p k a calculations suggest storage of an excess proton in ... · release proton in an...

doi:10.1006/jmbi.2001.4902 available online at http://www.idealibrary.com on J. Mol. Biol. (2001) 312, 203±219

pKa Calculations Suggest Storage of an ExcessProton in a Hydrogen-bonded Water Networkin Bacteriorhodopsin

Velin Z. Spassov1,4, Hartmut Luecke2, Klaus Gerwert3* andDonald Bashford1*

1Department of MolecularBiology, The Scripps ResearchInstitute, 10550 North TorreyPines Road, La JollaCA 92037, USA2Department of MolecularBiology and BiochemistryUniversity of California, Irvine3205 BioSci II, IrvineCA 92697-3900, USA3Ruhr-Uni Bochum, LehrstuhlfuÈ r Biophysik, UniversitaÈtsstr.150, GebaÈude ND 04 NordD-44780, Bochum, Germany4Institute of BiophysicsBulgarian Academy of Sciences1113 So®a, Bulgaria

Present address: V. Z. Spassov, MScranton Road, San Diego, CA 9212

Abbreviations used: bR, bacteriorFourier transform infrared (spectros

E-mail addresses of the [email protected]

0022-2836/01/010203±17 $35.00/0

Calculations of protonation states and pKa values for the ionizablegroups in the resting state of bacteriorhodopsin have been carried outusing the recently available 1.55 AÊ resolution X-ray crystallographicstructure. The calculations are in reasonable agreement with the availableexperimental data for groups on or near the ion transport chain (the reti-nal Schiff base; Asp85, 96, 115, 212, and Arg82). In contrast to earlier stu-dies using lower-resolution structural data, this agreement is achievedwithout manipulations of the crystallographically determined heavy-atom positions or ad hoc adjustments of the intrinsic pKa of the Schiffbase. Thus, the theoretical methods used provide increased reliability asthe input structural data are improved. Only minor effects on the agree-ment with experiment are found with respect to methodological vari-ations, such as single versus multi-conformational treatment of hydrogenatom placements, or retaining the crystallographically determinedinternal water molecules versus treating them as high-dielectric cavities.The long-standing question of the identity of the group that releases aproton to the extracellular side of the membrane during the L-to-M tran-sition of the photocycle is addressed by including as pH-titratable sitesnot only Glu204 and Glu194, residues near the extracellular side thathave been proposed as the release group, but also an H5O2

� molecule in anearby cavity. The latter represents the recently proposed storage of therelease proton in an hydrogen-bonded water network. In all calculationswhere this possibility is included, the proton is stored in the H5O2

� ratherthan on either of the glutamic acids, thus establishing the plausibility ontheoretical grounds of the storage of the release proton in bacteriorho-dopsin in a hydrogen-bonded water network. The methods used heremay also be applicable to other proteins that may store a proton inthis way, such as the photosynthetic reaction center and cytochrome coxidase.

# 2001 Academic Press

Keywords: bacteriorhodopsin; electrostatic model; H-bonded network;Zundel proton; proton release
*Corresponding authors
Introduction

This paper reports calculations, using a semi-macroscopic electrostatic model, of the states of

SI Inc., 96851, USA.hodopsin; FTIR,copy).ding authors:

protonation of various ionizable groups in the

ground state of the light-driven, trans-membrane

ion pump, bacteriorhodopsin. In particular, we

have modeled various alternative sites for the sto-

rage of a proton that is released to the extracellular

side of the membrane early in the photocycle,

including the possibility that this proton resides in

a hydrogen-bonded water network inside the pro-

tein rather than on any particular protein side-

chain.

# 2001 Academic Press

204 Bacteriorhodopsin pKa Calculations

Bacteriorhodopsin (bR) is a transmembraneproton-transport protein for which there exists awealth of structural and mechanistic informationfrom a variety of sources, including visible lightand FTIR spectroscopy, electron microscopy, elec-tron diffraction, X-ray crystallography, and NMRspectroscopy; and it has become a prototype forother transmembrane proteins whose functionincludes ion transport, such as the photosyntheticreaction center and cytochrome c oxidase.1 ± 4 Theretinal chromophore is bound to a lysine side-chain of bR by a Schiff base linkage, which in theground state of bR, is protonated. Excitation bylight causes a rapid isomerization of the chromo-phore triggering a series of protonation statechanges involving the Schiff base and several othergroups in bR, as well as structural transitions, thatultimately result in the release of a proton to theextracellular side of the membrane, and a protonuptake from the cytoplasmic side.5 ± 8 The cycleinvolves intermediates that are designated, J, K, L,M, N, and O, in order of their appearance. Of par-ticular interest here is the release of a proton froma group, X, to the extracellular surface of the pro-tein during the L-to-M transition, coupled to themovement of a proton from the Schiff base toAsp85.

The identity of the group X, upon which therelease proton is stored in the ground state,remained unknown even after the identities of anumber of other groups in the proton transportchain were established. As more complete andaccurate structural models became available, itappeared that a close pair of glutamic acid residuesnear the extracellular surface, 194 and 204, werewell positioned to play the role of group X. Site-directed mutagenesis of these residues clearlyshowed that they were involved in proton release,and early FTIR experiments appeared to suggestthat one or the other these groups was itself groupX.9 ± 13 But recently, time-resolved nanosecond stepscan FTIR experiments by Rammelsberg et al.13

exclude protonation changes of R82, E204, E194 orother side-chains in this region during the tran-sition to the M state, ruling out the identi®cation ofthese groups as the release group. Instead, theseexperiments showed that an IR continuum absorp-tion band present in the ground state disappearsduring the transition to M, when the proton isreleased. Spectroscopic studies on a number ofmodel systems have shown that such continuumbands are characteristic of an excess proton withinan hydrogen-bonded network;14 and in ab initio cal-culations of an excess proton in water, the ¯uctu-ation of the excess proton between oxygen atomsin species such as H5O2

� and higher-order com-plexes are predicted to give rise to continuum IRbands.15 It was therefore proposed that the disap-pearance of the continuum band in the L-to-Mtransition is related to the deprotonation of theproton release group, and that group X was there-fore an excess proton within a hydrogen-bondednetwork involving at least two internal water

molecules.13 Recently, FTIR experiments on deuter-ated samples have provided additional support forthis proposal.16 An H5O2

� molecule in a proteincavity is the minimal model for such a proteinrelease group.

Although the FTIR results provide strong evi-dence for the chemical character of the releasegroup, they cannot resolve its speci®c location.Speci®c water positions within several cavities inthe extracellular half of the protein are provided bya recent bR structure determined at 1.55 AÊ resol-ution by X-ray crystallography,17 but the X-ray datado not give direct evidence of protonation states.Furthermore, consideration of typical pKa valuesmake it seemingly implausible that a proton wouldreside preferentially on a species such as H5O2

�

rather than on carboxylic acid groups. We thereforetake an approach integrating the available exper-imental data with theoretical calculations aimed at®nding a speci®c model for the storage of therelease proton, and evaluating its plausibility byenergetic calculations using semi-macroscopic elec-trostatic models that have proven successful in thepast for studies of protonation states and pKa valuesin proteins, including bacteriorhodopsin.18 ± 23 Thismight also provide a paradigm for studies of otherproton transporting membrane proteins, such as thephotosynthetic reaction center and cytochrome coxidase, in which IR continuum bands have alsobeen observed.

In addition, the availability of high-resolutionstructural data, including internal water molecules,makes it possible to re-visit the problem of calcu-lating the titration properties of other functionallyimportant groups in bR, to see whether improvedstructural data result in improved predictions, asone would hope, and to compare models treatinginternal water molecules explicitly to models treat-ing water-®lled cavities as cavities of high-dielec-tric continuum. Because of the high quality of thestructural data, we have taken a conservativeapproach to structural modeling, generally prefer-ring to leave heavy-atom positions unchanged. Anextension of the usual theoretical models used insemi-macroscopic pKa calculations was necessaryto incorporate the idea of H5O2

� as an ionizable sitewithin a protein.

Results

Since a major aim of this work is to explore theground-state location of the extracellular releaseproton, the present calculations were designed toallow for each of the following alternative locationsthat have been proposed on experimentalgrounds:11 ± 13 Glu204, Glu194 or a hydrogen-bonded water network, so that their plausibility ontheoretical grounds can be evaluated. Calculationswere performed using structural models that dif-fered as to whether crystallographic water mol-ecules were explicitly included or whether theywere removed, so that water-®lled cavities were

Bacteriorhodopsin pKa Calculations 205

represented as cavities of bulk-water-like dielectric;whether a single conformer was used or whether amulti-conformer calculation with respect to hydro-gen-atom placements was done; and whether thepossibility of an H5O2

� molecule in a protein cavitywas included. In all cases, glutamic acid residues194 and 204 were included as possible proton sto-rage sites. Other aims of the work are to determinewhether pKa values and ionization states for othergroups involved in the photocycle can be predictedwhen a high resolution (1.55 AÊ ) X-ray crystallo-graphic structure17 is used rather than the lower-resolution structures used in the ®rst calculationsof this kind for bR,18 and whether this agreementcan be achieved without the ad hoc structuremanipulations, or the ®xing of the Schiff base pro-tonation that were previously required. For thisreason, the residues considered as ionizable are notcon®ned to the proton-release region, but includeionizable groups throughout the molecule, includ-ing the Schiff base. In most calculations here, nochanges are made to the crystallographically deter-mined heavy-atom positions, otherwise changesare small and con®ned to a few atoms.

