing extracellular pH favorsprotonation of the extracellular proton-binding (or rather, proton-release) site.This also means that the increase of the cytoplasmic pH and the decrease of theextracellular pH, as a result of proton pumping, will make the pump less e�cientby making reverse proton transfer more favorable and forward proton transferless favorable than initially.

Previously, we applied the same reasoning to the analysis of AC photoelectricdata obtained from interfacial electron transfer, as described in Section 5.4. Wewere able to change the time course of the photosignal by varying theconcentration of the electron donor in the aqueous phase. We observed that whenthe rate of reverse electron transfer is enhanced by an increasing donorconcentration, the relaxation time constant (tp) is shortened and the amplitude ofthe signal is decreased [163]. Furthermore, there is evidence supporting thedecoupling of two interfacial electron transfers in the microsecond range.Therefore, the concept of local reaction conditions does apply to our modelsystem of a light-driven electron pump.

In analogy with the case of interfacial electron transfer in the above modelsystem, the expected behavior of B2 and B2 ', when the local pH is varied, wouldbe the following. B2 relaxation should be hastened and its peak amplitudedecreased at high intracellular pH, whereas B2 ' relaxation should be sped up andits peak amplitude decreased at low extracellular pH. This result is also expectedby chemical kinetics analysis, if the interfacial proton transfer obeys the law ofmass action, and if the second-order rate constant is a true constant independentof local pH.

While the di�erential experiment apparently worked in reconstituted bRmembranes, the resulting pH dependence is contrary to our expectation.Inspection of Fig. 51 reveals that the most prominent e�ect is the pH dependenceof the amplitude, but the pH dependencies of B2 and B2 ' are exactly opposite towhat is expected. While the pH e�ect on the relaxation time constants of B2 andB2 ' remain to be analyzed quantitatively, the amplitude e�ect is too prominent tobe ignored. If we insist upon interpreting the data in the framework of the law ofmass action, the only explanation is that the second-order rate constant ofinterfacial proton transfer is pH-dependent. That is, the pKa's of the intracellularproton-binding group and the extracellular proton-binding group are pH-dependent [35,38].

While a classical equilibrium constant is not supposed to be dependent upon theconcentration of any of its reactants, exceptions are not unusual in proteinchemistry. A well-known precedent is the oxygen-binding constant of hemoglobin,in which the initial binding of oxygen leads to conformational changes thatenhance further binding of oxygen (cooperativity). Proteins are well known forconformation-coupled changes known as allosteric e�ect; a protein molecule


responds to a localized change caused by binding of a ligand (modulatormolecule), which is transmitted over a long distance to a�ect a remote part (activesite) of the same molecule. The proton is one of the most important ligands thatprofoundly a�ect the conformation of bR [237]. It is also not unusual for a kineticconstant to be pH-dependent [238,239].

The above notion of pH-dependent kinetic constants can be regarded as aspecial case of a more general formulation of charge-conformation interactions inmacromolecules, proposed by Christophorov and co-workers [240±242]. Theseauthors pointed out that a charge being transferred in a photosynthetic apparatuscarries with it an intense local electric ®eld (0107±109 V/cm), which is far greaterthan an externally applied one (0105 V/cm) (cf. Section 15.3). It has been shownthat such local electric ®eld changes induce a profound change of macromolecularconformation, which takes place at a considerably slower time scale than thecharge transfer per se [243,244]. This slow change of conformation may a�ect thekinetic constant of the charge transfer, because the kinetic constant isconformation-dependent. A feedback loop is thus established in which theoutcome of initial charge transfer regulates further charge transfer. Collectively,the e�ect caused by such feedback loops is referred to as self-organization in thenonlinear dynamics literature.

The concept of self-organization epitomizes the view that self-reinforcingfeedback (positive feedback) in primordial chemistry was responsible for theappearance of order and highly organized structures [245,246]. Speci®c modelsbased on a self-organizing e�ect are often referred to as self-consistent models,because of the complexity of regulatory control exerted by feedback from thee�ect to the cause itself, and the frequent necessity of solving the governingequations implicitly; the governing equations merely spell out the conditions ofself-consistency.

Examples of self-organization phenomena abound. Ionic ¯uxes throughvoltage-gated ion channels in biomembranes generate localized electric ®elds,which alter the state of voltage-gated ion channels, and thus a�ect the ionic¯uxes per se [247]. Bioenergetic systems in which ¯uxes of charges (electrons orprotons) through speci®c charge-translocating path instead of water-®lled ionchannels may exhibit similar phenomena via charge-conformation coupling. Ourobservation of pH-dependence of B2 and B2 ' is an example in whichprotonation and deprotonation of surface proton-binding groups may a�ect theoverall conformation of bR (Note that surface protonation and deprotonationare the ®rst and the last step of the proton ¯ux, respectively). In Section 17,we shall discuss in detail how surface protonation/deprotonation may a�ect thebR photocycle. Furthermore, the photocycle kinetics may become highlynonlinear, because of the presence of yet another feedback loop caused bysurface-potential-dependent changes of local proton concentration (pH)[248,249].

Let us consider the nonlinear light dependence of electron transfer inphotosynthetic reaction centers. Christophorov and co-workers [240±242] appliedthe principle of charge-conformation interactions to bacterial photosynthetic


reaction centers and constructed a mathematical model to describe the e�ect ofmanipulating illuminating light intensity. They predicted that under a certainrange of low lighting condition, there exist two distinct average distances ofseparated charges (electrons and holes) corresponding to two (meta)stableconformations. Since the rate of charge recombination via electron tunnelingstrongly depends on the distance between the pair of separated charges, the twostable conformations will exhibit two di�erent kinetic rate constants of chargerecombination. Thus, in varying the intensity over a range of weak illumination,the model predicts a hysteresis phenomenon Ð the light dependence of the extentof charge transfers will be nonlinear and the light-dependence curve will tracedi�erent paths depending on whether the extent of charge transfer is measured ina light-increasing direction or in a light-decreasing direction. These predictions arein agreement with experimental observations in reaction centers of Chloro¯exusaurantiacus and in QB-containing reaction centers of Rhodobacter sphaeroides, butnot in QB-free reaction centers of the latter (presumably, because the range oflight intensity used in the experiment was still too high) [250,251].

Subtle regulation, implemented in terms of charge-conformation interactions,will be discussed in the context of intelligent materials in Section 19.2.

11. Why is chemical capacitance physically distinct from membrane capacitance?

The analysis and interpretation of AC photoelectric signals, presented inSections 8±10, di�er sharply from the mainstream approach, in which thetransient photoelectric signal is ®tted with several exponential terms. With theadvent of personal computers and data manipulating software, the latter approachbecame routine and popular. Two parallel tracks of literature have come tocoexist: the mainstream approach and our present approach of equivalent circuitanalysis. Because of the diametrically di�erent interpretations, it is unlikely thatboth represent the same physical reality. In fact, there has been a continuingcontroversy with regard to the concept of chemical capacitance, since itsintroduction [252,253] (see Section 20.2). Several questions have been raised. Is itreally necessary to invoke the concept of chemical capacitance in theinterpretation of fast photoelectric signals? Is chemical capacitance actually theordinary membrane capacitance in disguise? Is it an algebraic (theoretical) artifactin the mathematical analysis? Is it an experimental artifact due to the peculiarityof a particular experimental procedure, such as the method of membranereconstitution or the electrical measurement method? Since our laboratory alonewas responsible for the introduction of this concept, and since the data whichwere used to validate the concept were also obtained mostly in our ownlaboratory, independent proof from a separate laboratory is in short supply. We,therefore, bear the burden to demonstrate the validity of the concept and thevalidity of mathematical analysis beyond reasonable doubt.

In the present section, we shall demonstrate that the evidence, initially used by


other investigators to argue against the concept of chemical capacitance, actually

supports the concept instead. The greatest di�culty of the mainstream approach

seems to be the lack of agreement between di�erent laboratories. Thus, we shall

demonstrate that the discrepancy of data between laboratories can be reconciled

in terms of the concept of chemical capacitance. Readers who are not particularly

concerned with the controversy may skip the following discussion and proceed

directly to Section 12 with no loss of continuity.

The mainstream approach has continued to enjoy endorsement of the majority

of laboratories working with the problem of the AC photoelectric e�ect. In the

case of bR, decomposed exponential time constants are routinely compared with

the optical relaxation time constants of the photocycle, and the agreement, though

not impressive, was generally considered to be satisfactory. In Section 17, reason

for such an apparent agreement between the optical and the electrical time

constants will be presented.

A number of investigators have come to believe that the mainstream approach

is objective by virtue of the use of standard software for exponential

decomposition. The success of ®tting relaxation data to several exponential

functions is thus taken as evidence of the validity of the approach. In Section 20,

we shall demonstrate that the ®t is guaranteed by the lack of any constraints,

imposed by the data, on the decomposed exponential functions. In other words,

the parameters (amplitudes and time constants of the exponential functions) used

in the process of curve ®tting are subject to no constraints. Therefore, the success

of a ®t alone cannot be construed as validation of the mainstream approach.

We also subject the relaxation data to similar exponential decomposition; the

time constants ts and tl, used in the deconvolution process, were obtained by

exponential decomposition of the curve shown in Fig. 25(A). The equivalent

circuit model then makes a prediction and imposed a constraint on the data by

virtue of Eq. (9.16), as explained in Section 9.2. What was conspicuously di�erent

from the mainstream approach was the relatively small number of exponential

terms, 2, as compared to four or more exponential terms. That was the

consequence of the additional step of isolating a pure component.

In contrast, the mainstream approach made no attempt to separate the

individual components, before applying the exponential analysis, presumably,

because it was regarded as self-evident that the exponential decomposition

automatically separates the components. As we shall demonstrate in the following

sections, the latter assumption turns out to be false. Failure to apply the

additional step of setting constraints from a concrete model thus gave a false sense

of validity of the approach. On the other hand, discrepancies, such as demonstrated

in Section 11.4, could be dismissed in a wholesale manner by invoking the

complexity of biology, the inherent noisy nature of biological data, and our

ignorance, etc. In discussing an unrelated topic, we have previously demonstrated

how easy it is to `brush aside' a piece of unfavorable evidence, and how easy it is

to rescue a weak hypothesis by proposing additional ones (p. 213 in Ref. [196]).

We think a better judgment can be made by viewing all available evidence as a


whole. The following discussion is intended to reconcile super®cially con¯ictingdata that appeared in the literature.

11.1. Experimental evidence in support of existence of series capacitance

The concept of chemical capacitance was initially proposed to ®ll the need tointroduce a series capacitance to the photosignal source, as demanded by ourexperimental data. The data were obtained from an arti®cial Mg-porphyrin-containing BLM that is coupled to a redox gradient [163], as described in Section5.4.

Our ®rst clue was a small, but discernible, variation of the photocurrentrelaxation time course, depending on the condition of the pair of calomelelectrodes being used to record the short-circuit current. This condition turned outto be the resistance of the electrodes. In our measurement set-up, this resistance iscomprised mainly of the access impedance that is located between the point wherethe voltage is being clamped and the membrane surface. The presence of a ®nitenon-zero access impedance leads to a deviation of the measurement conditionfrom an ideally short-circuit condition. The variation of the photosignal suggeststhat the source impedance is comparable to the electrode resistance (about 20 kOfor a pair of calomel electrodes). This means the source impedance must havedeviated considerably from its DC value of approximately 109 O to a much lowervalue at the megahertz range, where the measurement was being made. The latterimplies the existence of a reactance in the membrane. We suggested that thisreactance is a capacitance (chemical capacitance) that is connected in series withthe photosignal source [162,163].

Bacteriorhodopsin data in support of the existence of a series capacitance was®rst reported by Drachev et al. [152]. These investigators developed severalingenious methods to reconstitute bR into a planar membrane. Using one of thesemethods, they ®rst incorporated bR into phospholipid vesicles and then let thevesicles fuse with a plain (non-pigmented) planar BLM, as described in Section5.3. The photovoltage from such a membrane in response to a square-wave lightpulse is shown in Fig. 8(A). The waveform of the photoresponse could betransformed into the one, shown in Fig. 8(B), by either adding CCCP to theaqueous phases or by shunting the photovoltage with an external resistor. In otherwords, the transformed membrane responded to the onset of illumination with along square-wave light pulse by a spike-like waveform (on-overshoot), and to thetermination of illumination with a nearly symmetrical waveform of oppositepolarity (o�-overshoot) [184].

The characteristic waveform of on-overshoot and o�-overshoot is the `signature'of a linear RC high-pass ®lter and is often referred to as di�erential responsivity(Section 19.3). Their data thus demand the presence of a series capacitance placedin the photocurrent path leading to the external instrument. Their proposedbutton model (Fig. 52) satis®es this requirement [254]. While the membranecapacitance (C3) of the vesicle is in parallel with the signal source, the membranecapacitance (C2) of the planar membrane at the contact region (containing no bR


molecules) is indeed in series with the signal source. Thus, the membranecapacitance C2 and the internal resistance (r ) of the photoemf source in the vesicleconstitute a high-pass RC ®lter. Therefore, their interpretation is qualitativelyconsistent with their data. Note that Drachev et al. [184] have arrived at the samemathematical model (a high-pass RC ®lter circuit) as we did in Sections 9.

However, the data of Drachev et al. [152] could also be explained in terms ofthe concept of chemical capacitance [31,153,183]. Recall that the variation of tm

may have a profound e�ect on the waveform of an AC photosignal, induced by along square-wave light pulse. What CCCP or an external shunt does to themembrane is reduce the charging time constant tm (see Eq. (9.11)). When tm fallsbelow the critical value tmc, the waveform will be transformed from a monotonicrise and decay, as in Fig. 8(A), into a new waveform characterized by an on-overshoot and an o�-overshoot, as in Fig. 8(B) (see also Fig. 24). In order words,both the button model and the concept of chemical capacitance can qualitativelyexplain the data shown in Fig. 8. While quantitative veri®cation of the equivalentcircuit associated with chemical capacitance has been furnished, no quantitativeveri®cation of the button model has ever been reported.

Independent evidence in support of the button model was provided by Kagawaet al. [255]. Kagawa and co-workers ®rst formed a planar plain BLM by means ofTakagi±Montal method (Fig. 53). Preteoliposomes prepared from puri®ed F0±F1

ATPase were then introduced into one side of the membrane (the cis side) andallowed to fuse with the planar BLM. Proteoliposomes were assumed to attachedto the BLM without actual fusion, as stipulated by the button model. They thenlowered the water level of the trans side in order to `stretch out' the adhered

Fig. 52. High-pass RC ®lter circuit of `button' model. Capacitors for three regions Ð regular planar

BLM, contact region, and vesicle Ð are represented by C1, C2, and C3, respectively. Here, C3 is series

capacitor which, together with resistor r in vesicle region, forms linear high-pass RC ®lter. (Reproduced

from Ref. [254])


liposomes. When the water level was restored, a new BLM was again formed withF0±F1 ATPase then fully inserted into the bilayer, as they assumed. Presumably,such a maneuver was necessary to render the electrical event of proton pumpingobservable. Here, every detail in the chain of events corroborated the buttonmodel so well that the interpretation of Kagawa et al. was immediatelyconvincing.

Before one rushes to accept the report of Kagawa et al. as evidence in supportof the button model, one must critically examine the chain of events described inFig. 53. There were three possible consequences when the water level of the transside was lowered: (a) the two monolayers of the BLM were separated, as can besimulated by splitting two strips of Scotch1 tape (No. 810) that are stucktogether, (b) the BLM ruptured when the monolayer of the trans side was beingpulled away from the monolayer of the cis side, as can be simulated by splittingtwo similarly attached mailing labels (e.g., Avery1 Label No. 4013), and (c) theBLM remained intact in place. First, let us consider two forces: the adhesive forcebetween water and the polar head groups of the monolayer at the trans side, andthe cohesive force between hydrocarbon tails of the two monolayers (hydrophobicinteractions). If the cohesive force is stronger than the adhesive force, the BLMwould remain intact (possibility (c)). Otherwise, one must consider another forcein addition: the lateral cohesive force that holds phospholipids together within amonolayer. Only if this latter force is su�ciently strong could the two monolayersbeen successfully separated without breaking the BLM. In view of the notoriousfragility of a Takagi±Montal membrane (see Section 6.6), it is unlikely that thetwo monolayers could be successfully separated as stipulated by Kagawa et al.Since Kagawa et al. were able to measure an electric current from theirpreparation, the membrane was obviously not ruptured. Thus, the third event wasmost likely. The interpretation of Kagawa et al. is therefore highly questionable.

If the button model is accepted without a doubt, the interpretation of Kagawaet al. certainly has the `ring of truth'. If, however, the button model is called into

Fig. 53. Fusion of F0±F1 liposome to planar bilayer. See text for explanation (Reproduced from Ref.

[255])


question, the chain of events depicted in Fig. 53 is suddenly reduced from anexperimental `fact' to `®ction'. Perhaps the maneuver of changing the water leveldid help in promoting fusion of the vesicles, but the observation could beinterpreted as a consequence of mechanical perturbation caused by lowering andraising of the water level alone. The interpretation proposed by Kagawa et al. iscertainly not the only possible explanation of the e�ect. Strictly speaking, theobservation of Kagawa et al. cannot be used to support the button model becausedoing so is tantamount to circular reasoning.

We now turn to the crucial question: which one represents the real physicalpicture: the button model or chemical capacitance? Instead of proving which oneis correct, we shall show which one leads to an inconsistency.

Drachev et al. [152] also found the same waveform transformation induced byCCCP or by a shunt resistor in another experiment, in which bR was incorporatedby adding the purple membrane directly to the membrane forming solution, thusbypassing the step of vesicle fusion. This self-contradiction seems to negate theinterpretation of Drachev et al. [184]. Drachev et al. were apparently aware of theproblem, but they `resolved' the problem by stipulating that there are `water-containing closed chinks (cavities) between the plasma membrane surface and someparts of the sheets associate with this membrane' [254]. Certainly, a spontaneouslyformed water cavity gives rise to a series capacitance as does the button model, andcan, in principle, accounts for di�erential responsivity. But there is no independentevidence. In fact, Drachev et al. [254] noted that the electron microscope studyrevealed no vesicular structures in the bR sheet preparation.

The validity of the button model is an important issue, because the model hasbeen widely accepted, and has become the basis of additional experimentation andinterpretation [185,255,256]. Here, we must point out that there has never beenany morphological evidence or other independent evidence in support of thepresence of spontaneously formed water cavities, nor has there been any attemptto demonstrate its speculated presence. Thus, the above-mentioned inconsistencyremains to be explained.

Additional experimental evidence, in support of the existence of a seriescapacitance, comes from the study of the Mg-porphyrin-containing BLMmentioned earlier [163]. The pulsed-light-induced fast photoelectric signal from thelatter membrane under a pseudo-®rst-order regime follows a bi-exponentialrelaxation time course. The initial rise of the photosignal has a polarity that isconsistent with light-induced electron transfer from the membrane to the aqueouselectron acceptor (ferricyanide), but the signal does not decay monotonically tothe baseline, but rather shoots below the baseline and then rises gradually backtowards the baseline. The signal itself can be varied by changing the redoxcomposition of the aqueous phase, thus changing the pseudo-®rst-order rateconstant. However, as long as a pseudo-®rst-order regime is maintained, therelaxation time course can always be ®t with two exponential terms in accordancewith Eqs. (9.13) and (9.16). As explained in Section 9.2, this relationship impliesthat the measured photocurrent satis®es the condition of a zero time-integral,discovered by Hagins and McGaughy [157]. This empirically found relationship


suggests the existence of a series capacitance, and was the clue that led us to theequivalent circuit shown in Fig. 23.

The method of membrane reconstitution, used by Trissl and Montal [154] andHong and Montal [156] to produce an ERP-like signal, allows only a capacitativecurrent to be observed, because the insulating nature of Te¯on precludes thepassage of a DC photocurrent. Thus, the condition of a zero time-integral isguaranteed (Section 6.7). However, the zero time-integral condition would haveremained valid even if bR had been reconstituted into a genuine BLM, whichallows the DC photocurrent to coexist with the AC photocurrent. This is becausethe lowered source impedance in the high-frequency range allows the ACphotocurrent to be preferentially ampli®ed (that is what a high-pass ®lter does; seealso Section 9.1). We have shown that, under the measurement conditions thatallow the AC photocurrent to be resolved, the DC photocurrent is actually buriedin the noise. This is true both for bR membranes and for the Mg-porphyrin-containing BLM. The frequency-dependent source impedance thus allows the ACphotocurrent to be preferentially selected over the DC photocurrent, and, in fact,allows faster AC photocurrent components to be ampli®ed preferentially overslower AC components.

Without speci®cation of the measurement condition, the amplitude is not agood indicator of the underlying chemical processes. The information coded bythe amplitude can also be deceptive. This is illustrated by a comparison of the B1and the B2 components measured under a near-short-circuit condition and underan open-circuit condition (Fig. 9). Whereas the B2 seems to be larger than the B1component under open-circuit conditions, the opposite is true under near-short-circuit conditions [156]. In addition, the decay times of both components aresigni®cantly shortened. This behavior was predicted by the equivalent circuitanalysis.

Similar observations have been reported by Drachev et al. [257] in their study ofreconstituted rhodopsin membranes: the ratio of the R1 to the R2 peakamplitudes changes from 0.014 to 0.16, when the shunt resistance is varied from50 MO cm2 to 2 kO cm2 (see Section 13.1).

11.2. Relationship between photovoltage and photocurrent

Caution must be exercised in measuring a short-circuit current, which demandsthat the access impedance be considerably less than the source impedance. Thepresence of a chemical capacitance presents a pitfall for unsuspicious investigators.Since the source impedance of the membrane can be as low as 10 kO at 1 MHz, itis no longer good enough to have an ampli®er with an input impedance of 107 O(that of a commercial picoammeter) for short-circuit measurements. An intendedshort-circuit measurement could turn out to be actually a measurement under anear-open-circuit condition. The telltale evidence of this problem is provided by a®rst-derivative relationship between the photocurrent and the photovoltage, whichwas frequently cited by Trissl [166] to validate his photocurrent measurement:


Isc�t�AdVoc�t�dt

, �11:1�

where Isc�t� is the short-circuit current and Voc�t� is the open-circuit voltage.Super®cially, the above relation is consistent with the elementary notion that

photocurrent that charges and discharges a membrane capacitance is proportionalto the rate of change of the voltage across the capacitance. But it is important torealize that the two variables must be measured under the same condition in orderto maintain a ®rst-derivative relationship, whereas the open-circuit voltage and theshort-circuit current are measured under extremely di�erent conditions. Thus, thetwo variables, Isc�t� and Voc�t�, are inappropriately mixed in Eq. (11.1). Thefallacy of Trissl's interpretation can be made apparent by the following analysis.

Let us consider a simple case of the RC circuit shown in Fig. 54. Thecapacitance Cm is initially charged to a certain voltage. Its discharge is thenmonitored by a measuring device with an input resistance (or impedance) Re.There are two paths for the discharging process. The capacitance is dischargedpartly by the current I(t ) through the measuring device, and partly by the currentIr�t� through the membrane resistance Rm. The total discharging current Ic�t�,being the rate of disappearance of the charge Q(t ) on Cm, can be expressed as a®rst-derivative relationship:

Ic�t� � ÿdQ�t�dt� ÿCm � dV�t�

dt, �11:2�

which is valid under all conditions, including open-circuit and short-circuit.Now let us consider separately the open-circuit condition (condition 1) and the

short-circuit condition (condition 2), and use the subscripts 1 and 2 to denotevariables or functions under the open- and short-circuit conditions, respectively.

11.2.1. Condition 1 (open-circuit)An open-circuit condition can usually be achieved, if the measuring device is an

Fig. 54. Diagram explaining relationship between measured photocurrent and measured photovoltage,

as access impedance varies. Circuit parameters are de®ned in text.


electrometer with an input impedance, which is much greater than the membraneresistance:

�Re �1>> Rm: �11:3�Therefore, the current going through the electrometer (�I�t��1) should be negligiblecompared with the ionic current �Ir�t��1, i.e.,�

Ir�t��1>>

�I�t��

1, for all t: �11:4�

Thus, we have�Ic�t�

�1� �Ir�t�

�1��I�t��

11�Ir�t�

�1, for all t: �11:5�

Also, the open-circuit voltage, [V(t )]1, satis®es the following equation:�V�t��

1� �Ir�t�

�1�Rm, for all t: �11:6�

It can readily be shown that both �Ir�t��1 and �Ic�t��1 relax with an exponentialtime constant of approximately RmCm. Therefore, the open-circuit voltage �V�t��1also relaxes with the same time constant.

11.2.2. Condition 2 (short-circuit)Now, in order to make a short-circuit measurement, the access impedance must

be made much smaller than the membrane resistance:

�Re �2<<Rm: �11:7�We have�

Ir�t��2<<�I�t��

2, for all t: �11:8�

�Ic�t��2 becomes almost equal to the short-circuit current, [I(t )]2:�Ic�t�

�2� �Ir�t�

�2��I�t��

21�I�t��

2, for all t: �11:9�

Again, elementary analysis reveals that �Ic�t��2 relaxes with a time constant ofapproximately �Re�2 � Cm. Therefore, the short-circuit current [I(t )]2 has a fasterrelaxation than the open-circuit voltage [V(t )]1, of which the time constant RmCm

is much greater. In general, Eq. (11.1) is not valid because: (a) Isc�t� relaxes fasterthan Voc�t� does, and (b) the time-derivative of an exponential time function isalso one with the same time constant. Then, why did Trissl observe the ®rst-derivative relation (11.1) repeatedly?

11.2.3. Interpretation of Trissl's ®rst-derivative relationshipFrom the above analysis, it is obvious that the ®rst-derivative relationship, as

interpreted by Trissl, is in general not valid. In order to trace the reason behindTrissl's observation, let us now critically examine Trissl's experimental procedures.


Trissl used an electrometer with an input characteristics (1014 O; 20 pF) and apicoammeter (Keithley 427 with an input impedance of 107 O) to measure theopen-circuit photovoltage and the short-circuit photocurrent, respectively. Thus, ifthe reconstituted bR or rhodopsin membrane were represented by Fig. 54, asTrissl had assumed, the open- and short-circuit conditions would have beenadequately met, he would not have observed a ®rst-derivative relationship. Butthen why did Trissl observe the ®rst-derivative relationship (11.1)?

Trissl's observation can be explained, if there exists an additional circuit path(not included in Fig. 54) that contains a impedance lower than that of thepicoammeter, so that this third path provides a more e�ective short-circuitingthan does the measuring device or Rm. As a result, the measurement conditionremained virtually unchanged even if a picoammeter was used instead of anelectrometer. In other words, unbeknownst to the experimenter, the presence of athird unsuspected, but much leakier, path invalidates the intended short-circuitcondition. Therefore,�

Ic�t��11�Ic�t�

�2: �11:10�

It follows from Eqs. (11.2), (11.9) and (11.10) that

�I�t��

21ÿ Cm

�dV�t�

dt

�1

, �11:11�

which is exactly (11.1), the ®rst-derivative relationship reported by Trissl.The third path, which causes internal short-circuiting, can be realized by a

photocurrent path that includes the chemical capacitance, as shown in Fig. 23.The presence of chemical capacitance diminishes the source impedance of thephotosignal in the high-frequency range, rendering the use of a picoammeterinappropriate for a short-circuit measurement. In other words, while thephotosignal was recorded as a current signal by the picoammeter, themeasurement condition was actually closer to open-circuit than to short-circuit.The presence of Cm alone, while diminishing the membrane impedance at the highfrequency, could not have caused the same e�ect, as already shown by the aboveanalysis. Trissl's observation thus inadvertently supports the presence of areactance other than the membrane capacitance Ð the chemical capacitance.

11.3. Additional evidence

The Gouy±Chapman analysis in Section 8 demonstrates that the chemicalcapacitance is comprised of the same three fundamental capacitances as theordinary membrane capacitance does. Can the series capacitance be the ordinarymembrane capacitance in disguise [252,253]? In this section, we shall presentadditional evidence showing that the ordinary membrane capacitance cannotpossibly ®ll the role of the series capacitance [31].

Consider the process of proton transfer in the purple membrane, which


generates a membrane potential with a positive polarity at the extracellular side(Fig. 55(A)). In Fig. 55(B), the photoemf Ep, which drives the photocurrent fromthe intracellular side to the extracellular side, is connected in series to Cm. Thisarrangement results in Cm being charged negatively at the extracellular side, andthus gives rise to a photovoltage across Cm that happens to be opposite to what ismeasured experimentally. In order to obtain the correct polarity of thephotovoltage, Cm must be connected in parallel with the photoemf, as shown inFig. 55(C). Thus, it is not possible to con®gure Cm as a series capacitance.

The physical distinction between the ordinary membrane capacitance and thechemical capacitance can be further demonstrated by considering the three chargedistribution patterns on the three fundamental capacitances, i.e., Cd�l � (Cd on theleft-hand side of the diagram), Cg, and Cd�r� (Cd on the right-hand side). Asshown in Fig. 56, the charge distribution pattern that appears in an ordinarymembrane capacitance, in the OD model, and in the IPT model, constitute threedistinct ways of charging the three fundamental capacitance elements. Byconsidering all possibilities of arranging the polarities on each of the threefundamental capacitances, we shall argue that all patterns can be classi®ed as

Fig. 55. Diagram explaining di�erence of polarity of series capacitance and parallel capacitance. (A)

Diagram shows direction of forward proton transfer, which causes excess positive and negative charges

to accumulate at extracellular and intracellular surfaces, respectively. (B) Membrane capacitance Cm is

placed in series with photoemf Ep�t�. Proton current, driven by Ep�t� from intracellular side to

extracellular side, charges extracellular side of Cm negatively, relative to intracellular side Ð opposite

to actual situation shown in Diagram A. (C) Membrane capacitance is placed in parallel with

photoemf. Resulting charging process renders extracellular side of Cm positive, relative to intracellular

side Ð consistent with actual situation.


either one of the three types shown in Fig. 56, and that these three types are notinterconvertible. This is readily done by considering the number of polarityreversals as one examines the polarity on each pair of plates constituting all threecapacitances, starting from left to right.

Type I patterns (found in an ordinary membrane capacitance) are characterizedby the persistence of the same polarity in all three elements: (+, ÿ), (+, ÿ),(+, ÿ) or (ÿ, +), (ÿ, +), (ÿ, +), with no reversal of polarity. Type II patterns(found in IPT model) are characterized by a single reversal of polarity: (ÿ, +),(+, ÿ), (+, ÿ) or (+, ÿ), (ÿ, +), (ÿ, +). Type III patterns (found in the ODmodel) are characterized by two reversals of polarity: (+, ÿ), (ÿ, +), (+, ÿ) or(ÿ, +), (+, ÿ), (ÿ, +). This simple geometric analysis indicates that there arethree and only three distinct patterns of charge distributions. It also indicates thatthe charge pattern generated by an AC photoelectric e�ect cannot be duplicatedby an ordinary membrane capacitance.

The charge distribution patterns in the IPT or the OD model re¯ects thepeculiar localization of the photosignal source, being at the membrane±waterinterface and at the membrane interior, respectively. In contrast, when anordinary membrane capacitance is charged, the voltage source always residesoutside of the membrane Ð in fact, outside of the two double layers (in the caseof ionic current driven by a di�usion potential) or even in the external device (inthe case of charging the membrane with an electronic pulse generator).

Fig. 56. Charge distribution pattern of three capacitances in IPT model, OD model and ordinary

membrane capacitance. See text for explanation. (Reproduced from Ref. [31])


11.4. Reconciling data reported by other laboratories

It is instructive to examine the discrepancy exhibited in Table 5[168,192,258,259±261]. Data of Drachev et al. [168] were obtained under an open-circuit condition, and the time constants are the longest among the six groups.They correctly identi®ed t4 as the pure membrane RC relaxation time constant,but failed to realize the distortion of the remaining three time constants. On theother hand, the data of Fahr et al. [258] were obtained at a near-short-circuitcondition (see below). Thus, the discrepancies shown in Table 5 are indeedexpected by the bioelectrochemical approach, because of the di�erence inmeasurement conditions (access impedance).

The peril of continuing to ignore the impact of interaction between the chemicalcapacitance and the ordinary membrane capacitance, during a photoelectrictransient, is further illustrated by more recent data reported in the sameconference proceedings volume by two separate laboratories on the same subject(Fig. 57). Both Moltke et al. [262,263] and Gergely and VaÂ roÂ [264] studied a bRmutant, of which the residue 212 aspartate group had been replaced withasparagine (D212N ). Both groups reported the time courses of the observed ACphotoelectric signals on a logarithmic time scale, showing both fast and slowrelaxation processes. Those two sets of data look similar, but are not identical.Super®cially, the negative peak in Fig. 57(A) corresponds to the negative peak inFig. 57(B), but the time scale has been shifted by two to three orders ofmagnitude.

