photochemical dissociation in optically dense solutions: applications to photolyzed carboxymyoglobin...

Photochemical Dissociation in Optically Dense Solutions: Applications to Photolyzed Carboxymyoglobin (Mb*CO)

FRANK G. FLAMINGO and J A M E S O. ALBEN* Department o[ Physiological Chemistry, Ohio State University, Columbus, Ohio 43210

Photodissociation of ligands has made important contributions to the understanding of function and structure of heme proteins. Here we present a theory for photochemical dissociation that is not limited by the assumption of previous analyses of optically thin samples, and apply it to interpretation of the photodissociated state of carboxymyoglobin (Mb*CO). Equations are derived and presented in terms of the effects of absorbance, [Iog~o(ls//)= A, the probability of absorption of light quanta per unit surface areal, and the potential for dissociation, D (maximum probability of photodissociation per unit surface area; a linear function in time of photolysis), for both monochromatic and polychromatic light sources. When monochromatic light is used, we show that for large absorbances (A > 2) the fractional photolysis increases as (log D)/A, and may appear to "saturate" even though well below completion. For polychromatic light intensities and absorbances, the theory predicts that the near-infrared tail of the absorbance band of carboxymyoglobin should be sufficiently transparent to allow the radiation to penetrate the sample, yet still have a significant absorptivity such that complete photodissociation is possible. An optically thick myoglobin-CO sample il- luminated with a tungsten lamp was observed to behave somewhere between these two theories. These theoretical relations may be useful in the analysis of photolysis data from optically dense solutions and as a guide for future experimental design. Index Headings: Infrared; Methods, analytical; Techniques, spectro- scopic; UV-Visible spectroscopy; Mathematical modeling, photolysis; Quantum efficiency; Beer-Lambert relations.

INTRODUCTION

Quantitation of the chemical changes caused by irra- diation is an important concern for many photochemists and spectroscopists. Knowledge of the progress of photolytic reactions is often necessary in order to accurately interpret spectral changes. Biological spectroscopists have historically used light to initiate a chemical reaction. Heme-proteins are especially appropriate for these studies. The photochemistry of myoglobin or hemoglobin can be made very simple. These proteins normally transport (bind and dissociate) dioxygen in living systems, but will also bind carbon monoxide, which pho- todissociates with a quantum yield of one and is readily measured in both bound and photolyzed states by Fou- rier transform infrared spectroscopy. The photolysis of hemeprotein-CO complexes has long been used to ad- vance our understanding of biological systems. Photoly- sis of heme-proteins has also made important contributions to our understanding of cytochromes and related systems. The photochemical action spectrum of carboxy cytochrome oxidase was first determined by Warburg and Negelein 1,2 by use of light at different wavelengths

Received 16 December 1983; revision received 4 May 1984. * Author to whom all correspondence should be addressed. Present

address: Department of Physiological Chemistry, Ohio State Uni- versity College of Medicine, 1645 Nell Avenue, Columbus, OH 43210.

to reverse the carbon monoxide inhibition of respiration in yeast cells. The release of inhibition depended on the wavelength and the intensity of the activating light and on the coefficient of light absorption. This prompted Warburg to develop the mathematical theory of photochemical decomposition ~,3 to describe the transition between the inhibited and the activated systems. The theory was, however, limited by the assumption of an optically thin solution. More recently, Brunori and Giacometti 4 have investigated the effects of such factors as the protein moiety, type of ligand, wavelength, and solvent composition on the photosensitivity of hemes. Though they allow for some loss of light intensity, they too assume that only a small fraction of the incident photodissociating radiation is absorbed by the sample. While this is true for most visible transmission spectroscopy experiments, it may not be true for those techniques that require optically dense samples for sensitiv- ity, such as extended x-ray absorption fine structure (EXAFS), electron paramagnetic resonance (EPR), and MSssbauer spectroscopy. The difficulty of completely photodissociating heme ligands in these samples, which typically require absorbances between 1 and 3, and sometimes considerably higher, has not been generally appreciated.

The purpose of this paper is to explore the relations between light intensity and photolytic reactions as a function of optical density. The theory is developed in two stages. The first is strictly valid only for photolysis by monochromatic (e.g., laser) light. The second allows the absorptivity (and hence absorbance) and light intensity to vary with frequency. The limitations of these theoretical approaches are discussed and both are compared with observed data for thin and optically thick samples of carboxymyoglobin. The reaction to be con- sidered is MBCO -~ Mb*CO, where thermal relaxation is neglected at the low temperatures that are employed here. Abbreviations used are the following: MbCO, ferrous carboxymyoglobin; Mb*CO, ferrous carboxymyoglobin after photolysis of the CO; deoxy-Mb, ferrous myoglobin; met-Mb, ferric myoglobin; CcO, cytochrome c oxidase.