Calculations involving only the Schiff base andstandard side-chains as ionizable groups werecarried out using the now-standard combination ofmulti-site titration methods with a model assumingmacroscopic electrostatics with atomic detail(MEAD model) for the effects of the proteinenvironment on ionization energetics.18,24 Exten-tions to this methodology to allow the possibilityof H5O2

� as a proton storage site, and multiplehydrogen atom placements, are described in The-ory, Methods and Structural Models. That sectionalso provides an outline of the standard theory,including de®nitions of several quantities used inpresenting the results, pKhalf (the closest analog topKa in a coupled, multi-site system), pKintr, and the``Born'' and ``background'' terms.

In some cases the calculated pKhalf values arebelow 0 or above 15, and some care is needed inthe interpretation of the results. Since the calcu-lations are based on either a single conformer, or amodel with conformational ¯exibility limited tohydrogen atoms, extreme pKhalf values should beunderstood as predictions that it is not possible toprotonate (in the pKhalf < 0 case) or deprotonate (inthe pKhalf > 15 case) the site within the normal pHrange while keeping the structure unchanged. Thisimplies that any actual titration of these groupswould be energetically coupled to structuralchanges not accounted for in the model. In particu-lar, a number of sites are known to remain in par-ticular protonation states throughout the pH rangein which bacteriorhodopsin is stable, so that thesesites should be coupled to the acid or alkalinedenaturation of the protein. It is to be expectedthat extreme pKhalf values will be calculated forsuch sites.18

Electrostatic potentials in the channels

Internal cavities large enough to be occupied byone or more water molecules were located by asimple algorithm that checked possible solvent-sized probe positions on a cubic lattice for overlapwith protein heavy-atoms, and by graphical exam-ination to distinguish internal pockets from theexternal surface. It was con®rmed that all internalcrystallographic water molecules fall into thesecavities, except for one water molecule making avery short H-bond with Asp115. The boundaries ofthese cavities are displayed in Figure 1 where theyare also colored according to electrostatic potential.

Immediately below (to the extracellular side of)the Schiff base is a water accessible cavity, andbelow that is a second, larger cavity. We denotethese cavities as ECu and ECd, respectively. Theyare separated by the guanidinium group of Arg82which forms both a steric and (for proton trans-port) an electrostatic barrier between the two cav-ities. ECd is near the extracellular membranesurface, in direct contact with glutamic acid resi-dues 194 and 204, which have been implicated inthe proton release. If residues 194 and 204 are bothdeprotonated, ECd contains a strong negative elec-trostatic potential. However, if one of these resi-dues is protonated, the cavity's potential becomesmildly positive. Therefore, ECd is an attractive can-didate for the possible location of a proton storedin a hydrogen-bonded water network providedGlu194 and Glu204 are deprotonated.

The change in color of the ECd cavity inFigure 1(a) from deep red at the bottom to pink atthe top re¯ects the fact that the electrostatic poten-tial is substantially more negative in the bottompart of the pocket, near the negative charges of theglutamate residues, than at the top, near Arg82.This fact is of particular signi®cance in the H5O2

�

calculations described subsequently.

Models without explicit water

The simplest model for protonation state calcu-lations, which we denote here as S, is a single con-former with no explicit water molecules. Theinternal cavities, which in the crystal structure con-tain water molecules, here are ®lled with high-dielectric (e � 80) continuum. The hydrogen atompositions were those generated by the HBUILDand the minimization procedure described inTheory, Methods and Structural Models. Thesingle-conformer version of the protein titrationtheory was used. In contrast to previousstudies18,20 ± 22 based on older structural models,there was no ad hoc adjustment of the Schiff-basepKmod, or re-positioning of the Arg82 side-chain oralteration of any other protein heavy-atom pos-itions from the crystallographic structure.

The calculated pKhalf values, as well as the Bornand background terms contributing to the intrinsicpK, are shown in Table 1. The �pKBorn termsre¯ect the energetic penalty of burying the charged

Figure 1. Internal cavities in bacteriorhodopsin andtheir electrostatic potential. The protein backbone isshown in yellow and the membrane surfaces as greenmeshes. The extracellular side is at the bottom. Selectedside-chains are also shown. The irregular shapes are thesurfaces of internal cavities found by the methodsdescribed in the text. These surfaces are colored from


forms of ionizable groups in the low-dielectric pro-tein interior, and tend to be larger for more loca-lized charges. Thus, these terms are consistentlylarge and positive for buried carboxylic acidgroups, while for the buried arginine residues andthe Schiff base they are negative and of lesser mag-nitude. The �pKback terms re¯ect electrostatic inter-actions with non-titrating polar groups, such as thebackbone amides, and often compensate for theBorn terms of buried groups, particularly in morehydrophilic regions of the protein. Finally the inter-actions between ionizable groups produce furthereffects, which may be quite strong in regionswhere several such groups are clustered together,to produce the individual site titration curves fromwhich the pKhalf values are extracted (see Theory,Methods and Structural Models).

The resulting pKhalf values are in good generalagreement with the available experimentalmeasurements. The Schiff base and Asp96 havevery high calculated pKhalf values, which are con-sistent with the ®nding that in the ground statethese groups remain protonated until the alkalinedenaturation point. The high pKhalf value forAsp96, which must be in the protonated state inorder to act as a proton donor to the Schiff base inthe M-to-N transition, is mainly the result of thelarge, positive �pKBorn term which is not signi®-cantly compensated by the background term in therelatively hydrophobic region where Asp96 is bur-ied. In contrast, the Schiff base has a relativelysmall negative �pKBorn term, because the positivecharge of the protonated state is delocalized overthe retinal, which tends to reduce the penalty ofburial. Its high pKhalf is due to favorable inter-actions between its positive charge and nearbynegative charges, primarily Asp85 and Asp212.Asp85, the recipient of a proton in the L-to-M tran-sition, has a calculated pKhalf of 1.7, which is some-what lower than the experimentally measured pKa

of the acid-induced purple to blue transition (2.6).Asp212 and Arg82, which are part of the counter-ion complex just below (on the extracellular sideof) the Schiff base, are predicted to be in theircharged forms throughout the pH range in whichthe protein is stable, in agreement with experiment.The charged forms of the Schiff base and its coun-terion complex (glutamate residues 85 and 212,and Arg82) are stabilized by the strong site-siteinteractions between these groups, which is morethan suf®cient to offset the Born terms. A largeupward pKa shift is predicted for Asp115, in agree-

red to blue for more negative to more positive electro-static potential, respectively. The potential is calculatedby the MEAD potential program, according to the calcu-lated state of protonation at neutral pH (see Table 1),except as noted for the sub-®gures. The ECd cavity isjust below Arg82 and the ECu cavity is just above it.(a) Both Glu194 and Glu204 are assumed to be deproto-nated. (b) Like (a) except Glu194 is protonated.

Table 1. pK values calculated for single conformation without explicit water (model S)

Sitea pKmod �pKBornb �pKback

b pKintr pKhalf Experiment55 ± 58

Arg7 12.0 ÿ3.0 2.1 11.1 14.6Glu9 4.4 5.2 ÿ5.6 4.0 0.2Lys30 10.4 ÿ10.3 11.7 11.8 14.1Asp36 4.0 3.6 ÿ5.4 2.2 <0.0Asp38 4.0 1.3 0.2 5.5 3.5Lys40 10.4 ÿ4.0 1.0 7.4 7.7Lys41 10.4 ÿ2.7 0.8 8.5 12.9Glu74 4.4 0.2 0.4 5.0 4.6Arg82 12.0 ÿ6.0 ÿ4.1 1.9 >15.0 >13.8Asp85 4.0 10.3 ÿ6.5 7.8 1.7 2.6Asp96 4.0 10.1 ÿ1.7 12.4 >15.0 >12.0Asp102 4.0 0.4 0.4 4.8 3.2Asp104 4.0 1.8 ÿ1.2 4.6 < 0.0Asp115 4.0 11.6 ÿ5.1 10.5 8.4 > 9.5Lys129 10.4 ÿ0.6 0.1 9.9 10.0Arg134 12.0 ÿ6.4 11.3 16.9 >15.0Lys159 10.4 ÿ3.7 ÿ0.6 6.1 10.5Glu161 4.4 0.4 0.2 5.0 3.7Arg164 12.0 ÿ1.7 4.2 14.5 >15.0Glu166 4.4 2.7 ÿ0.1 7.0 < 0.0Lys172 10.4 ÿ2.3 0.2 8.3 7.1Arg175 12.0 ÿ6.3 4.5 10.2 12.8Glu194 4.4 9.6 ÿ2.5 11.5 >15.0 c

Glu204 4.4 9.6 ÿ6.0 8.0 < 0.0 c

Asp212 4.0 10.5 ÿ8.5 6.0 < 0.0 < 2.5Arg225 12.0 ÿ6.5 3.5 9.0 0.5Arg227 12.0 ÿ0.2 0.9 12.7 14.0SB (216) 7.0 ÿ3.3 ÿ1.7 2.0 >15.0 >12.0

a Tyrosine residues were also included, but all were found to have pKhalf values well above 15.b The �pK are the pK equivalents of ��GBorn and ��Gback of equation (2). pKint � pKmod � �pKBorn � �pKback.c The ``release group'' is believed to involve Glu194 or Glu204 or a network of water molecules near these residues. It is certainly

protonated at neutral pH. Experimental work indicates a release-group pKa value of 9.5,32 or 9.0 (R. Rammelsberg & K.G., unpub-lished results).


ment with experiment, but the magnitude of theshift is somewhat under-predicted. The calcu-lations predict very high pKhalf values for all tyro-sine residues, which is consistent with the ®ndingthat no tyrosinate is seen in the ground state at pHvalues below 12.25

As for the glutamic acid residues 194 and 204,which have been suggested as candidates for theproton release group, 194 is predicted to be proto-nated throughout the pH range in which the pro-tein is stable, while 204 is predicted to bedeprotonated. Thus, the S model is consistent with194 acting as the release group, but it should bepointed out that an excess proton in the internalwater is not included as a possibility in this model.FTIR experiments exclude a protonation change ofeither 194 or 204 during the photocycle of thewild-type.13 Furthermore, if either of these groupsis protonated in the BR state at neutral pH, it isunlikely that the H-bonding is not changed duringthe photocycle. Such H-bonding changes wouldhave been observed by FTIR, as in the case ofD115, which is seen undergoing changes in the H-bonding environment in the K, L, M and N inter-mediates. It therefore seems very unlikely thateither Glu204 or Glu194 are protonated at neutralpH.13 In summary, if the possibility of H5O2

� as aproton storage site is excluded, Glu194 is predicted

to be the proton-release group, but this contradictsthe experimental results.