The main factor responsible for the discrepancy was the use of di�erentreconstitution methods. Moltke et al. adsorbed purple membranes to lipid-impregnated polyethylene, whereas Gergely and VaÂ roÂ immobilized oriented purplemembranes in gels. The discrepancy can be understood in light of our equivalentcircuit analysis. A gel membrane is very leaky, causing the photoelectric signal tobe internally short-circuited. Thus, even though an open-circuit measurement wasintended, the measurement condition was, inadvertently, much closer to short-circuit than to open-circuit conditions. It was commonly known to investigators,

Table 5

Time constants of AC photoelectric signal of bacteriorhodopsin membranes (reproduced from Ref.

[205])

Source t1 (ms) t2 (ms) t3 (ms) t4 (ms)

Fahr et al. [258] 1.3 17 0.06 0.9

DeÂ r et al. [192] 25 150 2.4 5.8

Keszthelyi and Ormos [259] 4.4 81 2.5 8

Ray®eld [260]a 57 1.06 13

Trissl [261]a,b 115 4.5 640

Drachev et al. [168] < 0.2 200 2 1000

a t1 not reported.b t4 derived from Fig. 1(d) in Ref. [261].


who used the gel membrane method, that the relaxation time course of thephotosignal measured under open-circuit conditions is very close to that measuredunder short-circuit conditions. This latter observation is expected when themembrane is internally short-circuited. In other words, reduction of Re andreduction of Rm have the same e�ect in reducing tm.

In Table 5, the data of Fahr et al. were supposed to be obtained under a short-circuit condition, but we think that the condition was not quite close to the idealshort-circuit condition for the following reasons. If the condition were truly short-circuit, t2 would approach the true photochemical relaxation time constant of B1,that is tp � 12:3 ms. However, their data can still be reconciled with what weunderstand from the analysis in Section 9. Fahr et al. reported the accessimpedance to be 500±1000 O and a membrane capacitance of 05 nF, resulting ina tm value of 2.5±5 ms. From Eq. (9.22), a crude estimate of the true B1 relaxationtime constant can be obtained: tp � 2t1 � t2=tm � 8±18 ms. Our measured valuefalls within this range. Unfortunately, most other investigators did not even reporta crude estimate of the access impedance or the membrane capacitance. It istherefore not possible to rescue their data by a similar reconstruction.

12. Analysis of DC photoelectric signal from bacteriorhodopsin

The primary physiological function of bR is pumping (translocating) protonsacross the purple membrane, and the e�ciency and the e�ectiveness of thephotoconversion is evaluated by analyzing the DC photoelectric e�ect; the ACphotoelectric e�ect is essentially an inevitable side e�ect that diminishes thee�ciency of photoconversion. Suppression of the AC photoelectric response and/

Fig. 57. Photovoltages from reconstituted D212N membranes, plotted against logarithmic time scale.

(A) Data reported by Moltke et al. were shown. (B) Data reported by Gergely and VaÂ roÂ were also

shown for comparison. (Reproduced from Refs. [262] (A) and [264] (B))


or enhancement of the DC photoelectric response can be construed as majorobjectives in biomembrane-based arti®cial solar-energy conversion research. Byincreasing the proportion of separated charges that do not recombine relative tothose that do recombine, the conversion e�ciency can be increased. Methodologyfor evaluating the DC conductivity is therefore of great technical andtechnological importance.

Many reports about the DC photoelectric e�ect of reconstituted membranescontaining either natural or synthetic pigments have appeared in the past threedecades. Comprehensive summaries of these activities can be found in reviews byTien [29,173]. The DC photoelectric e�ect in a reconstituted bR-containingmembrane was ®rst reported by Drachev et al. [151]. Additional reports from anumber of laboratories have appeared since then [152,181,182,185,189,190,200,254,265±276].

Studies of the DC photoelectric e�ect are routinely carried out by using a longsquare-wave pulse from a continuous light source equipped with a shutter control[163] (cf. Fig. 24). Investigators routinely reported the DC photoresponses eitheras photovoltages (under open-circuit conditions) and/or photocurrents (undershort-circuit conditions). At a more fundamental level, the light-induced proton-pumping activity can be analyzed in terms of the photovoltaic e�ect and thephotoconductive e�ect. In equivalent circuit analysis, these e�ects can be evaluatedin terms of the parameters photoemf (photoelectromotive force) andphotoconductance (the terminology will be precisely de®ned in the next section).While a photovoltaic e�ect has been demonstrated in numerous cases, evidence insupport of the existence of a signi®cant photoconductivity was often indirect andsometimes ambiguous, except in the special cases in which the photoconductivee�ect is not accompanied by a photovoltaic e�ect [277±279]. This is because asingle act of measurement of either a photocurrent or a photovoltage does notallow for a photovoltaic e�ect and a photoconductive e�ect to be unequivocallydistinguished; two independent measurements are required. This requirement isful®lled by a measurement method, the null current method, which was previouslydeveloped by Hong and Mauzerall for a light-driven electron-transporting BLM[280,281].

A membrane exhibits a photovoltaic e�ect, if a voltage source appears inresponse to illumination, but disappears upon cessation of illumination. Thephotovoltaic e�ect (light-induced emf generation) is measurable as a light-inducedvoltage across the membrane under open-circuit conditions, or as a light-inducedcurrent which traverses the membrane under short-circuit conditions. Aphotoconductive e�ect exists, if a conductive path for electric current through themembrane is created, enhanced, or suppressed by illumination. A photovoltaice�ect may also be accompanied by a photoconductive e�ect, because thegeneration of a photovoltaic e�ect often requires the creation of a speci®cphotoconductive path, in addition to the ionic di�usion path that also exists in theabsence of illumination and/or in the absence of the pigment. The ionic di�usionpath allows a transmembrane voltage- and/or concentration-gradient to drive anionic current through it.


The separation of the photoconductive path from the ionic di�usion path isessential in the data analysis. The photoconductive path allows the passage ofprotons only, and it provides a speci®c translocating mechanism for protons, oftenagainst an existing electrochemical gradient of proton, i.e., active transport ofprotons. In contrast, the ion transport through the ionic di�usion channel ispassive in nature, and is driven by the electrochemical gradient of ions selectivelyspeci®ed by the channel. The ionic di�usion path in an arti®cial BLM (known asthe ionic leakage channel) is usually non-speci®c and is permeable to several smallions, unless a special ion channel-forming or ion-carrier agent is also present.

On the other hand, a pure photoconductive e�ect can exist without theconcurrent photovoltaic e�ect, as can be demonstrated by the following example.Mauzerall and Finkelstein [277] investigated a BLM that was doped with iodineand iodide ions. In their system, the ionic conductance of the BLM is enhancedby the doping, because of the formation of polyiodide ions, which have a higherpartition coe�cient in the membrane phase than monoiodide, Iÿ. Thus, themembrane-bound polyiodide ions can carry current across the BLM, if a biasingpotential is applied across the membrane. Illumination photochemically destroyspolyiodide ions in the membrane, resulting in the reduction of this voltage-drivencurrent. Thus, a negative photoconductivity without a concurrent photovoltaice�ect was demonstrated, because a photoresponse could not be demonstrated inthe absence of the applied membrane potential. In fact, there was no ionic currentwithout the biasing transmembrane voltage, because there were no emf sourcesother than the applied biasing voltage in the BLM system.

In a reconstituted bR membrane, a photovoltaic e�ect clearly exists, because aphotovoltage and a photocurrent can be demonstrated separately, uponillumination, without a biasing transmembrane voltage. However, the possibilityof coexistence of both the photovoltaic and the photoconductive e�ects makestheir separation somewhat problematic. For example, it is well documented thatthe photocurrent of a reconstituted bR membrane is initially dependent on thelight intensity, but reaches saturation at a higher intensity. A number ofinvestigators have attributed this light dependence to the photoconductance,whereas we found the contrary (see Section 12.4). The null current methodprovides a general approach designed to deal with this problem in a systematicway.

12.1. Equivalent circuit for DC photoelectric e�ect

The ®rst step toward the application of the null current method is to choose anappropriate equivalent circuit. Fig. 58 shows the three equivalent circuits, two ofwhich were proposed in our previous study of the Mg-porphyrin-containing BLM[280]. Model A is consistent with the equivalent circuit, shown in Fig. 23, for therepresentation of the AC photoelectric e�ect. The chemical capacitance is omitted,because no capacitative events are being considered in the steady state. Themembrane capacitance is, however, retained for the convenience of describing thestored charges in conjunction with the appearance of photovoltages. Note that the


resistances Rp and Rs are combined into a single element, Gp, which is the DCphotoconductance and is equal to the reciprocal of (Rp � Rs). Here, a potentialsource of confusion in terminology exists and a word of clari®cation is warranted.The use of Gp to represent the DC photoconductance implies that it is thereciprocal of Rp. In reality, the parameter (Rp � Rs) is almost identical to Rs, sinceRs � Rp. Thus, Gp is practically the reciprocal of Rs instead. This potential sourceof confusion is unfortunate, but can be avoided with this reminder.

Although Model A is preferred because it is consistent with the equivalentcircuit for the AC photoelectric e�ect, Models B and C are also shown for thepurpose of subsequent discussion (see Section 12.7). The di�erence among thethree models are as follows (see Table 6). Ep in Model A drives a photocurrentthrough a speci®c proton-translocating (photoconductive) path Gp, but notthrough the nonspeci®c ionic di�usion path Gm. In contrast, both Ep in Model Band Ep in Model C drive a photocurrent through both Gp and Gm. Under open-circuit conditions, the capacitance Cm in Models B and C will be charged to thefull value of Ep, and the open-circuit photovoltage V0 will be equal to Ep, with thetop plate of Cm being positively charged as indicated. In Model A, the capacitanceCm will be charged with the same polarity as in Models B and C, but thephotovoltage V0 may or may not attain its expected full value of Ep, because Gm

in Model A acts as a current shunt. The full expected value of V0 can be attainedin Model A, only if Gm � Gp. Thus, in general, the photovoltage will be reducedin Model A, but not in Models B and C, if Gm is increased by the action of anionophore. On the other hand, the (short-circuit) photocurrent in Model A willnot be a�ected by increasing Gm, but the photocurrent will be increased in ModelsB and C, if Gm is increased by ionophore action. A special case of Model C, inwhich Gm is zero before the addition of a proton ionophore, represents thesandwich model (see Section 12.7.2). In the absence of ionophores, neither DCphotocurrent nor DC photovoltage is observable; the addition of a protonionophore renders them observable. However, an AC photocurrent and an AC

Fig. 58. Three models of equivalent circuit. Ep is photoemf. Gp is photoconductance. Gm is ionic

leakage conductance, originally present in the planar BLM before incorporation of pigment. Cm is

membrane capacitance. V0 is open-circuit photovoltage. In Model A, photoconductive path Gp and

ionic di�usion path Gm are separate. Photoemf drives current through Gp, but not directly through Gm.

In Models B and C, photoemf drives current through both of them directly. Gp and Gm are connected

in parallel in Model B, but in series in Model C. (Reproduced and modi®ed from Ref. [280])


photovoltage should become observable (Gm is replaced with a capacitor, since aninsulating membrane possesses a capacitance). The latter has not been reported inthe literature.

12.2. Null current method

The null current method was fashioned after the principle of potentiometry inelectrochemistry. The accurate value of an unknown source of emf must bedetermined under a condition which allows no current to ¯ow through the emf.This can be implemented by counterbalancing the unknown emf with a knownand adjustable one, so that no current ¯ows through the unknown emf. The null-current condition is achieved, when and only when, the two emf sources are equalbut of opposite polarity.

We use a voltage-clamp circuit, which is similar to that shown in Fig. 19(B), toimplement the null current method. The command voltage E allows us to imposea transmembrane potential across the membrane, and is, therefore, also referredto as the clamping voltage. The parameters, such as photocurrent, photoemf andphotoconductance, are then measured as a function of the membrane potential. Inaddition, the command voltage E can also be used as the voltage source to supplyan o�set voltage for counterbalancing the photoemf Ep, whereas the end point ofsuch a maneuver can be monitored via the same current output of the ampli®erthat gives the value of the photocurrent. The procedure of a null-currentmeasurement is illustrated by the schematic diagram in Fig. 59(A), and an actualexample is shown in Fig. 59(B).

Let us consider Model A in Fig. 58. For the sake of simplicity, let us assumethat Gp is much greater than Gm, so that Gm can be regarded as e�ectively zero,i.e., the parallel current path through Gm can virtually be ignored. We furtherassume that the conductance Gp has the same magnitude in the dark as duringillumination. These restrictions will be subsequently relaxed after an intuitivepicture is presented.

At the beginning of a null-current measurement, the clamping voltage is set to 0and the illuminating light source is also turned o� (current level 1). While the lightsource remains o�, the clamping voltage is then set to a pre-selected value Vc, andthe current changes by settling at a new value (level 2), after a brief capacitativetransient (not shown). While the clamping voltage is maintained at Vc, the

Table 6

E�ect of increasing Gm

Parameters Model A Model B Model C

Photovoltage Decrease No change No changea

Photocurrent No change Increase Increase

a If Gm is initially zero, only an AC signal is observable. The addition of an ionophore brings about

the DC signal.


Fig. 59. Null current method shown schematically (A) and with actual data from bR-containing BLM

(B). Aqueous solution contained 0.1 M NaCl and 0.5 mM LaCl3. Measurement was made at pH 6.9

and 27.58C, with instrumental time constant of 1 s. Conditions, which include clamping potential and

illumination, are indicated below record. First measurement was `light on' and `light o�' operation,

which allowed Ip to be measured at desired clamping potential, e.g., 0 mV. Transient spikes were

manifestations of AC photoelectric e�ect (di�erential responsivity; see Section 19.3). In second

measurement, clamping potential was adjusted to obtain null-current condition, which was reached at

ÿ19 mV. See text for further details. (Reproduced from Ref. [281])


illuminating light is then turned on. The current changes, again after a briefcapacitative transient (shown in Fig. 59(B) but not in Fig. 59(A)), by settling atyet another new value (level 3). The di�erence, level 3 minus level 2, gives the DCphotocurrent, Ip (corresponding to the clamping voltage Vc). While theillumination continues at a ®xed level, the clamping voltage is then adjusted to anew value V 0c, so that the measured current is tuned back to level 2, i.e., the endpoint of tuning is the new voltage V 0c that is required to cancel (nullify) the DCphotocurrent. In other words, by applying an o�set voltage, ÿE0 � �V 0c ÿ Vc�, itis su�cient to abolish the DC photocurrent and move the measured current fromlevel 3 back to level 2 (the pre-illumination level).

By invoking the principle of potentiometry, the o�set voltage (V 0c ÿ Vc) can betaken as equal to the photoemf (Ep) at the clamping voltage Vc, but with anopposite polarity, i.e.,

Ep � ÿÿV 0c ÿ Vc

�� E0: �12:1�

Subsequently, the clamping voltage is then brought back to Vc, so as to ascertainthat the measured current actually returns to level 3, which is the level attainedbefore applying the o�set voltage. When the light is ®nally turned o�, themeasured current settles back to level 2, again after a brief capacitative transient.Finally, with the light remaining o�, the clamping voltage is returned to zero, andthe measured current is brought back to level 1, again after a capacitativetransient. This completes the cycle of measurement in which two acts ofmeasurement have been performed: the measurement of the photocurrent Ip (level3 minus level 2), and the measurement of the photoemf E0. The DCphotoconductance, Gp, is then obtained by dividing the DC photocurrent with thephotoemf by virtue of Ohm's law.

Gp � Ip

E0: �12:2�

By varying the value Vc in a systematic way, both the DC photocurrent and theDC photoemf can be measured as a function of the transmembrane (clamping)voltage, Vc. The DC photoconductance Gp can be determined as a function of thetransmembrane voltage by repeatedly using Eq. (12.2).

Note that the background ionic di�usion conductance in the absence ofillumination, Gm, can also be obtained from the measured currents shown in Fig.59(A) by dividing the current (level 2 minus level 1) with the applied voltage Vc,again by virtue of Ohm's law.

A null-current measurement can be interpreted in an intuitive way as follows.When a net voltage of (V 0c ÿ Vc) is applied to the membrane during steadyillumination, the current responds by shifting from level 3 to level 2. Theconductance under this circumstance (the photoconductance Gp, or, morerigorously, the combined conductance (Gp � Gm), if Gm cannot be ignored) can beobtained in a way similar to the measurement of Gm above. Eq. (12.2) is thus re-derived without resorting to the concept of potentiometry, but simply by invoking


Ohm's law instead. Thus, the null current method is similar to the methoddescribed above for the measurement of Gm, except for the fact that it is beingperformed during illumination. In brief, Gm and Gp, as determined by the nullcurrent method, are the DC conductances measured in the dark and during steadyillumination, respectively.

We shall refer to the above determined photoemf and the photoconductance asthe apparent photoemf and the apparent photoconductance, since additionalcorrections of these directly measured values are required, when the restrictionsimposed earlier are relaxed. First, when Gm is comparable to Gp, the shuntinge�ect of Gm must be taken into account. Shunting will reduce the measured valueof the apparent photoemf by a factor of Gp=�Gp � Gm�, as is intuitively evidentfrom the consideration of the e�ect of a voltage divider in elementary electronics.Again by intuitive reasoning, the apparent photoconductance so measuredactually contains a contribution from Gm, i.e., the apparent photoconductancerepresents the combined value of (Gp � Gm). Rigorous proof for these conclusionscan be found in Appendix A.2.1.

Another correction is required, if Gp is zero in the dark, so that no current canbe driven through Gp by the applied potential Vc. As will be shown in Section12.4 for bR, Gp is zero in the dark and is activated by illumination to a ®xed non-zero value. We shall refer to this behavior as step-function photoswitching of theproton-translocating channel (photoconductive path). In this case, when Gp

suddenly turns non-zero upon illumination, both Vc and Ep can each drive acurrent through Gp. Both currents will be treated as photocurrents by thede®nition given above. This would not be the case, if Gp has the same valueduring illumination as in the dark, because the Vc-driven current has already beenincluded as part of the dark current (see explanation in Appendix A.2.2).

Thus, Eqs. (12.1) and (12.2) must be replaced by

Ep � E0 � Gp � Gm

Gp

ÿ Vc, �12:3�

and

Gp � Ip

E0ÿ Gm, �12:4�

respectively. In other words, the measured photoemf by means of the null currentmethod as described by Eq. (12.1) is the apparent photoemf, the e�ectiveness ofwhich is reduced by shunting whereas the measured conductance duringillumination actually contains a contribution from the dark ionic conductance.The photoconductance as determined by Eq. (12.2) is more appropriately referredto as the combined conductance during illumination (Gp � Gm), or simplyapparent photoconductance, for brevity. Since Gm can be independently measured,the true photoemf Ep and the true photoconductance Gp can be calculated byvirtue of Eqs. (12.3) and (12.4). The derivation of Eqs. (12.3) and (12.4) can befound in Appendix A.2.1.


Finally, a few words of caution are in order. In view of experimentalmeasurement errors, the parameters that are directly measured, such as (Vc ÿ V 0c)and Ip, are more accurate than the remaining parameters. The combinedconductance (Gp � Gm), being a ratio of two measured parameters, is thereforesubject to a greater error. By the same token, the propagation of errors makes thecalculated value of the true photoemf Ep quantitatively less reliable.

12.3. Null-current analysis of DC photoelectric data

For reconstitution of bR membranes, we use either the original method ofDancshaÂ zy and Karvaly [181] (Section 6.1) or its variant with a Collodion ®lmformed according to the recipe of Drachev et al. [189] (Section 6.3). The lightsource is a continuous argon-ion laser beam with the main output at 515 nm (UVoutputs ®ltered). In the case of a BLM, formed by the method of DancshaÂ zy andKarvaly, the laser beam is focused to illuminate only the thin bilayer region in thecenter rather than the thick Plateau±Gibbs border. In the case of Collodion ®lms,the entire membrane is illuminated. The background ionic conductance Gm is alsoroutinely measured. It is done before and after the fusion of purple membranes,but in the absence of illumination. Additional experimental details can be foundin Ref. [281].

A typical photocurrent response (under a short-circuit condition) exhibits atransient peak at the onset of step illumination with a square-wave pulse, followedby a sustained stationary (DC) current (Fig. 59(B)). Upon cessation ofillumination, a negative transient peak appears before the current level is restoredto the previous dark level. Qualitatively, the waveform is consistent with theprediction of the equivalent circuit shown in Fig. 23; the transient peaks aremanifestations of the AC photoelectric e�ect (Fig. 24). However, the two peaksexhibit an asymmetry; the positive peak is more prominent and is decaying fasterthan the negative peak. Interpretation of this asymmetry will be given in Section12.4. For the purpose of investigating the DC photoelectric e�ect, these transientpeaks can be temporarily ignored.

The DC photocurrent (Ip) as a function of the membrane voltage is shown inFig. 60(A). The sign convention of Ip is that the positive membrane current ¯owsfrom the compartment, where purple membrane fragments were added (cis side),to the compartment free of purple membrane fragments (trans side). The signconvention of the applied membrane voltage is such that a positive appliedvoltage will drive a positive current, i.e., the trans side is the zero voltagereference. The voltage dependence of the photocurrent is almost linear, butdeviation from linearity is sometimes observed. At about ÿ70 mV thephotocurrent becomes zero, and the polarity is reversed below ÿ70 mV.

The apparent photoemf, as determined directly by the null current method, isshown as a function of the membrane voltage in Fig. 60(B) (open invertedtriangles). The true photoemf, which was corrected for shunting by Gm and for theapplied potential according to Eq. (12.3), is also plotted (®lled inverted triangles).It is seen that the voltage dependence of the apparent photoemf is similar to that


Fig. 60. Steady-state photoelectric response of bR-containing BLM. Aqueous solution contained 0.1 M

NaCl and 0.5 mM CeCl3. Measurements were made at pH 6.9 and 248C. (A) Measured photocurrent

Ip is shown as function of membrane voltage. (B) Photoemf Ep, as determined by null current method,

is shown as function of membrane voltage. Apparent photoemf is shown as open inverted triangles,

whereas true photoemf, calculated by means of Eq. (12.3), is shown as ®lled inverted triangles. (C)

Apparent photoconductance (Gp � Gm) (open squares), which is equal Ip=E0, measured dark

conductance (Gm) (open triangles), and true photoconductance (Gp) (®lled circles), calculated by means

of Eq. (12.4), are shown. Each set of data was ®tted with straight line by least-square method.

Conductance data were also connected with line segments, for easy data reading. All data were taken

from same membrane. (Reproduced from Ref. [281])


of the photocurrent, but the true photoemf has virtually no voltage dependence.The sign convention for Ep is that a positive photoemf will drive a positivephotocurrent (from the cis side to the trans side).

As explained in Section 12.2, the apparent photoconductance, which iscalculated by means of Eq. (12.2), contains the contribution of the ionicconductance, and is therefore labeled as (Gp � Gm) (open squares in Fig. 60(C)).The ionic conductance (Gm) as a function of the membrane voltage is also plotted(open triangles). Subtraction of these two sets of data allows for the calculation ofthe pure photoconductance Gp, which is shown in Fig. 60(C) as ®lled circles. Allthese conductances are ohmic (no voltage dependence).

The absolute values of these conductance, as well as the photocurrent and thephotoemf, varied from membrane to membrane, and we were thus prevented frompooling the repeated measurements together to obtain statistics. The data shownin Fig. 60 are typical. The descriptions to be presented below will be based oncollective features from repeated experiments under the same or similarconditions.

For a given membrane, the combined conductance during illumination(Gp � Gm) is consistently found to be two to three fold higher than the darkconductance Gm. This means that Gp is either of about the same magnitude as Gm

or twice as large. For conditions used in Fig. 60, (Gp � Gm) is 50215 n0/cm2,whereas Gm is 1725 n0/cm2. Therefore, Gp is about 33215 n0/cm2 (Here, theunit n0/cm2 is identical to nS/cm2 or nmho/cm2 commonly used by physiologists).

The combined conductance (Gp � Gm) is greater than the dark conductance.The increase is not spectacular; the photoconductance Gp is only slightly greater(about two fold) than the ionic conductance Gm. Without illumination, theincorporation of the purple membrane into the BLM does not change thebackground conductance, i.e., Gp � 0 in the dark. Illumination turns on both thephotoemf and the photoconductance Gp.

Unlike the claim of Bamberg et al. [182], photosignals from our reconstitutedmembranes were usually su�ciently large in amplitude for accurate measurements,without the aid of proton ionophore-induced enhancement. However, wefrequently use multivalent cations to enhance the adsorption process.Occasionally, su�ciently large photosignals can be observed, without the aid ofmultivalent cations or ionophores. It has been reported that La3+ has an e�ect onthe AC photoelectric signal [189]. But we found that La3+ has no direct e�ect onthe DC photoelectric signal. The presence or absence of multivalent cations doesnot alter the conclusions drawn for the DC photoelectric e�ect.

In Fig. 61, the light dependence of the photocurrent, the true photoemf and thetrue photoconductance are shown. The data were obtained from a Collodionmembrane reconstituted according to the method of Drachev et al. [189] (seeSection 6.3). The photocurrent was shown to have a linear dependence at lowlight intensity, but eventually becomes saturated; any further increase of the lightintensity had no additional e�ect (Fig. 61(A)). A similar light dependence isexhibited by the true photoemf (Fig. 61(B)). The half-saturation level of thephotocurrent and the photoemf is about 0.059 W/cm2. The true photoconductance


Fig. 61. Light dependence of photocurrent (A), photoemf (B), and photoconductance (C). Both

photoemf and photoconductance have been corrected, by means of Eqs. (12.3) and (12.4). Data were

measured, at 228C, from Collodion membrane of 2 mm2. Ionic conductance Gm was 0.5 n0/cm2.

Aqueous solution contained 0.1 M KCl, bu�ered with 50 mM L-histidine at pH 7.0. Both photo-

current and photoemf were each ®tted with exponential curve, with half-saturation light intensity of

59 mW/cm2. Photoconductance was ®tted with straight line. (Reproduced from Ref. [281])


(Gp) is shown in Fig. 61(C). Gp is virtually independent of the laser light intensity(it varies25% in the range from 0.045 to 1.4 W/cm2).

12.4. Interpretation of DC photoelectric data

Our own data shown in Figs. 60 and 61 thus con®rmed a number ofobservations, previously reported in the literature. The photocurrent is voltage-dependent and it reverses its polarity at a certain potential, i.e., the I±V curve islinear and intercepts the voltage axis [151,185,254,267,269,274]. The photocurrentexhibits an initial linear dependence and reaches saturation as light intensityincreases [270]. Beyond that, there are important di�erences in our interpretation.The salient feature of the null-current analysis is summarized as follows.

12.4.1. Step-function photoswitching of proton-translocating channelIt is of interest to compare the present results of photoconductance

determination with what we observed previously in the Mg-porphyrin-containingBLM [280]. Super®cially, the magnitude of Gp shown in Fig. 60(C) seems to benot much di�erent from that of Gm. However, one must realize that Gp is zero inthe dark; illumination changes the overall conductance from its value in the dark(Gm) to a signi®cantly higher value (Gp � Gm). Therefore, the e�ect of illuminationis quite signi®cant and there is little doubt that illumination opens a speci®cphotoconductive path. In contrast, it is noted that Gp of the Mg-porphyrin-redoxBLM is non-zero in the dark and illumination does not increase Gp any further[163,280]. This is because the latter system transports electrons in the dark, butbR does not transport protons in the dark (Mg porphyrins undergo redoxreactions in the dark).

The null-current analysis attaches the light dependence to the photoemf ratherthan to the photoconductance without any prior assumptions. It is of interest toobserve that the magnitude of the photoconductance is independent of the lightintensity in the range used in this study. Of course, the photoconductance dependson light for its existence. However, once it is turned on by light, thephotoconductance quickly reaches its full (saturation) magnitude in the samerange of light intensity, where the photoemf is still linearly light-dependent. Werefer to this characteristic as the step-function photoswitching of the proton-translocating channel. This characteristic is important for the interpretation of thevoltage dependence of the photocurrent.

While we attribute the light dependence of the photocurrent to the samedependence of the photoemf, other investigators have assigned the dependence tothe photoconductance, instead. Hermann and Ray®eld [185] postulated a voltage-independent current generator shunted by a light-dependent conductance, in orderto interpret their data quantitatively. SzaboÂ and Bamberg [282] reported a light-dependent photoconductance, which saturates at 0.59 W/cm2. Here, we have madeno prior assumption about light dependence in our measurements and analysis,and have come up with an opposite result. The light-saturation level determinedby SzaboÂ and Bamberg is somewhat higher than ours. Our reported value was


probably underestimated. The light intensity (power) was read directly from alight meter attached to the argon-ion laser and the beam area was estimated fromburning of an exposed Polaroid ®lm by the laser beam. We therefore placedlimited con®dence on the absolute magnitudes of our light intensitymeasurements. However, the measurements of relative magnitudes of data shownin Fig. 61 are considered reliable.

12.4.2. Interpretation of voltage dependence of photocurrentBy means of the null current method, we found that the apparent photoemf is

linearly dependent on the applied potential, but the true photoemf and the truephotoconductance is not, i.e., Gp is ohmic. The voltage dependence of thephotocurrent can be simply interpreted as follows. As explained in Section 12.2and documented rigorously in Appendix A.2.1, the step-function photoswitchingof Gp allows for the both the (true) photoemf and the applied transmembranepotential (Vc) to drive proton currents through bR's proton-translocating channel.Therefore, the measured (apparent) photoemf also contains a contribution fromthe applied membrane potential. The photocurrent thus contains a constantfraction, which is driven by the true photoemf, and an additional fraction, whichis driven by the applied potential and is linearly proportional to the appliedpotential. Incidentally, this feature is not a consequence of the shunting e�ect. Ifthe voltage-driven fraction of the photocurrent is excluded, the remaining fractionbecomes independent of the applied potential and, therefore, the true photoemf isindependent of the applied potential. The polarity reversal of the photocurrentobserved at ÿ70 mV is caused by the increasing in¯uence of an opposing appliedpotential. Thus, the determination of the intercept of the voltage axis is analternative way to determine the photoemf (which is a common practice in I±Vanalysis). The value 70 mV compares favorably with the average values of thephotoemf as determined by the null current method, 77210 mV. Our model forthe DC photoelectric e�ect of bR thus appears parsimonious, and the DCphotoelectric data appears `transparent'. It is of interest to note that no suchmodi®cation is necessary for the above-described Mg-porphyrin-redox BLMsystem [163,280] (see Appendix A.2.2).

An alternative interpretation of the polarity reversal has been proposed byBamberg et al. [269]. These investigators suggested that the polarity reversal iscaused by the presence of two populations of purple membrane sheets in thesystem, with the majority of the purple membrane sheets being incorporated inone orientation, but a much smaller fraction being oriented in the reversedirection. Thus, when the photocurrent decreases as a negative voltage is applied,the increasing photosignal, attributed to the other minor fraction, might berevealed. However, this explanation is inconsistent with the observation of Gavachet al. [270], which was also con®rmed in our laboratory. Whereas the stationaryphotocurrent is reversed at a certain applied voltage, the transient positive peak isnot reversed. This transient peak re¯ects the AC photoelectric current and itspolarity can be regarded as an indication of the orientation of the majority of bRmolecules inside the model membrane. Gavach et al. interpreted the voltage


dependence as the e�ect of variation of the surface potential of the membrane,which in¯uences the degree of protonation of certain donor sites that areseparated from the site of the photoemf.

Nagel et. al. [275] succeeded in expressing bR in oocytes of Xenopus laevis andmeasured the DC photocurrent directly by means of the patch-clamping method.Again, they found nearly linear voltage dependence of the DC photocurrent.However, no polarity reversal was observed up to ÿ165 mV. They cited the lackof polarity reversal as a support for the interpretation of polarity reversal in termsof two populations of bR orientation, previously proposed by Bamberg et al.[269]. In their patch-clamp measurement, presumably there is only one orientationof bR in such a way that all bR molecules pump proton in the outward direction.Possible nonlinearity of the voltage dependence prevents extrapolation of thephotocurrent to estimate the voltage, where polarity reversal can be achieved. Thepresence or absence of polarity reversal can only regarded as unsettled for thedirect patch-clamp measurement. In a more recent report by Nagel et al. [276], thevoltage-clamp measurements show little evidence of nonlinearity in the range ofÿ160 to +60 mV.

Our interpretation of the voltage dependence in terms of the step-functionphotoswitching of the proton-translocating channel thus appears much simplerthan these alternative interpretations.