METHODS

Sperm whale myoglobin was obtained from Pentex and used without further purification. The myoglobin was dissolved in distilled water, centrifuged for 1 h at 5000 rpm and concentrated to about 12-16 mM in either an AMICON pressure filter (for large volumes) or a MINICON ultrafiltration device (for small volumes), both manufactured by Amicon Corp, Lexington, MA.

116 Volume 39, Number 1, 1985 0003-7028/85/3901-011652.00/0 APPLIED SPECTROSCOPY © 1985 Society for Applied Spectroscopy

The protein solutions were then deaerated by repeated evacuation and refilling with argon. We accomplished reduction by mixing in a slight stoichiometric excess of 1 M deoxygenated sodium dithionite solution buffered with 1 M potassium phosphate to pH 7.4. (The pH of the buffer was 8.6 before dithionite addition.) The sample was then equilibrated with CO after evacuation. At this point one sample was injected between a pair of CaF2 windows separated by a 0.095-mm spacer and then frozen by a closed-cycle helium refrigerator (aqueous MbCO). To a second MbCO sample of about 5 mL was added 0.5 mL of CO-saturated glycerol. This was then put into a Visking No. 8 dialysis tubing and inserted within a 100 mL test tube filled with CO and CO-saturated glycerol, to extract the water. The resultant protein paste was then squeezed onto a CaF2 window with a 0.38-mm spacer and pressed with a second window before being frozen in the helium refrigerator (glycerol sample). The resulting high concentration produced an optically thick sample.

Low temperatures (10-280 K) were conveniently obtained by use of a Lake Shore Cryotronics helium refrigerator, model LTS-21-D70C. Cryostat cell temperature was measured by use of a Lake Shore Cryotronics digital thermometer, model DRC-70, with a calibrated silicon diode probe.

Infrared spectra were obtained with a Digilab FTS- 14D infrared interferometer fitted with an InSb detector cooled by liquid nitrogen. Interferograms were collected at 2 cm i resolution through a 15-bit A/D converter and signal averaged into 32-bit computer words, which were used for all further computations. Single-beam spectra result from the real part of the Fourier transforms of 1 to 8192 signal-averaged interferograms. At 2 cm -1 resolution, multiple scans are begun every 3.6 s. The photolysis data are taken with progressive increases in the number of scans signal-averaged with time. There is no additional averaging or smoothing of the data.

Visible spectra were obtained with a Cary model 17DX spectrometer, adapted to be controlled by a micropro- cessor with the On-Line Instrument System model 3820 data system. At each wavelength, 8 light-chopper cycles were signal-averaged before progression to the next wavelength, a process which required about 15 min to collect a scan of 400 data points. The identical sample was observed in both the visible and infrared spectrom- eters.

Photodissociation of the heme-CO was accomplished with continuous radiation from a 500 W tungsten lamp focused through a slide projector and optically filtered through glass and water. The energy reaching the sample was measured with a YSI-Kettering model 65 radi- ometer equipped with a black body probe.

THEORY

The mathematical models are based upon the Beer- Lambert relation with the simplifying assumptions that (1) there is no ligand dissociation in the dark; (2) once photolyzed the ligand remains dissociated from the iron for the duration of the experiment, i.e., the rate of re- combination of ligand with iron is very small relative to photolysis; and (3) the absorptivity of the sample does

not change appreciably upon photolysis. Assumptions 1 and 2 are good approximations for heme systems at low temperature (T <10 K for MbCOS; T <140 K for cytochrome oxidase-CO6). Assumption 3 may be valid for the region of visible absorbance peaks (e.g., 579 for MbCO), but not in the near-IR, where the absorptivity is very low, and the photolyzed species may absorb quite differently. No attempt was made to include the effects of light scattering due to devitrification, which may be significant at low temperatures. 7,8,~

The absorbance is given by A = ac e, where a (mM -1 cm 1) is the absorptivity of the sample (a measure of the probability of absorption of the exciting radiation by the molecule), c (mM) is the concentration of the sample and e (cm) is the thickness of the sample. (We have chosen to use the units of moles and millimolar (mM) in this paper rather than the more convenient units of molecules and molecules per cm 3 in order to correspond with the units of concentration commonly used in the chemical literature to be cited later.) At low absorbance the photochemical dissociation constant is defined as the rate of the photodissociation of ligands divided by the number of sites within the sample and is proportional to a.¢.Io, where ¢ is the quantum yield, the ratio of the number of photodissociated ligands to the number of quanta absorbed by molecules in their ground state (i.e., not previously dissociated), and Io (mol quanta cm -2 s -i) is the intensity of the incident radiation per unit surface area. We will then define the potential for dissociation as D = a~Iot, where t (s) is the time, so that Iot is a measure of the total number of quanta per unit area striking the sample after time t, and a¢ is the total probability that photolysis will result per incident quantum.