To explore whether ¯exibility with respect tohydrogen-bonding arrangements could in¯uencethe results, calculations were performed thatallowed for variable hydrogen atom positions inthree distinct regions of the protein: Asp115/Asp96; Asp85/Asp212; and Glu194/Glu204. Ineach case, four possible hydrogen positions wereincluded for each carboxylic acid: protonation oneither of the two oxygen atoms, and for each case,the syn or anti orientation for the proton. For thestates in which both members of a close pair wereprotonated, all 16 possible arrangements wereincluded, so that correlations between proton pos-itions within close pairs was fully accounted for.The multi-conformational formulation described inTheory, Methods and Structural Models was used.We denote this set of calculations as the MCmodel.

The pKhalf values calculated using the MC model(Table 2) are very similar to those from the single-conformer calculation for most residues, the excep-tion being Asp115, whose pKhalf value is now insigni®cantly better agreement with experiment.Examination of the calculated populations of thevarious conformers shows that in most cases, oneconformation is strongly preferred over others, andthat the preferred conformer is the same one found

Table 2. pK values for multi-conformer calculation with-out explicit water molecules (model MC)

Site pKhalf Experiment

Asp96 >15.0 >12.0Asp115 9.7 >9.5Asp85 1.8 2.6Asp212 <0.0 <2.5Glu194 >15.0 a

Glu204 <0.0 a

The calculation includes all the same residues shown inTable 1, but here only sites treated by the multi-conformationalformalism are shown. Results for the other sites are essentiallyidentical to Table 1.

a See footnote c of Table 1.


in the H-placement scheme used to prepare thesingle-conformer calculation. In effect, the multi-conformer calculation has provided a test of theinitial proton-placement scheme, and the resultsindicate that the initial placements were correct inthe sense of obtaining optimal electrostatic inter-actions.

Models with crystallographic water molecules

Calculations were also carried out in which all23 crystallographic water oxygen positions wereretained. These include seven water molecules ininternal cavities between the Schiff base and theextracellular membrane surface, and three in cav-ities between the Schiff base and the cytoplasmicsurface.17 Hydrogen atom positions were builtonto the crystallographic oxygen atom positionsfor all of these water molecules, by the proceduredescribed in Theory, Methods and StructuralModels. Regions occupied by these water mol-ecules are treated as ``protein'' as far as the dielec-tric model is concerned, which means that theinterior region now is nearly all assigned a dielec-tric constant of 4, with only a few small interiorpockets of high-dielectric continuum. Therefore,the partial stabilization that was previously pro-vided to buried charges by the high-dielectricpockets in the above calculations (generally

Table 3. Single-conformer calculation with explicit water (mo

Site �pKBorn �pKback

Lys30 ÿ10.3 11.3Arg82 ÿ7.4 5.8Asp85 11.5 ÿ11.8Asp96 10.5 ÿ1.6Asp115 11.7 ÿ6.3Lys159 ÿ3.8 6.2Arg175 ÿ6.3 4.5Glu194 10.3 ÿ8.5Glu204 10.6 ÿ7.6Asp212 11.5 ÿ11.5SB (216) ÿ3.4 0.4

The calculation includes all the same residues shown in Table 1,proton transport, or whose calculated pKhalf value differs signi®cantl

a See footnote a of Table 1.

reducing the magnitude of the �pKBorn term), isnow removed, but interactions of the charged formwith the explicit water dipoles (now entering inthe �pKback term) may provide compensatingstabilization.

The results of a single-conformer calculationwith explicit water, which we denote as model WS(Table 3) are largely similar to the results withoutexplicit water, but there is a striking reversal of theroles of glutamic acid residues 194 and 204. Glu204now remains protonated throughout the pH rangein which the protein is stable, while Glu194remains deprotonated. Thus, the Glu194/Glu204pair still stores one proton, but the proton nowresides on Glu204 rather than Glu194. As before,the possibility of the release proton as an excessproton in the internal water network is notincluded in this model.

The pKhalf value of Asp115 calculated usingmodel WS is signi®cantly lower than that calcu-lated using the corresponding model with no expli-cit water (model S) and thus farther from theexperimental result. The MC results, discussedabove, suggest that this may be related to thechoice of the Asp115 proton position. The WSmodel correctly predicts the Asp85 pKa value to beshifted downward, but overestimates the magni-tude of the shift. This is in contrast to the S model,which gives better agreement with experiment. Onthe whole, the single-conformer model with expli-cit water predicts the same protonation states asthe model without explicit water, apart from the194/204 reversal and the borderline protonationstate of Asp115; but the quantitative agreementwith available experimental pKa data is not asgood. This may be because the WS model does notallow the explicit water molecules to re-orient inresponse to protonation changes, while the high-dielectric interior cavities of the S model are able torespond by polarization changes.

The next model, WMC, allows for ¯exibilitywith respect to hydrogen-bonding arrangements,and limited re-orientation of the explicit water mol-ecules. It was designed to focus on the in¯uence ofwater molecules in the ECd pocket on the position-

del WS)

pKintr pKhalf Experiment

11.4 13.210.4 >15.0 >13.83.8 <0.0 2.612.9 >15.0 >12.09.4 7.0 >9.512.8 >15.010.2 11.86.2 <0.0 a

7.4 >15.0 a

4.0 <0.0 < 2.54.0 >15.0 >12.0

but here only sites which are either known to be involved iny from that calculated in the S model are shown.

Figure 2. pH titration of Glu194 and Glu204 in modelWMC (explicit water, multiple conformations). Thecurve for the sum of the protonation of Glu194 andGlu204 shows that throughout the normal pH range,one proton is present on the pair. This proton is sharedbetween Glu194 and Glu204. This is in contrast to pre-ceding calculations where either 194 or 204 holds theproton exclusively (Tables 1, 2 and 3).


ing of the putative release proton on either Glu194or Glu204, or the possibility of the two residuessharing the proton. As in the MC model, all 16possible ways of positioning two protons on theside-chains of residues 194 and 204, and all eightways of positioning one proton on the pair areincluded in a multi-conformer calculation. For eachof these proton con®gurations, as well as for thedoubly deprotonated state, water hydrogen pos-itions were re-built using the HBUILD and mini-mization procedure described in Theory, Methodsand Structural Models. This allows the water mol-ecules to re-orient in response to changes in theprotonation state. In order to avoid biasing thecalculations in favor of more protonated states, anequal number of overall conformers (16) wasincluded for the doubly protonated state, the statewith Glu194 alone protonated, the state withGlu204 alone protonated and the doubly deproto-nated state. In the doubly protonated case, therewere already 16 conformers, but in the other cases,additional conformers were created by combiningglutamic acid proton con®gurations for that par-ticular state with water con®gurations that hadbeen generated for other protonation states. As aresult, a total of 64 conformations are included.The multi-conformer formalism is then applied.The energetic cost of this water re-orientation isaccounted for by the reference-state energy differ-ences calculated by the CHARMM22 energy func-tion and MEAD-based solvation effects (seeTheory, Methods and Structural Models). Again,the water molecules were treated only as H2O, andnot as possible sites of protonation.

The calculations using this model predict a pH-dependent sharing of a proton between glutamicacid residues 194 and 204 (Figure 2). The fractionof the proton on 204 is higher, but this result issensitive to the details of the water positions andorientations, and thus to the ®ne details of the crys-tallographic structure determination and thehydrogen-building procedures. Essen et al.26 haveproposed that both 194 and 204 could serve jointlyas a release group, with nearby water moleculesexerting a signi®cant in¯uence.

In both this calculation and the WS model calcu-lation, the inclusion of explicit water moleculesrather than a pocket of high-dielectric continuumtends to shift the equilibrium towards the protona-tion of Glu204 rather than Glu194. Examination ofthe preferred water orientations shows a semi-line-ar chain of hydrogen bonds (Arg82-W403-W404-Glu194) connecting the negatively charged Glu194with the positively charged side-chain of Arg82,leading to enhanced stabilization of the state inwhich Glu204, rather than 194, holds a proton.This effect occurs in both the WS and WMCmodels but its energetic consequences in the latterare not so strong as to cause complete occupancyof the state with Glu204 protonated.

Models with H5O2� in release channel

A model that allows for the possibility that therelease proton is stored in a hydrogen-bondedwater network has been prepared by building anH5O2

� molecule near the Glu194/Glu204 pair.H5O2

� is the minimal model for the storage of aproton in a low-barrier, water-water hydrogenbond of the type that has been proposed to beresponsible for the observed continuum band inthe FTIR difference spectra.13 We note that someprevious computational studies22,27 included H3O�

as an ionizable site within the Schiff base-counter-ion complex, but this does not pertain to the ques-tion of the release proton or the continuum band.

The placement of the H5O2� is the main dif®culty

in constructing such a model. The ECd pocketshown in Figure 1(a) was chosen as a likelylocation since it is near residues 194 and 204 on theextracellular side, and mutations of 204 and 194have signi®cant in¯uence on the continuum band(R. Rammelsberg et al., unpublished results). Thispocket has a strong negative potential when resi-dues 194 and 204 are deprotonated. The ECu pock-et can be excluded because the mutation,Asp212Asn, has no in¯uence on the continuumband.13 The ECd pocket is bounded by the glutamicacid dyad on its extracellular side, and by Arg82on the opposite side. In the crystal structure, thispocket contains three water molecules denotedW403, W404 and W405, and it is suf®ciently largeto accommodate a fourth water molecule as well.