12.4.3. Interpretation of spike-like waveform of photocurrentThe step-function photoswitching of Gp also provides a simple explanation of

an anomalous waveform of the DC photocurrent upon stimulation by a longsquare-wave light pulse. Elementary analysis indicates that a linear RC high-pass®lter exhibits a waveform similar to what is evident in Fig. 59(B) and that thepositive spike and the negative spike should be symmetrical (see Eqs. (9.6), (9.7),(9.17), (9.18), (9.26) and (9.27), in Section 9). Analysis based on the ACphotoelectric e�ect explains the waveform characteristic of the high-pass ®lterresponse. But the latter does not explain the slight asymmetry shown in Fig. 59(B)(cf. Fig. 1 in Ref. [254]). The positive spike peaks more prominently and decaysconsiderably faster than the negative spike. This observation is consistent with thefact that Gp is zero in the dark. The hastened relaxation during illumination islikely caused by the sudden increase of Gp, which is equivalent to a light-induceddecrease of the resistance that was previously designated as Rs in Fig. 23 (Rs � 1in the dark, but Rs � 1=Gp in the light).

The asymmetry of the two spikes shown in Fig. 59(B) is not unique to the bRsystem. Fig. 62(A) shows an open-circuit voltage recorded intracellularly from anintact giant chloroplast of Peperomia metallica [283]. The waveform of thephotoresponse to a long square-wave light pulse looks similar to what we reportedin Fig. 59(B). Upon the addition of valinomycin (a K+ ionophore), in thepresence of 30 mM K+, the decay of both spikes became faster than the control,but retained the asymmetry of their amplitudes, whereas the DC photovoltagelevel became diminished. A similar waveform also appears in a BLM reconstitutedfrom the puri®ed reaction center of Rhodobacter sphaeroides [284] (Fig. 62(B)),


and from the subchromatophore pigment-protein complex of Rhodospirillumrubrum [184,285]. These observations are consistent with the concept of chemicalcapacitance and the step-function photoswitching, taken together (cf. Section 9.3).

In the above discussion, we have invoked our own interpretation of thetransient peaks as the manifestation of the AC photoelectric e�ect [30]. However,several versions of alternative interpretation of the transient spike waveform areavailable. A widely accepted interpretation, based on incomplete fusion of bR-vesicles to a planar membrane, was proposed by Drachev et al. [254]. We haverefuted that interpretation in Section 11.1. Another interpretation, proposed byBamberg et al. [182], was based on the e�ect of an unstirred layer on the creationof a transient di�usion potential in the presence of a proton ionophore. Theproton uptake from the cytoplasm and its release from the extracellular surfaceare faster than the di�usion of protons in water; a transient transmembraneproton gradient, which is greater than its steady-state value, could, in principle,appear upon step illumination. However, the polarity of the di�usion potentialwill be opposite to that of the stationary photocurrent, and, therefore, cannotpossibly generate the spike waveform upon illumination. A similar argumentapplies to the spike signal upon cessation of illumination.

12.5. I±V analysis

In classical electrophysiology, equivalent circuit analysis is usually carried out interms of an I±V (current±voltage) curve. It is therefore instructive to compare it

Fig. 62. Photoelectric signals from photosynthetic membranes in response to long square-wave light

pulse. (A) Open-circuit photovoltage was recorded intracellularly from intact chloroplast of Peperomia

metallica. Control signal, taken before addition of valinomycin, is shown at left, and e�ect of adding 1

mM valinomycin and 30 mM potassium ions in external medium is shown at right. (B) Sample of

photosynthetic reaction center of Rhodobacter sphaeroides (8 mM), supplemented with 100 mM of

ubiquinone-10, were reconstituted into BLM. One of two aqueous phases contained 25 mM reduced

cytochrome c, and other contained 1 mM ferricyanide. See text for discussion. (Reproduced and

modi®ed from Refs. [283] (A) and [284] (B))


with the null current method. The I±V analysis is straightforward if the I±Vcurves are linear. The current±voltage relationship can be described by

I � G�Vÿ E�, �12:5�

where E is the emf and G is the conductance. Thus, an I±V curve going throughthe origin is an indication of the absence of an emf source. Conversely, a non-zerointercept of the I±V curve on the voltage axis is evidence for the existence of anemf source. The conductance G is simply the slope of the I±V curve, or simply theratio of the short-circuit current (i.e., the I intercept) and the open-circuit voltage(i.e., the V intercept). Implicit in this description is that both the emf and theconductance are constant and not dependent on the membrane voltage. Theapplication of the null current method in this case is a trivial exercise; themagnitude of the emf E can be read directly from the V intercept because E � Vwhen I � 0.

In the case of nerve excitability, the I±V curve is non-linear. However, it can beshown that the emf (di�usion potential) is still constant. Therefore, the non-linearity is entirely attributable to the membrane conductance, which is voltage-dependent. It is necessary to invoke the concept of slope conductance (the ®rstderivative of the I±V curve), which is usually di�erent from the cord conductance(the conductance as de®ned by Eq. (12.3)). The slope conductance and the cordconductance becomes identical, if and only if, the I±V curve is linear. How theproblem was solved was described by the classical work of Hodgkin and Huxley[207].

Among a number of I±V analyses performed on bR membranes, the report ofCaplan and Fischer [273] is the most rigorous and is, therefore, of great interest tous. These authors determined the I±V curve in the dark as well as duringillumination. They found that both I±V curves are linear, but their slopes di�ersigni®cantly (Fig. 63). Based on the intuitive picture above, these I±V curvesindicate that there is a signi®cant di�erence of conductance measured in the darkand during illumination. Both curves have a non-zero V intercept. Thisobservation indicates the existence of both a dark emf (electromotive force notinduced by light) and a photoemf. These authors thus assumed the separation of adark-conductance channel and a light-conductance channel; the light-conductancechannel is closed in the dark (equivalently, we combine the two channels, butallow the conductance to be switched by light). They used an equivalent circuitshown in Fig. 64. By solving simultaneous equations involving three RC circuits,they were able to determine all the parameters.

Caplan and Fischer explicitly considered the `dark' conductive path to bedistinct from, and in parallel with, the photoconductive path. In our system, the`dark' conductive path does not exist, because there was no dark voltage detectedand because the incorporation of bR did not raise the conductance above thebackground ionic conductance. This is tantamount to setting E d

m to zero and Rdm

to in®nity in Fig. 64. With the exception of this di�erence, their equivalent circuitis identical to ours. It is of interest to note that both the I±V analysis and the


Fig. 63. I±V curve analysis of DC photoelectric signals from reconstituted bR membranes. (A) Data

from membrane, prepared by means of ®eld-orientation method, are shown. (B) Data from membrane,

prepared by means of surface-orientation method, are also shown. See Fig. 64 for meaning of symbols.



null-current analysis make the assumption that an externally applied potential cano�set the photoemf (see Eq. (12.5)). In other words, an applied potential can drivea current through the photoconductive path (proton-translocating channel) ineither direction. However, the I±V analysis makes an additional assumption thatthe photoemf is voltage-independent, whereas the voltage independence of thephotoemf is an experimental result in our approach; the null-current analysismakes no such a prior assumption.

In the study of Caplan and Fischer, the magnitude of the combinedconductance is about 1.3 to 1.9 times that of the dark conductance, whereas ourreported value of the measured conductance during illumination is two to threetimes that of the dark (ionic) conductance. A dark emf was also observed byHiggins et al. [266], but not by Drachev et al. [254]. In the absence of additionalinformation, we tentatively attribute the di�erence to the use of di�erentreconstitution methods.

By substraction of data represented by the two I±V curves shown in Fig. 63, acurve showing the voltage dependence of the photocurrent, similar to what wepresent in Fig. 60, can be constructed Ð the resulting photocurrent exhibits apolarity reversal.

Fig. 64. Equivalent circuit proposed by Fischer and Caplan in their I±V analysis. Subscripts or

superscripts s, m, d, and l designate salt, membrane, dark and light, respectively. E0 is voltage

measuring device, I is current measuring device, and E is external voltage source. R1 and R2 are

resistances of two electrodes, and Ee is electrode o�set emf. Experiment was performed ®rst with salt

solution only (Rs), then with plain membrane in place (Rm and Em), and ®nally with reconstituted bR

membrane (Rdm and E d

m for dark channel, and Rlm and E l

m for light channel). Im, I dm and I l

m are

currents through three above circuits. See text for further explanation. (Reproduced from Ref. [273])


12.6. E�ect of ionophores

The e�ects of FCCP, CCCP and nystatin were studied using the null currentmethod. We have con®rmed the widely reported observation that FCCP or CCCPenhances the photocurrent from a reconstituted bR membrane. A typicalphotocurrent response in the presence and in the absence of FCCP is shown inFig. 65(A). The presence of 0.01 mM FCCP causes the photocurrent to increase bya factor of 2 or more, especially when a positive potential is applied. The voltagedependence is enhanced by FCCP and the I±V curve deviates signi®cantly fromlinearity with its concave side pointing upward.

In response to the addition of FCCP, the apparent photoemf is signi®cantlyreduced and the voltage dependence becomes insigni®cant (Fig. 65(B)). The truephotoemf obtained after corrections using Eq. (12.3) is also shown (Fig. 65(C)).The errors become so large that the voltage dependence appeared erratic frommembrane to membrane. Therefore, it is di�cult to draw any reliable conclusionfor the voltage dependence.

In contrast, the e�ect of FCCP on Gm and Gp are fairly consistent frommembrane to membrane. The presence of 0.01 mM FCCP also increases the truephotoconductance Gp as well as the ionic conductance Gm more than 10 fold (Fig.65(D)). In addition, both Gp and Gm become signi®cantly voltage-dependent.These voltage-dependent changes are symmetrical with regard to the polarity ofthe membrane potential; the application of a positive potential has the same e�ectas that of a negative potential of the same magnitude. Although Gp is greater thanGm before FCCP is added, Gp and Gm become about equal afterwards.

The e�ect of CCCP is shown in Fig. 66. CCCP causes a similar e�ect as FCCPdoes on bR membranes: the photocurrent is enhanced and both Gm and Gp areincreased. However, CCCP is less potent and 0.1 mM CCCP is required to achievecomparable e�ects. Again, the e�ect on the photoemf is erratic. It is not certainwhether CCCP decreases the true photoemf. The voltage dependence of Gm andGp is not conspicuous.

Experiments have also been carried out with nystatin, a known ionophore forchloride ions (Fig. 67). Its e�ect on bR membranes is in sharp contrast to those ofCCCP and FCCP. Nystatin inhibits the photocurrent (Fig. 67(A)) and increasesthe ionic conductance Gm, but has no e�ect on the photoconductance (Fig.67(D)). The decrease of the true photoemf by the addition of nystatin is probablyreal (see Section 12.8), but the voltage dependence is not certain (Fig. 67(C)).

12.7. Evaluation of membrane reconstitution methods

Several important questions have been raised about the nature of bRmembranes reconstituted by means of the DancshaÂ zy±Karvaly method. Are bRmolecules perfectly oriented in the reconstituted membrane? Which direction dothey orient? Are these molecules completely incorporated in the bilayer? Our studyof the DC photoelectric e�ect of bR o�ers new criteria and experimental evidencefor examining or answering these questions.


Fig.65.E�ectofFCCP.Aqueoussolutioncontained

0.1

MNaCland0.5

mM

LaCl 3.Controldata

points,taken

before

additionofFCCP,are

shownas

open

symbols,whereasdata

taken

after

additionofFCCP(®nalconcentration0.01mM

)are

shownas®lled

symbols.Photocurrent(A

;diamond),apparent

photoem

f(B;hexagon),truephotoem

f(C

;invertedtriangle),andtruephotoconductance

Gp(D

;circles)

aswellasionic

conductance

Gm(D

;triangles)

are

shown.Foreasy

data

reading,data

points

oftruephotoem

fare

connectedwithlinesegments.Truephotoem

fcurves

are

also®tted

withstraightlines

by

least-square

method.Measurements

weremadeatpH

6.9

and248C

.(R

eproducedfrom

Ref.[281])


Fig.66.E�ectofCCCP.Aqueoussolutioncontained

0.1

MNaCland0.5

mM

LaCl 3.Symbols

usedin

graphshavesamemeaningasin

Fig.65.Final

concentrationofadded

CCCPwas0.1

mM.Measurements

weremadeatpH

6.9

and258C

.(R

eproducedfrom

Ref.[281])


Fig.67.E�ectofnystatin.Aqueoussolutioncontained

0.1

MNaCland0.5

mM

LaCl 3.Symbols

usedin

graphshavesamemeaningasin

Fig.65.Final

concentrationofadded

nystatinwas4mg

/ml.Measurements

weremadeatpH

6.9

and238C

.(R

eproducedfrom

Ref.[281])


Similar questions can also be raised with regard to other membranereconstitution methods. Is a Collodion membrane really a thick ®lm rather than inbilayer con®guration, as its inventors have maintained? Is fusion of bR-vesicleswith a planar BLM really incomplete? Our study of both the AC and the DCphotoelectric e�ect of bR o�ers some insight.

12.7.1. Orientation of bR moleculesAccording to the literature, membranes reconstituted by means of the

DancshaÂ zy±Karvaly method, or the vesicle fusion method, or the method ofCollodion ®lm exhibit a preferential orientation, in such a way that the proton ispumped from the cis side (the side where purple membrane fragments or vesiclesare added) towards the trans side. By comparing the AC and the DC photoelectricsignals, we deduced that the B1 component of the AC photoelectric signal has apolarity opposite to that of the DC photoelectric component, whereas the B2component has the same polarity as the DC photoelectric signal. Thus, the cis sidecorresponds to the cytoplasmic side of the purple membrane. This assignment isconsistent with the assignments reported by DancshaÂ zy and Karvaly [181] andBamberg et al. [182]. The same assignment was made with regard to bRmembranes reconstituted in the Collodion membrane. Collodion membranespossess su�cient mechanical stability to allow for both the DC and the ACphotoelectric measurements to be performed on the same membrane so that thepolarity assignment is unequivocal.

The consistent observation of a photovoltaic e�ect in bR membranesreconstituted by means of these methods is a testimony that there is a certaindegree of preferential orientation among the incorporated bR molecules, but thereexists no unambiguous experimental evidence indicating a perfect orientation.Bamberg et al. have suggested an imperfect orientation of bR molecules, whichare comprised of two populations with opposite orientations. They thus explainedthe linear voltage dependence and the polarity reversal of the DC photocurrent.However, we have provided an alternative interpretation. As a consequence, itremains inconclusive as to whether there are two populations of orientation.

12.7.2. Is bR completely incorporated in a reconstituted membrane?According to conventional wisdom, the DancshaÂ zy±Karvaly method is

perceived as a method that does not fully incorporate bR into a genuine bilayermembrane. The method depends on the adsorption of purple membrane sheets tothe bilayer structure of a pre-existing planar BLM. Bamberg et al. [182] suggestedthat the purple membrane sheets were not incorporated into the bilayer structure,but were instead bound to the surface of the bilayer, forming a sandwich-likestructure (Fig. 68), referred to herein as the sandwich model. Their conclusion wasbased on the following observation. The stationary (DC) photocurrent wasextremely low in their system unless gramicidin A or some other ionophore thatforms proton-di�usion channels (not to be confused with the proton-translocatingchannel of bR) was also added. Thus, a proton which was pumped across themembrane system would encounter a resistance both in passing through the


purple membrane sheet (Rp) and in passing through the lipid bilayer (Rm). Theyproposed that the ionic di�usion channel formed by gramicidin A would facilitatethe passage of protons through the lipid bilayer proper and thus lower Rm.

The sandwich model is represented by Model C in Fig. 58. Our observation thatthe conductance during illumination (Gp � Gm) is consistently greater than thedark conductance, and adsorption of the purple membranes has no detectablee�ect on the dark conductance appears to contradict this model. Here, we shalltentatively ignore the conclusion reached by the null-current analysis. We simplyfocus our attention of the determination of conductance by applying atransmembrane potential in the dark and during illumination.

Referring to Fig. 68, and assuming that the BLM is uniformly covered by thepurple membrane sheets without any bare spots, the total resistance (Rt)encountered by the proton current traversing the sandwich-like assembly shouldbe equal to the (series, not parallel) sum of the resistance of the BLM alone (Rm),and the resistance of the purple membrane (Rp). Here, the parameter Rm is theinverse of the membrane ionic conductance Gm, mentioned earlier (Rm � 1=Gm inModel C). The parameter Rp is the inverse of the photoconductance Gp

(Rp � 1=Gp in Model C). The sandwich model (Model C) predicts that Rt > Rm,because Rm and Rp are connected in series (Rt � Rm � Rp). However, our

Fig. 68. `Sandwich' model. Purple membrane is adsorbed onto surface of BLM, but is not completely

incorporated (fused) into it. Rm is resistance through plain BLM, and Rp is resistance through purple

membrane patches, i.e., Rm � 1=Gm and Rp � 1=Gp. Rt is resistance encountered by protons in crossing

both BLM proper and attached purple membrane patches, i.e., Rt � Rm � Rp. While relationship

Rt > Rm, predicted by this model, clearly holds if purple membrane forms continuous layer on BLM

surface, it also holds if purple membrane patches are discontinuous and coverage is incomplete.



experimental measurements repeatedly point to the contrary. Adsorption of purplemembranes does not change the conductance in the dark. Illumination causes theconductance to rise signi®cantly above the background level. Our experimentalobservations thus contradict the sandwich model. Admittedly, the uniformcoverage assumption mentioned above may be unrealistic. But the adjustment forthe incomplete coverage does not invalidate the prediction that Rt > Rm.Incidentally, the e�ect of shunting (within the purple membrane sheets) on themeasurement of Gp does not a�ect the validity of the above argument.

Our experiments using the proton ionophore FCCP and CCCP further castdoubts upon the sandwich model. According to the sandwich model, FCCP orCCCP should decrease the ionic resistance Rm, and should thus decrease thephotoresistance Rt as a whole. It is possible that Rp may be so small that Rt isapproximately equal to Rm, but Rt should never become smaller than Rm. In ourexperiment, addition of FCCP or CCCP to the aqueous phases decreases Rm.However, the relationship Rt<Rm remains valid. This result again contradicts thesandwich model.

One possible explanation for our data is that the DancshaÂ zy±Karvaly methoddoes completely incorporate bR into the BLM, instead of just being attached tothe external surface. Additional evidence comes from our previous study of Mg-porphyrin-containing BLM. In our investigations, Mg porphyrins were routinelydissolved ®rst in the membrane-forming solution. A BLM was then formed fromsuch a preparation. The thinning process was visually monitored for the telltaleappearance and coalescence of `black holes' (Section 6.1). It is extremely unlikelythat our Mg-porphyrin data were obtained from a thick membrane. Two Mg-porphyrin experiments will be described to further substantiate this point: oneaddressing the problem of a thick membrane [163] and the other the problem ofincomplete vesicle fusion [183].

In Fig. 69, the illuminating light beam was focused to a fraction of the thinBLM and was scanned slowly across the diameter of a BLM (diagram d ). Boththe peak AC photocurrent and the DC photocurrent were monitored. It is evidentthat the AC photocurrent appears only in the thin bilayer region (trace a ),whereas the DC photocurrent appears in both the thin bilayer region and in thethick Plateau±Gibbs border, which anchors the BLM to a supporting Te¯onpartition (trace b ). Furthermore, the DC photocurrent is more prominent in thePlateau±Gibbs border than in the thin bilayer region. There is an asymmetry ofthe Plateau±Gibbs border Ð the thick border at the top of the bilayer is biggerthan that at the bottom of the BLM (because excess decane solution ¯oats to thetop due to gravity). The DC signal is more prominent at the top Plateau±Gibbsborder than at the bottom one, and the transition zone on the scanned trace a(which shows partial overlap of the light beam and the thick region) is larger on atop than at the bottom. Since the AC signal is capacitative in nature, thicknesshas a profound e�ect on both Cm and Cp. It is understandable why the AC signalis more prominent at the thin region but undetectable at the thick Plateau±Gibbsborder. On the other hand, the DC signal is less sensitive to the variation ofcapacitances as a result of variation of the thickness. However, the thick Plateau±


Gibbs border absorbs at least 104 time more photons than the bilayer region, and,therefore, the DC signal is more prominent at the thick region. In the aboveexperiment, the light source of the AC signal is a pulsed argon-ion laser with apulse duration of about 50 ms. It elicits both DC and AC photocurrents. But theDC component is overshadowed by the AC component and is not evident in tracea (see Section 9.1 for explanation based on source impedance).

The DC component can be rendered observable, however. When the pulsed-laser-elicited photosignal was subjected to an e�ect that is tantamount to low-pass®ltering, the remaining (DC) signal was found to be more prominent at thePlateau±Gibbs border than at the thin region, again showing the asymmetry(signal c ). In view of the result of the `scanning' experiment, it is unlikely that onecan elicit an AC signal from a thick membrane. We thus infer indirectly that themembrane, formed by means of the DancshaÂ zy±Karvaly method, is actuallybilayer thin, and the incorporation of bR is complete.

Fig. 70 shows AC photosignal from a plain (non-pigmented) planar BLM, towhich Mg-octoethylporphyrin-containing phospholipid vesicles were added to the

Fig. 69. `Scanning' experiment. Photocurrent response to focused light beam is shown as function of

distance across BLM. BLM contained amyl ester of Mg mesoporphyrin IX. Light source was argon-ion

laser (50 ms duration) for traces a and c, and Xe arc lamp (continuous light) for trace b. Peak AC

photocurrent response to argon-ion laser pulse (trace a) was obtained by means of boxcar integrator,

with aperture time of 25 ms. DC photocurrent response to Xe arc light (trace b) was obtained by

voltage-clamping at 0 mV, with instrumental time constant of 1 s. Heavily ®ltered response (low-pass

®lter time constant 1 s) to laser pulse is also shown (trace c). Light beam was focused to about one-

sixth of diameter of BLM (thin region: 1.96 mm), and was scanned vertically across diameter of BLM,

at constant speed, over time interval of about 5 min. Arrows indicate points, where light beam reached

aperture or departed completely from it. Te¯on partition, together with BLM, is shown schematically

(diagram d). Aperture, where BLM and thick Plateau-Gibbs border reside, had area of 3 mm2.



cis (right) side, whereas an electron acceptor potassium ferricyanide is added tothe trans (left) side. The hydrophilic ferricyanide ion penetrates a BLM with greatdi�culty, and neither electron acceptor nor electron donor was added to the cisside. Electron transfer between Mg porphyrin and ferricyanide cannot occur at adistance as large the membrane thickness. We have previously demonstrated thatan AC photosignal generated by interfacial electron transfer between membrane-bound Mg porphyrin and aqueous-solution-bound ferricyanide takes place at asingle membrane±water interface: the interface where both Mg porphyrin andferricyanide are within reach of each other [286]. Therefore, an AC photosignalcan be observed only if Mg porphyrin molecules are actually present near themembrane surface of the trans side.

As Fig. 70 shows, an AC photosignal appeared in a matter of minutes andcontinued to grow in amplitude as time passed. This experiment suggests that Mgoctaethylporphyrin reached the trans side either by di�usion or by virtue of acomplete fusion of the vesicles. Thus, in spite of its almost universal acceptance byinvestigators, there is no compelling evidence in support of the button model.

The same argument can be raised against the conventional interpretation ofexperiments conducted in Collodion ®lms. As commonly held by mostinvestigators, including Drachev himself, the lipid ®lm supported by the Collodionmembrane is not bilayer thin and, therefore, it is unlikely that bR spans the entirethickness of the lipid membrane supported by the Collodion ®lm. However, the

Fig. 70. `Fusion' experiment. Lipid-soluble pigment Mg octaethylporphyrin was ®rst incorporated into

phospholipid vesicles. Aqueous suspension of these vesicles was then added to aqueous phase of cis side

(see inset). Potassium ferricyanide (10 mM) was then added to trans side. BLM contained no pigment

initially. Photoresponses were recorded immediately after addition of vesicles and potassium

ferricyanide (0 min), and then 4 and 7 min after addition. Light source was dye-laser pulse (1 ms at 590nm). (Unpublished data of F.T. Hong, E. Heyer, A. Finkelstein and D. Mauzerall) (Reproduced from

Ref. [183])


fact that bR responds to the pH change at the extracellular side in the`di�erential' experiment (the side opposite to where the purple membranefragments were incorporated, see Fig. 51) indicates that the lipid ®lm on theCollodion membrane was actually bilayer thin.

The prime evidence which was used to judge the thickness of membranesreconstituted with various methods and to support the sandwich model and thebutton model is the marked enhancement of stationary DC photocurrent byproton ionophores. The enhancement e�ect has been replicated in a number oflaboratories including ours [185,272,274]. However, it turned out that there is acompletely di�erent explanation of proton ionophore action: a direct action onthe pigment itself in addition to the e�ect on passive proton conductance (see nextsection). Since an alternative interpretation can be found for the ionophore action,it loses its compelling nature in support of the conventional view.

12.8. Mechanism of ionophore action

Our null-current analysis indicates that the enhancement e�ect of protonionophores cannot be explained by shunting of Gm alone; there is possible directaction on bR itself. Referring to Fig. 58 and Table 6 (Section 12.1), the equivalentcircuit of Model A predicts that the short-circuit photocurrent is independent ofshunting, but Models B and C predict an increase of the photocurrent, when Gm

increases. On the other hand, Model A predicts that the photovoltage will bedecreased by shunting, whereas Models B and C predict no changes in themeasured photovoltage. It is well known that FCCP or CCCP decreases the open-circuit photovoltage. This latter experimental fact contradicts Models B and C,but the enhancement of the photocurrent is consistent with Models B and C, butnot with Model A. Thus, it is di�cult to come up with a consistent interpretationby assuming that the only e�ect of FCCP and CCCP is to create an ionicdi�usion path for proton. Perhaps, FCCP and CCCP exert a direct action on bRin addition.

Our null-current analysis shows that FCCP and CCCP increase both Gp andGm, but nystatin increases Gm without a�ecting Gp. On the other hand, nystatininhibits the photocurrent rather than enhances it. In reference to Model A, thise�ect can be caused by a genuine decrease of the true photoemf (see Fig. 67(C)).FCCP and CCCP enhances the voltage dependence of both Gp and Gm, but thevoltage dependence then becomes symmetrical; reversing the applied membranepotential has no apparent e�ect on the voltage dependence of Gp and Gm.However, the enhanced voltage dependence of Gp is unlikely to be directlycoupled to the e�ect on Gm. The increase of Gp is sometimes more dramatic thanthe increase of Gm but sometimes less dramatic. The cause of this variability is notpresently clear. It is suggested that the ionophoric action on Gp may not be tightlycoupled to the action on Gm, although the mechanisms may be similar or evenrelated. The cause for the symmetric voltage dependence of Gp and Gm isunknown. It may be caused by a voltage-dependent partition coe�cient of theionophores, commonly observed in BLM studies. The action of nystatin reinforces


our suspicion that FCCP and CCCP may have direct action on bR. However, wehave no clues about its molecular mechanism. On the other hand, the lack ofnystatin action is expected by the sandwich model, because nystatin is not aproton ionophore. Conversely, no direct action of nystatin on bR is expected.

At this point, the presence of similar action of proton ionophores on Gp and Gm

and the lack of action of nystatin on Gp seem to support the sandwich model.But, from the analysis presented above, the experimental evidence based onmeasured conductance in the dark and during illumination seems so direct that weare almost certain that the sandwich model in its present form does not apply toour reconstitution membrane system. A BLM reconstituted by means of theTakagi±Montal method [202,203], which o�ers the possibility of an unambiguousincorporation of bR, may resolve the problem in the future.

More recently, Li et al. [287] studied the square-pulsed-light-inducedphotoelectric signals from a LB ®lm that contained bR on an indium tin-oxide(ITO) electrode (Fig. 71). They found a signi®cant increase of the transientphotocurrent amplitude with the addition of FCCP. Since no DC photocurrentcan possibly be detected with such an arrangement (see Section 19.3 for theinterpretation of the transient photosignal), the enhancement must be due to thee�ect of FCCP on the AC photoemf rather than due to its e�ect on the protonconductance. It is most likely due to the direct FCCP action on bR, which wespeculated above.

Possible direct action of CCCP on bR is also relevant to the discussion on thevalidity of the button model. Let us refer to Fig. 52. Drachev et al. [254] studiedthe e�ect of CCCP, gramicidin A and external shunting on the induction ofdi�erential responsivity and found detailed subtle di�erences.

They found that addition of gramicidin A, which forms K+, Na+, and H+

channels through the thin (bilayer) membranes, but not thick ones, decrease thephotoresponse without lowering of the resistance of the planar membrane in thelight. The observation was consistent with the button model, since the planarmembrane was thick (no e�ect on R1 and R2) and the attached vesicle was thin(causing R3 to decrease). On the other hand, CCCP, which is a mobile H+-carrierthat a�ects both thin and thick membranes, should decrease both R1 and R3.They found that the lowering of the photoresponse by CCCP parallels that of theplanar membrane resistance, measured both in darkness and light. They alsofound that a decrease in external resistance R4 not only lowers the amplitude ofthe photoresponse, but also induces di�erential responsivity; again the proposedexplanation was consistent with the button model.

However, the subtle di�erence of gramicidin A and CCCP e�ects can also beinterpreted in the framework of chemical capacitance, by taking into account thepresent analysis of the DC photoelectric e�ect of bR. CCCP, which increases bothGp and Gm, is expected to decrease the light resistance and reduce the amplitudeof the photovoltage. On the other hand, gramicidin A, being a channel-formingantibiotic, may be similar to nystatin and have a lack of direct action on bR: itincreases Gm, but has no e�ect on Gp. We have no photoelectric data ofgramicidin A-treated bR membranes to verify this hypothesis. Additional


assumptions, needed for our alternate interpretation, are that the vesicles actuallyfused and that islands of thin bilayer appear among the thick region of the planarmembrane. Note that there is a subtle di�erence in our interpretation ofphotoconductance (reciprocal of light resistance) as Gp, as compared to that ofDrachev et al., who made no distinction between Gp and Gm.

13. AC photoelectric signal from other pigments

The OD and the IPT models and the equivalent circuit analysis presented inSection 10 for bR can be generalized to describe the AC photoelectric e�ect inmembranes that contain other pigments. Light elicits vectorial charge separationand recombination in these membranes. The moving parts in the photoelectricevent need not be protons; they can be electrons or other small charged particles,such as inorganic ions. Thus, the interfacial proton transfer model can begeneralized to the interfacial charge transfer (ICT) model. We have previouslydemonstrated that the oriented dipole and the interfacial charge transfer modelscan account for phenomenologically di�erent observations in arti®cial BLMreconstituted from various organic dyes or pigments [30]. It is not necessary toconstruct di�erent models in order to account for the di�erences in thecharacteristics of these photosignals. In this section, we shall examine the ACphotoelectric signals originating from other retinal proteins and photosyntheticreaction centers.

Fig. 71. E�ect of FCCP on transient photocurrent of bR. Photocurrent response was measured from

six-layer LB ®lm of bR, deposited on indium tin-oxide (ITO) electrode, under illumination with long

square-wave pulse of green light (560 nm). Signals were taken before and after FCCP addition.

Transient spikes are manifestation of AC photoelectric e�ect (see Fig. 24 and Section 19.3 for further

explanation). (Reproduced from Ref. [287])


13.1. Early receptor potential

Earlier experimental data about the early receptor potential (ERP) wererecorded from genuine photoreceptor membranes. Recent data using reconstitutedmembranes are available but scanty. We shall interpret the ERP data in terms ofthe concept of chemical capacitance.

13.1.1. Direct measurement of ERP in reconstituted membranesTakagi and coworkers were the ®rst to reconstitute rhodopsin into a BLM, by

means of the Takagi±Montal method [202]. Subsequently, Darszon et al. [155]used the method to identify a transient photoelectric signal in the reconstitutedrhodopsin membrane as the ERP that was originally discovered by Brown andMurakami (Section 5.1). Bauer et al. [288] attached bovine rod disc outer segmentmembranes to a lecithin BLM and studied pulsed-light-induced ERP-like signal.Drachev et al. [257] reconstituted rhodopsin into a Collodion membrane andanalyzed the measured AC photoelectric signal. Shown in Figs. 72(A) and (B) isthe open-circuit photovoltage from such a membrane in response to a 530 nmlaser ¯ash plotted at three di�erent time scales. Phase I shown in Fig. 72(A)corresponds to Component I of bR as reported by Drachev et al. [168] (Fig.12(B)). In other words, phase I corresponds to the R1 component. Likewise,Phases II and III are similar to Components II and III in Fig. 12(B), and are,therefore, equivalent to the R2 component. The magnitude of Phase I isapproximately 100 times smaller than that of the positive phase (phases II andIII). The positive phase is correlated with the formation of metarhodopsin II,measured as an increase in the 390 nm absorbance (cf. Fig. 11). This correlationestablished the identity of Phase II as being primarily the R2 component.

The di�erence in the amplitudes of the two components was found to decreasewhen the membrane was shunted with an external resistance (Fig. 72(C)). As themembrane resistance was reduced from 50 MO cm2 to a level (2 kO cm2) that iscomparable to that of the outer segment membrane, the negative-to-positive phaseratio changed from 0.014 to 0.16. The time course of the shunted photosignalappeared to be similar to that of the ERP measured in vivo. The formalidenti®cation of the negative phase with R1 and the positive phase with R2 isjusti®ed.