Initially, we explored the possibility that theH5O2

� molecule could be formed by using the oxy-gen positions from W403 and W404. These twowater molecules form a hydrogen-bonded bridge

Figure 4. Individual site titration curves from modelPW, which includes the possibility of H5O2

� as the pro-ton release group. The three lower curves pertain to theindividual sites listed in the legend. The upper curve isthe sum of the three lower curves. Above pH 4, oneproton is present and resides mostly in the H5O2

� form,though it is partly shared with Glu204.


between the side-chains of Glu194 and Arg82. Pre-liminary protonation-state calculations showedthat this H5O2

� readily converts to 2H2O through-out the pH range, because of its interaction withthe positive charge of Arg82. However, aCHARMM energy minimization of this initialH5O2

� position with the water oxygen atom nearGlu194 (the W404 oxygen) restrained, caused theother oxygen atom (from W403,) which has a highB-factor and elongated density in the X-ray crystal-lographic study, to move away from the arginineand into an unoccupied region of the pocketbetween the carboxylate groups of glutamate resi-dues 194 and 204. (During this minimization theposition of other water and protein atoms wasrestrained, and residues 194 and 204 were deproto-nated.) It was then possible, without steric clashes,to re-®ll the vacated W403 position with a watermolecule having the original W403 oxygen coordi-nates. In effect, the empty fourth water positionnoticed in this pocket in the crystal structure, aposition very near the dyad, became occupied bythe extra oxygen atom needed to change W404from H2O to H5O2

�. The resulting model is shownin Figure 3. It should be emphasized that as far asheavy-atom positions are concerned, none of thecrystallographically determined coordinates havebeen altered; the model only introduces one newoxygen position.

The methods described in Theory, Methods andStructural Models for treating H5O2

� as a titrating``site'' in a protein were then applied to this struc-tural model. We refer to this as the PW (protonatedwater) model. The resulting titration curves for theH5O2

� and the two glutamic acid residues areshown in Figure 4. Below pH 0, the two glutamic

Figure 3. The H5O2� model and its environment in the

lower extracellular side pocket, ECd.

acid residues are protonated but H5O2� is in the

2H2O form. As the pH increases from 0 to 3, thistwo-proton state of the complex changes to a one-proton state, and the remaining proton is sharedbetween H5O2

� and Glu204, with the H5O2� receiv-

ing between 75 and 85 % of the proton. This situ-ation persists throughout the range between pH 4and 15. To explore the robustness of these resultswith respect to the choice of the pKmod value ofH5O2

� (see Theory, Methods and StructuralModels), a calculation was done at pH 7.0 with thepKmod value lowered by 1. The resulting fractionalprotonations of H5O2

� and Glu204 were 0.35 and0.65, respectively. Thus, in a calculation that allowsfor the possibility of a proton in an internal hydro-gen-bonded water network in the proton releaseregion, such a proton does indeed occur preferen-tially to a proton on the glutamic acid dyad,although uncertainty as to pKmod values canreduce, but not eliminate the fraction residing onH5O2

�. The pKhalf values of other groups are similarto those of the S model which is the non-H5O2

�

model most similar to this one (Table 4).The region of Glu204/294 is somewhat disor-

dered in the crystal structure.17 The side-chains ofGlu194, Glu204, Ser193, and water molecule 403have high B-factors. Furthermore, the H5O2

� pos-ition modeled by the above procedure produced anumber of unusually short oxygen-oxygen dis-tances between the extra oxygen atom and heavyatoms from the crystallographic structure, althoughstrong electrostatic interactions more than offsetunfavorable van der Waals interactions. Thismotivated additional calculations to explore thesensitivity of the results to structural variations.

Table 4. Models allowing H5O2�

Site PW model PWR (relaxed) model

pKint pKhalf pKintr pKhalf

Glu9 4.5 0.2 4.6 1.0Lys30 11.0 12.3 11.2 12.7Asp85 3.9 <0 3.9 <0Asp115 10.7 8.8 10.6 8.8Glu194 11.6 0.9 10.9 <0Glu204 12.3 1.3 10.4 <0Arg225 6.9 < 0 6.9 <0Arg227 12.7 14.3 12.7 14.3H5O2

� ÿ8.8 a ÿ7.9 a

The sites shown in Table 1 were included in the calculations, but only results differing by >0.2 pK unit from Table 1 (model S) areshown.

a Result is a complex titration curve (see Figures 4 and 5).

Figure 5. Individual site titration curves from modelPWR, a relaxed variant of model PW (see Figure 4). Inthis case, the proton resides entirely on H5O2

� through-out the normally accessible pH range.


A structural model was therefore prepared by anenergy minimization that allowed apparentlydisordered (high B-factor) heavy atoms to relax.Starting with the above PW model, energy mini-mizations were performed in which the heavyatoms of the side-chains of Ser193, Glu194 andGlu204 and the oxygen atoms of water 403 and theH5O2

� were allowed to move with only weak har-monic constraint. As before, all hydrogen atomswere allowed to move without constraint. The pro-tonation states were the same ones used for thePW model preparation. The largest heavy-atommovements were seen for the Oe atoms of Glu194(0.46 AÊ r.m.s.d.). The Oe atoms of Glu204 movedby 0.28 AÊ ; the Og atom of Ser193 moved by 0.17 AÊ ;one of the oxygen atoms of H5O2

� moved by0.32 AÊ ; and water molecule W403 moved by0.15 AÊ . We designate this relaxed model as PWR.The calculations for the ionization states of thismodel (Table 4, relaxed-model column, andFigure 5) give the result that the proton remains onthe H5O2

� throughout the pH range, while effectson other groups are relatively small. The tendencyof the release proton to prefer the H5O2

� formrather than a glutamic acid is even stronger in thiscalculation than in the PW model. There is no dis-cernable sharing of the proton in Figure 5. Sharingof the proton with Glu204 occurs only if the pKmod

for H5O2� is arti®cially lowered to the unrealistic

value of ÿ4.7, as compared to the pKmod value ofÿ1.7 adopted here (see Theory, Methods and Struc-tural Models).

Discussion

In general, good agreement was obtainedbetween the calculations and previously publishedexperimental results for the protonation states and,where available, the pKa values of ionizable resi-dues on, or closely involved in the ion transportpathway. Inclusion of conformational variabilitywith respect to proton placement improved theaccuracy of the calculated pKa values in a fewcases, and in other cases served as a check on theinitial proton placements while leaving the calcu-

lated pKa values unchanged. It might be thoughtthat inclusion of explicit water molecules ininternal cavities should be preferred over the mod-eling of water-®lled cavities as pockets of highdielectric constant, particularly when water pos-itions are available from X-ray crystallographic stu-dies. However, in the usual formulation ofelectrostatic continuum models for pKa calcu-lations, this amounts to treating the water mol-ecules as dipoles that do not re-orient even whenadjacent side-chains change their ionization state.On the other hand, a high dielectric cavity is ableto polarize in response to such events, althoughthis can only be a crude model of the actualresponse of the cavity water. In the present work,calculations of both kinds were tried, includingcalculations allowing for limited explicit water re-orientation through the minimization protocol. Theresults were generally similar, but inclusion ofexplicit water molecules in a single-conformercalculation led to somewhat worse agreement withexperimental pKa values than the treatment ofinternal water as high-dielectric cavities.


In early computational studies of the protonationstates of the ground state of bacteriorhodopsin18,21

based on a more approximate structural modelderived from cryo-electron microscopy data,28 sat-isfactory agreement with experiment could only beobtained by manipulation of the Arg82 side-chainposition. Since the data did not provide densitycorresponding to this side-chain, it was initiallymodeled in a ``down'' orientation away from theSchiff base. In order to provide enough stabiliz-ation of aspartate negative charges to predict bothAsp85 and Asp212 to be deprotonated, Arg82 wasmoved into an equally plausible `ùp'' orientationnear these aspartate side-chains.18,21 In some casesit was also necessary to add an ad hoc positive termto the intrinsic pK of the Schiff base to force it toremain protonated.18 From this work it wasobvious that the pK value of Asp85 depends onthe position of Arg82, and that movement ofArg82 can in¯uence the pK of Asp85 and could bepart of the proton release trigger. Such movementis actually found now in the M state.29,30 It is grati-fying that in the present work, using a high resol-ution crystallographic structure, and a Schiff-basecharge model based on high quality density-func-tional calculations, no manipulations of heavy-atom coordinates or pKintr values were required toobtain good agreement with experiment.

The actual position of the guanidinium group, asrevealed by the new crystal structure, is midwaybetween the ``down'' and `ùp'' positions. The ECu

cavity (Figure 1) corresponds approximately to theold `ùp'' position, and the ECd cavity correspondsto the old ``down'' position. In the present calcu-lations, the stability of the release proton in thehydrogen-bonded network involves a balancebetween the stabilizing effect of negative chargefrom Glu194 and Glu204, and the destabilizingeffect of the positive charge of Arg82. Indeed,Arg82 is thought to serve as a crucial link in achain of conformational changes that trigger pro-ton release.3,22,31

As for the groups which have previously beenproposed as the group X, which releases a protonto the extracellular side during the L-to-M tran-sition, the computational models that do not allowfor the proton to be stored in water predict thateither Glu204 and Glu194 holds the proton, or thatthe proton is shared between them, depending onthe model details. A previous MEAD-type study23

of various side-chains as possible proton releasegroups found that Glu204, but not Glu194, couldact as the release group; but this study was basedon older structural models in which Glu194 waspositioned differently, and not in such close associ-ation with Glu204. In the development of a mini-mal model for a proton stored in a hydrogen-bonded water network, we found that the mostplausible location was the lower part of the ECd

cavity shown in Figure 1. A position for an H5O2�

molecule was found that allowed for favorableinteractions with Glu204 and Glu194 in their car-boxylate forms, while avoiding direct contact with

the positively charged side-chain of Arg82(Figure 3). When this H5O2

� site was included inthe protein titration model and allowed to competefor the release proton with the two glutamic acidresidues, it was found that the proton did indeedreside preferentially on the H5O2

�. The calculationstherefore indicate that a proton in a hydrogen-bonded network of internal water molecules is anenergetically plausible candidate for the storage ofthe release proton as proposed on the basis ofobservation of a broad continuum band in theFTIR difference spectra.13

In all of the computational models, the protonrelease group, be it Glu194, Glu204 or H5O2

�, con-tinues to hold the proton up to a pH value of 15 ormore. This is in contradiction to experimental ®nd-ings that the release group has a pKa of 9-9.532 (R.Rammelsberg et al., unpublished results). In thecalculations, the fully deprotonated state is highlyunfavorable because the two negatively chargedglutamate residues are very close together,whereas the protonation of one of the glutamateresidues, or of a nearby water dimer eitherremoves this repulsive interaction or provides acompensating attractive interaction, respectively. Itseems likely that in the real protein, deprotonationof the release group under alkaline conditionswould cause Glu194 and Glu204 to move apart tolower the energy of the fully deprotonated state.Since none of the model calculations allow for pH-induced changes of heavy-atom positions, this ave-nue is closed, and the calculations over-predict thepKa. The crystal structure of the ground statesuggests a fairly high degree of conformationalmobility in this region,17 and in the recent crystal-lographic structure of the M state the region under-goes signi®cant conformational change relative tothe ground state, including a movement of theArg82 guanidinium group towards the extracellu-lar side.29,30 It therefore seems plausible that thedeprotonation of the release proton at around pH 9in the ground state is accompanied by a shift to amore locally M-like structure in the region of theECd pocket.

The ECd pocket in which the H5O2� is located is

large enough to accommodate four water mol-ecules, and three are seen in the crystallographicstructure. Our H5O2

� positioning is consistent withone of these three observed crystallographic wateroxygen positions, combined with a fourth oxygenposition in a vacant region of the pocket. In proteinX-ray crystallography, typically only well-orderedwater molecules show up in the density. Remain-ing cavities may or may not be ®lled with staticallyor dynamically disordered water molecules. (Anexample of a borderline case is water 403 in theECd pocket, which, as evidenced by its B factorand elongated density, is partially disordered.17)Thus, while there is no positive crystallographicevidence for the added oxygen atom position thatwe have modeled, it is not inconsistent with thecrystallographic data.


Examination of the electrostatic potentials in thepocket, and preliminary titration calculations indi-cated that both of the oxygen atoms of H5O2

� mustbe within hydrogen bonding distance of the carbo-nyl oxygen atoms of the glutamate side-chains 194or 204, in order to be stable as H5O2

� (rather thanas 2H2O). A hydrogen bond with the Ser193 side-chain also provides crucial stabilization. Veryrecently, mutation of Ser193 to Cys has been foundto abolish the continuum band observed in thewild-type, and to delay proton release (R. Ram-melsberg et al., unpublished results). H5O2

� modelswith oxygen atom positions ``higher'' in the pocketare unsustainable because of unfavorable inter-action with the positively charged Arg82 at the topof the pocket. We also made preliminary calcu-lations based on a model in which the releaseproton was stored as H3O�; but in titration calcu-lations this model collapsed to H2O and a protonon either Glu194 or Glu204 (results not shown). Inany case, a release proton stored as H3O

� wouldnot account for the continuum band, while H5O2

�

is the minimal model that does account for it. Amore extended ionized water system, such asH7O3

�, could also account for a continuum band,but it appears from the crystal structure that thiscould only occur by incorporating a third oxygenposition that would be farther from the glutamateresidues and closer to guanidinium group ofArg82. This would seem to be less energeticallyfavorable than the H5O2

� case, so no attempts weremade to model ionized water complexes largerthan H5O2

�. The electrostatic and steric barrierimposed by the Arg82 guanidinium group appearsto provide a ``ceiling'' on any ionized water net-work storing the release proton, while the negativecharges of the glutamate 194 and 204 carboxylategroups provide a ``¯oor.`` In view of these structur-al constraints, and the lack of any other pocketswith strong negative potential in the putative pro-ton-releasing region of the protein, we believe thatif the release proton is indeed stored in an internalwater network, as suggested by FTIR spectro-scopy13 and the present results, it must be veryclose to the H5O2

� position that we have modeled.Finally, in the recently obtained M-statestructures,29,30 ECd no longer exists as a closedpocket, but is opened to the extracellular side, andthe arrangement of the polar and charged groupslining it is substantially changed. The identi®cationof this pocket as the proton storage site is consist-ent with its disruption in the state from which theproton has presumably been released.

As mentioned in the Introduction, it would at®rst seem implausible that H5O2

� would be pre-ferred over a glutamic acid as the location of a pro-ton, because the typical pKa value of a glutamicacid, 4.4, is higher than that of H5O2

� (approxi-mately ÿ1.7). Burial of these groups would makethe pKa difference even greater, by penalizing theformation of both glutamate and H5O2

� relative tothe neutral forms. Two effects compensate forthese tendencies in the calculations. First, because

the charge of H5O2� is delocalized across two water

molecules, it does not suffer as large a Born deso-lvation penalty as a more compact species, such asH3O� would do. Second, the H5O2

� has very strongfavorable interactions with the negative charges ofthe two glutamate residues: its interaction energieswith Glu194 and Glu204 are equivalent to 17.4 and14.4 pK units, respectively. If the proton were toinstead reside on either Glu194 or Glu204, thesefavorable interactions would be lost, although theunfavorable interaction equivalent to 8.4 pK unitsbetween the two glutamate residues would also belost. The net interaction energy terms among thesethree groups (Glu194,204 and H5O2

�) thus favorsprotonation of the H5O2

� by 23.4 pK units, which isenough to compensate for the pKintr difference of21.1 between Glu204 and H5O2

� (see Table 4).

Theory, Methods and Structural Models

The calculations are based on the idea that thedifference between the titration behavior of ioniz-able groups in a protein, and a group of the samekind in a model compound is caused mainly bydifferences in the electrostatic effects in the proteinversus the model compound. It is further supposedthat these electrostatic effects are adequatelydescribed by the following semi-macroscopicmodel: the solvent region is represented by a conti-nuum having the bulk dielectric constant of waterew; the region inside the protein, membrane ormodel compound has a dielectric constant ein,which is a parameter of the model; the charge dis-tributions of the protein or model compound,including both forms of the titratable groups, aremodeled by atomic partial charges. The boundarybetween the interior and exterior of the molecule isthe Connolly molecular surface33 which is de®nedby the atomic radii and coordinates through ahypothetical process of rolling a solvent-sizedprobe sphere over the atomic spheres. The electro-static potential f is then determined by the Poissonequation:

re�r�rf�r� � ÿ4pr�r� �1�where the charge distribution r is de®ned by atom-ic partial charges, and the dielectric constant e(r) isein or ew according to the region in which r falls.This equation can be solved by the ®nite-differencemethod.34 We refer to this electrostatic model asMEAD (macroscopic electrostatics with atomicdetail). The use of the MEAD model for calcu-lations of ionization states in proteins has beendescribed;18,24 but in the present work some vari-ations from the usual methods, particularly theinclusion of H5O2

� as a titratable site, allowance forvariable hydrogen-atom positions, and the pre-sence of a membrane, require a fairly detaileddescription of the theoretical methods.


A side-chain as a titratable site in protein

Because the present study includes considerationof H5O2

� as a titrating site, it is necessary todescribe the ideas and assumptions underlying thestandard treatment of ionizable side-chains to jus-tify the extension of these methods to an H5O2

�

molecule in a protein cavity. The standard schemestarts with Tanford & Kirkwood's35 observationthat if one has a matrix of site-site interactions Wij,and a set of ``intrinsic pKa`` values, where the pKintr

of a site is de®ned as the pKa that it would have ifall other sites were neutralized, it is then possiblein principle to calculate the full ionization behaviorof the protein as a function of pH. The calculationsof the pKintr values are based on the assumptionthat any difference between the pKintr and the pKa

of a corresponding model compound pKmod is duepurely to electrostatic effects.