The e�ect of shunting on the negative-to-positive phase ratio can readily beunderstood if we assume that the electrogenesis process in rhodopsin is similar tothat in bR. The change of ratio from 0.014 to 0.16 is expected from the e�ect ofthe reduction of tm as stipulated in Fig. 24. In fact, Hong and Montal [156] haveshown that, in bR, the B1/B2 ratio of the two peaks increases dramatically inswitching from an open-circuit condition to a near-short-circuit condition (Fig. 9)(see Section 11.1).

Also of interest is the observation of the reversal of polarity of the ERP signal,if a 347 nm laser pulse is delivered after a 530 nm ¯ash (Fig. 73). Such a signal issimilar to the photoreversal potential discovered by Cone [159] (Fig. 10). Thereversal potential was shown to originate from metarhodopsin II, and can be


eliminated by hydroxylamine treatment, which prevents accumulation ofmetarhodopsin III, whereas the normal ERP was una�ected by such a treatment.

In a previous analysis of ERP, we suggested that the R2 component may begenerated by interfacial proton transfer [209]. This suspicion is reinforced byseveral experimental observations. The e�ect of alkalinization of the incubationmedium, during the bleaching of digitonin extracts of rhodopsin, or a suspensionof rod outer segment fragments has been interpreted as the protonation ofrhodopsin at the stage of metarhodopsin II. As shown in Fig. 11, the appearanceof R2 coincides with the formation of metarhodopsin II. Furthermore, by using apenetrating synthetic anion as a probe, Bolshakov et al. [289] have shown that the

Fig. 72. E�ect of shunting on ERP. Rhodopsin was reconstituted into Collodion membrane.

Photosignals were elicited with 15 ns-laser pulse at 530 nm (A and B), or at 500 nm (C). Records A

and B show ERP at three di�erent time scales. Fast negative Phase I (seen in A) corresponds to R1.

Slow positive Phases II and III (seen in B) correspond to R2. Resistance of Collodion membrane was

50 MO cm2 in Records A and B, but was shunted with external resistance of 2 kO cm2 in Record C.

Experimental conditions in Record C were otherwise identical to those in A and B. Amplitude ratio

R1/R2 of two components was 0.014 before shunting, but became 0.16 after shunting. (Reproduced

from Ref. [257])


R2 component has such a polarity that the disc interior is positive and thecytoplasmic side is negative. The polarity of the R2 component determined by thisexperiment is consistent with the interpretation that R2 is generated by a protonbinding from the cytoplasmic side. However, these tentative conclusions are basedon indirect inference.

The direct experimental evidence was provided by Shevchenko et al. [290], whoassayed protonation and deprotonation of two populations of reconstitutedrhodopsin-containing vesicles.

13.1.2. Direct assay of protonation and deprotonationShevchenko et al. [290,291] ®rst prepared photoreceptor disc membranes with

normal orientation from cattle retina, by means of a previously establishedmethod. Rhodopsin vesicles with inverted orientation were then obtained byrepeated freeze-thawing. The inversion was, however, incomplete. The separationof these two populations was implemented by a�nity chromatography on aconcanavalin A-Sepharose column [292]. The principle of separation is based onthe presence of two oligosaccharides near the N-terminus (see Fig. 4). Theseoligosaccharides are sequestrated inside a normally oriented vesicle (i.e., C-terminus out and N-terminus in), but become exposed upon inversion and thuscan bind to the concanavalin A-Sepharose column, thereby becoming separatedfrom the normal population. The inverted vesicles can be eluted subsequently witha solution containing methyl-a-D-mannopyranoside.

Light-induced protonation or deprotonation on the exposed vesicle surfaceswere assayed by monitoring the characteristic absorbance of pH indicator dyebromocresyl purple. The result is shown in Fig. 74. Illumination of the vesicles

Fig. 73. Kinetics of metarhodopsin II electrogenesis. Rhodopsin preparation was ®rst illuminated with

31 consecutive 530 nm ¯ashes, followed by single 347 nm ¯ash. Both fast phase (A) and slow phase (B)

are shown. (Reproduced from Ref. [257])


with normal rhodopsin orientation causes alkalinization of the medium, indicatinglight-induced proton binding (Fig. 74(A)). Illumination of the vesicles withinverted orientation, however, causes no acidi®cation of the external medium (Fig.74(B)). In fact, there is a slight alkalinization instead. Shevchenko et al. attributedthe alkalinization of the normally oriented vesicles to light-induced proton uptakeat the cytoplasmic domain of rhodopsin, whereas they attributed the slightalkalinization of the medium by the supposedly inverted vesicles to gradualrestoration of the normal orientation. In support of their interpretation, theydemonstrated re-inversion by repeated chromatography of a presumably pureinverted vesicle fraction. Furthermore, they observed time-dependent re-inversionof a pure inverted sample and were able to correlate the degree of proton uptakewith the duration of storage. They also concluded that there is no light-inducedproton release at the intradiscal domain of rhodopsin (N-terminal side), andtherefore, no light-induced proton pumping across the membrane.

Following the observations of Shevchenko et al., we further conclude that thereis no counterpart of the B2 ' component in ERP, because there is no protonrelease. Our interpretation of the R2 component in terms of proton uptake(charge separation) and its reverse reaction (charge recombination) is supportedby an additional observation of Shevchenko et al. They observed a slow partialrestoration of pH in the dark, indicating proton release to the cytoplasmicaqueous phase.

The direct observation of acidi®cation or alkalinization of the medium,associated with the photoreversal potential, further con®rms the aboveinterpretation. The sample was ®rst illuminated with a 500 nm ¯ash, and theexpected e�ect of a rapid alkalinization of the medium took place. After a one-minute interval, the sample was then illuminated with a 365 nm ¯ash. A rapid

Fig. 74. Light-induced pH changes in suspension of photoreceptor discs. Record A was taken from

discs with normal rhodopsin orientation, whereas Record B was from discs after freeze-thawing, which

caused disc inversion (turning inside-out). Trace a shows photoresponse with 100 mM bromocresyl

purple in medium. Trace b shows response without bromocresyl purple in medium. Trace c shows true

pH change (di�erence of trace a and trace b), whereas trace d shows calibrated addition of HCl.

Samples were illuminated with ¯ash of xenon lamp (4 ms pulse duration), resulting in bleaching of 40%

of rhodopsin. Rhodopsin concentration was 14 mM in Record A, and 25 mM in Record B.



acidi®cation of the medium was observed instead. However, if the life time ofmetarhodopsin II was reduced by the addition of hydroxylamine (formingretinochrome), then illumination with a 365 nm ¯ash would not cause acidi®cationof the medium (Fig. 75). It is apparent that protons are released during thephotoreversal potential.

In summary, experiments of Cone, Drachev et al., and Shevchenko et al.established that the R2 component is associated with a light-induced protonuptake at the cytoplasmic domain of rhodopsin (C-terminal side) at the time offormation of metarhodopsin II.

13.2. AC photoelectric signal from halorhodopsin

Halorhodopsin (hR) is the second most abundant retinal protein inHalobacterium salinarium. It is one of the three retinal proteins in the redmembrane fraction [61]. Its primary function is conversion of absorbed lightenergy into a transmembrane Clÿ concentration gradient. Since hR and bR have a62% homology with regard to their retinal binding pocket [55], we suspected theprimary event of charge separation may be similar in both pigments. We thereforeexpected the existence of a signal analogous to B1, to be named the H1 component.In view of hR's function, interfacial chloride ion transfers must take place at bothmembrane surfaces. We also expected the existence of signals analogous to the B2and the B2 ' components, to be named theH2 andH2 ' components.

Because of the relatively small amount of hR in the wild-type cell of H.salinarium, as compared to bR, it is necessary to obtain hR from a bR-freemutant (strain OD2-W). Halorhodopsin membrane fragments were prepared bymeans of a method developed by Steiner and Oesterhelt [293]. Puri®ed membranefragments were then reconstituted into liposomes (vesicles) by means of a methoddeveloped by Duschl et al. [294] or directly used, depending on the thin ®lmreconstitution methods being used. In reconstituting hR membranes by means ofthe TM method, we used hR liposomes as the starting material. However, we usedpuri®ed hR membrane fragments directly to make ML thin ®lms.

The fast photoelectric response in a TM ®lm so reconstituted is shown in Fig.76 [295]. The photosignal is analogous to the fast photoelectric signal from bR.We found that the H2 component is not sensitive to the pH change, but issensitive to the change of the Clÿ concentration in the aqueous phase. In a Clÿ-free medium, such as 0.1 M sodium citrate, the H2 component is quite prominent.If the Clÿ-free electrolyte solution is then replaced by 0.1 M KCl, the H2 peak issuppressed. The suppression of the H2 component is reversible; it can be restoredby replacement with the Clÿ-free solution again.

In the ML thin ®lm, reconstituted from hR membrane fragments, the signallooks like B1, and is insensitive to both the pH change and to the change ofchloride ion concentration. A Q-tip experiment, similar to that described inSection 10.11, was performed on the ML thin ®lm. The diminutive signal afterstripping still shows no dependence on the Clÿ concentration. We thus regard thiscomponent as the H1 component.


Using a long square-wave light pulse to illuminate a reconstituted hRmembrane, Bamberg et al. [296] elicited a photoelectric response similar to whatwe observed in bR membrane, as reported in Section 12 (Fig. 59(B)). Theobservation of the photosignal requires the presence of Clÿ. In addition to the DCphotocurrent, they also observed the characteristic asymmetric `spikes'. Theyinvoked the button model to explain the waveform. Again, we found it su�cientto invoke the concept of chemical capacitance and the step-function switchingfeature of the photoconductance to explain the appearance of asymmetric spikes.It is also worth noting that we did not used fused vesicles for reconstitution ofbR.

Recently, Kalaidzidis et al. [297] reported AC photoelectric signals of hRisolated from Natronobacterium pharaonis. The latter hR di�ers from that ofHalobacterium salinarium in several characteristics, including the photocycle, andthey identi®ed a Clÿ-dependent component.

13.3. AC photoelectric signals from photosynthetic reaction centers

Historically, the AC photoelectric e�ect in arti®cial membranes was ®rstdemonstrated in a BLM reconstituted from a chloroplast extract [148]. Typicalphotoresponses are shown in Fig. 77 [298]. Photosynthetic reaction centers ofRhodopseudomonas viridis or Rhodobacter sphaeroides can be puri®ed in a

Fig. 75. pH changes in suspension of fragments of photoreceptor discs, during light-induced transition

of metarhodopsin II into product P. Experimental conditions were: trace a, 100 mM NaCl, pH 6.0;

trace b, 100 mM NaCl, pH 6.0 (sample illuminated with 365 nm light 30 min after ®rst ¯ash); trace c,

100 mM NaCl, 100 mM hydroxylamine, pH 6.0. Rhodopsin concentration was 12±25 mM.

Concentration of bromocresyl purple was 100 mM. Arrows indicate instant of illumination of sample

with 500 nm light (4 ms pulse duration) and with 365 nm light (10 s illumination duration).



Fig. 76. Photoelectric signals from reconstituted halorhodopsin thin ®lms. (A) Change of photosignal,

measured from TM ®lm, was reversible, when aqueous solution was changed from KCl (pH 6) to

sodium citrate (pH 6), and vice versa. H1 and H2 components have opposite polarities: positive and

negative, respectively. (B) Photosignals from ML ®lm (H1 component only) in KCl (pH 7) and in

sodium citrate (pH 6), before stripping with cotton swab, are shown to be superimposable. (C)

Corresponding photosignals, after stripping with cotton swab, are also shown to be superimposable.

All measurements were made at 258C. (Reproduced from Ref. [295])

preparation suitable for membrane reconstitution. Packham et al. [284] succeededin reconstituting a puri®ed reaction center sample of Rhodobacter sphaeroides intoa BLM. Evidence for the existence of an AC photoelectric signal can be found inthe spike-like waveform of the photoelectric response elicited by a long square-wave pulse of light (400 ms) (Fig. 62(B)).

Hara et al. [299] immobilized puri®ed reaction centers Rhodopseudomonas viridison a solid electrode by means of a technique called avidin±biotin coupling [300].Avidin has four binding sites for biotin. Macromolecules (such as bR) orsupramolecular complexes (such as the reaction centers) can be derivatized withbiotin at selected surface domains. The surface of a solid support can also be soderivatized. Coupling of both derivatized reaction center complexes and thederivatized solid surface allows for oriented bacterial reaction centers to form athin ®lm on the solid surface. Plating with a reference electrode on the thin-®lmsurface completes a photoactive assembly, from which an AC photoelectric signalcan be elicited by a light pulse, as shown in Fig. 78(A).

Keszthelyi and co-workers [301] immobilized a sample of isolated and orientedphotosynthetic reaction center of Chlamydomonas reinhardtii into a gel ®lm, using amethod developed by DeÂ r et al. [192] (Section 6.4). Fig. 78(B) shows two similar fastphotoelectric responses from the gel ®lm, obtained with two di�erent sampleorientations between the electrodes. The samples were oriented by an applied DCelectric ®eld prior to immobilization.

The waveform of both signals, shown in Fig. 78, exhibits a biphasic relaxation,as expected from an AC photoelectric signal. The measurement of data fromChlamydomonas reaction center warrants a comment. A gel ®lm is highlypermeable to small inorganic ions. Therefore, the parameter Rm is small comparedto the input impedance of the open-circuit voltage measuring device, which is partof the access impedance. In other words, the gel ®lm is short-circuited internallyby the leaky ®lm. Thus, the parameter tm is diminished according to Eq. (9.11)and becomes smaller than tmc, so that the photosignal is biphasic instead ofmonophasic (see Fig. 24 and Section 9.3 for explanation). Although the data werereported as photovoltages, the measurement was performed under a near-short-circuit condition.

14. Comparison of bacteriorhodopsin and photosynthetic reaction centers

Both bR and chlorophyll-based photosynthetic reaction centers convertabsorbed photon energy into a transmembrane proton gradient, which issubsequently utilized to synthesize ATP. The chlorophyll-based photosyntheticmembranes also convert part of the absorbed light energy into the reducingequivalents, such as NADPH or NADH, to be utilized in many biosyntheticprocesses.

Super®cially, the chlorophyll-based photosynthetic membranes resemblemitochondria more than they do the purple membrane; both a chlorophyll-basedphotosynthetic membrane and a mitochondrial membrane contain many


Fig. 77. Photoelectric responses from chlorophyll-containing BLM. (A) Response to microsecond xenon

¯ash, with 10 mM FeCl3 in one side of two aqueous phases, is shown. Delivery of xenon ¯ash is

indicated by arrow. Dark RC response of BLM is also shown (lower trace). (B) Photoresponse, with

FeCl3 in one side of two aqueous phases and with applied voltage (ÿ10 mV), is shown. (C) Slow decay

phase of photoresponse is shown. RC response is also shown (inset). (Reproduced from Ref. [298])


prosthetic groups, which form a linear path known as the electron transport chain;the proton gradient is generated via a multi-step process, in which the chargebeing transferred is primarily the electron. There is no such counterpart in thepurple membrane; the transmembrane charge carrier is always the proton.

However, the underlying electrochemical processes in the purple membrane aregenerically similar to those in the chlorophyll-based membranes. We shall give abrief account of the structural organization of the chlorophyll-based system inorder to facilitate subsequent discussion. Readers interested in more detail shouldconsult standard review articles [302±308].

14.1. Photosynthetic reaction center of Rhodopseudomonas viridis

The photosynthetic reaction center of Rhodopseudomonas viridis was among the®rst membrane-bound protein complexes, of which the three-dimensional structurehas been determined to the level of atomic resolution [309,310] (Fig. 79). Thecomplex consists of four protein subunits, known as H, L, M, and the cytochromesubunits. The H subunit is located mainly at the cytoplasmic side with a single a-helical loop inserted into the core of the reaction center apparently as an anchor.The cytochrome subunit contains four heme prosthetic groups. The L and Msubunits are transmembrane proteins that form the sca�old to hold the prostheticgroups together with optimal relative spatial distances and optimal geometriccon®gurations. These prosthetic groups exhibit a two-fold symmetry and each halfof them are embedded in the L and the M subunits, respectively.

The primary electron donor is a dimer, the `special pair', formed by twobacteriochlorophyll b molecules from both the L and the M subunits. Having thelowest redox potential among the various prosthetic groups, the `special pair' isthe primary electron donor. Photoexcitation causes an electron to be transferredfrom the `special pair' to the electron acceptor bacteriopheophytin. There is an

Fig. 78. Pulsed-light-induced photoelectric responses in reconstituted photosynthetic membranes. (A)

Puri®ed photosynthetic reaction centers of Rhodopseudomonas viridis were immobilized, by means of

avidin±biotin coupling technique, on transparent metal electrode. (B) Puri®ed photosynthetic reaction

centers of Chlamydomonas reinhardtii were oriented and immobilized in gel. (Reproduced from Refs.

[299] (A) and [301] (B))


additional pair of bacteriochlorophyll b molecules, known as the voyeur ormonomer bacteriochlorophyll, which is positioned between the `special pair' and thebacteriopheophytin molecule. It is not completely settled whether the monomerbacteriochlorophyll molecule actually participates in the electron transfer from the`special pair' to bacteriopheophytin. The electron is further transferred frombacteriopheophytin to a hydrophobic quinone, menaquinone, QA, in the Lsubunit. Symmetrically positioned in the subunit M is a similar quinone,ubiquinone QB. QA of the L subunit is a tightly bound quinone, whereas QB ofthe M subunit is mobile and serves as a shuttle to carry electrons (and protons) tothe cytochrome b/c1 complex. On the extracellular (periplasmic) side, a peripheralprotein cytochrome c2 serves as a water-soluble mobile electron shuttle thattransfers electrons to the cytochrome subunit. Functionally, only the L subunit isfully utilized in electron transfer (electron transport chain ).

14.2. Structurally di�erent systems with similar functional design

The scheme shown in Fig. 79 for the reaction center of Rhodopseudomonas

Fig. 79. Schematic of reaction center of Rhodopseudomonas viridis. There are four protein subunits: H,

L, M and cytochromes (Cyt). BCLP and BCMP, which form dimer (`special pair'), are

bacteriochlorophylls from L and M branches, respectively. BCLA and BCMA are voyeur

bacteriochlorophylls from L and M branches, respectively. BPL and BPM are bacteriopheophytins

from L and M branches, respectively. QA is the tightly bound quinone of L branch, and QB is loosely

bound quinone of M branch. Cytochrome c2 (Cyt c2) is peripheral protein in periplasmic space.



viridis can be cast as a series of electrochemical reactions, which we refer to inSection 10.13 as coupled consecutive charge-transfer reactions. The resultingscheme (Fig. 80) looks similar to that for the purple membrane (Fig. 50).Photoexcitation in the reaction center causes an electron to be transferred to BPhor QA and the charge separation generates a hole: the oxidized `special pair',SP+. Likewise, photoexcitation of bR causes a proton to be transferred from theprotonated Schi� base to the carboxylic group of D85, generating a `negativehole': the deprotonated Schi� base.

In Section 10.13, we have pointed out that the minimum requirement of a light-driven proton pump is that at least one of the steps of the coupled consecutivecharge-transfer reactions is light-driven; a highly irreversible step is not anabsolute requirement. On the other hand, charge recombination results indissipation of converted light energy. The structural organization of the reactioncenter of Rhodopseudomonas viridis provides us with a glimpse of how Naturemanaged to optimize the light-driven proton pump. The underlyingelectrochemical principles are best illustrated with the analysis described in areport by Kuhn [311]. The major features of that analysis will be highlighted here.

Apparently, separating charges in the form of a transmembrane proton gradientis the primary objective of biological photon energy conversion. The membranedielectric, which is a relatively good insulator, constitutes a major barrier for theseparated charges to recombine directly by retracing the original charge-transferpath in the reverse direction. Instead, the separated charges must recombine viaan external circuit loop, so that useful work can be performed. By coupling toATP synthetase, the dissipation of the electrochemical gradient of protons can beutilized to synthesize ATP from ADP and inorganic phosphate.

However, charge separation across a biomembrane over a distance of 60 AÊ

cannot be accomplished in a single step; the maximal distance electrons can tunnelquantum-mechanically in a single step is about 10±15 AÊ . It is therefore necessaryto break the process down to a number of successive coupled consecutive charge-transfer reactions, each of which covers a small distance, as depicted above.

The rate of forward or reverse electron transfer between an electron donor andan electron acceptor is determined by the di�erence of their redox potentials, orthe di�erence of free energy DG. The more exothermic the reaction is (i.e., morenegative DG), the faster the forward electron-transfer rate is and the slower thereverse electron-transfer rate is. Thus, one approach to minimize chargerecombination is to make the electron-transfer reaction highly exothermic.However, for a scheme of multi-step coupled electron-transfer reactions, thecumulative DG means energy loss in the form of heat dissipation, and is thusenergetically unacceptable. A compromised approach is to allow most of thetransfer steps to be highly reversible, i.e., with small DG.

Fig. 81(A) shows the spatial relation of the photo-excited `special pair' D, themonomer bacteriochlorophyll W1, and bacteriopheophytin W2. The photo-excitedelectron is transferred from D to W2 in 2.8 ps. In 200 ps, the electron reaches QA.In 270 ns, cytochrome, the secondary electron donor, further reduces the oxidized`special pair', D+. The separated charges now almost span the entire thickness of


the membrane. The secondary quinone in the M branch (QB) is reduced in about100 ms. So far, the charge separation is implemented by electron-hole pairformation. But when QB is reduced, it picks up two electrons from QA, as well astwo protons from the adjacent aqueous phase:

1

2QB � 1

2QÿA �H �4

1

2QBH

2 � 1

2QA: �14:1�

QB, being a mobile charge carrier in the membrane phase, becomes electricallyneutral and feeds both electrons and protons to cytochrome b/c1 complex. Whenan electron is eventually transferred to the mobile charge carrier cytochrome c2 inthe periplasmic aqueous phase, a proton is released, stoichiometrically, into theperiplasmic space. Cytochrome c2 then feeds the electron to the cytochromesubunit of the reaction center, and thus completes the process of the so-calledcyclic electron ¯ow. It is through this mechanism of electron±proton co-transport,in the direction opposite to the initial electron ¯ow, that an electron-mediatedphotocurrent leads to the generation of a transmembrane proton gradient, insteadof a redox gradient.

In order to minimize the impact of reverse electron transfers, the photo-energized electron must be separated from the hole (D+) as fast and as far aspossible. This large distance, which amounts to 30 AÊ , cannot be covered by a

Fig. 80. Coupled consecutive electron-transfer reactions with electron-proton co-transport in reaction

center of Rhodopseudomonas viridis. SP is `special pair', BCh is voyeur bacteriochlorophyll, BPh is

bacteriopheophytin, QA and QB are tightly bound and loosely bound quinone, respectively. Electron-

transfer reactions in cytochrome b-c1 complex are simpli®ed to single step, so are those in four bound

cytochromes on periplasmic surface. Cyt c2 is peripheral protein cytochrome c2. Dotted arrows indicate

di�usion of QB and Cyt c2. Reverse reactions are not shown. (Reproduced from Ref. [43])


single step of electron tunneling. It requires the bridging provided by an extendedp-electron system, which is formed by three molecules (D, W1, W2). The freeenergy levels of D

�, W1 and W2 are closely matched, so that the forward electron

transfer is almost devoid of energy loss (Fig. 81(B)). The reverse reactions arefurther retarded by a combination of three mechanisms. First, there is vibronicrelaxation of the reduced QA (Aÿ) and a decrease of the free energy level byabout 0.4 eV, so that the reverse reaction, traversing the original path via W1 andW2 but in the reverse direction, becomes more endothermic. Second, the p-electron system is spatially arranged in a bent (banana-shaped) structure. Thus,the direct straight-line path through the s-portion of the L protein subunitpresents a shorter path for electron tunneling, but the tunneling probabilitythrough this s-portion is drastically reduced. Third, the hole, D+, created by

Fig. 81. Spatial arrangement (A) and energy levels (B) of electron transport chain in reaction center of

Rhodopseudomonas viridis. D is `special pair'. W1 is voyeur bacteriochlorophyll. W2 is

bacteriopheophytin. A is tightly bound quinone QA. D ' is secondary electron donor cytochrome. See

text for explanation. (Reproduced from Ref. [311])


oxidation of D, is re®lled with an electron from the secondary donor D '(cytochromes). The probability of reverse electron transfer from QA back to D+ isthus further reduced. Readers interested in further details should consult Kuhn'soriginal treatise [311].

Presently, a comparable three-dimensional structure of bR with atomicresolution is lacking. The detailed structure of the transmembrane proton-translocating path is only partially known. Except for the initialphotoisomerization of the chromophore, charge separation in the form ofelectron-hole generation is absent. The Schi�-base proton-binding site correspondsto the primary charge (proton) donor. The free carboxylate group of aspartateresidue 85 (D85) corresponds to the primary proton acceptor. The free carboxylicacid group of aspartate residue 96 (D96) corresponds to the secondary protondonor. The Schi�-base proton-binding site switches from a con®guration withproximity to D85 to another with proximity to D96 during the M1 to M2

transition (deportonation/reprotonation switch). The thermodynamic analysis ofthe bR photocycle performed by VaÂ roÂ and Lanyi [128] is particularly relevant toour discussion.

As shown in Fig. 82, the free energy levels of most intermediates are closelymatched, showing little free energy loss in each successive photochemicalreactions, except at the M1 to M2 transition. Furthermore, the decrease of the freeenergy at that transition has a large contribution from the entropy change. VaÂ roÂand Lanyi thus concluded that the main molecular switch (deprotonation/reprotonation switch), which greatly reduces the probability of chargerecombination, is the M1 to M2 transition. The principles cited by Kuhn forretarding the charge recombination in the bacterial reaction center is replicated inbR, but with a completely di�erent molecular construction.

Recent work by Lanyi and his coworkers has greatly elucidated the mechanisticdetail of the deprotonation/reprotonation switch. Interested readers are referred totwo recent articles about their local access model [312,313].

15. Comparison of bacteriorhodopsin and rhodopsin

15.1. Molecular processes of visual transduction

The primary function of the visual photoreceptor membrane is light-signalsensing, i.e., utilizing light as a means to code information from the outside world.The photoreceptor is characterized by its high sensitivity and its broad dynamicrange. Based on the psychophysical measurement of Hecht and co-workers [314],it is known that a single photon, if absorbed by rhodopsin, is su�cient fordetection of the light signal by a photoreceptor, under an optimal (dark adapted)condition. The dynamic range of the rod receptor sensitivity covers 9 orders ofmagnitude through processes known as dark and light adaptation.

It has subsequently been shown that the neural excitation of a visualphotoreceptor is manifested as a hyperpolarization of the photoreceptor


Fig. 82. Enthalpy (A), entropy (B), and free energy (C) changes of various photointermediates, relative

to bacteriorhodopsin, during photocycle. Greatest free energy and entropy changes occur at M1 to M2

transition. (Reproduced from Ref. [128])


membrane potential in vertebrate eyes [106]. In contrast, the excitation of theinvertebrate photoreceptor membrane is a depolarization. These membranepotential changes are, in turn, mediated by light-induced decrease or increase ofthe Na+ permeability, respectively. The active Na+ transport from thecytoplasmic space to the extracellular space generates a transmembrane Na+

gradient. The active transport is carried out in the inner segment by the sodium±potassium ATPase (Na+±K+ pump).

A relatively high Na+ permeability of the plasma membrane at the outersegment in the dark causes a massive in¯ux of Na+ current. Illumination of avertebrate retina causes the Na+ permeability to decrease suddenly; the moreintense the illumination is the more marked the decrease is. The light-inducedalteration of the Na+ in¯ux is manifest as the a wave of the electroretinogram,which is identical to the late receptor potential (LRP) mentioned in Section 5.1.Thus, the transduction of the initially absorbed photon energy into the regulationof Na+ in¯ux incurs an energy ampli®cation of 100,000 fold.

Since rhodopsin molecules are located in the outer segment disc membranes,whereas the Na+ channel proteins are located in the outer segment plasmamembrane, rhodopsin molecules are separated from the Na+ channel proteins bya considerable distance. Thus, visual transduction involves the transformation of alocal event of photobleaching of rhodopsin to the global event of Na+

permeability change. The lack of membrane continuity between the discmembrane and the plasma membrane (except near the junction of the outer andinner segments), and the time delay of 1.7 ms between the initiation ofphotobleaching of rhodopsin and the onset of LRP suggest that an electricalconduction mechanism (e.g., electrotonic spread) is unlikely. It is now known thatvisual transduction is made possible by the cyclic GMP cascade (see Section 4.1).

15.2. Why is ERP not necessarily an epiphenomenon?

It is apparent that the functional role of rhodopsin is completely di�erent fromthat of bR. E�ciency of light energy conversion is not the central issue, but thesensitivity and the dynamic range of light sensing are. Why then does ERPresemble the fast photoelectric signal of bR so much? What is the physiologicalsigni®cance of ERP? These are not trivial questions, in view of the manysimilarities between rhodopsin and bR. Both rhodopsin and bR are single-chainpolypeptides that are folded into seven a-helices that span the membrane. Bothhave their C-termini located at the cytoplasmic side of the membrane and bothutilize vitamin A aldehyde as the chromophore, which is attached to the apo-protein by means of a Schi�-base linkage to the e-amino group of a lysine residuelocated on the a-helix closest to the C-terminus. As in bR, deprotonation of theSchi� base is an obligatory process in metarhodopsin I to II transition, and isessential in activation of transducin [315]; glutamate 113 is the Schi�-base protonacceptor [316]. The similarity and di�erence between the two retinal proteins aresummarized in Table 7.

A surprising exception is the apparent lack of amino-acid sequence homology.


However, the more than super®cial resemblance of their AC photoelectric signalsarouses a suspicion that the similarities between the two pigments are not limitedto the super®cial structural resemblance. Yet the conventional wisdom in visualphotoreceptor physiology seems to conclude that ERP represents electricalmanifestations of the photochemical events, but does not represent the excitationof the rods per se [139]. ERP has been commonly dismissed as an epiphenomenon,implying that it is an evolutionary vestige with no important physiologicalfunction. However, Pak [139] has not completely ruled out the possibility of stillunidenti®ed and silent processes intervening between the generation of ERP andthe excitation of the rods. It is instructive to examine the major arguments behindthe rationale of such a conclusion.

Two reasons have often been singled out to discredit the possible physiologicalimportance of ERP: (a) the amplitude of ERP is too small, and (b) the ERP-likesignals are ubiquitous. Shortly after the discovery of ERP, similar fastphotoelectric signals were found in many di�erent pigment-containing tissues,such as pigmented epithelia of the eyes and chloroplasts [317] (Fig. 83). After thediscovery of the BLM technique, there were many reports of the AC photoelectrice�ect in arti®cial BLMs containing various types of pigments or organic dyes [30].The ubiquity of ERP-like signals is suggestive of their lack of speci®city, but doesnot constitute proof that ERP has no physiological role. Its ubiquity isunderstandable, if we recall that many pigments and organic dyes become reactiveupon illumination, and some even undergo electron-transfer reactions (chargeseparation), if suitable electron acceptors are present in the vicinity. Yet electrontransfer and charge separation are fundamental processes in photosynthesis, andpossibly also in vision. Both bR and rhodopsin store substantial amounts of the

Table 7

Comparison of bacteriorhodopsin and rhodopsin (reproduced from Ref. [43])

Common features

1. Transmembrane proteins (7 transmembrane a-helices)2. Chromophore (retinal) bound to a lysine residue via a Schi�-base linkage

3. C-terminus located on the cytoplasmic surface

4. Similar photochemical intermediates

5. Primary event: chromophore photoisomerization and rapid charge separation

6. Major conformational changes: M14M2, and metarhodopsin I4 II, respectively

7. Similar displacement photocurrent signals

8. Proton uptake taking place at the cytoplasmic surface

Di�erences

Bacteriorhodopsin Rhodopsin

1. Photon energy converter 1. Photon signal transducer

2. Photocyclic reactions 2. Photobleaching reactions

3. Transports protons 3. Does not transport protons

4. Conducting polymer 4. Non-conducting polymer


absorbed photon energy as charge separation, during photoisomerization of thechromophore [133,134,318,319]. Warshel [47] has modeled the energy storage interms of charge separation.2 We suspect that the signal components, such as R1,B1 and H1, are manifestations of such charge separation (see Section 10.10).