The usual formulation, which is incorporatedinto several computer programs for protein electro-statics, including the MEAD suite used here18,36 is:

pKintr � pKmod ÿ��GBorn ��Gback

2:303RT�2�

where ��GBorn is the difference between the Born-like solvation energy of the partial charges of thetitrating group in its protonated versus deproto-nated form in the protein versus the model com-pound, and ��Gback is the correspondingdifference of differences for the interaction of thetitrating site with non-titrating charges in the pro-tein or model compound (e.g. the peptide back-bone). To put the assumptions involved in arrivingat equation (2) more formally, let PAH and PAdenote the protein with the site under consider-ation protonated or deprotonated, respectively,and all other sites neutralized. Let AH and Adenote the protonated and deprotonated forms ofthe corresponding model compound for whichpKmod is presumed to be known. Consider the ther-modynamic cycle:

Scheme 1.

where the vertical lines represent ``alchemical'' pro-cesses corresponding to ``cutting out'' the modelcompound from the protein, as suggested inFigure 1 of Bashford & Karplus.24 Because 2.303RT, pKintr � m�PAH ÿ m�PA ÿ m�H � , for the proteinand a similar expression applies to the model com-pound, we can write:

pKintr � pKmod ÿ�m�prot ÿ�m�deprot

2:303RT�3�

where we have introduced �m�prot � m�PAH ÿ m�AH

and �m�deprot � m�PA ÿ m�A, the differences in chemi-cal potential associated with the vertical lines ofthe thermodynamic cycle. These differences can beexpressed as:

�m� � �Gelec ��Gne ��Gchem �4�where the elec component is the change in electro-static interactions with the surroundings in theprotein versus the model compound, the ne com-ponent is the change in non-electrostatic non-bonded interactions, and the chem component isfor any changes not accounted for by the ®rst two,such as the alteration of chemical bonds impliedby the process of ``cutting out'' the model com-pound from the protein. Clearly, �Gelec will bequite different for the protonated and deproto-nated forms. But �Gne should be nearly the same,since the protonated and deprotonated forms aresterically very similar; and �Gchem should benearly the same provided the cut is made farenough from the titrating functionality that there isno through-bond in¯uence on its pKa value. (Inthis work, for ionizable side-chains of amino acidresidues, we follow the common practice of takingthe model compound to be the residue and its two¯anking backbone peptide groups.24 In Asp, forexample, the cuts are then four covalent bondsaway from the carboxylic acid group.) The essen-tial approximation of the standard method for cal-culating pKintr is that the �Gne and �Gelec termswill be the same for m�prot and m�deprot, so thatequation (3) becomes:

pKintr � pKmod ÿ�Gelec;prot ÿ� Gelec;deprot

2:303RT�5�

The usual expression for pKintr (equation (2)) isthen essentially equation (5), re-written in terms ofBorn and background electrostatic contributions(see Bashford & Gerwert18 for the speci®c details ofthese terms).

The same solutions of equation (1) from whichthe ��GBorn and ��Gback terms are obtained canalso be used to obtain the matrix of site-site inter-actions Wij. The fractional protonation of any par-ticular site in a protein with N titratable sites canthen be calculated by a Boltzmann-weighted aver-age over the 2N possible protonation states, or by asuitable approximation of such an average.37 Hav-ing determined the protonation as a function of pHfor each site, the pKhalf of a site is de®ned as thepH at which that site is half protonated. The pKhalf

value is thus roughly analogous to the pKa valueof a molecule with a single ionizable group.

H5O2� as titratable site within protein

Consider an H5O2� molecule con®ned within a

protein cavity as a titrating site which, upon depro-


tonation, becomes a pair of water molecules withinthe protein cavity. We wish to treat this as a ``site''within the framework of the usual methods of cal-culating ionization states of proteins. In this case,the thermodynamic cycle of Scheme (1) becomes:

Scheme 2

.

where P( . . . ) denotes a species con®ned in the pro-tein cavity, and in the upper reaction, the speciesare in bulk water. Here, the two vertical arrowsrepresent not the alchemical ``cutting out'' processof Scheme (1), but rather the transfer of an H5O2

�

molecule, or a dimer of water molecules, respect-ively, between the protein cavity and the bulk. Thechemical potential differences between the speciesin protein and in solution can again be dividedinto electrostatic and other components, as inequation (4), but in the present case there is nocovalent bond breaking as previously representedby �Gchem. If we once again assume that the non-electrostatic components of �m� do not changebetween the protonated and deprotonated forms(i.e. the difference between the interaction of awater dimer and H5O2

� with the protein cavity ispurely electrostatic) then we again obtain equation(5), which is equivalent to the standard formula,equation (2).

It remains to choose an appropriate pKmod valuecorresponding to the top equilibrium in Scheme(2). The dif®culty is that in the deprotonated form,our ``model compound'' becomes a water dimer inbulk water, that is, Kmod is the dissociation con-stant for the reaction H5O2

� $ (H2O)2 � H�:

Kmod � ��H2O�2��H��H5O�2 �

�6�

It would not be correct to use H5O2� $ 2H2O � H�,

as the top reaction, because in the protein reaction(bottom row of Scheme (2)) the proton is acceptedby a pre-formed water dimer within the cavity. Ifwe suppose that an excess proton in bulk waterexists partly in the form H3O

� or oxonium (prob-ably coordinated by other water molecules tomake larger complexes, such as H9O4

�, as proposedby Eigen38), and partly in the form H5O2

�, as pro-posed by Zundel,14 we can express the overall pro-ton activity as [H�] � [H3O�] � [H5O2

�]. Thenequation (6) becomes:

Kmod � ��H2O�2��H5O�2 � � �H3O��H5O�2 �

� ��H2O�2��1� 1=a��7�

where a � [H5O2�]/[H3O

�]. In these expressions[(H2O)2] refers to the concentration of water mol-ecule pairs that have a suitable hydrogen-bondedgeometry to be converted to H5O2

�. For a givenmicroscopic state of a sample of N water mol-ecules, one can, in principle, describe them as a col-lection of N/2 water pairs, and then enquire as towhat fraction of them, f, meet the criteria of beingreadily convertible to H5O2

�. Using a total waterconcentration of 55 mole/l, and taking the negativelogarithm of equation (6):

pKmod � ÿ log f �55=2��1� 1=a�� ÿ1:7ÿ log f �1� 1=a�=2 �8�

Given the strongly H-bonded structure of water, itis likely that a high fraction of the water moleculesare participating in dimers that have a suitablegeometry for protonation to H5O2

�, therefore fshould be close to 1. If one supposes that the pro-ton in water occurs as a roughly equal mixture ofH5O2

� and oxonium,39 then a � 1. Combining thesesuppositions about f and a, one ®nds log f(1 � 1/a)/2 � 0, and pKmod � ÿ 1.7. Admittedly, theabove derivation of the pKmod value is approxi-mate, but uncertainties corresponding to even anorder of magnitude in f or a correspond to uncer-tainties in pKmod of only approximately 1. There-fore, in using this value one should check whetherthe ®nal results are sensitive to pKmod variations oforder 1.

Membrane, dielectric boundary and charges

In this work, we model the membrane simply asan in®nite dielectric slab having the same dielectricconstant ein as the protein interior. In using the®nite-difference method to solve equation (1), it isnecessary to specify f on the outer boundary ofthe ®nite-difference lattice (i.e. Dirichlet boundaryconditions40). In many applications to biomoleculesit is common to set this potential to zero, or to usea simple analytical approximation, such as Cou-lomb's law. However, these approximations maylead to signi®cant error in the case of an in®nitedielectric slab. We therefore use the method ofimages40 to ®nd the lattice boundary potential of aset of atomic partial charges in or near an in®nitedielectric slab. Since the membrane in the presentcase is transverse to the coordinate z-axis, theobvious de®nition for e(r) for a protein-membranesystem is that it is ein if r is either in the protein orif the z coordinate is between the two values thatde®ne the two surfaces of the membrane. How-ever, bacteriorhodopsin, like many membranespanning proteins, is known to have internalwater-®lled pockets or channels that lie betweenthe two membrane surfaces, and in some cases, we


wish to be able to model these pockets as havingthe bulk water dielectric constant ew. Therefore, wede®ne the ein region as follows: all points which liewithin the protein interior, and all points whichare between the top and bottom surfaces of themembrane and outside of a 10 AÊ cylinder whoseaxis is transverse to the membrane and passesthrough the center of the protein. The proteinboundary used in this de®nition is the molecularsurface,33 including the surface of interior pockets.In other words, a point is outside the protein if it ispossible to ®nd a position for a solvent-sized(1.4 AÊ ) spherical probe such that the point fallsinside the probe, but the probe does not overlapany atoms of the molecule; otherwise the point isinside the protein.

The use of the method of images describedabove, which is incorporated into the softwareused here, is valid only for the Poisson equation,and not for the Poisson-Boltzmann equation,which would be needed in order to include salteffects. Therefore, we had to choose betweenincluding salt effects or including the membrane.Preliminary calculations including salt, but nomembrane, or a membrane but no salt, showedthat the membrane effects on calculated pKhalf

values were much larger, so we chose to includethe membrane effects. The effects of the mem-brane's lipid head-group charges are also notincluded. It is expected that these would be largelycancelled by salt effects as an electrical double-layer is formed, and that calculations with headgroups, but no salt, would be worse than calcu-lations without head groups at all.

In early applications of the MEAD method toprotein pKa calculations the charge distributionsused included the full set of atomic partial chargesfor the non-titrating charges, but titrating groupswere modeled as having their formal charge con-centrated on a single point.24,41 Later, this single-site-charge restriction was lifted18 so that the titrat-ing site could also be described by atomic partialcharges, but uncertainty as to proton placementwas re¯ected by ``smearing'' the hydrogen-atomcharges between heavy atoms. For example, theprotonated form of glutamic or aspartic acid wasmodeled by distributing the hydrogen partialcharge between the two oxygen atoms of the car-boxylic acid group. In the present work we makean explicit placement of all hydrogen atoms anduse atomic partial charges without smearing.

Multi-conformer case

In several cases (see Results) ensembles of struc-tural models were generated which differed fromone another as to the positions of the labile hydro-gen atoms in the ionizable groups. Some cases alsoincluded variation of water hydrogen-atom pos-itions as well. Calculations were then done in a

{ Tripos Inc., SYBYL, St. Louis, Missouri, USA.

way that allowed the system to select which mem-bers of this ensemble were most populated at var-ious pH values. This was done by calculating theprotonation of each site as a function of pH foreach member of the ensemble, using the single-conformer methods described above, and thencombining the results using integrals over protonbinding isotherms, which allow the pH-depen-dence of the free energy of a conformationalchange between two members, A and B, of theconformational ensemble to be expressed as:

�GAB�pH� ÿ�GAB�pHo�

� 2:302RT

Z pH

pHo

�QB�pH0� ÿQA�pH0��dpH0�9�

where the Q are either the total charge or totalnumber of protons bound in state A or B.42 ± 44

Using this formula, and the values of Q providedby the calculations for the individual members ofthe ensemble, the relative population of all mem-bers of the ensemble can be found at any pH, pro-vided that the ratios are known at some referencepH, pHo. The average ionization of individual sitesas a function of pH can then be obtained byweighting the results of the single-conformer calcu-lations according to these ratios.

This leaves the problem of selecting a referencepH, and ®nding the relative populations of confor-mers at that pH. In calculations including only theconformational variability of the labile protons, thesolution is simple. The reference pH is selected suf-®ciently high that all of the labile protons (typicallycarboxylic acid protons) are dissociated. Then allmembers of the ensemble become identical andhave identical free energies and populations(�GAB(pHo) � 0). If the hydrogen atom positions ofwater molecules are also considered as ¯exible, itis again convenient to choose high pH so that allrelevant ionizable groups are deprotonated, but inthis case, variation as to water hydrogen atomsremains. Here, we calculate these energy differ-ences using the CHARMM22 force ®eld, with thedielectric constant set to 4.0 to maintain consist-ency with the MEAD calculations, and solventeffects are treated by the MEAD model.

Structural models, parameters and programs

All calculations are based on the 1.55 AÊ X-raycrystallographic structure of Luecke et al.17

(PDB45,46 entry 1C3W). With a very small numberof exceptions, noted in Results, all heavy-atom pos-itions from this structure were left unchanged. Themissing loop, Thr157-Glu161, was constructedusing the loop-building facility of the SYBYL mol-ecular modeling system{ Hydrogen-atom positionswere initially generated using the HBUILDalgorithm47 as implemented in the CHARMM com-puter program,48 and then energy minimized usingthe CHARMM22 force ®eld49 and the ABNR mod-ule of CHARMM with all heavy atoms ®xed.

Figure 6. Structure of lysine-reti-nal with atom names used inTable 5.


In addition to atomic coordinates, MEAD calcu-lations require atomic charges and radii. (The radiiare used to de®ne the dielectric boundaries.) Theradii used are taken from Bondi,50 and whereavailable, the atomic partial charges are taken from

Table 5. Lysine-retinal charges calculated from DFT andused in calculations

Atoma Charge

Protonated Deprotonated

CE ÿ0.102 ÿ0.020HE1(2) 0.146 0.089NZ ÿ0.260 ÿ0.474HZ 0.346 0.000C15 0.054 0.368H15 0.205 0.057C14 ÿ0.487 ÿ0.507H14 0.213 0.193C13 0.305 0.244C20 ÿ0.358 ÿ0.321H20(3) 0.136 0.108C12 ÿ0.413 ÿ0.373H12 0.227 0.224C11 0.032 ÿ0.053H11 0.157 0.170C10 ÿ0.345 ÿ0.349H10 0.204 0.188C9 0.173 0.138C19 ÿ0.263 ÿ0.219H19(3) 0.116 0.087C8 ÿ0.300 ÿ0.330H8 0.205 0.208C7 ÿ0.076 ÿ0.129H7 0.172 0.189C6 ÿ0.243 ÿ0.301C5 0.081 0.024C18 ÿ0.329 ÿ0.269H18(3) 0.128 0.095C4 ÿ0.108 ÿ0.085H4(2) 0.092 0.064C3 ÿ0.089 ÿ0.081H3(2) 0.066 0.047C2 ÿ0.192 ÿ0.188H2(2) 0.057 0.040C1 0.604 0.690C16 ÿ0.454 ÿ0.436H16(3) 0.101 0.088C17 ÿ0.427 ÿ0.436H17(3) 0.101 0.088

a Notations like H19(3) indicate that there are three hydrogenatoms attached to the heavy atom, C19, and each has the indi-cated charge.

the CHARMM22 force ®eld. However, this force®eld does not have partial charges for either theprotonated or deprotonated form of the retinalSchiff base, for H3O

�, or for H5O2�, so charges were

determined by density functional calculations forthese species. These calculations were carried outusing the Amsterdam Density Functional program(ADF).51 A triple-zeta basis set size and frozen coreorbitals are used for all atoms. (In ADF this is``basis set IV.``) For the exchange and correlationpart of the density functional, the local densityapproximation of Vosko et al.52 (VWN) with thethe Becke gradient correction53 and Perdew corre-lation term54 were used. The atomic partial chargesare then obtained using electrostatic potential ®t-ting. The resulting charges for the retinal Schiffbase are shown in Table 5 and Figure 6. Thecharges for H5O2

� are shown in Table 6.The electrostatic calculations are carried out

using the MEAD computer program suite18,36

which uses the ®nite-difference method was usedto solve the Poisson equation. The ®nite-differencelattices were arranged according to a focusingscheme: a 653 grid with 1.5 AÊ spacing centered onthe molecular center was followed by a 653 gridwith a 0.25 AÊ spacing centered on each particulartitrating site. The interior regions were assigned adielectric constant of 4.0. The model-compoundpKa values used were as follows: retinal Schiffbase, 7; Asp, 4.0; Glu, 4.4; Arg, 12.0; Lys, 10.4. Allresidues of the above types were included as ioniz-able groups in the calculations. Tyrosine residueswere considered as ionizable with a model com-pound pKa of 9.6, in the ®rst set of calculations,but since it was found here and in previous work18

Table 6. H5O2� charges calculated from DFT and used in

calculations

Atom Charge

Protonated Deprotonateda

O(2) ÿ0.654 ÿ0.834Bridge H 0.432 0.417Periph. H 0.469(4) 0.417(3)

a Charges for the deprotonated form are taken from theTIP3P water model.


that tyrosine side-chains were always predicted toremain protonated, subsequent calculations treatedthem as ®xed in their protonated state.

Acknowledgments

This work was supported by grants from the NationalInstitutes of Health (GM45607 and GM59970) and theDeutsche Forschungsgemeinschaft (SFB-394 and SFB-480). We are grateful to Professor Lou Noodleman fordiscussion and assistance with DFT calculations.

References

1. Oesterhelt, D. (1998). The structure and mechanismof the family of retinal proteins for halophilicarchaea. Curr. Opin. Struct Biol. 8, 489-500.

2. WikstroÈm, M. (1998). Proton translocation by bacter-iorhodopsin and heme-copper oxidases. Curr. Opin.Struct. Biol. 8, 480-488.

3. Haupts, U., Tittor, J. & Oesterhelt, D. (1999). Closingin on bacteriorhodopsin: progress in understandingthe molecule. Annu. Rev. Biophys. Biomol. Struct. 28,367-399.

4. Okamura, M. Y., Paddock, M. L., Graige, M. S. &Feher, G. (2000). Proton and electron transfer in bac-terial reaction centers. Biochim. Biophys. Acta, 1458,148-163.

5. Gerwert, K., Hess, B., Soppa, J. & Oesterhelt, D.(1989). Role of Asp96 in proton translocation bybacteriorhodopsin. Proc. Natl Acad. Sci. USA, 86,4943-4947.

6. Gerwert, K., Souvignier, G. & Hess, B. (1990). Simul-taneous monitoring of light-induced changes inprotein side-groups' protonation, chromophore iso-merization and backbone motion of bacteriorhodop-sin by time-resolved FTIR. Proc. Natl Acad. Sci. USA,87, 9774-9778.

7. Lanyi, J. K. & Varo, G. (1995). The photocycles ofbacteriorhodopsin. Israel J. Chem. 35, 365-385.

8. Heûling, B., Souvignier, G. & Gerwert, K. (1993). Amodel-independent approach to assigning bacterior-hodopsin's intramolecular reactions to photocycleintermediates. Biophys. J. 65, 1929-1945.

9. Balashov, S. P., Imasheva, E. S., Govindjee, R. &Ebrey, T. G. (1996). Titration of aspartate-85 inbacteriorhodopsin: what it says about chromophoreisomerization and protein release. Biophys. J. 70, 473-481.

10. Richter, H.-T., Brown, L. S., Needleman, R. & Lanyi,J. K. (1996). A linkage of the pKas of Asp85 andGlu204 forms part of the reprotonation switch inbacteriorhodopsin. Biochemistry, 35, 4054-4062.

11. Dioumaev, A. K., Richter, H. T., Brown, L. S., Tanio,M., Tuzi, S. & SaitoÃ , H. et al. (1998). Existence of aproton transfer chain in bacteriorhodopsin: partici-pation of Glu194 in the release of protons to theextracellular surface. Biochemistry, 37, 2496-2506.

12. Brown, L. S., Sasaki, J., Kandori, H., Maeda, A.,Needleman, R. & Lanyi, J. K. (1995). Glutamic acid204 is the terminal proton release group at the extra-cellular surface of bacteriorhodopsin. J. Biol. Chem.270, 27122-27126.

13. Rammelsberg, R., Huhn, G., LuÈ bben, M. & Gerwert,K. (1998). Bacteriorhodopsin's intramolecular pro-

ton-release pathway consists of a hydrogen-bondednetwork. Biochemistry, 37, 5001-5009.

14. Zundel, G. (1999). Hydrogen bonds with large pro-ton polarizability and proton transfer processes inelectrochemistry and biology. Advan. Chem. Phys.111, 1-217.

15. Lobaugh, J. & Voth, G. A. (1996). The quantumdynamics of an excess proton in water. J. Chem.Phys. 104, 2056-2069.

16. Wang, J. & El-Sayed, M. A. (2000). Proton polariz-ability of hydrogen-bonded network and its role inproton transfer in bacteriorhodopsin. J. Phys. Chem.ser. A, 104, 4333-4337.

17. Luecke, H., Schobert, B., Richter, H.-T., Cartailler,J.-P. & Lanyi, J. K. (1999). Structure of bacteriorho-dopsin at 1.55 AÊ resoultion. J. Mol. Biol. 291, 899-911.