The small amplitude of ERP can also be readily understood in view of our newunderstanding of the generation mechanism. While the driving `force' of manycommon bioelectric signals resides outside of the membrane phase (e.g., thetransmembrane di�usion potentials of Na+ and K+ in the generation of actionpotential), the driving `force' (photoemf) of ERP is residing either inside themembrane or at the membrane±water interface. Such processes of electri®cation inthe membrane are partially shielded from direct outside observation by the di�usedouble layers, because of the charge screening e�ect. As a consequence, externallyrecorded ERP signals do not re¯ect the true intensities of local electric ®elds insidethe membrane or at the membrane surfaces. Furthermore, many earlyinvestigations of ERP relied on extracellular recording, which further reduces theobserved signal amplitude. Based on a simple calculation, we have previouslyspeculated the presence of a positive surface potential in association with theappearance of the R2 component of ERP [209]. We further stipulated that amodest surface potential of 50 mV could readily generate an electric ®eld, whichmay be more intense than that generated by a typical transmembrane potential ofthe same magnitude. This speculated surface potential and the associated intense

Fig. 83. ERP-like photosignals from pigmented eye cup without retina, from eye of albino rat (retina

only), and from green leaf of gout weed. Top row: high temperature (25, 30, 468C, respectively).

Middle row: medium temperature (5, 16, 308C, respectively). Bottom row: low temperature (ÿ0.5, 0,168C, respectively). Arrows mark onset of 400 ms ¯ash. (Reproduced from Ref. [317])

2 Shieh et al. [320] proposed an alternative energy-storage mechanism based on steric strain.


electric ®eld were subsequently experimentally observed by Ca®so and Hubbell[321,322].

15.3. E�ect of surface potential

Ca®so and Hubbell [321,322] took advantage of an interesting property of anegatively charged hydrophobic ion named tetraphenyl borate, TPBÿ. While smallinorganic ions have extremely limited solubility in the membrane, TPBÿ has asigni®cant solubility in the membrane phase, because of the reduction of its Borncharging energy, caused by low charge density in an organic ion of substantialsize. The amount of TPBÿ partitioned into the membrane phase depends on itsaqueous concentration or, more precisely, on its local concentration in the di�usedouble layer (i.e., surface concentration). Since TPBÿ carries a negative charge, itsaqueous surface concentration can be regulated by the membrane surfacepotential. Ca®so and Hubbell derivatized TPBÿ with a paramagnetic functionalgroup, so that its partition into the membrane phase can be monitored by meansof electron paramagnetic resonance. Thus, they were able to position a probe ofthe surface potential at the vicinity of the membrane surface. Using this technique,they observed giant signals re¯ecting the appearance of a positive surfacepotential, which they correctly attributed to ERP.

Fig. 22(A) and (B) illustrate how a modest surface potential can generate anintense electric ®eld near the membrane surface (cf. Section 10.13.4). The diagramsshow the charge-density pro®le, r�x�, and the electric potential pro®le, C�x�,across a membrane of thickness d, which is initially uncharged. As a result oflight-induced proton binding, the membrane surface at the left aqueous phasebecomes positively charged, and a positive surface potential appears there. The netpositive charges on the left surface are compensated jointly by net negativecharges both in the adjacent double layer and in the opposite double layer.

The potential pro®le indicates that a positive surface potential also appears onthe opposite interface, even if the opposite surface is not charged. This is becausethe membrane is so thin that the in¯uence of the surface charges extended acrossthe membrane and reaches the other interface. Without this extension, interfacialcharge transfer would not be directly detectable via a pair of electrodes placedacross the membrane, but would remain detectable with a localized probe, such asTPBÿ.

Electri®cation of one interface generates electric ®elds both in the two di�usedouble layers and inside the membrane. Since the electric ®eld, E(x ), is given bythe negative slope of the potential pro®le, ÿdC�x�=dx, and since the membrane isthicker than the double layers, the electric ®eld is much stronger inside the doublelayers than inside the membrane. Pulsed-light stimulation generates aconcentration jump of small anions in the double layers with a risetime,determined by the ionic cloud relaxation time (less than a nanosecond for smallions in a physiological solution) or by the risetime of the surface potential,whichever is slower.

Assuming a Boltzmann distribution of the ions in the double layers, in


accordance with their electrochemical potential, the interfacial concentrations canbe considerably higher or lower than the corresponding bulk concentrations, forcounterions and co-ions, respectively.

Consider a monovalent anion. Since RT/F is 25.6 mV at 258C, theconcentration of a monovalent anion increases e-fold for an increase of every 25.6mV of the surface potential (e � 2:71828, R is the universal gas constant, T is theabsolute temperature, and F is the Faraday constant). For a divalent anion, ittakes only 12.8 mV to achieve the same e�ect. A surface potential thereforeprovides an excellent switch to cause a highly localized concentration jump ofsmall ions, especially multivalent ions. However, multivalent ions are alsodramatically more e�ective in charge screening, leading to a reduction of thesurface potential. The intensity of the interfacial electric ®eld is partially preserved,because of a concurrent reduction of the Debye length or, loosely speaking,reduction of the thickness of the double layer.

15.4. Trigger mechanism of visual transduction

From the foregoing discussion, it is apparent that the light-induced surfacepotential provides an excellent switch. Such a mechanism is attractive for visualtransduction, because it ful®lls several important requirements. A reliable photontrigger must have a fast risetime. From the previous analysis, a surface-potential-based mechanism is faster and more reliable than a ionic-di�usion-mediatedmechanism. Processes mediated by ionic di�usion have a risetime in themillisecond range. For example, LRP, which is of ionic origin, has a risetime ofthat magnitude (latency of 1.7 ms). Since the cyclic GMP cascade involves bothchemical reactions and di�usion (of peripheral proteins), visual transductionimposes a requirement that a mechanistic trigger must operate in a time rangeconsiderably faster than milliseconds.

In view of the nonlinear nature of visual transduction and the requirement of abroad dynamic range, it is advantageous for the mechanistic trigger to operate ina localized and linear fashion, with regard to the stimulating light intensity. Theseengineering requirements, though by no means absolute, are neverthelessconveniently ful®lled by ERP.

The next step is to examine the consistency and the compatibility of such atrigger mechanism with established facts in the photoreceptor physiology.

15.5. Visual photoreceptor membrane as ®eld-e�ect transistor

The absence of proton pumping, demonstrated by Shevchenko et al. [290], isconsistent with rhodopsin's role of being a photon energy sensor, rather than aphoton energy converter, as discussed in Section 13.1. In addition, their ®ndingthat the proton-uptake by photoexcited rhodopsin occurs at the cytosolic surface,together with Cone's demonstration of the correlation between R2 generation andthe metarhodopsin I to II transition, reinforces our suspicion that the positivesurface potential associated with R2 may be the mechanistic trigger that initiates


transducin binding and activation; the positive surface potential appears at theright place and at the right time.

Exactly how a positive surface potential may initiate transducin activation canonly be speculated at present. It could be due to a simple electrostatic interactionwith the formation of a salt bridge between transducin and metarhodopsin II. Itcould also be due to a sudden concentration jump of a key unknown regulatoryion or small charged molecule. Mutagenesis experiments have begun to dissectsome of the topographical parts of rhodopsin that are critical for transducinbinding. Referring to Fig. 4(A), the second, third, and fourth cytoplasmic loops ofmetarhodopsin II cooperate in the binding of transducin, but not the ®rst loopand the C-terminus [323]. The Glu±Arg (E134±R135) pair at the top of helix IIIin loop i2 has been found to be critical in transducin activation, and reversal ofthe pair abolishes the mutant's ability to activate transducin, but not its binding[324]. However, the proton-binding site responsible for R2 is not clear. Fahmyand Sakmar [325] found glutamate 134 (E134) to be crucial in regulating the pHdependency of transducin binding: protonation of glutamate 134 favors binding ofrhodopsin to transducin. Glutamate 134 is also involved in proton uptakereactions [326,327,328]. By comparing a number of naturally occurring andmutant G-protein-linked receptor molecules, Oprian [329] has demonstratedstructural similarity at the ligand-binding domain, if one treats the covalentlybound retinal in retinal proteins and the non-covalently bound ligands, such asbiogenic amines and hormones, as being equivalent. A similar approach, withregard to the G-protein-binding domain, will probably shed light on the bindingmechanism of transducin and other G proteins. A recent report aboutthyrotropin-releasing hormone (TRH) indicates that its binding of G protein isnot mediated merely by random collision, but rather through an elaborate two-step gradient-like process [330]. Thus, the search for a mechanistic switch oftransducin binding is justi®ed.

Activated transducin continues to activate PDE, until the bound GTP ishydrolyzed. However, this latter process is very slow, and, therefore, allows theactivity of activated transducin to last for tens of seconds. Its rapid turn-o�requires binding of a 48 kD peripheral protein: arrestin (Section 4.1).

The price for this rapid `reset' process, instead of the passive photochemicalrelaxation entailed in rhodopsin photobleaching, is paid in the currency of ATP,which phosphorylates rhodopsin. Massive photophosphorylation is a prerequisitefor arrestin binding. Again, all these events take place at the cytoplasmic surfaceof the visual membrane. Massive photophosphorylation also implies theconcurrent appearance of a massive negative surface potential. Note that the onsetof a negative surface potential is time-shifted with respect to the onset of R2-related positive surface potential, so that it takes place at the beginning ofdeactivation of photo-excited rhodopsin. We suspect that the appearance of anegative surface potential (or the decrease of an existing positive surfacepotential), accompanying the massive phosphorylation, may be the mechanistictrigger for the accelerated deactivation of photo-excited rhodopsin.

That the trigger for the deactivation may be electrostatic in nature is supported


by the ®nding that arrestin has a high a�nity for heparin, other polyanions, andinositol hexaphosphate, and these negatively charged species compete for itsbinding to phosphorylated rhodopsin [331].

Readers familiar with the rhodopsin literature may raise an important questionhere. Most of the experiments that led to the elucidation of the c-GMP cascadewere performed in the solution phase and using photoreceptor disc-membranefragments. These fragments usually do not form sealed (leak-proof) membranevesicles and therefore cannot sustain a transmembrane potential in general. Apertinent question is: does a surface potential exist on these membrane fragments?The answer is yes. Unlike a di�usion potential, which disappears upon rupture ofa membrane, a surface potential persists, even in broken membrane fragments, asindicated by the Gouy±Chapman analysis described in Section 8 Ð the derivationwas performed speci®cally under a short-circuit condition, and is, therefore,applicable to broken membrane fragments in an electrolyte solution.Bioenergeticists usually distinguish two types of potentials: localized anddelocalized. A di�usion potential is delocalized and vanishes upon membranerupture, whereas a surface potential is localized and persists in brokenmembranes.

Thus, by means of an orchestrated time sequence of surface potential changes atthe cytoplasmic domain, the photoreceptor disc membrane may operate like a®eld-e�ect transistor (FET) or phototransistor. Here, the surface potential changesare equivalent to the base voltage change, which regulates the current ¯ow fromthe power supply to ground via the emitter and the collector in a transistor. Theanalogy is more than just ®gurative. The main points of experimental observationin support of this mechanism are summarized in Table 8.

It must be pointed out here that the above-outlined trigger mechanism of visualtransduction is presently speculative. While the proposed mechanism must besubjected to experimental veri®cation, it is of interest to ascertain experimentallywhether it is a viable mechanism. Its viability can be demonstrated by means ofan experimental prototype developed by Drain et al. [279,332].

These investigators studied the voltage-driven transmembrane transport ofTPBÿ across a BLM. At the same time, they con®gured the BLM in such a waythat light illumination generates symmetric positive surface potentials on both

Table 8

Visual photoreceptor membrane as a phototransistor (Compiled from Ref. [34])

1. The cyclic GMP cascade takes place at the cytoplasmic surface.

2. Binding of transducin to metarhodopsin II leads to its activation.

3. The formation of metarhodopsin II involves the net uptake of a proton at the cytoplasmic side.

4. The rise phase of the ERP R2 component is time-correlated with the formation of metarhodopsin II.

5. The polarity of the R2 component is consistent with the proton uptake at the cytoplasmic surface.

6. The photophosphorylation of rhodopsin at its cytoplasmic surface occurs during the deactivation of

visual transduction.

7. The above events are associated with a surface-potential change at the cytoplasmic surface.


Fig. 84. Experimental prototype showing switching of ionic currents, based on light-induced surface

potentials. (A) BLM contained lipid-soluble Mg octaethylporphyrin (3.6 mM). Aqueous solution

contained electron acceptor methyl viologen (Aÿ), in equal concentrations on both sides (20 mM).

Tetraphenyl borate ions, Bÿ, were partitioned into membrane at region of polar head groups of lipid.

Photoactivation of Mg octaethylporphyrin formed P+ and generated two symmetrical positive surface

potentials, which increased surface concentration of Bÿ, but decreased surface concentration of

tetraphenylphosphonium ions. (B) Ionic current, carried by 1 mM tetraphenyl borate ions, increased

50% upon illumination with laser pulse (1 ms). (C) Ionic current, carried by 5 mM of

tetraphenylphosphonium ions, decreased 25% upon illumination. In both B and C, spike on left was

capacitative transient upon application of transmembrane potential of +50 mV. Light pulses are

indicated by arrows. (Reproduced from Ref. [279])


surfaces of the membrane. These surface potentials are generated by a light-induced electron transfer from the membrane-bound Mg octaethylporphyrin to anaqueous electron acceptor of equal concentrations in the two aqueous phases (Fig.84(A)). No macroscopic photovoltaic electric signal can be detected, because thephotocurrents generated by interfacial electron transfers at both surfaces are equalin magnitude, but opposite in polarity. Nevertheless, the positive surfacepotentials induced by light at the two membrane surfaces increase the adjacentsurface concentration of the negatively charged TPBÿ with a fast risetime (Fig.84(B)). Correspondingly, a sudden increase of ionic current carried by TPBÿ isdetected. As expected, if TPBÿ is replaced by positively chargedtetraphenylphosphonium (TPP+), light illumination would cause a suddendecrease of the ionic current (Fig. 84(C)). This surface-potential-induced change ofionic concentration would have been even more pronounced if the ionic speciesbeing transported were multivalent. These experiments demonstrated that asurface-potential-based switching mechanism is eminently viable, at least in thedesign of molecular devices. Whether it actually takes place in the visualphotoreceptor remains to be tested.

16. Comparison of bacteriorhodopsin and halorhodopsin

As shown in Fig. 3, bacteriorhodopsin (bR) is similar to halorhodopsin (hR) inits primary and secondary structures. These two pigments share considerableamino-acid sequence homology. The transmembrane part of bR is 36%homologous to hR, and the conserved residues are concentrated in thechromophore-binding region [333,334,335]. Both pigments are comprised of seventransmembrane a-helical segments, with the C-terminus facing the cytoplasmicside. Both pigments use retinal as the chromophore, and illumination causes it toundergo trans to cis isomerization. Yet, when hR is illuminated, it pumps chlorideions instead of protons [61,296,336].

In view of the structural similarity, it is not surprising that the photoelectricsignals in bR and hR are similar (Section 13.2). Both the B1 and the H1components have a submicrosecond risetime and are insensitive to changes of theionic composition in the aqueous phase, and both B1 and H1 re¯ect light-inducedintramolecular charge separation (OD mechanism). The slower component, B2 orH2, is strongly a�ected by changes of ionic compositions. The dependence ofthese signals on aqueous proton and Clÿ concentrations, respectively, is consistentwith the interpretation that B2 represents interfacial proton transfer, whereas H2represents interfacial Clÿ transfer. Thus, with appropriate modi®cations, theinterfacial proton transfer (IPT) mechanism can be naturally generalized tobecome the interfacial charge transfer (ICT) mechanism (Fig. 20). Incidentally, theICT mechanism was originally developed to explain the AC photoelectric signalgenerated by interfacial electron transfer in a Mg-porphyrin-containing BLM[163].

There are good reasons to suspect an intimate relationship between bR and hR.


What structural di�erences lead to the di�erences of their functional roles is anintriguing question. Based on comparative studies of more than half a dozenretinal-containing proteins and their mutants, especially those of bR and hR,mechanistic models of ion transport have been advanced [61,231±233,335,337,338].The key step of proton translocation in bR is the cyclic deprotonation/reprotonation of the Schi� base when the chromophore undergoesphotoisomerization. During deprotonation, the primary acceptor of this Schi�-base proton is the carboxylate group of aspartate residue 85 (D85). Thedeprotonated Schi� base is reprotonated through aspartate residue 96 (D96).Halorhodopsin lacks the aspartate residues corresponding to D85 and D96 in bR.Thus, in the Clÿ translocation cycle, the Schi� base remains protonated [339].Deprotonation does, however, take place through a side reaction (see below). Thatsuccessive protonation and deprotonation of the Schi� base are absolutelyrequired for proton transport is consistent with the absence of vectorial protontransport in: (a) the bR mutant in which the aspartate residue in D85 is replacedwith asparagine (D85N ), (b) bR at low pH in which D85 is fully protonated, and(c) hR in which proton acceptor/donor groups, such as D85 and D96, are missing.

That bR and hR are intrinsically equipped with the mechanism to transporteither H+ or Clÿ was ®rst suggested by Keszthelyi and coworkers [340±342].These investigators found that a stationary (DC) photocurrent from reconstitutedbR appears at pH 0.55 in the presence of HCl, but found no such current at thesame pH in a Clÿ-free medium. They suggested that bR pumps Clÿ instead ofprotons, because the proton acceptor D85 is blocked by acidi®cation and therequired M state is absent at low pH. Thus, bR may have a dual pumpingmechanism built into it, but only proton pumping takes place under physiologicalconditions.

Another intriguing possibility was raised by Oesterhelt and coworkers[334,343,344]. By studying the photoelectric signal from a reconstituted hRmembrane, they demonstrated that hR can be made to pump protons instead ofClÿ. Normally, under white light or green light illumination, hR pumps Clÿ.However, a green photon absorbed by hR generates a photointermediate H410 asa side reaction. If, however, additional blue light is administered after blue lightillumination, hR can pump protons with the help of the enriched H410 state (two-photon process).

More recently, Sasaki et al. [345] reported the conversion of bR into a chlorideion pump. The conversion is caused by replacing aspartate 85 residue withthreonine (D85T ). Brown et al. [346] found in D85T that glutamate 204 (E204)becomes protonated when Clÿ is added. VaÂ roÂ et al. [347] found that, when azideis bound to the Clÿ-binding site, it functions as an acceptor of the Schi�-baseproton during the photocycle and that, after deprotonation of the Schi� base,protons are released. Apparently, another molecule of azide shuttles protons fromthe cytoplasmic side to the extracellular side. These results indicate that theproton- and the chloride-pumping mechanisms are intimately related and Clÿ

plays a prominent role.Photoelectric responses of D85T and D85N have been analyzed by Tittor et al.


[348] and Ganea et al. [349]. They interpreted the data in terms of anIsomerization/Switch/Transfer (IST) model [231].

That bR is intrinsically equipped with the capability to transport Clÿ is alsosupported by our observation on the Clÿ-dependent AC photocurrent at low pH(Section 10.8). Whereas the mutant D212N lacks the B2 component in neutral tohigh pH, it exhibits a Clÿ-dependent signal at low pH, which has the samepolarity as B1, i.e., opposite to that of B2 in neutral to high pH [219].

This low-pH B2 signal also exists in membranes reconstituted from wild-typebR [227]. In addition, the B2 component disappears completely at pH 2.7. The B2component reverses its polarity when pH falls below 2.7. These observationsjustify the designation of the low-pH and the high-pH B2 signals as two separatesubcomponents, B2-a and B2-c, respectively. The dichotomy seems clear-cut ÐB2-a is Clÿ-dependent but B2-c is not (except for the non-speci®c ionic strengthe�ect). That B2-a and B2-c may be generated by two fundamentally di�erentmechanisms is further suggested by the observation that B2-a and B2-c can beabolished selectively and independently, either by point mutation or by chemicalinhibitors (Sections 10.7±10.9). There seems little doubt that, in the absence ofClÿ, there is no cytoplasmic interfacial proton transfer at low pH. Super®cially,this observation favors the interfacial Clÿ transfer mechanism. This interpretationis also in line with the interpretation that bR pumps Clÿ instead of H+ at lowpH. However, the possibility that the Clÿ-dependence of B2-a re¯ects modulationof interfacial proton transfer by Clÿ cannot be ruled out.

While exactly how Clÿ a�ects the generation of B2-a signal cannot beascertained from photoelectric measurement alone, some mutant studies suggestthe following. As mentioned above, acid blue bR does not pump protons and thedecay of the excited state of retinal is prolonged [350]. Logunov et al. [351] foundthat Clÿ catalyzes the retinal photoisomerization process of acid purple bR andsome bR mutants. They concluded that the bound Clÿ compensates for the loss ofthe negative charges of the carboxylic group of D85 and/or D212 caused either byneutralization at low pH or by residue replacement in D85N and D212N mutants.Our observation of the reversal of the Clÿ e�ect on B2, by the subsequentaddition of DIDS or SITS, can thus be interpreted as the prevention of criticalClÿ binding.

It is instructive to compare the e�ect of halide ions and concomitantlyadministered DIDS or SITS on hR. DIDS and SITS are potent inhibitors of theerythrocyte anion transporters [352±354]. They act by binding, with a 1:1-stoichiometry, to the transmembrane domain of band 3 protein of the erythrocyte.Halorhodopsin has also been shown to transport bromide (Brÿ) and iodide (Iÿ)ions [355], but iodide is transported less e�ciently than Brÿ and Clÿ. Schobertand Lanyi [356] suggested that two Clÿ-binding sites exist in hR. In an attempt todetermine these Clÿ-binding sites, they added several inhibitors of chloride iontransport to reconstituted hR membranes. However, they found no e�ect of DIDSand SITS on Clÿ transport in reconstituted hR membranes. The only inhibitorsthat have any e�ect at all were certain alkanoic acid derivatives known as MK-196 and MK-473. These compounds have an inhibitory e�ect on chloride ion


transport. In assuming that bR has a transport mechanism for Clÿ similar to thatof hR, it would be reasonable to suspect that bR also transports Brÿ and Iÿ

under similar conditions. However, the absence of any observed Iÿ e�ect ininducing the B2-a component casts some doubt on whether our observation isrelevant to Clÿ pumping.

Although no de®nite conclusions about the molecular mechanism of Clÿ

dependence of the B2-a component can be made presently, our results corroboratethe prevailing view that bR pumps Clÿ instead of protons at low pH. Thus, bRand hR may actually have a common motif for ion transport [334]. The pair ofretinal proteins provide another example of the economy of Nature's design e�ortÐ a theme which recurs in Sections 14, 15 and 18.

17. Correlation between electrical and optical responses

A signi®cant portion of our current knowledge about bR has been derived fromspectroscopic studies of the photocycle kinetics. The present bioelectrochemicalanalysis of the AC photoelectric relaxation thus presents an independentdescription of the photochemical relaxation of bR. In contrast, the mainstreamapproach decomposes the transient photoelectric signal in several exponential

Table 9

Electrical and spectral relaxation of bacteriorhodopsin membrane (reproduced from Ref. [135])

Source t1 (ms) t2 (ms) t3 (ms) t4 (ms) t5 (ms)

Keszthelyi and Ormos [259]

Electricala 4.4 81 2.5 8.0

A408a 81 7.9

A522a 3.7 91 8.5

A635a 2.2 9.2

DeÂ r et al. [192]

Electricalb 25 150 2.4 5.8

A403b 28 73 6.2

A638b 2.3 6.6

Electricalc 30 89 3.4

A403c 40 3.2 72

A638c 1.8 2.9 84

Drachev et al. [168]

Electrical < 0.2 15±70 10.5 (3.6, 11)d 1000

A412e 14, 68 3 (1.1, 3.2)d

A640e 5±10

a Purple membrane in distilled water oriented by an electric ®eld.b Purple membrane in distilled water oriented by an electric ®eld and immobilized in gel.c Purple membrane in 100 mM KCl oriented by an electric ®eld and immobilized in gel.d Computer-resolved time constants.e Measured from an aqueous suspension of purple membrane.


terms and then constructs an ad hoc kinetic model to describe the process.Interpretation of data in terms of this kind of ad hoc model often relies heavily oncorrelation of the photoelectric data with the photocycle data. Thus, the validityof interpretation of the AC photoelectric e�ect depends on the validity ofinterpretation of photocycle data. Each time, the photocycle underwent anoverhaul, it was necessary to revise the photoelectric interpretation. Just howreliable is the correlation between electrical and optical responses? An examinationof data compiled in Table 9 reveals a serious problem.

In Table 9, both the electrical and the optical relaxation data of bR membranesfrom three laboratories are compiled. Both Keszthelyi and Ormos [259], and DeÂ ret al. [192] regarded their optical data to be in good agreement with their ownelectrical data. On the other hand, Drachev et al. [168] reported that spectralrelaxation at 412 nm seems to be faster than its electrical counterpart.Comparison of these data shows that data from di�erent laboratories are not ingood agreement, whereas the agreement between electrical data and optical dataseems to be better, as long as both sets of data are from the same laboratory. Inother words, the optical data show a variability that is correlated with that of theelectrical data. A simple explanation for this strange phenomenon is presentedbelow.

We have shown in Section 11.4 that the discrepancy in the electrical relaxationdata, reported by various laboratories, is a consequence of the di�erence in themeasurement conditions and/or the di�erence in the structure of modelmembranes. The variation in the electrical relaxation may in turn a�ect thephotocycle relaxation by virtue of charge-conformation interactions (see Section10.13.4).

Although some electrical measurements in Table 9 were reported in terms ofphotocurrents, they were not carried out under strictly short-circuit conditions (seeSection 11.2). Therefore, the transmembrane potential showed a transient change,which has exactly the same time course as the measured photocurrent for thefollowing reason. Because the membrane potential equals the voltage drop (whichis equal to the product of current and resistance) across the access impedance, andthe access impedance may be fairly constant over the time range of interest, thispotential is proportional to the photocurrent. In other words, the variable portionof electric ®eld to which bR is exposed is proportional to the photocurrent.Therefore, it is likely that the spectral relaxation of the photointermediate merelyfollows the time course of the apparent electrical relaxation.

The e�ect of the transmembrane electric ®eld on photokinetic processes of bRhas been demonstrated by Tsuji and Neumann [357], who observed electric-®eld-induced structural and spectral changes in a bR membrane. Drachev et al.[168,358] also found that the electric ®eld, generated by light under open-circuitconditions, induced a change in spectral relaxation, and were forced to shunt themembrane with ionophores, in order to eliminate this electric-®eld dependence andfacilitate a (locally, but not globally) consistent interpretation of their data.

In addition to the externally applied electric ®eld, there exist internal electric®elds associated with the membrane surface potentials. Stationary surface


potentials arise from the predominantly negative charges of the phospholipid headgroups [359,360]. Additional surface charges are generated upon ¯ash lightstimulation, because of the protonation/deprotonation at the exposed region ofbR, giving rise to light-dependent surface potentials associated with the B2 andthe B2 ' components. The existence of such a variable surface potential has beendemonstrated in the purple membranes by Tokutomi et al. [361], Carmeli et al.[362], and Ehrenberg and Berezin [363]. Here, we further point out that theincrease of the surface potential at the intracellular interface (protonation) and thedecrease of the surface potential at the extracellular interface (deprotonation)combine to generate an additional electric ®eld across the membrane, which is notreadily detectable by conventional electrical measurements [249,364]. This internalelectric ®eld can lead to conformational changes of bR, thus a�ecting the bRphotocycle [362,365,366]. This latter possibility has an important implication tothe interpretation of salt and pH-induced changes in the electrical and opticalsignals of bR membranes, as discussed in detail in Section 10.13.4.

It has been reported that the bR chromophore undergoes two major shifts ofabsorption spectrum between pH 0 and 7 [1,367±369]. At pH above 3, bR exhibitsan intense purple color in the ground state. Between pH 3 and 1, the purplemembrane turns blue (known as the blue form; absorption maximum shifting to605 nm; pKa � 2:9), and the purple membrane no longer pumps protons. BelowpH 1, the blue form again turns to purple (known as acid purple; absorptionmaximum shifting back to 565 nm; pKa � 0:5). Acid purple has been treated as anew species that is di�erent from the native one [370]. It also does not pumpprotons [189]. Muccio and Cassim [371] indicated that the acid-induced change israther localized and involves only minor changes in the membrane tertiarystructure, localized near the retinyl chromophore with no secondary structureinvolvement. Their data showed no change in the membrane crystalline structure.

Our photoelectric data show that the pH-induced change is indeed highlylocalized and is largely con®ned to the exposed region of the bR molecule. The B1component, which re¯ects internal charge separation, remains totally unalteredfrom pH 0 to 11. The pH-induced changes are limited to the B2 and the B2 'components, which re¯ect processes of surface protonation and deprotonation,respectively. Thus, from an electrochemical point of view, bR is largely unalteredover this wide range of pH. The pH-induced spectral shift is secondary to thelocalized conformational change due to proton binding. This view is shared byBakker-Grunwald and Hess [372], who interpreted the observed e�ect ofpolyelectrolytes as changes in local surface potentials. It is also consistent with theconclusion that the chromophore is in¯uenced by nearby ionizable groups [371](cf. Refs. [373,374,375]). Such a localized conformational change has also beeninvoked to explain the observation that the blue form can be induced at neutralpH by low concentrations of sodium dodecyl sulfate [376]. A similar mechanismmay also be involved in the inhibition by water-soluble carbodiimides of the acid-induced blue transition in the purple membrane [377,378]. The validity ofconsidering a localized conformational change is not limited to pH-inducedchanges of the absorption spectrum. Our analysis of the AC photoelectric signal


showed that B2 is vulnerable to prolonged drying and to ¯uorescamine treatment,but not the B1 component. In addition, the B2 component is sensitive to changesof the electrolyte composition, whereas the B1 component is not.

A discussion of the salt e�ect on the absorption spectrum of bR is relevanthere. The blue transition of the purple membrane can also be induced bydeionization, implemented either by repeated washing of the purple membraneswith distilled water [379] or by the addition of EDTA [365]. The subsequentaddition of a small amount of divalent cations or large amounts of monovalentcations can restore the purple color. Ca2+ and Mg2+ are thus suspected to beresponsible for the purple color. Corcoran et al. [380] suggested that more thanone metal cation may be involved in the Schi�-base deprotonation. Speci®cbinding of metal cations to bR is proposed to explain the observations [381,382].El-Sayed and coworkers [383±385] have shown that Ca2+-binding sites are dividedinto three classes. Most of the low-a�nity binding sites of Ca2+ in bR are surfacesites [384], whereas the two strong binding sites seem to interact with the aminoacids within the retinal-binding pocket of bR [385]. They also found that thestrong Ca2+-binding sites are localized within the protein monomer unit, and notbetween the molecules within the trimeric structure. More recently, Tuzi et al.[386] investigated the high-a�nity cation-binding sites of bR by means of solid-state 13C-NMR spectroscopy, and found similar spectra for two kinds of bluemembranes: (a) deionized membranes at pH 4 and (b) acid blue membrane at pH1.2. They concluded that there are high-a�nity cation-binding sites on both theextracellular and intracellular regions (surfaces) of bR. In addition, one of thepreferred cation-binding sites is located at the loop between the helix F and Gnear residue Ala 196. Furthermore, the bound cations undergo rapid exchange (lifetime shorter than 3 ms) among various types of cation-binding sites.

Chang et al. [365] have considered three possible mechanisms of the bluetransition: (a) the e�ect of divalent cations in reducing the negative surfacepotential, (b) binding of divalent cations to speci®c sites, and (c) conformation-dependent chelation similar to the mode of action of calmodulin. The surface-charge density (and hence the surface potential) is a�ected by divalent-cationbinding. Removal of the divalent cations enhances the negative surface potentialand hence increases the local (surface) concentration of protons near themembrane surface, thus leading to the protonation of critical carboxyl groups athigher pH than in the native purple membrane.

Kimura et al. [379] reported that high salt concentration lowers the pKa of theblue form conversion, and that deionization induces a blue form that isindistinguishable from that induced by low pH. They further showed that theobservation is consistent with the charge screening e�ect, since the native purplemembrane carries negative surface charges.

Szundi and Stoeckenius [370,387] found that partially delipidated purplemembrane could undergo the blue transition by acid titration, but not bydeionization, and argued that the blue transition is controlled by the protonconcentration only and does not require the presence of other cations.Furthermore, extraction of lipids from deionized native membranes converts their


color from blue to purple. The e�ect of divalent cations is implemented indirectlythrough their e�ect on the surface-charge density of lipids.

Here, we must point out that charge screening has a two-fold e�ect on the pH-induced localized conformational change during a transient photoelectric response.Charge screening, due to high salt concentration, ®rst alters the surface potentialarising from existing membrane surface charges. The surface potential, in turn,alters the interfacial pH. As a consequence, the rate of proton uptake and its backreaction may be altered by virtue of the law of mass action. In addition, the pKa

of the proton-binding site may also change. These e�ects, in turn, a�ect the rateof development of additional surface potential caused by proton binding. All theseevents have an impact on the localized conformational state, and thus mayin¯uence the transient absorption spectrum of bR. This kinetic complexity mayhave contributed to additional di�culty in the analysis of some spectral data.

By treatment with halides, the acidi®ed blue membrane may also be restored toa purple form [369], which appears to be almost identical to the neutral pH-purpleform [388]. Renthal et al. [389] investigated this blue-to-purple transition bystudying the Clÿ e�ect at low pH. They tested several surface charge models, butcould not ®nd reasonable agreement unless unrealistically large numbers oftitratable groups near pH 0 are assumed. Their data are in agreement with amodel proposed by Braiman et al. [390], in which protonation of tyrosinate 185and aspartate 212 as well as Clÿ binding to arginine 82 are invoked. A moredetailed discussion about the halide e�ect on bR at low pH is presented in Section16.

Photoelectric studies of the acid-blue and acid-purple forms of bR have beenreported by Moltke and Heyn [391]. Using the conventional analysis of thephotoelectric signal, these authors have concluded that there is no net chargetransfer in the acid-blue and acid-purple forms. Liu et al. [24,25] have previouslystudied the e�ects of various bu�ers on the photoelectric signals. Their workincludes the cations and anions being analyzed in Section 10. But the di�erence inmethodology and interpretation sets the present report apart from those whichfollow the mainstream approach. The multiple e�ect of pH and cations on thepurple membrane has been reviewed by Jonas et al. [392].

The e�ect of local reaction conditions on heterogeneous reactions in the purplemembrane also has a signi®cant impact on the conventional use of transientabsorption spectra of aqueous suspensions as a means of identifying thephotointermediates. In the above discussion, the spectral properties of bR weretreated as functions of protonation state of proton-binding groups. In an intactmembrane, proton-binding groups are subject to di�erent conditions at the twomembrane surfaces. Therefore, the relaxation of transient absorption spectrummay depend on pH values of both aqueous phases, i.e., two independent pHvariables instead of just one. Thus, depending on the pH di�erence at the twomembrane surfaces, protonation/deprotonation and the resulting surface potentialsmay follow two separate relaxation time courses. At the same time, it is possiblethat the associated absorption spectrum may also have two distinct decay timeconstants, owing to the possible dependence on local electric ®elds at both


surfaces. This peculiar e�ect may also appear with regard to other localconditions, such as ionic strength, salt composition, and presence ofpharmacological agents, etc. Without taking into account the above-indicatede�ects, di�culties may arise, when data obtained from intact membranes arecompared with data obtained from broken membrane fragments in bulk phases.

Although there is validity in using ¯ash photolysis data to assign reactionintermediates, assigning two distinct intermediates, solely because of the presenceof two distinct decay time constants, can sometimes be misleading. Furthermore,it may become impossible to consistently explain a group of data, if one fails torealize the presence of two independent experimental variables (one for each sideof the two aqueous phases). In this regard, we suspect that some complex schemesproposed for the bR photocycle may not be necessary or justi®able. This problemwas discussed by Hessling et al. [393] in their proposed factor analysis andalternative method of spectral decomposition.

The possibility of chemical decoupling also has an important implication to theinterpretation of ¯ash photolysis data of bR. Since a true photostationary state ofcharge movement may not be achieved during a transient ¯ash excitation, perhapsone should not be surprised to ®nd that a later intermediate (e.g., O intermediate)could rise faster than the decay of its precursor (e.g., M intermediate) undercertain conditions. Thus, stoichiometry (ratio of proton pumped and photonsabsorbed) bears a very di�erent meaning in a transient analysis than in a steady-state analysis. In order to avoid confusion, the molecular step to which thestoichiometry is associated must be speci®ed.

In summary, photoreactions of bR in an intact membrane present a peculiarsituation in which the rules derived from solution phase photochemistry may notbe applicable. Particularly important is the e�ect of local electric ®elds generatedby photoreactions themselves. Contrary to common belief, these local electric®elds persist, even in broken membrane preparations. As stipulated by a fairlygeneral formulation of charge-conformation interactions, the interactions betweenphotochemical reactions and local electric ®eld generation in¯uence each other ina feedback manner (cf. Section 10.13.4). In other words, neither factors can betreated as independent variables. The ensuing nonlinearity should not beoverlooked, when complex reactions schemes are being contemplated. Thiscaution applies both to photoelectric and spectroscopic data.

18. Retinal protein research and arti®cial solar-energy conversion

For a number of years since the discovery of bR, applied research of bR hasbeen pursued by investigators devoted to the investigation of arti®cial solar-energyconversion. That a reconstituted bR membrane or thin ®lm respond toillumination as a photovoltaic device has been amply demonstrated by manyinvestigators. Considerable e�orts have been devoted recently to the elucidation ofthe proton-translocating path. Here, we shall discuss the electrical characteristicsof the bR membrane that are relevant for a solar cell.


A bR membrane or thin ®lm has sometimes been described as a photodiode.However, our experimental result described in Section 12 indicates that theproton-translocating channel is not recti®ed; the current driven by the appliedvoltage encounters the same resistance in either direction during illumination, i.e.,bR is not a photodiode in the strict sense (Fig. 85). The notion that the photoemfand the applied transmembrane voltage are interchangeable for driving atransmembrane proton current is, however, consistent with the basic principle ofbioenergetics.

According to chemiosmotic theory [9,10,11], the converted energy by bR

Fig. 85. Schematic diagram comparing recti®cation in conventional photodiode and step-function

photoswitching in bR. Plus and minus signs indicate polarity of photovoltage under open-circuit

conditions. Gf and Gr are forward conductance and reverse conductance of photodiode, respectively.

Photoactivation causes photocurrent to ¯ow in forward direction, as indicated. Elicited photovoltage

back-biases photodiode (under open-circuit conditions), and drives current in reverse direction during

illumination, thus canceling part of (forward) photocurrent. But reverse current encounters much

greater resistance than forward current (recti®cation: Gr � Gf ). In photodiode, charge recombination in

dark is minimized because of recti®cation. There is no recti®cation in bR; forward photocurrent (driven

by light) and reverse current (driven by back-biasing voltage) encounter same resistance (1=Gp). Note

that externally observed photocurrent is actually di�erence (algebraic sum) of voltage-independent

light-driven current and voltage-driven (and, therefore, voltage-dependent) current. Constancy of

measured true photoemf, as membrane potential varies, indicates that illuminated bR's ability to

maintain net `driving force' is not a�ected by back-biasing. In bR, charge recombination in dark is

minimized because of step-function photoswitching (Gp � 0 in dark)


photoreaction is stored as a transmembrane electrochemical gradient of protons.Furthermore, both the electrical component (DV) and the chemical component(DpH) of this gradient are equivalent and are both available for ATP synthesis.Thus, our photoelectric data provide a quantitative demonstration that the twoparts of electrochemical energy are interchangeable bioenergetically.Metaphorically, the process is tantamount to equal currency exchange ratesregardless of buying or selling. Were there a recti®cation, the interconversionwould not be equal, because the IR drop would be more in the back-biasingdirection than in the forward-biasing direction (di�erence between buying andselling rates in currency exchange).

Recti®cation is an important property of a photodiode to minimize energy lossdue to charge recombination; the resistance which the photocurrent encountersduring (internal) charge recombination is much higher than the forward resistanceduring charge separation. As for achieving a good energy conversion e�ciency,bR apparently relies on a di�erent strategy than recti®cation. We argue here thatstep-function photoswitching allows bR to prevent wasteful dissipation of convertedenergy, in the absence of illumination.

The generation of a transmembrane proton gradient is the intermediate stepbetween photon energy conversion and bioenergetic synthesis of ATP. Theformation of the transmembrane electrical gradient (i.e., the photovoltage)constitutes a situation similar to back-biasing of a photodiode. Back-biasingprovides the driving force to drive protons back into the cell.3 In principle, thereare several ways the electrochemical potential can drive protons back to thecytoplasm: (a) protons re-entering the cell via a reverse proton ¯ow through thesame proton-translocating channel in bR, (b) protons or other small ions re-entering the cell via leakage through the phospholipid portion of the purplemembrane, and thus dissipating the converted energy, (c) protons re-entering thecell via the proton-transport channel of ATP synthetase (in the reverse direction),thus synthesizing ATP, (d) protons re-entering the cell via the ¯agella motorapparatus, and thus powering the motion of the ¯agellas, and (e) protons re-entering the cell to power a co-transport system (symport or antiport). The ®rsttwo possibilities would lead to wasteful dissipation of the converted energy. Theyare prevented (or minimized) in the purple membrane by step-functionphotoswitching (in the dark) and by having a relatively small area of phospholipidportion in the two-dimensional crystalline structure of the purple membrane [52].In the reconstituted bR BLM, Gp in the dark is considerably smaller than Gm.This property means that the insulation against a proton back¯ow, in the dark,via the proton-translocating channel is much more e�ective than the insulation ofphospholipid portion of the arti®cial BLM. Quantitative comparison of Gp andGm in a native purple membrane is not available. But we think that the ratioGp=Gm during illumination should be much greater in the native purple membrane

3 Strictly speaking, the proton back¯ow is driven both by the electrical component and by the chemi-

cal component, of the electrochemical potential.


than in our experimental system, because reconstitution in our experimentalsystem could not have achieved the same high density of bR packing as in thenative purple membrane.

From a mechanistic point of view, recti®cation in a photodiode is moreimportant in the dark than during illumination. While light-induced chargeseparation encounters the forward resistance (1=Gf in Fig. 85), chargerecombination during illumination and in the dark encounters a much higherresistance (1=Gr in Fig. 85). The bR data indicate that photon energy conversionis still possible without recti®cation. The lack of recti®cation in the purplemembrane may be the consequence of the universal presence of reverse reactionsin the scheme of coupled consecutive charge-transfer reactions (Figs. 50 and 80).How net forward charge transfers are still possible, in spite of the lack ofrecti®cation, is discussed in Section 14.2. Thus, by means of step-functionphotoswitching, bR achieves the same goal (in the dark, at least) as does a siliconphotodiode by means of recti®cation.

We further suspect that the step-function photoswitching mechanism of thelight-dependent electron-transfer channel may also be present in a chlorophyll-based photosynthetic membrane. As shown in Fig. 62, the asymmetrical transientcurrent spikes that appear upon the onset and the cessation of illumination of agiant chloroplast from Peperomia metallica [283] suggest that the electron-conduction path in the photosynthetic reaction center may also be activated onlyby light, thus preventing electron back¯ow in the dark. Evidence from directelectrical measurement of Gp (as compared to Gm) is presently lacking. But, if thisinterpretation is correct, then it appears that Nature has implemented the samedesign principle by using completely di�erent molecular constructs (cf. Sections14±16).

19. Retinal protein research and molecular electronics

In recent decades, retinal protein research has taken a new turn. Thedevelopment of `Biochrom' ®lms by Vsevolodov and co-workers [394±398] inPushchino, Russia, marked the advent of bR as an advanced material ininformation technology. These investigators took advantage of the photochromicproperty of bR to construct an imaging device. As mentioned earlier, illuminationof bR with yellow or orange light converts it from a purple-colored material to ayellow-colored one (blue-absorbing M state). Vsevolodov and coworkerssubstituted the chromophore of bR with a synthetic analog of vitamin A and wereable to alter the photocycle kinetics and prolong the lifetime of the M state. Thismodi®ed bR was used to construct an imaging device that can record an imagethat lasts for minutes. The image can be erased by illuminating the device withblue light. In addition, by treating the exposed Biochrom ®lm withhydroxylamine, the image can be retained inde®nitely. Whether being used as atransient imager or as a micro®lm, Biochrom ®lms exhibit superb quality in termsof cyclicity, resolution, etc.


Another landmark achievement was made by Hampp et al. [399±401], whenthey constructed a dynamic holographic ®lm (both transmission- and re¯ection-type), using a genetic mutant of bR in which the aspartate at residue 96 wasreplaced with asparagine (D96N ). The bR ®lm can be con®gured for holographicinterferometry or for holographic pattern recognition. The versatility o�ered bybR, in conjunction with genetic engineering technology, is presently exceedingmost synthetic organic photonic materials.

19.1. Bacteriorhodopsin as advanced material

Proteins have traditionally been perceived as being fragile owing to theirvulnerability to denaturation. Bacteriorhodopsin is a notable exception. Thepopularity of bR as an advanced material for device construction is due to itsthermal and chemical stability. The relatively high temperature of the naturalhabitat of H. salinarium confers an unusual heat-resistance (808C). Rothschild andcoworkers [402] have demonstrated that bR, when con®gured in a thin ®lm, canwithstand temperature as high as 1408C. Bacteriorhodopsin is also resistant toacidic pH. We routinely carried out electrical measurements at pH as low as 0.The resistance to denaturation by acidic conditions is also enhanced bycon®guring D212N in a thin ®lm [403]. Data from the mutant D212N shown inFig. 86 is an example. D212N is considerably less stable than the wild-type bR.While wild-type bR in an aqueous suspension can survive pH as low as 3 formany months, D212N mutant denatures in less than three days under the samecondition. Yet, a TM ®lm reconstituted from D212N continued to exhibit an ACphotoelectric signal for nine consecutive days, while the pH of the aqueous phasewas maintained between 0.5 and 0.9. The reason for this thin-®lm enhancedstability is not known.

Another reason accounting for bR's popularity is its versatility for deviceconstruction. The versatility of biomaterials is illustrated by the concept ofintelligent materials.

19.2. Concept of intelligent materials

In a workshop sponsored by the US Army Research O�ce on Smart Materials,Structures and Mathematical Issues [404], the concept of smart materials wasproposed to usher in a research e�ort to embed functional materials (such assensors and actuators) in conventional structural materials in order to impart thematerials with self-regulatory properties. The concept of intelligent materials is thedescendant of the concept of smart materials, as applied to functional molecularmaterials. Japanese investigators further extended the concept to its extreme, bydemanding that the intelligent materials include sensor, processor, and actuatorfunctions, all residing in a single molecule. According the Science and TechnologyAgency of Japan, intelligent materials are `substances/materials with the ability torespond to environmental conditions intelligently and manifest their functions'


[405]. We shall illustrate the concept of intelligent materials using bR as anexample.

Consider again the di�erential experiment (Section 10.13). We interpret the dataas a consequence of pH-dependent binding constant of proton-binding sites at themembrane surfaces. While the detailed mechanism is not known, its physiologicalsigni®cance is clear in reference to the minimalist model shown in Fig. 50. Forexample, decreasing extracellular pH and increasing intracellular pH caused byproton pumping will eventually reduce the throughput rate of forward protontransfer, if the proton binding constant is pH-independent (i.e., pKa is pH-independent). However, if the pKa of the extracellular proton-binding group isalso decreased at low pH, the equilibrium will be shifted in favor of forwardproton transfer (i.e., proton release) in competition with charge recombination(proton binding). Similarly, the increase of pKa of the intracellular proton bindingsite at high pH will favor further intracellular proton binding. Thus, in spite ofthe `back (proton) pressure', which appears as a result of proton pumping, theinterfacial proton-transfer steps do not become rate-limiting prematurely and thepumping e�ciency is signi®cantly enhanced, as compared to the minimalist model.This is reminiscent of the cooperative e�ect exhibited by the sigmoid-shapedoxygen binding of hemoglobin mentioned in Section 10.13. In apparent de®ance

Fig. 86. Photocurrents from TM ®lm of D212N, maintained at pH between 0.5 and 0.9, over period of

nine days. Signals are shown without normalization (A), and with normalization to positive peaks (B).



of Le ChaÃ telier's principle, oxygent binding is actually enhanced as more andmore oxygen molecules are bound to hemoglobin: the sigmoid-shaped oxygenbinding curve of hemoglobin thus allows more oxygen to be bound in the lung,where the oxygen tension is high, and allows more oxygen to be released in thetissue, where oxygen tension is low, i.e., the oxygen-binding constant is oxygen-dependent.

The oxygen-binding curve of hemoglobin also undergoes pH-dependent shift(Bohr e�ect ). In the tissue, where pH is low, the oxygen-binding curve shifts tothe right, causing more oxygen to be released than if there were no such a shift.Conversely, in the lung, where pH is high, the shift in the opposite directionallows for more oxygen to be bound to hemoglobin than otherwise. The Bohre�ect allows the performance of hemoglobin to be enhanced beyond what isexpected of a system without the e�ect. This feature of providing extraperformance is the hallmark of intelligent materials.

Now consider the model of coupled consecutive proton-transfer reactions again(Fig. 50). The minimum requirement for the scheme to pump protons is that atleast one of the steps for proton transfer is initiated by light energy. Equilibrationon the basis of Le ChaÃ telier's principle will ensure the equilibrium to be shifted tothe right in the reactions preceding the Schi�-base deprotonation and in thereactions following that. It will work even in the presence of signi®cant reverseproton transfers. The pumping e�ciency can be further enhanced by the presenceof an irreversible step Ð the M1 to M2 transition (see Section 14.2) Ð and/ormore than one light-assisted step, as stipulated in Honig's model [230]).

In our discussion for establishing the concept of local reaction conditions, weinferred that at least one slow step exists between the surface-proton uptake orrelease and the initial light-driven charge separation during photoisomerization. Ifso, then either B2 or B2 ' or even both may be light-assisted. This is because theintervening slow step prevents propagation of chemical equilibrium from thehydrophobic center to the surface proton-binding (or proton-releasing) group.

The enhanced performance of bR as a proton pump is also re¯ected in its DCphotoelectric e�ect, which essentially re¯ects the throughput rate of protonpumping, and hence its overall e�ciency. Thus, bR's `intelligence' lies in its step-function photoswitching capability, which minimizes energy dissipation indarkness (Sections 12 and 18).

Thus, bR is actually more intelligent than the minimalist machine suggested bythe model of Fig. 50. It is apparent that bR acquired this extraordinaryintelligence through billions of years of evolution. However, we have pointed outthat material intelligence must be evaluated in the context of the intendedapplications [406]. Biomaterials, in general, and bR, in particular, are oftenutilized for purposes completely di�erent from Nature's original intent, asexempli®ed by Biochrom ®lms and dynamic holograms based on mutant D96N.Thus, bR may appear insu�ciently intelligent for these purposes, because Naturenever had our speci®c applications in mind. Modi®cations of the native moleculesare often called for. With the advent of modern genetic techniques [217,407±414],it is possibly to produce intelligent materials in the laboratory in a compressed


Fig. 87. Motion-sensitive sensor array based on AC photoelectric e�ect of bR. (A) Cross section of

photocell, formed by immobilizing bR on transparent electrode, is shown: 1, SnO2 transparent

conductive layer; 2, purple membrane LB ®lm (typically six to ten layers); 3, aqueous electrolyte gel

layer (200 mm thick); 4, Au layer (01000 AÊ ) as counter-electrode; 5, Te¯on ring space; 6, glass

substrate. (B) Indium tin oxide (ITO) electrode, patterned with 64 pixels for image-sensing, is shown.

Pixels of ITO (2.5 mm by 2.5 mm, 1000 AÊ thick transparent layer) were patterned as 2D array on glass

plate; each pixel had separate wire leading to four-edge terminals along sides, for interfacing with

ampli®er circuit. (C) Photocurrent, generated in each pixel by square-wave light pulse of about 200 ms

duration, is shown. Positive and negative spikes of `on' and `o�' responses, respectively, are

characteristic of response of high-pass RC ®lter to square-wave pulse of applied current (see also Fig.

24). (D) Photoresponses to step illumination exhibits di�erential responsivity. Amplitude of photosignal

transient is proportional to change of light intensity. (Reproduced from Refs. [211] (A, B, C) and [416]

(D))


time scale by forcibly providing bacteria (which constitute the expression system)with the desired assembly codes.

19.3. Molecular devices based on photoelectric e�ect of bR

In addition to the photochromic property, the photoelectric property of bR hasalso been exploited for device construction [415]. A prototype based on the ACphotoelectric property of bR was constructed by Miyasaka and co-workers[211,416] (Fig. 87). Their design consists of a two-dimensional array of 64 (8 � 8)square pixels (2.5 mm � 2.5 mm) on optically transparent indium tin oxide (ITO)electrodes (Fig. 87(A) and (B)). Each pixel has a separate wire (300 mm width)leading to the terminals aligned at four edges for connection with an externalparallel circuit for signal ampli®cation. The entire surface of the pixel-bearing sideof the ITO substrate is coated with an LB ®lm of purple membranes. A Te¯onring spacer (200 mm thick) is placed on the electrode so as to surround the pixel

Table 10

Pigment-containing membranes exhibiting di�erential responsivity (reproduced and modi®ed from Ref.

[420])

Reference Pigment source Reconstitution method

Miyasaka et al. [211] bR Thin ®lm on ITO electrode

Wang et al. [417] bR Thin ®lm on ITO electrode

Boyer et al. [421] bR Thin ®lm on ITO electrode

Robertson and Lukashev [419] bR Thin ®lm on ITO electrode

Robertson and Lukashev [419] bR mutant Thin ®lm on ITO electrode

Hermann and Ray®eld [185] bR Fused liposomes

Drachev et al. [254] bR Fused liposomes

Higgins et al. [266] bR Fused liposomes

Bamberg et al. [269] bR Fused liposomes

Mirsky et al. [274] bR Fused liposomes

Braun et al. [422] bR Fused liposomes

Drachev et al. [152,254] bR Mixed pm sheets

Bamberg et al. [182] bR Attached pm sheets

Seta et al. [267] bR Attached pm sheets

Fuller et al. [281] bR Attached pm sheets

Ullrich and Kuhn [423] Cyanine dye Black lipid membrane

Schadt [424] Vitamin A aldehyde Black lipid membrane

Schadt [424] Vitamin A acid Black lipid membrane

Drachev et al. [184] Rh. rubrum Attached chromatophore

Barsky et al. [285] Rh. rubrum Attached chromatophore

Drachev et al. [425] Rh. rubrum Fused liposomes

Packham et al. [284] Rh. sphaeroides Black lipid membrane

Ajiki et al. [426] Rps. viridis Thin ®lm on ITO electrode

Vredenberg and Bulychev [283] Peperomia metallica In vivo (patch clamp)

Bamberg et al. [296] hR Fused liposomes

Hegemann et al. [427] hR Fused liposomes

Bamberg et al. [343,428] hR Attached pm sheets


array, and the enclosed cavity is ®lled with a viscous electrolyte composed of 6%carboxymethylchitin and 1 M KCl (pH 7±8). A gold-coated glass plate that servesas a counter-electrode covers the electrolyte layer, and the outer joint of thesandwiched cell is shielded with an epoxy adhesive. These photosensor arrays arecapable of mobile image extraction and edge detection in real time.

The photocurrent from each pixel is converted to voltage by a separateampli®cation and display circuit that controls each pixel of a light-emitting diode(LED) display. A typical photocurrent output, in response to step illumination, isshown in Fig. 87(C). A positive and a negative spike of photocurrent appears withthe onset and the cessation of illumination, respectively. The waveform of thephotocurrent response is characteristic of a high-pass RC ®lter as explained inSection 9.3 (see also Fig. 24). Within the operating range of illuminating light, thepeak photocurrent amplitude is a linear function of the intensity (Fig. 87(D); seealso Ref. [417]). The sensor array responds to multiple steps of illumination insuch a way that the transient photocurrent amplitude is proportional to thechange of the level of illumination instead of the level per se. This type ofresponse is referred to in the biosensor literature as di�erential responsivity[211,417]. The waveform showing di�erential responsivity is what is expected in ahigh-pass linear RC ®lter response. The linearity of the response, as demonstratedby using a multi-step light pulse, is also expected by a linear ®lter, such asrepresented by our equivalent circuit shown in Fig. 23.

The interpretation of di�erential responsivity is, however, controversial.Di�erential responsivity was ®rst demonstrated in a reconstituted bR membraneby Drachev et al. [151,152] (see Fig. 8(B)). They proposed a mechanism based onthe attachment of bR-containing vesicles to a planar BLM (referred as the buttonmodel in Section 11.1; see Fig. 52). Alternatively, both Koyama et al. [418] andwe interpret di�erential responsivity as the manifestation of light-induced chargedisplacement. A third interpretation was proposed more recently by Robertsonand Lukashev [419]. The latter investigators observed that a pH-dependent steady-state electric signal can be detected from an ITO electrode without attached bR®lms. They inferred that di�erential responsivity is caused by a light-induced localpH change on the ITO electrode surface. However, di�erential responsivity is notunique to bR thin ®lms associated with an ITO electrode, as indicated by datacompiled in Table 10 (see also Ref. [420] for detail).

The original observation of Drachev et al. [152,184,254] did not involve an ITOelectrode, nor did our own observation of di�erential responsivity in a bR-containing BLM (see Fig. 59(B)). In fact, di�erential responsivity appears in awide variety of pigment-containing membranes of either arti®cial or naturalorigin, such as BLMs that contain halorhodopsin [296,343], bacterial reactioncenter [284], cyanine dye [423], vitamin A acid or aldehyde [424]. It could even berecorded from a giant chloroplast by means of intracellular recording, i.e., underconditions devoid of an ITO electrode and adsorbed vesicles [283] (see Fig. 62(A)in Section 12.4.3). On the other hand, a photocell which is comprised of achromatophore ®lm (from Rhodopseudomonas viridis ) and an attached layer ofelectron mediator, sandwiched between two ITO electrodes, also exhibits


di�erential responsivity [426]. Here, photostimulation of the thin ®lm assemblyleads to changes of redox potential at the electrode surface instead of pH changes.Clearly, a local pH change on the ITO electrode surface is not a prerequisite fordi�erential responsivity.

What all these membranes have in common is light-induced charge separationand recombination in a pigment-containing membrane rather than the use of anITO electrode or the presence of attached vesicles on a planar BLM. Bycomparing photoresponses under pulsed and continuous wave laser excitations,El-Sayed and coworkers [429,430] identi®ed a B3 component of the ACphotosignal as the component responsible for the generation of spike. B3 is asignal slower than B1, B2, and B2 '. Presumably, the latter faster components aresuppressed by the low-pass RC ®lter, which is often used in conjunction with DCmeasurements. With regard to the consideration that is necessary in decidingamong competing hypotheses, an epistemological comment is given in Section 20(see also Ref. [420]).

Boyer et al. [421] have also exploited di�erential responsivity of bR and haveconstructed a color discriminatory photosensor. These investigators utilized areversible transformation of the native bR570 into a structurally and spectrallymodi®ed bR480 form, in the presence of the halogenated general anestheticen¯urane. Stimulation with light of two di�erent wavelengths, 570 and 480 nm,generates two similar transient photocurrents with reversed polarity. Thesephotosignals are reminiscent of the normal ERP and its photoreversal potential,respectively (Sections 5.4 and 13.1).

Both Trissl [431] and Ray®eld [432] have constructed an ultrafast photodiodefrom bR. That an oriented bR thin ®lm constitutes a photocell is apparent fromour equivalent circuit analysis. However, the claim that it is also a photodiode isnot evident (see Section 18).

Two additional prototypes utilized the AC photoelectric e�ect: an arti®cialneural network developed by Horonian and Lewis [433] and an arti®cial retinadeveloped by Birge and co-workers [434]. It is worth noting that both designsexploit the bR-analog of the photoreversal potential. In the design of the arti®cialneural network, patches of bR thin ®lms that are connected by a pair oforthogonal array of electrodes form the individual synapses in the neural network.The degree of conversion from the B570 state to the M state, and vice versa, areregarded as the synaptic strength. The signals being transmitted along the path ofthe network are the regular AC photoelectric signals, described in Section 10, andits photoreversal potential with an opposite polarity. The latter is generated byillumination of the M-state-enriched bR with blue light. Thus, the polarity of theAC photosignal transmitted in the neural network depends on the color ofinterrogating light beam, but the amplitude of the photocurrent depends of therelative proportion of the B570 state and the M state. Haronian and Lewisdemonstrated that it is possible to read the synapse without erasing its content.While the write scheme uses the B570 to M transition, the read scheme use ayellow beam to e�ect the K to L transition which is followed, with a brief delay,by a red beam to convert L back to K. Readers interested in the detail of how the


neural network operates to generate a truth table, unique to the layout, shouldconsult Haronian and Lewis' original paper [433].

In the design of an arti®cial retina, using bR as the light-sensing material, Birgeand co-workers [434] constructed a 256� 256 array of charge-sensitivesemiconductor elements (CID, charge-injection device array) with 15 mm spacingbetween the elements in both dimensions to monitor the AC photocurrent ofeither polarity. The passivation layer that is normally deposited on top of theseelements was replaced by a thin ®lm of bR in polyvinyl alcohol photographicgelatin. The array is then covered with a BK7 glass slide coated with ITO.Essentially, they use the x±y addressability of the CID array as a two-dimensionalspatial multiplexer to monitor the charge, deposited on the CID surface by thephoto-excited bR thin ®lm. In addition to an increased density, the array hasrandom access capability. Instead of using the LB technique, the latter design usesan applied electric ®eld to orient bR molecules, prior to ®xation in a polymericmatrix.

From the above discussion, it is evident that bR is a bifunctional electronicmaterial [415], which is sensitive both to light and to ions, such as H+, Clÿ, andCa2+. In the motion detector developed by Miyasaka et al., bR is con®gured as aphoton sensor. Alternatively, bR can be explored for its ion sensitivity. Tanabe etal. [435] con®gured bR as an ion-sensitive ®eld e�ect transistor (ISFET) for H+

sensing. Seki et al. [436] con®gured halorhodopsin as an ISFET sensor for thedetection of Clÿ, and demonstrated a linear relationship of the gate outputvoltage and the Clÿ concentration. The operation of these ISFET sensors dependson light for its action, since no ion sensitivity can be demonstrated in the absenceof light. In other words, these sensors are addressable with light. It is thuspossible to implement `multiplexing' in a sensor array, by sequentiallyinterrogating individual sensors with light. In these prototypes, the sensors wereaddressed with steady light. We suggest here the use of pulsed light to interrogatethese sensors, so as to gain the advantage of speed, as well as sensitivity; the ACphotoelectric e�ect of bR and hR possesses a picosecond risetime, and the ACsignal amplitude is at least two orders of magnitude greater than that of the DCphotosignal.

19.4. Reverse engineering and biomimetic science

The discussion, presented in Sections 14±16 and 18, highlights the insight thatcan be gained by reverse engineering Nature's photobiological membranes. Natureutilizes di�erent molecular materials to implement the same design principle, ascan be seen from a comparison of bR and the bacterial reaction center. Naturemay also cast the same molecular functionality for di�erent functional roles. Ifour hypothetical trigger mechanism for visual transduction turns out to be correct,it will serve as such an example; Nature casts the molecular functionality of light-induced proton binding either for photosynthesis or for vision. The photogatedion conductor designed by Drain et al. [279,332], based on the hypothetical triggermechanism of visual transduction, was an example of biomimetic science. It is an


unusual case that the principle is still pending veri®cation but the experimentalapplication has already worked.

Similarity between di�erent photobiological membranes highlights the essenceof the designs. Di�erence between them can also inspire new designs. The mostconspicuous absence in the bR system is the long-distance electron transfer,although the end result of both the purple membrane and the bacterial reactioncenter is the same: generation of a transmembrane proton gradient. Comparisonreveals the obviously important reactions involving quinone and quinoidcompounds. These compounds are characterized by concurrent electron- andproton-transfer reactions. A typical reaction is:

�19:1�

The quinoid compounds include menaquinone and ubiquinone, in the reactioncenter of purple phototropic bacteria, and plastoquinone, NADP+-oxidoreductase, and perhaps also water, in the chloroplast of green plants andcyanobacteria. In splitting water to form molecular oxygen, two protons and twoelectrons are extracted from water, rendering water marginally quali®ed to beclassi®ed as a quinoid compound. We have pointed out that a metal electrodecoated with oriented purple membrane is incapable of generating a DCphotocurrent for lack of an appropriate electrodic reaction. `Reverse-engineering'the photosynthetic apparatus and the quinoid compounds suggests that the abovereaction may be run backward, enabling a conversion of proton current, generatedby photo-excited bR, to electron current, suitable for transmission through themetal electrode to the outside world. That is, a suitably engineered quinoidcompound may be used to interface the bR-generated DC photocurrent to themetal electrode.


20. Philosophical digression

In the analysis of the AC photoelectric e�ect presented in Section 10, wehave abandoned the conventional practice of ®rst decomposing the measuredphotoelectric signal into a number of exponential components by means ofcurve ®tting and then interpreting each time constant as a true photochemical(and/or photoelectric) relaxation time constant (brie¯y referred to as exponentialanalysis ). Our alternative approach reverses the two steps and does not takethe directly measured time constants at their face value. However, byemphasizing mathematical modeling and downplaying direct exponential curve®tting, we have inadvertently helped create an impression that the mainstreamapproach and our alternative (bioelectrochemical) approach constitute a dualityof valid approaches, of which the choice is only a matter of convenience or amatter of taste. This is however an illusion generated by the following possiblefactors.

First, any one who utilizes exponential analysis to analyze an ACphotoelectric signal always succeeds in obtaining a set of exponential timeconstants. Second, the exponential time constants so obtained are in agreementwith those of the photocycle, albeit only crudely. This fortuitous agreement, forwhich we o�er a bioelectrochemical explanation (Section 17), gives itspractitioners a false sense of con®dence. The unsuspicious faith to such apractice is further reinforced by confusing a mathematical technique with amathematical or physical model. Exponential analysis is a mathematicaltechnique which maps the transient signal from the time domain to thefrequency domain, and is therefore tantamount to Laplace transform. Eachdiscrete time constant is represented as a discrete peak in the transformed(amplitude vs. frequency) curve (see Section 20.5).