18. Bashford, D. & Gerwert, K. (1992). Electrostaticcalculations of the pKa values of ionizable groups inbacteriorhodopsin. J Mol. Biol. 224, 473-486.

19. Yang, A.-S., Gunner, M. R., Sampogna, R., Sharp, K.& Honig, B. (1993). On the calculations of pKas inproteins. Proteins: Struct. Funct. Genet. 15, 252-265.

20. Sampogna, R. V. & Honig, B. (1994). Environmentaleffects on the protonation states of active site resi-dues in bacteriorhodopsin. Biophys. J. 66, 1341-1352.

21. Engels, M., Gerwert, K. & Bashford, D. (1995).Computational studies on bacteriorhodopsin: confor-mation and proton transfer energetics. Biophys.Chem. 56, 95-104.

22. Scharnagl, C., Hettenkofer, J. & Fischer, S. F. (1995).Electrostatic and conformational effects on the pro-ton translocation steps in bacteriorhodopsin: analysisof multiple M structures. J. Phys. Chem. 99, 7787-7800.

23. Sampogna, R. & Honig, B. (1996). Electrostatic coup-ling between retinal isomerization and the ionizationstate of Glu204: a general mechanism for protonrelease in bacteriorhodopsin. Biophys. J. 71, 1165-1171.

24. Bashford, D. & Karplus, M. (1990). pKa`s of ionizablegroups in proteins: atomic detail from a continuumelectrostatic model. Biochemistry, 29, 10219-10225.

25. Herzfeld, J., Das Gupta, S. K., Farrar, M. R.,Harbison, G. S., McDermott, A. E. & Pelletier, S. L.et al. (1990). Solid-state 13C NMR study of tyrosineprotonation in dark-adapted bacteriorhodopsin. Bio-chemistry, 29, 5567-5574.

26. Essen, L.-O., Siegert, R., Lehmann, W. D. &Oesterhelt, D. (1998). Lipid patches in membraneprotein oligomers: crystal structure of the bacterior-hodopsin-lipid complex. Proc. Natl Acad. Sci. USA,95, 11673-11678.

27. Sandberg, L. & Edholm, O. (1997). pKa calculationsalong a bacteriorhodopsin molecular dynamicstrajectory. Biophys. Chem. 65, 189-204.

28. Henderson, R., Baldwin, J. M., Ceska, T. A., Zemlin,F., Beckmann, E. & Downing, K. H. (1990). Modelfor the structure of bacteriorhodopsin based onhigh-resolution electron cryo-microscopy. J. Mol.Biol. 213, 899-929.

29. Luecke, H., Schobert, B., Richter, H.-T., Cartailler,J. P. & Lanyi, J. K. (1999). Structural changes inbacteriorhodopsin during ion transport at 2 AÊ

resolution. Science, 286, 255-261.30. Luecke, H., Schobert, B., Cartailler, J.-P., Hans-

Thomas, R., Rosengarth, A., Needleman, R. & Lanyi,J. K. (2000). Coupling photoisomerization of retinal


to directional transport in bacteriorhodopsin. J. Mol.Biol. 300, 1237-1255.

31. Scharnagl, C. & Fischer, S. F. (1996). Conformational¯exibility of arginine-82 as source for the hetero-geneous and pH-dependent kinetics of the primaryproton transfer step in the bacteriorhodopsin photo-cycle: an electrostatic model. Chem. Phys. 212, 231-246.

32. Govindjee, R., Misra, S., Balashov, S. P., Ebrey, T. G.,Crouch, R. K. & Menick, D. R. (1996). Arginine-82regulates the pKa of the group responsible for thelight-driven proton release in bacteriorhodopsin.Biophys. J. 71, 1011-1023.

33. Connolly, M. L. (1983). Solvent-accessible surfaces ofproteins and nucleic acids. Science, 221, 709-713.

34. Press, W. H., Flannery, B. P., Teukolsky, S. A. &Vetterling, W. T. (1986). Numerical Recipes. The Art ofScienti®c Computing, Cambridge University Press,Cambridge, UK.

35. Tanford, C. & Kirkwood, J. G. (1957). Theory ofprotein titration curves. I. General equations forimpenetrable spheres. J. Am. Chem. Soc. 79, 5333-5339.

36. Bashford, D. (1997). An object-oriented program-ming suite for electrostatic effects in biological mol-ecules. In Scienti®c Computing in Object-OrientedParallel Environments (Ishikawa, Y., Oldehoeft, R. R.,Reynders, J. V. W. & Tholburn, M., eds), vol. 1343of Lecture Notes in Computer Science, pp. 233-240,ISCOPE97, Springer, Berlin.

37. Bashford, D. & Karplus, M. (1991). Multiple-sitetitration curves of proteins: an analysis of exact andapproximate methods for their calculation. J. Phys.Chem. 95, 9556-9561.

38. Eigen, M. & De Maeyer, L. (1958). Self-dissociationand protonic charge transport in water and ice. Proc.Roy. Soc. ser. A, 247, 505-533.

39. Marx, D., Tuckerman, M., Hutter, J. & Parrinello, M.(1999). The nature of the hydrated excess proteon inwater. Nature, 397, 601-604.

40. Jackson, J. D. (1975). Classical Electrodynamics, Wileyand Sons, New York.

41. Antosiewicz, J., McCammon, J. A. & Gilson, M. K.(1994). Prediction of pH-dependent properties ofproteins. J. Mol. Biol. 238, 415-436.

42. Tanford, C. (1970). Protein denaturation. C. theoreti-cal models for the mechanism of denaturation.Advan. Protein Chem. 24, 1-95.

43. Schellman, J. A. (1975). Macromolecular binding.Biopolymers, 14, 999-1018.

44. Yang, A.-S. & Honig, B. (1994). Structural origins ofpH and ionic strength effects on protein stability.Acid denaturation of sperm whale apomyoglobin.J. Mol. Biol. 237, 602-614.

45. Abola, E. E., Sussman, J. L., Prilusky, J. & Manning,N. O. (1997). Protein Data Bank archives of three-dimensional macromolecular structures. In Methodsin Enzymology (Carter, C. W., Jr & Sweet, R. M.,eds), vol. 277, pp. 556-571, Academic Press, SanDiego.

46. Abola, E. E., Bernstein, F. C., Bryant, S. H., Koetzle,T. F. & Weng, J. (1987). Protein Data Bank. InCrystallographic Databases-Informaton Content, SoftwareSystems, Scienti®c Applications (Allan, F. H.,Bergerhoff, G. & Sievers, R., eds), pp. 107-132, DataCommission of the International Union ofCrystallography, Bonn. Cambridge, Chester.

47. BruÈ nger, A. T. & Karplus, M. (1988). Polar hydrogenpositions in proteins: empirical energy placementand neutron diffraction comparison. Proteins: Struct.Funct. Genet. 4, 148-156.

48. Brooks, B. R., Bruccoleri, R. E., Olafson, B. D.,States, D. J., Swaminathan, S. & Karplus, M. (1983).CHARMM: a program for macromolecular energy,minimization, and dynamics calculations. J. Comp.Chem. 4, 187-217.

49. MacKerell, A. D., Jr, Bashford, D., Bellott, M.,Dunbrack, R. L., Jr., Evanseck, J. D. & Field, M. J.et al. (1998). All-atom empirical potential for molecu-lar modeling and dynamics studies of proteins.J. Phys. Chem. ser. B, 102, 3586-3616.

50. Bondi, A. (1964). Van der Waals volumes and radii.J. Chem. Phys. 68, 441-451.

51. te Velde, G., Bickelhaupt, F. M., Baerends, E. J.,Fonesca Guerra, C., van Gisbergen, S. J. A., Snijders,J. G. & Ziegler, T. (2001). Chemistry with ADF.J. Comput. Chem. 22, 931-967.

52. Vosko, S. H., Wilk, L. & Nusair, M. (1980). Accuratespin-dependent electron liquid correlation energiesfor local spen density calculations: a critical analysis.Canad. J. Phys. 58, 1200-1211.

53. Becke, A. D. (1986). Density functional calculationsof molecular bonding energies. J. Chem. Phys. 84,4524-4529.

54. Perdew, J. P. (1986). Density-functional approxi-mation of the correlation energy of the inhomo-geneous electron gas. Phys. Rev. ser. B, 33, 8822-8824.

55. Balashov, S. P., Govindjee, R., Imasheva, E. S.,Misra, S., Ebrey, T. G. & Feng, Y. et al. (1995). Thetwo pKa`s of aspartate-85 and control of thermalisomerization and proton release in the arginine-82to lysine mutant of bacteriorhodopsin. Biochemistry,35, 8820-8835.

56. Zscherp, C., Schlesinger, R., Tittor, J., Oesterhelt, D.& Heberle, J. (1999). In situ determination of transi-ent pKa changes of internal amino acids of bacterior-hodopsin by using time-resolved attenuated totalre¯ection Fourier-transform infrared spectroscopy.Proc. Natl Acad. Sci. USA, 96, 5498-5503.

57. Metz, G., Siebert, F. & Engelhard, M. (1992). Asp85

is the only internal aspartic acid that gets protonatedin the M intermediate and the purple-to-bluetransition of bacteriorhodopsin. FEBS Letters, 303,237-241.

58. Brown, L. S., Bonet, L., Needleman, R. & Lanyi, J. K.(1993). Estimated acid dissociation constants of theSchiff base, Asp85 and Arg82 during the bacterior-hodopsin photocycle. Biophys. J. 65, 124-130.

Edited by G. von Heijne

(Received 1 March 2001; received in revised form 1 July 2001; accepted 1 July 2001)

p k a calculations suggest storage of an excess proton in ... · release proton in an...

Documents