Once the exponential time constants have been obtained, an ad hocequivalent circuit model is then constructed to quantitatively describe theexperimental data. The mainstream approach becomes problematic, when data,reported by di�erent laboratories, or reported by the same laboratory atdi�erent times and under di�erent conditions, are compared (cf. Tables 5, 9and 10, and Fig. 57; see Sections 11.4, 17 and 19.3). However, complexity ofbiology provides an easy escape route for dismissing the discrepancy as beingwithin an acceptable range of error. This latter explanation has seldom beenquestioned, in part because di�erent laboratories usually utilized di�erentreconstitution methods (and measurement conditions), leaving su�cient room toaccommodate the observed discrepancy. As explained in the analysis presentedin the bulk of this article, the two alternative approaches are incompatible andsometimes even led to diametrically opposite conclusions. Here, we shall take acritical look at the strength and weakness of both approaches. We shalldistinguish a numerical or mathematical model from a physical or molecularmodel. The relationship between experimental data, mathematical models(numerical or equivalent circuit models) and physical (or molecular) models areshown in Fig. 88.


20.1. Experimental data, mathematical models and physical models

It is important to point out that exponential analysis is utilized not only in themainstream approach but also in the bioelectrochemical approach. What sets thebioelectrochemical approach apart from the mainstream approach is thedecomposition of the AC photoelectric signal into several molecular componentsby physical means, prior to exponential analysis. In accordance with ourequivalent circuit, each component contains two exponential time constants. Theseexponential time constants together with several other directly measured electricparameters are then used as input parameters to compute the predicted signal timecourse, according to the equivalent circuit model shown in Fig. 23. The intrinsicphotochemical relaxation time constant can then be extracted by equivalent circuitanalysis (brie¯y referred to as deconvolution). Here, the equivalent circuit can beregarded as a mathematical model, of which the circuit elements (or parameters)may or may not be attached with physical meaning.

In contrast, the time constants obtained by exponential analysis in themainstream approach give rise to a numerical model directly, which is comprisedof a number of exponential functions, each of which describes the time course of aseparate component. But these components may not be related to separatechemical processes in a one-to-one correspondence. Almost without exception, theassociated equivalent circuit (mathematical model) contains only a singlecapacitance Ð the membrane capacitance.4 Of course, such a simple circuit isincapable of generating a multi-exponential signal waveform, if the photoemf istaken as a d-function (for pulsed light stimulation). The complex multi-exponential waveform of the photosignal must therefore be attributed to the

Fig. 88. Relationship between experimental data, numerical models, equivalent circuit models, and

physical models. Arrows indicate direction of `mapping' data to models with increasingly detailed

structure. Some steps may be bypassed, as indicated by dotted arrows (short cuts). Alternatively,

equivalent circuit model can be treated as numerical model with detailed structure.

4 The mainstream approach sometimes proposes an equivalent circuit similar to Model A of Fig. 58

to decribe both the AC and the DC photoelectric signals. But the validity of the latter equivalent circuit

model is often not rigorously scrutinized (see below).


photoemf per se, i.e., the photoemf becomes a multi-exponential function asdetermined by exponential analysis. That the validity of such an assumption ishighly questionable can be made apparent if one only makes an attempt toexamine the change of the measured signal waveform when the measurementcondition is switched from open- to short-circuit, or vice versa. Experimentally,such a maneuver generates data with a drastically di�erent relaxation time course,in which both amplitudes and relaxation kinetics are altered by short-circuiting.The e�ect of such a maneuver is shown in Fig. 9 for bR. Incidentally, similar dataof rhodopsin has been reported by Drachev et al. [257] (see Section 13.1.1). Theyfound a signi®cant change of both amplitudes and relaxation kinetics of R1 andR2 when the reconstituted rhodopsin membrane was shunted with an externalresistor (Fig. 72). What they did was tantamount to `tuning' the access impedanceand to convert an open-circuit measurement to one closer to short-circuit. It is nowonder that what they observed parallels what is evident in Fig. 9 for bR.

The same e�ect can also be ascertained by: (a) testing an equivalent circuitactually constructed from discrete electric components and using a programmablewaveform generator to simulate the multi-exponential waveform (or simplerwaveforms such as d-function), or (b) simply performing a computer simulation ofthe equivalent circuit. Either way, the investigator should be able to quickly ®ndout that the output-signal waveform does depend on the value of the accessimpedance, and a ®rst-derivative relationship, as reported by Trissl, cannot holdtrue (see Section 11.2).

The mainstream investigators have gradually realized the distortion e�ect of themembrane RC relaxation process and have begun to acknowledge the presence ofthe pure membrane RC time constant among the time constants determined byexponential analysis [26,27,437,438]. But they still have not fully appreciated theextent of distortion Ð just about every time constant is a�ected.5

Thus, the equivalent circuit associated with the numerical model derived directlyfrom exponential analysis must be considered ad hoc; each model is speci®callyconcocted for a speci®c measurement condition, but is incapable of predicting thechange of measured signal waveforms when the measurement conditions arevaried. Thus, the associated equivalent circuit usually does not even agree with thenumerical model obtained by exponential analysis.

The dramatic alteration of the relaxation time course, shown in Figs. 9 and 72,is not unique to the equivalent circuit with chemical capacitance. It is common toall circuits that contain one or more reactances in whatever con®guration,including those ad hoc circuits proposed by the practitioners of the mainstreamapproach. Revelation of such dependence will unmistakably warn investigatorsthat measured photoelectric relaxation data cannot be directly interpreted at theface value. The fact that the mainstream approach continues to enjoy its long-lasting popularity suggests that the practitioners of the mainstream approach have

5 The data of Drachev et al. [257], shown in Fig. 72, demonstrate the distortion e�ect of varying the

access impedance, but the data were treated as a mere isolated incident without explanation.


not bothered to check their proposed ad hoc equivalent circuit either by means ofan actually constructed analog electric circuit, by a computer simulation, or bysolving the relevant di�erential equations.

One of the reasons that persuades mainstream investigators to performexponential analysis of the data, prior to decomposing the photosignal into severalcomponents, is the concern about the possibility of introducing artifacts while thephotosignal is being decomposed into components by physical means. What theydid not realize is that, by recording the signal under open-circuit conditions, theyallowed the membrane RC relaxation process to distort the intrinsic photoelectricrelaxation process and, thus, inadvertently introduced artifacts. Data obtained bymeans of the tunable voltage-clamp method are not immune to such distortion.But the distortion can be undone by means of deconvolution. Open-circuit dataare technically much more di�cult to deconvolute, mainly because of the excessivedistortion caused by the membrane RC relaxation.

Let us now brie¯y recapitulate how the measured B1 signal is deconvoluted, asdescribed in detail in Section 10.2. Exponential analysis is ®rst applied to themeasured B1 signal. For reason explained in Section 9, the measured relaxationtime of a pure component such as B1 can always be ®tted with two exponentialtime constants (when the access impedance is not zero). Unlike the mainstreamapproach, the bioelectrochemical approach does not treat these time constants asintrinsic chemical relaxation time constants, but instead maps6 these data to amacroscopic mathematical equivalent circuit model, as shown in Fig. 23. Thismacroscopic model imposes a strict constraint on its own validity. Essentially, itpredicts the ratio of the two exponential terms found empirically by exponentialanalysis. Eqs. (9.13) and (9.16), which jointly specify the constraint on thephotosignal that represents a pure molecular component, can be regarded as thecorresponding numerical model. As explained in Section 9.2, there is no freeparameter that can be adjusted to `enforce' a ®t. In fact, a quantitative ®t can beachieved consistently under a variety of conditions, in which we, the experimenter,had no control to in¯uence the ®t. In other words, the numerical model and theequivalent circuit make a sharp prediction, as dictated by Eqs. (9.13) and (9.16).

In contrast, the mainstream approach does not propose a mathematical modelthat imposes constraints on the amplitude of each exponential terms (see alsoSection 20.5). This fact is often overlooked when the bioelectrochemical and themainstream approaches are compared.

In the bioelectrochemical approach, the macroscopic mathematical model takesthe form of an electric circuit. Physical meaning of these circuit elements wasestablished by virtue of two microscopic models (IPT and OD), from which themacroscopic model can be derived. In other words, the Gouy±Chapman andkinetic analysis presented in Section 8 allows us to map the macroscopic model totwo di�erent microscopic physical models. Thus, the correspondence between the

6 The term `map' used here carries the same meaning as understood in a representation theory, such

as linear algebra and group theory. It loosely means `correspond.'


macroscopic (mathematical) and microscopic (physical) models is not one-to-one.Furthermore, the two microscopic models, shown in Fig. 20, are not the only twothat correspond to the same macroscopic model, shown in Fig. 23. The buttonmodel of Drachev et al. [152,184] also corresponds to the same model. Thus, thesame macroscopic model actually represents all three microscopic physical modelsjust mentioned. While the button model bears no resemblance to the IPT modelor the OD model, all three models are featured with a capacitance that isconnected in series to the photocurrent source. The button model was eliminatedby virtue of internal contradiction (Section 11.1). A similar elimination process ledus to the tentative conclusion that the OD model is compatible with B1, whereasthe IPT model is compatible with B2 (see Section 10.10).

We could have used the standard method of exponential decomposition toobtain all the exponential terms ®rst, and then applied the equivalent circuitanalysis to the entire composite signal. But then an agreement between data andthe macroscopic model would not be as convincing, because decomposition of themolecular components would have been determined implicitly via curve ®tting,which requires adjusting of parameters.

20.2. Critique on concept of chemical capacitance

Since its inception in 1974, the concept of chemical capacitance has beencriticized as being the membrane capacitance in disguise (i.e., an algebraic artifact)or an experimental artifact [252,253]. In classical electrophysiology, there is oneand only one capacitance Ð the membrane capacitance. The bulk of experimentaldata obtained either in other laboratories or in our own repeatedly indicate the

Fig. 89. E�ect of varying illuminated membrane area on time course of photoelectric signal from ML

®lm of bR. Experimental conditions were similar to those in Fig. 25. Membrane was initially partially

illuminated (6%). Diameter of light beam was progressively increased from 6%, through 14%, 19%,

25%, 47%, 77% and, ®nally, 100%. Corresponding measured photoelectric signals were then

superimposed without normalization. Nearly perfect superposition of photosignals indicates that

photoresponses were in linear range in all measurements. (Reproduced from Ref. [205])


presence of two separate capacitances Ð one in series and another in parallel.However, Trissl continued to insist that the concept of chemical capacitance is anexperimental artifact. His main argument was based on an experimental practicewhich we adopted in the study of the Mg porphyrin BLM system. In our study ofthe latter system, the light beam was routinely focused on the thin bilayer regionof a BLM in order to avoid eliciting a photosignal from the thick Plateau±Gibbsborder of the BLM (cf. Fig. 69). Thus, the BLM was partitioned into anilluminated region and an unilluminated region. Trissl [252] argued that thepartitioning gives rise to the appearance of two separate (membrane) capacitances.In our study of the bR ML thin ®lms, there was no Plateau±Gibbs border and wewere free to illuminate the entire thin ®lm or a fraction of it. We found no changeof the apparent relaxation time course of the B1 component, when the illuminatedarea was varied stepwise from 6% to 100% (Fig. 89). The latter data weresubsequently criticized for the use of saturating intensity of stimulating light byTrissl [253] but he o�ered no explanation for the absence of variation of theobserved relaxation time course; Trissl's previous analysis expected such avariation. Furthermore, the photoelectric signal records shown in Fig. 89 can besuperimposed without normalization of their amplitude, indicating that themeasurements were actually carried out in the range of linear light response Ðnot in the saturating region, as claimed by Trissl. Apparently, our reportedintensity was inaccurate and so excessively high as to lead Trissl to believe thedata were generated by a saturating light pulse.

However, Trissl's criticism is not entirely without merits, because the measuredvalue of Cp is about 100 times lower than that predicted by Eqs. (8.22) and (8.28).In other works, our microscopic models failed to predict the measured value ofCp. The reason for this discrepancy will be discussed next.

Let us now examine the mathematical derivation of the concept of chemicalcapacitance (Section 8). The weakness of the derivation is inherited from theGouy±Chapman di�use double layer theory. There are a number of assumptionsthat form the cornerstones of the Gouy±Chapman theory: (a) the assumption ofsmear charges, (b) the assumption of the membrane surface as a mathematicalplane, (c) the assumption of uniform dielectric constants in the aqueous and themembrane phases, and discontinuity of the two dielectric constants at themembrane±water interface, and (d) the linearization in solving the Poisson±Boltzmann equations. In reality, these assumptions cannot be expected to holdtrue for the AC photoelectric e�ect under most experimental conditions. Anumber of reasons have been proposed to explain why the measured value of thechemical capacitance is so much smaller than the calculated value [31]. But we®nd it instructive to ask the opposite question: why does our macroscopicequivalent circuit model work so well in spite of the fact that it was derived underassumptions that deem unrealistic.

The essence of the AC photoelectric e�ect lies in the proclamation made byHagins and McGaughy [157]: the electric current associated with ERP satis®es thecondition of the zero time-integral (5.1). In other words, it is a capacitativecurrent. This notion has never been challenged amidst the controversy and thus


constitutes the only agreement between the mainstream approach and ourbioelectrochemical approach.

The immediate clue that led us to the concept of chemical capacitance was theempirically derived relationship (9.16). This equation indicates that the relaxationof the photosignal can be decomposed into two exponential terms of oppositepolarity; the ratio of the amplitudes equals the inverse of the ratio of the timeconstants. Geometrically, Eq. (9.16) implies that the area enclosed by the curveabove the baseline is equal to the area below the baseline. That is, the time-integral of the photocurrent eventually goes to zero. The equivalent circuit modelis a simple model that ful®lls this requirement and, at the same time, furnishes theexplanation as to why the relaxation of a ®rst-order or pseudo-®rst-order processleads to an apparent time course with two exponential decays. It is evident thatthe approximations and simpli®cation utilized in the derivation did not prevent itfrom capturing this essential feature. Instead, the approximations andsimpli®cation help suppress the concurrently distracting features and allow theessential feature to emerge.

An additional factor that also helps bring out the essential feature is thestrategy to separate the kinetic analysis from the electrical analysis. Since theelectrical events take place in time scales far removed from that of the chemicalevent, the electrical event in the aqueous phases can be handled by an electrostaticcalculation, and the electric ®eld inside the membrane can be regarded asconstant. In other words, the time dependence of the AC photoelectric event ishandled by chemical kinetic analysis, whereas the spatial dependence is handledby the electrostatic calculation. Without this simpli®cation, the computationalresult might become more accurate, but the physical picture would become moreobscure. As a consequence, the essential feature of the process may be lost in theintricacy of mathematical manipulations. In a short essay, with the title of`Simplicity and Transparence Ð Re¯ections of a Physical Chemist', Kuhnillustrated the same view with several personal examples [439].

The application of the Gouy±Chapman double layer theory allows theelectrostatic analysis to be cast in a three-capacitor model: a geometriccapacitance and two double-layer capacitances. The advantage of this formulationis the ready linkage between the microscopic molecular photoelectric event and themacroscopic electrical event. This link is crucial in establishing a macroscopicmodel with an unequivocal molecular interpretation. The three-capacitorformulation is fairly general in membrane biophysics. Everitt and Haydon [440]used it to describe the electrical capacitance (Cm in our present notation)quantitatively. Markin et al. [441,442] used it to quantitatively describe the directpassage of a hydrophobic ion, tetraphenyl borate, through a BLM (see also workof Ketterer et al. [443] and Andersen et al. [444]).

Why then did some practitioners of the mainstream approach ®nd conceptualdi�culty with the concept of chemical capacitance? The obvious reason seems tobe the unusual localization of the voltage source of the AC photoelectric e�ect(the photoemf Ep in our present notation) at the membrane surface or inside themembrane; the voltage sources in all other membrane systems, studied in the past,


are located outside of the membrane. A unifying view can be readily established ifone regards all these three-capacitor formulations as attempts to treat thephenomena of electrical polarization at and near the discontinuity of media, themembrane phase vs. the aqueous phase. In this regard, the AC photoelectric e�ectappears to be intimately related to the gating current for Na+ channels, recordedin giant axons of Loligo pealei [445,446].

The gating current is an externally measurable capacitative current associatedwith the charge displacement of the putative voltage sensor of the Na+ channelduring its opening and closing. It appears that the voltage source of the gatingcurrent also resides inside the membrane, i.e., the segment S4 of the Na+ channel[447,448]. It is assumed that the displacement of these charges are correlated withthe transition between di�erent channel states. The analysis of the gating currentprovides information about the voltage dependence of the channel states.Unfortunately, the detailed interpretation of such analysis is model-dependent,and re®nement of analysis often leads to an increasing number of conformationstates. The similarity between ERP (as well as the ERP-like signals) and the gatingcurrent suggests that the relaxation of the gating current may also be a�ected bythe measurement conditions, such as access impedance. The interpretation of thegating current analysis may be facilitated if the data are deconvoluted ®rst.

20.3. Tentative nature of physical models

We have debunked the mainstream approach by citing a number of apparentparadoxes and contradictions, of which the most serious one is the con¯ict withthe notion of the zero time-integral (Fig. 13). In contrast, the bioelectrochemicalapproach does not share this di�culty. But we avoid using the adjective `correct'to describe the bioelectrochemical approach, because all physical models andexplanations, no matter how attractive and elegant, are only tentative but notultimate. We do so, not because of modesty, but because of the sheer impossibilityto demonstrate the one-to-one correspondence between a model and the physicalreality. It is especially true if the model is a physical model instead of amathematical model. The interpretation of the button model of Drachev et al.(Fig. 15(B)) is a revealing example.

The button model correctly describes and explains the high-pass ®lter responseshown in Fig. 8. In essence, the button model leads to the same (mathematical)equivalent circuit model as do the two physical (microscopic) models shown inFig. 20 [184]. However, our two physical models are di�erent from each other. Inother words, the two physical models, representing drastically di�erent physicalreality, are consistent with the same abstract mathematical representation: anequivalent circuit with a series capacitance connected to the photoemf source. The`proof' or, more accurately, the tentative validation of a pre-conceived physicalmodel, can only be achieved by elimination of all possible alternatives [183]. Thisview is similar to that of a more general formulation, previously enunciated byAustrian-British philosopher Sir Karl Popper [449±451] in his attempt to resolvethe di�culty associated with the lack of a sound logical basis of Francis Bacon's


induction method (also known as Hume's problem).7 Here, our view can beregarded as a subset of Popper's formulation, as applied to physical models. Thesame view has subsequently be applied to numerical models by Oreskes et al.[452].

The main weakness of the button model is the internal contradiction describedin Section 11.1. An additional weakness of the button model is the lack of thedemonstration of quantitative agreement between the data and the model.

A more recent explanation of the high-pass ®lter feature proposed byRobertson and Lukashev [419] can be dismissed for its failure to explain mostdata reported in the literature except those measured with ITO electrodes (seeSection 19.3).

However, since we cannot prove that there exists no future alternative validexplanation, it is impossible for us to prove the `correctness' of our two physicalmodels. We thus have to be content with the tentative nature of a physical model.This attitude does not imply that we ought to be equally skeptical about everyphysical model. Rather, the credibility or plausibility of a physical model can beenhanced by its `track records' as time goes by: its ability to survive challengesand sophisticated experimental tests designed to reveal any serious ¯aws, and itsability to predict novel experimental phenomena. This point of view can beampli®ed by a Bayesian analysis to be described next.

20.4. Ockham's razor and Bayesian analysis

Ockham's razor serves as an implicit underpinning of science but has seldombeen explicitly cited. In traditional usages, Ockham's razor means: `amongcompeting hypotheses, favor the simplest', or `complexity must not be invokedwithout necessity'. In an article with a title identical to the present subsectionheading, Je�erys and Berger [453] applied the Bayesian method of statisticalanalysis to give Ockham's razor a quantitative evaluation and support. TheBayesian school views probability not as the conventional notion of frequency ofoccurrence of a certain event in an in®nite series of trials, but rather as the degreeof belief a certain event will occur in a single future trial. Thus, the Bayesiananalysis does not cast a hypothesis as being correct or incorrect but rather interms of the plausibility of a hypothesis. A Bayesian analysis thus assign a priorprobability to a hypothesis or physical model: P�HijI �, the probability thathypothesis Hi is correct given information I. As new data becomes available, thisprobability will be revised, as the plausibility or the level of con®dence has beenaltered after the new data become available. Cast in symbols of conditionalprobability and according to Bayes's theorem, the probability that the hypothesisHi is true, given both the prior information I and the new data D, is given as:

7 The author was not aware of the monumental work of Sir Karl R. Popper at the time when Ref.

[183] was published.


P�HijD&I� � P�DjHi&I�P�HijI�P�DjI� , �20:1�

where i � 1,2,3, . . . ,n, and P�DjHi&I � is the probability of observing the new dataD, given the initial information, I, and assuming that Hi is true. P�DjI � is thetotal probability of observing D given I, no matter which of the hypothesis turnsout to be true.

The biggest problem with the application of Eq. (20.1) to a real case is the wayto assign prior probability P�HijI �; it is rather subjective. Je�erys and Bergerassigned higher prior probabilities to models that are simpler. But what qualitiesconstitute simplicity? Usually, models with fewer parameters, especially feweradjustable parameters, are considered simple. In the present case, we shall dealwith the situation somewhat di�erently and even-handedly, without ®rst raisingthe question of simplicity.

Given the information available at the outset for the AC photoelectric e�ect, itis natural to consider the classical electrophysiological approach withoutmodi®cations. It is also natural to decompose a transient signal into severalexponential terms Ð a common practice in solution phase photochemistry. Inview of these facts, one must assign a higher prior probability to the mainstreamapproach than to the bioelectrochemical approach. Let us consider again the datashown in Table 5 (Section 11.4). Since there are six laboratories subscribing to themainstream approach, the odds are at least six to one in favor of the mainstreamapproach. Thus, a smaller prior probability is assigned to the bioelectrochemicalapproach. The actual odds could be even greater against our approach if wecounted the number of publications using either approach. Although it may notbe entirely appropriate to determine scienti®c truths by means of popular votes,we shall tentatively ignore this latter issue.

Since the di�erence of the two approaches in terms of the prior probability isnot overwhelming, the decisive factor will come from the conditional probabilityor plausibility given the challenge of new data. Here we must distinguish betweenold data on which the construction of the model was based, and new data whichappears after the models were cast. The mainstream approach utilizes curve ®ttingand ad hoc models, each speci®cally constructed for a speci®c occasion. Most ofthese models are ridden with freely adjustable parameters. Therefore, thegoodness-of-®t consideration is not called in question. It is the apparentdiscrepancy among these six laboratories that is at issue: none of theselaboratories proposed models that can predict the data of other laboratories, andnone has o�ered any explanation or even acknowledged the discrepancy. On theother hand, we have successfully explained the discrepancy on the basis of thedi�erence in the access impedance. Chronologically, our model was establishedbefore the appearance of these data [163]. We have also quantitatively predictedthe e�ect of varying the access impedance, using our own data. Since our modeldoes not possess any adjustable parameters, the model thus made sharppredictions that have a narrow range of the predicted value (e.g., the reciprocalrelation (9.16)). It is this latter reason that a�ords us to assign a signi®cantly


higher posterior probability P�DjHi&I � to the bioelectrochemical approach, so asto more than o�set the lower initial prior probability. As Je�erys and Berger haveargued, Bayesian analysis shows that a hypothesis with fewer adjustableparameters automatically scores an enhanced posterior probability.

In the spirit of Ockham's razor, the bioelectrochemical approach is simpler thanthe mainstream approach in the sense that a single model ®ts all types ofmembranes [30] whereas, in the mainstream approach, a speci®c ad hoc modelmust be concocted for each special case. Furthermore, those models o�er virtuallyno cross-prediction. For these reasons, we think that the bioelectrochemicalapproach possesses a higher degree of plausibility than the mainstream approach.

20.5. Postdiction, prediction and parsimony

The tentative nature of a physical model may lead to the doubt about the valueand usefulness of a physical model that one cannot absolutely prove. In order todeal with this concern, we shall cite an insightful analysis presented by Gauch[454], demonstrating that a (mathematical) model can be more accurate than itsdata from which it was constructed. This is mainly because data usually containnoise. A (mathematical) model, which enhances the pattern of the underlyingprinciple of data generation and ®lters the obscuring in¯uence of noise, cansurpass the data's accuracy in representing reality (cf. Ref. [439]).

For the sake of argument, Gauch examined two aspects of a model: postdictionand prediction. Postdiction refers to the agreement between the model and thedata on which the model is based. Prediction refers to the agreement between themodel and any future data. Here, the `future' data could have been part of thesame set of data used for postdiction that had been set aside for the purpose offuture testing of the model. They could have been data generated in the past inother laboratories, or the data to be generated by a future experiment suggestedby the model.

Most models perform well in postdiction for obvious reasons, and bRphotoelectric data found in the literature are no exceptions. But the true value ofa model is not just its explanatory power but rather its predictive power, especiallyits ability to guide future experimental designs.

The bioelectrochemical approach explains qualitatively the discrepancy shownin Table 5 (Section 11.4), and predicts quantitatively the e�ect of varying theaccess impedance (Fig. 26). The use of the diagram in Fig. 33 to explain theconcurrent diminution of the B2 peak and enhancement of the B1 peak is anotherexample of prediction in the strict sense, because the explanation was publishedprior to the appearance of the data it attempted to explain [156]. Based on dataobtained at one value of the access impedance, it is possible to make sharppredictions about both the amplitude and the time course of the photosignal atother values of the access impedance. It predicts the existence of a pH value atwhich the signal from a TM will be superimposable, after normalization, with thesignal from an ML Ð another sharp prediction with which the experimenter has


no adjustable parameters to play and has no control to in¯uence the ®t [227] (Fig.48(A)).

Let us examine why postdiction is easier to accomplish than prediction,especially in mathematical modeling. This is not just the simple consequence ofthe availability of data for postdiction, but is based on a mathematical theoremknown as the Weierstrass's Approximation Theorem [455], which proclaims, inplain language, that any mathematical curve can be ®t with a polynomial functionof a higher and higher degree (if necessary) to any degree of accuracy. It is thuspossible to run a polynomial curve through all the data points with any desireddegree of accuracy. This is a common practice in multiple regressional analysis.The time course of a signal is represented by an in®nite power series:

f�t� � a0 � a1t� a2t2 � a3t

3 � � � � : �20:2�However, this expansion of f(t ) is by no means unique. For example, f(t ) can beexpanded as an in®nite series made of polynomials such as the Legendrepolynomials and many others. Under a fairly general formulation, a continuousfunction f(t ) can be treated as a vector in an in®nite dimensional space, of whichthe power functions, 1, t, t 2, . . . , form a set of basis vectors for the coordinatesystem. Just as the Cartesian system is not the only coordinate system forordinary vectors, the power series expansion is not the only way to express anarbitrary continuous function. While the possibility of ®tting the time course of asignal to a power series of the form of Eq. (20.2) is always guaranteed, there is noguarantee for a physical meaning of parameters a0, a1, etc., and the (numerical)model may or may not be parsimonious.

A power series expansion is rarely, if ever, used in the analysis of chemicalrelaxation processes; it is simply the wrong kind of parametrization. For chemicalrelaxation processes initiated by either a d-function type or a step-function type ofperturbation (of either concentrations, temperature, or other physical conditions),it is most natural to express the process as a linear sum of exponential functionsof the form of

Pni�1 aiexp�ÿt=ti �, where ti (with i � 1,2,3, . . .) are discrete time

constants. Finding the time constants and the coe�cients is tantamount toperforming a Laplace transform to map the function from the time domain to thefrequency domain. There exist methods to perform the computation on a set of®nite data points [456±458]. Sometimes, accurate deconvolution of data may bedi�cult, especially if the data contain noise and/or possess an insu�cient dynamicrange. Since the Laplace transform of the function

Pni�1 aiexp�ÿt=ti � appears as a

curve with multiple spikes in the frequency domain, a `noise' spike can bemistaken as a discrete exponential term. Since two spikes may overlap to give theappearance of a single spike, the distinction between two closely clustered timeconstants and a single time constant may be problematic under noisy conditions.Therefore, the determination of the exact number of time constants may beuncertain.

Theoretically, the distribution of time constants may not be discrete and cansometimes become a continuum, i.e., the relaxation kinetics may be distributed


rather than discrete. In an attempt to analyze the waveform of the R2 componentof the ERP, Lindau and RuÈ ppel [459] found it impossible to describe the kineticswith a single exponential function. They cited this di�culty as evidence for theexistence of conformational substates of rhodopsin and proceeded to describe thewaveform with a scheme of distributed kinetics. This approach was duplicated byHolz et al. [19], who also decomposed the time course of the AC photoelectricsignal from a reconstituted bR membrane, in accordance with a scheme ofdistributed kinetics. In other words, the photosignal is characterized by acontinuous relaxation time spectrum with several broad peaks. They claimed thatthis model of distributed kinetics was found to be more appropriate than discrete®rst-order processes and suggested that the experimental data so analyzed indicatethe existence of conformational substrates with distributed activation energies.Their proposed scheme has become widely accepted and has generated aconsiderable following that many subsequent reports showed plots of therelaxation processes in the logarithmic time scale. However, this new approach isstill problematic. For example, both the data of Moltke et al. [262] and of Gergelyand VaÂ roÂ [264] shown in Fig. 57 pertain to the same bR mutant, and both wereplotted in a logarithmic time scale (Section 11.4). The mere juxtaposition of thetwo reports reveals a glaring discrepancy in the time domain where those peaksappear, and immediately demands an explanation or rationalization. It is easy tosuccumb to the temptation to reject one of the two as incorrectly executedexperimental data. However, the criteria to judge the validity of the experimentsare not apparent. Our alternative interpretation presented in Section 10.3 actuallysalvages both sets of data by attributing the discrepancy to the variation of ahidden parameter Ð the access impedance. Thus, both sets of data are `correct,'but pertain to di�erent experimental conditions. However, in light of ouralternative interpretation, the claim of Holz et al. becomes dubious. Perhaps,adoption of a continuous time spectrum and distributed activation energies istantamount to adoption of additional (free) parameters that improve the model'spostdiction at the expense of its prediction.

In solution phase photochemistry, the expansion of a time function usuallygives rise to a ®nite number of time constants, each of which can be related to adiscrete step of chemical reaction with either ®rst-order or pseudo-®rst-orderkinetics. In the case of the bR photocycle, investigators may encounter a situationthat there exist more time constants than the number of knownphotointermediates, as determined by their characteristic absorption spectra. A®nding like this often forced investigators to postulate a branching photocycle, ora photocycle containing two or more photointermediates with identical absorptionspectra but di�erent decay time constants. While these provisions are eminentlypossible, other explanations are also possible (cf. Section 17). In the case of theAC photoelectric e�ect, the concept of chemical capacitance and theaccompanying equivalent circuit analysis dictate that a single ®rst-order orpseudo-®rst-order relaxation is re¯ected in a bi-exponential decay except undertrue short-circuit conditions.

The mainstream approach insists upon matching each exponential decay of the


photoelectric signal to a photointermediate relaxation process. There is littlewonder why it has su�ered from internal inconsistency. Yet those ad hoc modelsbased on exponential analysis did well in postdiction in each individual case,because the exponential analysis guarantees that the numerical values ofexponential terms so obtained agree with the data (the data themselves impose noconstraints on the numerical values). Those ad hoc models perform rather poorlyin cross-prediction of data from other laboratories or own data obtained bydi�erent methods of reconstitution, because the models provided no provisions forthe e�ect of hidden factors such as access impedance.

In the bioelectrochemical approach, we insist that a signal with multipleexponential decays be ®rst separated, by means of physical methods, into distinctmolecular components, and each such component is then mathematically ®t withtwo exponentials. This approach profoundly in¯uenced the allocation of ourresources; we spent a great part of our e�ort in searching for experimentalmethods of component decomposition and spent little time in re®ning the modelwith more and more adjustable parameters in order to achieve better and better®t.

Since most data contain noise, the immediate goal of mathematical modeling isto recover the pattern (or signal) and ®lter the noise so as to enhance prediction.As demonstrated by Gauch with several speci®c examples, the model complexitya�ects the model accuracy di�erently with regard to postdiction and prediction.This is illustrated in Fig. 90, which plots postdictive and predictive accuracy aswell as pattern and noise as a function of the model complexity. Obviously, a

Fig. 90. Accuracy and parsimony of models. Because pattern is determined by relatively few major

factors, even simple models recover much of pattern in data set. Because noise is idiosyncratic and

complex, it is recovered more slowly, as model increases in complexity. Model's postdictive accuracy

develops from sum of pattern recovery and noise recovery. It increases quickly even in simple models,

and then tapers to slower increase. In contrast, predictive accuracy arises from pattern recovery minus

noise recovery. It also increases quickly in simple models, but then peaks at `Ockham's hill', and

subsequently decreases in increasingly complex models. (Reproduced from Ref. [454])


model cannot be too simple, or too simplistic. Thus, with a modest increase ofcomplexity, both the predictive and postdictive accuracy increase rapidly. This isbecause the pattern is captured e�ectively with relatively simple models. Thereason behind this is not totally clear unless one categorically attributes it toOckham's razor. In my opinion, this is in part due to the choice ofparametrization. Through experience and through prior accumulated knowledge,there is a tendency for experimenters to parametrize the system underinvestigation in such a way that only a small handful of parameters are involved.They hope other (hidden) parameters are so randomized that they can be takencare of by statistical analysis.8 Noise is often idiosyncratic and beyond theexperimenter's control, and is, therefore, recovered more slowly than the pattern.Postdiction, which is the sum of pattern and noise, thus continues to increase inaccuracy as the model's complexity rises. In contrast, prediction, which is thedi�erence between pattern and noise, goes through an optimum (Ockham's hill)when the model is moderately complex. Models that proceed beyond theOckham's hill are over®tting the data by increasingly capturing the noise feature.A parsimonious model, optimally capturing the pattern and discarding the noise,can thus be more accurate than the data set used in postdiction and can performwell in prediction.

There are two kinds of prediction, roughly classi®ed as interpolation andextrapolation. Interpolation can be interpreted as prediction governing data thatare obtained in similar and conventional ways and, therefore, more likely to beconsistent with the model being tested. In contrast, extrapolation can beinterpreted strictly in the literal sense but can also be interpreted as predictiongoverning future data obtained by a radically di�erent experimental design.Extrapolation gives the experimenter relatively little control over the manipulationof parameters of a model; extrapolation makes a model more vulnerable thaninterpolation does. It is this latter category of data that o�ers greatest challengesto a model, and thus carries the biggest weight in validation of a model ifsuccessful or in rejection of a model if unsuccessful. Because of the tentativenature of models, experimental tests for prediction or validation must be designedwith a spirit to reveal ¯aws of the model.

The Bayesian analysis itself has been criticized for its subjectivity. Thisobjection is especially acute for those who take the position of dichotomy injudging a hypothesis either as true or false: If a hypothesis is either correct orincorrect, why does the Bayesian school evaluate a model with the degree ofplausibility? From the above discussion, the Bayesian approach is actually quitecompatible with our present view about the tentative nature of physical models,and with the Popperian view [449±451].

In experimental science, the so-called `proof' of an explanation or a physicalmodel is often correlational in nature and is little more than a consistency check.But there is a wide variety of correlations or consistency checks: some are

8 Those non-random hidden (or uncontrolled) parameters are called systematic errors.


primitive but others are more sophisticated, some are redundant but others aremore comprehensive. As a result, conclusions so reached range from highlytentative to highly a�rmative. A mathematical model that gives quantitativepredictions is more plausible than an explanation that gives only qualitativepredictions, because the former o�ers more `points of contact'9 between the modeland the data than the latter and thus ¯aws of the model are more readily exposed.A parsimonious model with few or no adjustable parameters that give sharppredictions is more plausible than one with many adjustable parameters or onecapable of only broad predictions.

Critics of the Bayesian view will undoubtedly cite a number of extremelysuccessful physical models in the realm of physics or chemistry, many of whichinvolve rather sophisticated and high-powered mathematics. Some investigatorsbelieve that these mathematical models capture the ultimate and absolute truths.In my opinion, no matter how successful these mathematical models are, thecorresponding physical models must still be considered tentative, albeit highlyplausible, for two reasons. First, it is impossible to prove that there is one andonly one physical model that corresponds to the same highly a�rmedmathematical model. In mathematical jargons, the correspondence between aphysical model and a mathematical model is a homomorphism rather than anisomorphism. Second, there is no guarantee that novel data will not appear in thefuture to seriously challenge and undermine the presently accepted mathematicalmodel and, therefore, also the corresponding physical model. The numerousexamples of extremely successful and general mathematical models in physics andchemistry are not counter-examples to the Bayesian view, but are rather tributesto the supreme accomplishments of the human mind.

In science history, there is no lack of celebrated examples in which meticulouslydocumented and con®rmed science suddenly faced a need to carry out a completeoverhaul when confronted with novel and unusual data. This is the case withbiological sciences where complexity prevents all relevant parameters to bebrought under control.10 This is also the case even with physical sciences. Twoexamples that easily come to mind were the birth of quantum mechanics and ofspecial relativity for dealing with the physical world of extremely small dimension,and of speed comparable to the speed of light, respectively, starting whereclassical mechanics begins to fail. In this sense, the Bayesian school's view actuallyre¯ects more faithfully the tentative and step-by-step nature of science, andperiodic re®nements, alterations and revisions demanded by new data. Subjectivityof value judgment in science is not an aberration but indeed a way of life.

When a physical model is less than perfect, the decision to accept or to rejectthe model can be rather subjective. An example illustrating this point is the

9 See p. 30 in Ref. [460].10 Investigators working in structural biology may object to the Bayesian view. Our explanation is that

the physical models (or rather, the methodologies), which structural biologists use in interpreting exper-

imental data, have been established beyond reasonable doubt.


epicycle theory of Ptolemy for explaining the planetary motion. From hindsight,this theory is unsatisfactory but it survived and persisted for several thousandyears, because it did provide a reasonable explanation for the rather erraticapparent `looping' motion of planets. The quantitative agreement was far frombeing perfect but the expectation was not high at that time, either. Besides, betteragreements had been accomplished by introducing additional epicycles andoscillations Ð a geometric equivalent of introducing more and more adjustableparameters. Recall that Ptolemy did not have the bene®t of Newtonian mechanicsnor did he have access to NASA's vast collection of space exploration data. All hehad were data of planetary trajectories projected onto the two-dimensionalcelestial sphere, collected without the aid of a telescope. The discrepancy couldreadily be dismissed in the absence of an alternative competing explanation untilthe advent of the heliocentric theory of Copernicus.11 Based on high-precisionobservation data inherited from Tycho Brahe, Copernicus was able to produceevidence demonstrating that his theory could better explain the looping planetarymotion than Ptolemy's. Even so, he still had to face a life-threatening `uphill' ®ghtagainst the then-establishment.

In biomedical sciences, the expectation for sharp quantitative agreements hasnot been high for obvious reasons. Therefore, considerable latitude exists withregard to a decision to accept or reject a piece of evidence. In an article aboutinterpretation of behavioral experiments [196], we have pointed out that aninvestigator may choose to ignore unfavorable evidence and propose additionalhypothesis in order to rescue a weak hypothesis. In so doing, the investigatorsubjectively assigns a greater weight on a yet-to-be-tested hypothesis than onunfavorable experimental evidence furnished by critics or opponents. It is onlyappropriate that the readers are warned here that, in our critical analysis ofphotoelectric e�ects here, the present author is also not immune to this pitfall, notjust his critics. After all, decision making in science is far more subjective thanpundits believe or are willing to admit.

In dealing with modeling of the AC photoelectric e�ect, value judgment hasbeen an issue. Not every investigator viewed the discrepancy shown in Table 5(Section 11.4) with equal seriousness. Some regarded the variability as acceptablein biological modeling, given the relative greater variance in biologicalexperiments, as compared to physical experiments. Some others suggested shiftingof speci®c columns in the table to bring data from di�erent groups to a betteragreement with one another. Our objection to these manipulations is as follows.The signal-to-noise ratios of the original data had not be su�ciently degraded toallow for comfortable overlap of variances of these data. Furthermore, eachcolumn in Table 5 bears speci®c correspondence to a speci®c component, andshifting of columns is thus not permissible. However, the critics are right inpointing out the discrepancy between the measured and the theoretical value of

11 Note that the probability P�HijD&I � in Eq. (20.1) is in¯uenced by the number of available compet-

ing hypotheses.


chemical capacitance. Thus, the value of chemical capacitance, calculated by theformula derived on the basis of the Gouy±Chapman analysis, predicts theexperimental value poorly (microscopic prediction), but the equivalent circuitanalysis predicts the experimental results with reasonable accuracy (macroscopicprediction). As we pointed out in Section 20.2, the poor microscopic prediction isin part inherited from the Gouy±Chapman theory and in part a consequence ofthe necessity to perform experiments under conditions outside of the range of therestrictive assumptions. In spite of being a forerunner of the Debye±HuÈ ckeltheory, the Gouy±Chapman theory has never attained the popularity enjoyed bythe Debye±HuÈ ckel theory, because of its poor microscopic performance, andbecause it has never been tested at the macroscopic level, until the theory wasresurrected by the advent of membrane biophysics (reviewed by McLaughlin[461]). Membrane biophysics must confront both the microscopic and macroscopicaspects of the electrical phenomena, and the Gouy±Chapman theory serves as avital conceptual link.

Although we are comfortable with the present performance of thebioelectrochemical approach, the discrepancy exhibited by the microscopic modelmight hold the clues to some deeper insight into interfacial properties of themembrane. We suspect that it may require very di�erent kind of data to bringabout the new insight still unknown to us. In view of the tentative nature ofscience, we would not be surprised if newer and better models are proposed in thefuture, with the assistance of novel and crucial data. In the absence of suchmodels, the present approach will continue to serve the purpose of macroscopicmodeling in the AC photoelectric e�ect.

21. Concluding remarks

Most, if not all, photobiological membranes exhibit photoelectric phenomena.Understanding of these phenomena constitutes an important part of ourknowledge about photosynthesis and vision. The basic knowledge of thephotoelectric phenomena is also important for technological applications in botharti®cial solar-energy conversion and in molecular electronic device construction.The main purpose of this article is to examine the photoelectric phenomena froma point of view of electrochemical surface science, and to relate macroscopicelectrical parameters to microscopic chemical parameters via equivalent circuitanalysis. The photoelectric phenomena in biomembranes are separated into twocategories: the AC and the DC photoelectric e�ects. This classi®cation is justi®ed,mainly because of the di�erence of the methodology of measurements. Thisclassi®cation also facilitates equivalent circuit analysis.

Although we depend heavily on data obtained from reconstituted bRmembranes for validation of the bioelectrochemical approach, the conceptualframework and the methodology are actually quite general. The reason behindthis generality is that the photoelectric phenomena are common to all pigment- ordye-containing membranes that are capable of light-induced vectorial charge


separation. The vectorial nature stems from the ®xed orientation of thephotopigment and the resulting asymmetry of the pigment-containing membraneswith regard to the inner and the outer aqueous phases; light-induced chargemovements always have a nonzero component perpendicular to the plane of themembrane surface. It is the involvement of light that sets the topic apart fromconventional electrophysiology, which deals successfully with bioelectricphenomena in non-photosensitive biomembranes. On the other hand, it is theinvolvement of membrane or thin ®lm con®guration that sets the topic apart fromconventional photochemistry, which deals mainly with solution phase phenomena.An e�ective approach to the problem of the photoelectric e�ects is the`intermarriage' of surface electrochemistry, which deals with the microscopicsurface chemical phenomena, and electrophysiology, which deals with themacroscopic electrical phenomena in biomembranes.

The photoelectric events in biomembranes are unique, because they are neithercompletely microscopic nor completely macroscopic phenomena. The spatial scalewithin which the photochemical events take place is often referred to asmesoscopic. As a result, new and unexpected phenomena appear. The conventionalelectrophysiology usually deals with electrical phenomena driven by a voltage (orcurrent) source that resides outside of the membrane per se, e.g., delocalized anddistributed in the two aqueous phases as a di�usion potential. The voltage sourcein a photobiological membrane resides either at the membrane±water interface orinside the membrane itself, and thus generates a mesoscopic event. There are noprecedents either in conventional (solution phase) photochemistry or inconventional electrophysiology. The development of the bioelectrochemicalapproach was motivated by the need to deal with the unique feature inphotobiological membranes.

We have introduced the concept of chemical capacitance and the method oftunable voltage clamp to deal with the AC photoelectric e�ect, and the nullcurrent method to deal with the DC photoelectric e�ect about a quarter centuryago. The bioelectrochemical approach was initially developed for the investigationof a model BLM system that is capable of light-induced vectorial electrontransfer. But it is the bR membrane system that convinced us that thebioelectrochemical approach is su�ciently general for most, if not all, pigment- ordye-containing membranes and thin organic ®lms.

Bacteriorhodopsin, being the simplest photosynthetic apparatus, allows us todeduce the minimal requirements, and, at the same time, permits us a glimpse ofNature's versatility in designing purposeful molecular functionality (concept ofintelligent materials). It is indeed a reductionist's dream come true.Bacteriorhodopsin, serving as a convenient link between photosynthesis andvision, a�ords us an unprecedented global perspective about all majorphotobiological membrane systems. It is also the integrationist's delight. Byexploring the underlying electrochemical principles, it is possible to penetrate thesuper®cial structural di�erence of various systems and ®nd the underlyingcommon features.

By its insistence upon the application of classical electrophysiology and


conventional solution phase photochemistry, the mainstream approach isinevitably plagued with discrepancies, contradictions, and apparent paradoxes.12

For those who hold the view that life processes cannot be fully comprehended interms of physics and chemistry (referred to as neo-vitalistic or new-mysterian13),these paradoxes and discrepancies are just additional supports of their view. In thepresent article, we have shown, by examples, that some of these apparentparadoxes and discrepancies are actually logical consequences of electrochemicalsurface science, as applied to these systems. By means of electrochemical surfacescience, it is often possible to provide a simple explanation for a complexbiological phenomenon.

Electrochemical surface science is probably the branch of existing science thatmainstream biologists most neglect. This is primarily due to the fact that majoradvances in biochemistry (biological chemistry) have been made in the area ofsolution phase chemistry. Yet life processes are carried out within the frameworkof complex structures, in which solution phases are compartmentalized by anintricate sca�old of membranes. Nevertheless, electrochemical surface science hasenjoyed some success especially in membrane related phenomena [461]. In view ofthe fact that many important biological functions are based on interactionsinvolving forces other than covalent bonding, electrochemical interactions may bejust as important as such well-known mechanisms as the van der Waalsinteraction and hydrogen bonding. Important phenomena such as self-assembly,antigen±antibody reactions, cell-to-cell recognition, enzyme substrate interactions,and receptor recognition, to name a few, may require electrochemical surfacescience for further mechanistic elucidation.

The electrochemical analysis of retinal proteins is more than just an academicinterest. Understanding based on electrochemical analysis has importanttechnological implications. Since the discovery of bR, investigators working on theproblem of arti®cial solar-energy conversion have maintained a keen interest inbR. Bacteriorhodopsin also has played a prominent role at this stage of researchand development of molecular electronics [463±470]. Molecular electronics evolvesfrom the increasing recognition that the microelectronic revolution will eventuallycome to a halt since the physical limit of miniaturization imposed by quantumand thermal e�ects is rapidly being approached. Construction of devices usingmolecular materials as the building blocks o�ers a promising alternative forcontinuing miniaturization; living organisms utilize molecular machines withphysical dimensions in the nanometer scale (nanobiology).

Unlike conventional microelectronic circuits which operate mostly on the basisof bulk properties of materials, biomachinery utilizes the mesoscopic properties ofbiomaterials and biostructures, and exploits both the underlying physics as well as

12 Optimists with ®rm mechanistic orientation would claim that there are no real paradoxes (in

science), but only our own temporary confusion.13 The term `new mysterians' was coined by Owen Flanagan, a philosopher at Duke University. See

Ref. [462] for a concise account.


chemistry for its functions, and implementing an architecture that is a far cryfrom the popular von Neumann type architecture of modern (sequential) digitalcomputers [471±473]. The rich repertoire of chemical reactions associated withcarbon-containing molecules provides virtually unlimited possibilities for ®ne-tuning molecular functions and allows intelligent materials to evolve. Anincreasing emphasis on the development of molecular devices also means anincreasing importance of understanding the electrochemical surface phenomena. Inthis article, we have illustrated the importance of biomolecules as advancedmaterials for device construction, using bR as an example. We have alsodemonstrated that basic research in photobiological systems can lead to insightthat can be translated into design principles in molecular electronics (biomimeticscience via reverse engineering). The validity of this approach is probablystemmed from Nature's `design philosophy'. It appears that Nature designedmolecular machines in modular forms. Nature is versatile; the same designprinciple may be implemented with completely di�erent types of molecules,whereas the same molecular functionality may be cast for diverse roles to servedi�erent purposes. Retinal proteins, which include the visual pigments and fourchemically similar proteins from H. salinarium, o�er an unprecedentedopportunity for investigators to systematically reverse engineer Nature's designs ofphotobiological systems.

The present article summarizes work on retinal proteins done in the author'sand his collaborators' laboratories. Our bioelectrochemical approach deviatessigni®cantly from the widely accepted mainstream paradigm. The mainstreamapproach usually started with simple ad hoc models and quantitative(mathematical) analysis with several free parameters. But the models often lackinternal consistency as well as predictive power. Our alternative approach requiresmore elaborate analysis, but the resultant models attain more predictive powerand generality than those in the mainstream approach. Here, the parsimonyexhibited by our alternative approach falls under the coverage of a broad guidingprinciple which was routinely but tacitly invoked by scientists, especiallyreductionists: the Ockham's razor. That simple mathematical modeling is possibleis frequently a consequence of reductionists' approach. As reductionists, we hadthe privilege to choose the suitable methods of reconstitution, to bring crucialexperimental conditions, including previously hidden parameters, under control.As a consequence, it is possible to analyze the photoelectric e�ects with linearmathematics.

Biology is inherently complex, and biologists tend to confront many morevariables than physicists do. For mathematical and physical models of biologicalphenomena, high precision is not generally expected. However, biologists mustresist the temptation to prematurely accept a given model by dismissing theremaining discrepancy as mere consequence of complexity in biology. Inevaluating various competing models, we are in favor of the Bayesian view that amodel is not to be judged as true or false but rather in terms of degree ofplausibility. We thus choose a model by eliminating all currently availablealternatives, but the choice must be regarded as a tentative one. Since the possible


future emergence of an alternative but better model cannot be excluded inadvance, it is not possible to prove a model absolutely.

Complexity in biology leaves plenty of room for subjective judgment ondiscrepancy or agreement. It also gives investigators the temptation tocategorically reject the future possibility of obtaining a mechanistic explanationfor biological phenomena (such as consciousness) which are refractory to repeatedattempts at mechanistic explanations. This is the emerging line of thinking of new-mysterians. In our opinion, the debate between the mechanistic view and the new-mysterian view is endless and futile. Whereas it is impossible to prove the validityof the mechanistic view by a ®nite number of successful examples, it is equallyimpossible to prove the validity of the new-mysterian view by the sheer absence ofan available mechanistic explanation to a speci®c problem. Historic lessonsabound which showed that when one was about to exhaust the capability ofexisting sciences, lingering puzzles actually ushered in a new science Ð a major`paradigm shift', according to science historian Thomas S. Kuhn [460]. In the caseof photoelectric phenomena in biomembranes, solving the puzzles does not requirea new science but, instead, an improved recombination of existing paradigms, anda fresh perspective made possible by infusion of electrochemical surface science.14

Acknowledgements

The author thanks Andrei Dioumaev, Elias Greenbaum, Norbert Hampp, HansKuhn, Dieter Oesterhelt, Hitoshi Shichi, and Klaus-Peter Zauner for criticalreading of the manuscript. The author thanks his collaborators, Janos Lanyi,Lowell McCoy, Mauricio Montal, and Richard Needleman. The authoracknowledges the intellectual in¯uence of his two mentors, Professor DavidMauzerall and the late Professor Alexander Mauro, both of The RockefellerUniversity, during the formative years. The author was bene®ted by countlessdiscussions and debates with his colleagues and with his critics, the list of which istoo long to be included here. The author is also indebted to the followingindividuals whose experimental work that forms the basis of this review: ManChang, Albert Duschl, Brian Fuller, Filbert Hong, Sherie Michaile, Baofu Ni,Ting Okajima, Michelle Petrak and Wita Wojtkowski. The author's research hasbeen support by the following grants and contracts: GM-20729, GM-25144, EY-03334 from NIH, Grant No. 34 from the American Heart Association ofMichigan, N00014-87-K-0047 from the O�ce of Naval Research, N60921-91-M-G761 from the Naval Surface Warfare Center, and Wayne State UniversityResearch Stimulation Funds.

14 The mainstream approach is based on a recombination of solution phase photochemistry and classi-

cal electrophysiology. The bioelectrochemical approach includes an additional paradigm: electrochemi-

cal surface science.


Appendix A. Equivalent Circuit Analysis

A.1. AC photoelectric e�ect

A.1.1. Photocurrent measured under tunable voltage-clamp conditionsWe shall ®rst set up a second-order ordinary di�erential equation for the

equivalent circuit shown in Fig. 23 [163]. There are seven unknown variables: ic,qm, ip, qp, is, ir, and I. Two of the seven needed simultaneous equations aresupplied by the following de®nitions:

ic � dqm

dt, �A1�

ip � dqp

dt: �A2�

The remaining ®ve equations are obtained by invoking the Kirchho�'s rules:

I � ic � ir � ip � is, �A3�

IRe � ÿirRm, �A4�

isRs � qp

Cp

, �A5�

IRe � Ep ÿ qp

Cpÿ ÿip � is

�Rp, �A6�

ÿ qm

Cm

� Ep ÿ qp

Cp

ÿ ÿip � is�Rp: �A7�

By eliminating ir, is and I, from Eqs. (A3)±(A6), and by using the de®nition (9.11)for tm, we have

ic � RpCm

"Ep

tmRp

ÿ qp

tmRpCp

ÿ�

dqp

dt� qp

RsCp

��1

tm

� 1

RpCm

�#: �A8�

By di�erentiating Eq. (A7), multiplying through by ÿCm, and using Eqs. (A1),(A2), (A5) as well as the de®nition for tp, Eq. (9.2), we have

ic � RpCm

"d2qp

dt2� 1

tp

dqp

dtÿ 1

Rp

dEp

dt

#: �A9�

By combining Eqs. (A8) and (A9), and eliminating ic, we have


d2qp

dt2��

1

RpCm

� 1

tp

� 1

tm

�dqp

dt��

1

tptm

� 1

RpCmRsCp

�qp

� 1

Rp

dEp

dt� 1

tm

Ep

Rp

: �A10�

The initial conditions for this di�erential equation are:

qp�0� � 0, �A11�and

ip�0� ��

dqp

dt

�0

� 0: �A12�

The di�erential equation can readily be solved by the method of Laplacetransform:

qp�t� � �1=ts ÿ 1=tm ��1=ts ÿ 1=tl �

�t0

Ep�u�Rp

exp

�uÿ t

ts

�du

ÿ �1=tl ÿ 1=tm ��1=ts ÿ 1=tl �

�t0

Ep�u�Rp

exp

�uÿ t

tl

�du,

�A13�

where ts and tl are de®ned, in Section 9.2, by Eqs. (9.9) and (9.10). Knowingqp�t�, it is then ready to obtain the explicit expression for I(t ) as given in Eq. (9.8).

A.1.2. Existence and uniqueness proofSolution of Eqs. (9.9) and (9.10) for Rp and Cp, when Rs is not small enough to

be negligible, is outlined here [163].The following Eqs. (A14) and (A15) are equivalent to Eqs. (9.9) and (9.10):

1

ts

� 1

tl

� 1

tp

� 1

tm

� 1

RpCm

, �A14�

1

tstl� 1

tptm� 1

RpCmRsCp: �A15�

We thus have

Cp �ÿ1=Rp � 1=Rs

�ÿ1=ts � 1=tl ÿ 1=tm ÿ 1=RpCm

� : �A16�

The explicit solution for Rp and Cp follows.

1

Rp

� P2��P2 �Q

p, �A17�


Cp � T2��T 2 ÿ tstl

R2s

r, �A18�

where

P � Cm

2

"S�

ÿt2m=tstl

�ÿ 1

RsCm � tm

#, �A19�

Q � SC 2m

RsCm � tm

, �A20�

T � tstl

2

�SCm

�1

tm

� 1

RsCm

�� 1

Rs

�tm

tstl

� 1

tm

��, �A21�

S � 1

ts

� 1

tl

ÿ 1

tm

ÿ tm

tstl

: �A22�

Thus, we have two pairs of solutions for Rp and Cp. We need to show that onlyone pair is physically meaningful and the other pair is physically absurd. FromEqs. (A14), (A15) and (A22), it follows that

S � tm

RpCm

�1

tm

ÿ 1

RsCp

�1 tm

RpCm

�1

ReCm

ÿ 1

RsCp

�: �A23�

For tunable voltage-clamp measurement with the access resistance Re<Rs, wehave S > 0 since Cm and Cp are roughly of the same order of magnitude. Thus,from Eqs. (A20) and (A21), we have Q > 0 and T > 0. As a consequence, we alsohave P�

��P2 �Q

p> 0 and Pÿ

��P2 �Q

p<0. Therefore, there is one and only one

physically meaningful solution for Rp:

1

Rp

� P��P2 �Q

p, �A24�

and the matching solution for Cp:

Cp � T��T 2 ÿ tstl

R2s

r, �A25�

because of the choice of Eq. (A24) for Rp. Cp must be real because of Eq. (A16),and also positive, considering Eq. (A18) and T > 0. This completes the existenceand uniqueness proof of Rp and Cp for the case with Re<Rs.


A.2. DC photoelectric e�ect: null current method

A.2.1. Zero dark conductanceThe validity of the null current method will be examined by an equivalent

circuit analysis, under the condition that the membrane conductance duringillumination di�ers signi®cantly from that in the dark [281]. For simplicity, weshall assume that the photoemf and the photoconductance is weakly dependent onthe membrane potential or not voltage-dependent at all. Under this assumption,the necessary change of the membrane voltage for achieving the null-currentcondition will not change the value of either the photoemf or thephotoconductance. Here, we shall also consider the e�ect of shunting by theparallel ionic di�usion path on the interpretation of the null-current measurement.

Referring to the diagram in Fig. A1, an external voltage source Vc and an o�setvoltage E0 are applied to the membrane under a short-circuit condition. Inpractice, Vc and E0 are combined into a single voltage source but are separatelylisted for the sake of clarity.

We shall consider three steps of the null-current measurement: (a) applying thepotential Vc in the dark, (b) while maintaining the applied potential Vc, the lightis turned on, and (c) while the light is on, an o�set potential E0 is introduced toachieve the null-current condition. By invoking Kirchho�'s rules, we obtain thefollowing equations:

i1Rp � Ep � Vc ÿ E0, �A26�

i2Rm � Vc ÿ E0, �A27�

Fig. A1. Equivalent circuit analysis of null current method. Capacitances are all ignored. Equivalent

circuit consists of photoconductive path (emf Ep and photoresistance Rp), and ionic di�usion path

(resistance Rm). Membrane is short-circuited by external voltage-clamp circuitry, which also provides

Vc and E0; Vc is applied voltage, and E0 is o�set voltage for achieving null-current condition.

Measured current i0 is split into two branches: i1 goes through photoconductive path, and i2 goes

through ionic di�usion path. See text for further explanation. (Reproduced from Ref. [281])


i0 � i1 � i2, �A28�where the symbols are de®ned in Fig. A1. These three equations are valid for allthree steps (conditions) listed above for the null-current measurement. Note that i1is the current through the photoconductive path and i2 is the current through theionic di�usion path.

A.2.1.1. Applying potential Vc in the dark (level 2 in Fig. 59(A)). The measuredcurrent i0 is the dark current, Id. Therefore, Id � i0 � i1 � i2. The o�set potential isnot applied: E0 � 0. In the absence of illumination, the photoemf is zero and thephotoconductance is not turned on: Ep � 0 and Rp � 1. By virtue of Eq. (A26),no current goes through Rp, and thus i1 � 0. Therefore, Id � i2. By virtue of Eq.(A27), we obtain

Id � Vc

Rm

: �A29�

A.2.1.2. Illuminating bR membrane while membrane potential is maintained at Vc

(level 3 in Fig. 59(A)). The measured current i0 shifts to a new value, which con-sists of both the dark current and the photocurrent, Ip, by our de®nition above:i0 � Id � Ip.

Since the o�set voltage has not been applied, we have E0 � 0. Therefore, byvirtue of Eq. (A27), we obtain

i2 � Vc

Rm

: �A30�

In view of Eqs. (A29) and (A30), we have i2 � Id. Thus, i1 � Ip, and, by virtue ofEq. (A26), we have

Ip � Ep � Vc

Rp

: �A31�

A.2.1.3. Enforcing the null-current condition during illumination (back to level 2 inFig. 59(A)). By applying the o�set voltage E0, the membrane current is shiftedback to the level prior to illumination, Id. Therefore, we have i0 � Id. Solving Eqs.(A26) and (A27) for i1 and i2, respectively, and substituting them into Eq. (A28),we have

Id � Ep � Vc ÿ E0

Rp

� Vc ÿ E0

Rm

: �A32�

Combining Eqs. (A29) and (A32) and solving the resultant equation for E0, weobtain

E0 �ÿEp � Vc

� � Rm

Rm � Rp

� ÿEp � Vc

� � Gp

Gp � Gm

, �A33�


which, after rearranging, becomes:

Ep � E0 � Gp � Gm

Gp

ÿ Vc, �A34�

which is Eq. (12.3) in Section 12.2. By combining Eqs. (A31) and (A33), weobtain

Ip

E0� Rm � Rp

RmRp

� Gp � Gm, �A35�

which becomes Eq. (12.4).Eq. (A31) means that the driving potential of the photocurrent includes both

the true photoemf and the applied membrane potential. This is because theapplied potential can drive current through Gp in either direction (i.e., withoutrecti®cation). Eq. (A33) means that the e�ectiveness of the driving potential isdiminished, because of shunting through a parallel ionic di�usion path Gm; theextent of shunting is weighted by the relative magnitude of Gm with respect to Gp.Eq. (A35) means that the apparent photoconductance obtained by dividing thephotocurrent with the o�set voltage is actually the combined conductance duringillumination (Gp � Gm). The e�ect of shunting by the parallel ionic di�usion pathis that the apparent photoemf is undervalued and the apparent photoconductanceis overvalued.

If, however, Gp � Gm, then Eq. (A33) becomes

E0 � Ep � Vc, �A36�

and Eq. (A35) becomes

Ip

E0� Gp: �A37�

Thus, in the absence of shunting, the null current method directly yields the truevalue of the photoconductance but the o�set voltage gives the sum of the truephotoemf and the applied potential.

A.2.2. Nonzero dark conductanceWe have previously applied the null current method to the Mg-porphyrin-redox

BLM system [163,280]. But the interpretation of the null-current data is somewhatdi�erent. In this latter system, the pigment-mediated conductance, Gp, has thesame value in the dark, i.e., Gp is not zero in the dark. In the derivation above,Eq. (A29) must be replaced by

Id � Vc

Rp

� Vc

Rm

, �A38�

Eq. (A31) must be replaced by


Ip � Ep

Rp

, �A39�

and Eq. (A33) must be replaced by

E0 � Ep � Rm

Rm � Rp

� Ep � Gp

Gp � Gm

: �A40�

Eq. (A35) remains valid.In other words, the term Vc in Eqs. (A31), (A33), (A34) and (A36) must be set

to zero. This is because the current driven through Rp by the applied potential hasalready been included in the dark current Id (see Eq. (A38)).

If Gp � Gm, Eq. (A40) becomes Eq. (12.1):

E0 � Ep, �A41�and Eq. (A39) can be rewritten as

Ip

E0� Gp, �A42�

which is identical to Eqs. (A37) and (12.2). Eqs. (A41) and (A42) are easilyvisualized intuitively in applying the principle of potentiometry.

A.2.3. DiscussionIt is of interest to look into the role of Vc in the generation of the photocurrent

in bR membranes and the lack of it in Mg-porphyrin BLM. The key is anassumption that is embedded in the derivation when we applied Kirchho�'s rulesabove. It is assumed that an external applied potential (Vc and/or E0) can pass acurrent through the pigment-conductance channel Gp in either direction (polarity)(see Eq. (A26)). This means that by applying a su�ciently large o�set voltage, it ispossible to reverse the proton (or electron, in the case of Mg-porphyrin BLM)current ¯ow through Gp. This also means that bR and the Mg-porphyrinmembrane exhibit no recti®cation. This assumption is of course the prerequisite ofapplying the principle of potentiometry, which pits an external applied potentialagainst the (true) photoemf. The validity of this assumption is justi®ed as long asthe results do not give rise to contradictions or a `bizarre' picture. In our presentanalysis, we have not encountered any problems that warrant casting doubt onthe validity of this assumption (but that does not guarantee that problems willnever arise in other pigment-containing membrane systems). It is of interest tonote that the conventional I±V curve analysis also makes this implicit assumptionalthough it has seldom been advertised.

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