Let I (x) be the intensity of the incident radiation per unit area at a depth, x, in from the surface of the sample. Its value is given by the Beer-Lambert relation which describes the absorption of radiation by a solution

I (x ) = Io'10 . . . . . . . Io'e -dnl°) . . . . . . . (1)

This radiation causes the photodissociation of N moles of ligand per unit surface area at a time, t, after initia- tion of continuous illumination. Of these photodissociated molecules an amount, dN, are contained within a volume of infinitesimal thickness, dx. The rate of change in dN with time is proportional to (1) the radiation intensity reaching this volume, I(x); (2) the fraction of molecules within this volume that may still be photolyzed, c dx - d N ; and (3) the probability that an incident quantum will cause photolysis, a4~; such that

~ t [ d N ( x , t ) ] = (ln lO)I(x)[c - dN(x , t ) ]a¢ . (2) dx

After integrating over time, substituting for I (x ) , and exponentiating the result, we obtain

d N ( x , t ) = c dx{1 - e - ( l n l O ) a c ¢ l ° t e - ( l " ' ° ) " c = } ( 3 )

We can then obtain the total quantity of photolyzed molecules per unit area by integrating d N ( x , t ) over the entire thickness of the sample, #. We then have

APPLIED SPECTROSCOPY 117

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Dissociation Potential, oe~Iot

Fie. 1. Fraction of the sample photolyzed vs. dissociation potential at constant values of absorbance. A, Monochromatic radiation. We calculated this plot from Eq. 5 through numerical integration while varying D and holding A fixed at the values 2, 3, 5, 10, 20, and 30. For larger values of D, Eq. 11 may be used to evaluate /(A,D). B, Polychromatic radiation. The absorptivity was defined to have a Gaus- sian bandshape centered at 17,200 cm * (580 nm) with a halfwidth of 300 cm 1 (about 11 nm). The source was a black body radiator at 3300 K. An was held fixed at the values 0.1, 1, 2, 3, 5, 10, 20, and 30. The curves were calculated from Eq. 12.

f O g N ( g , t ) = c dx{1 - e -(lnl°)'t'a'~'1°~ ( , . ,o ) ...... }. (4)

The absorbance of the sample is given by A = a c e and the photochemical dissociation potential by D = a¢Iot . When we divide Eq. 4 by the number of molecules per unit surface area in the total sample, cg, we obtain the fraction of the total sample that is photolyzed by monochromatic light. This fraction is given by

f0 1

f ( A , D ) = 1 - d y . e U. lO) , e ';°'°)Ay (5)

where y = x / g . Upon conversion of the exponential to base 10, Eq. 5 can be written as

A I I I I [ i I I I I i I ]

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FIG. 2. Fraction of the sample photolyzed vs. absorbance at constant values of the dissociation potential. A, Monochromatic radiation. We calculated this plot from Eq. 5 through numerical integration while varying A and holding D fixed at the values 1, 10, 102, 103, 104, and 105. To evaluate f(A,D) at large values of A and D see Eq. l l . B, Polychromatic radiation. The source was a black body radiator at 3300 K. The absorptivity was defined as in Fig. 1. Do was held fixed at the values 10, 102, 10 ~, 104, and l0 s. The curves were calculated from Eq. 12.

f O f(A,D) = 1 - d y . 10 - D ' ° A > (6 )

It is helpful to look at the fractional photolysis equations for small and large values of A and D. In the limit of very small A we can see from Eq. 5 that the fractional photolysis depends simply on D as

f ( D ) ~ 1 - e Un 10).D, A ~ 0 (7a) 1 - 10 v (7b)

so that even at very low absorbances a minimum light intensity is required for complete photodissociation. To see the trends in f at large D, we differentiate Eq. 5 with respect to D. The integral over the thickness of the sample can now be done in closed form, providing us with

Of 1 - lO) D e-"'°)A e-(~,lO) O} (8) OD - A . D . l n 10 {e (1. - - .

118 Volume 39, Number 1, 1985

For large values of A this reduces to

of 1 _ _ , ~ [ __ e - D . l n t0], A .-> 3 . OD A . D . l n 10ft

(9)

When D is also large this further simplifies to

A>_3,

of 1 aD ~ A . D . l n 10 '

D >> 1, but D.e a~nlo << 1.

(lO)

Under these conditions we see that f will increase as log D, i.e.,

1 f ( A , D ) ~ ~[log D + k], (11)

A >_3, D>> 1, but D . e A,,10 << 1.

Effects of Spectral Distribution. Heme proteins do not have constant absorption spectra, but rather their absorption spectra are very much frequency-dependent in the visible region. To include a frequency-dependence in the equations we must replace the absorptivity, quantum yield, and incident radiation intensity of Eq. 4 by the integral of these functions over frequency so that the fraction of the sample photolyzed will be given by

L 1 f o ff = 1 - d y . e - l . 10 d P . a ( D . ¢ ( 9 ) . I o ( ~ ) . t . e . . . . . . ) . . . . . . . . . . y

(12)

replacing Eq. 5. In these equations, Io(D is the number of photons per unit frequency per unit surface area striking the sample per second, and I0 is the sum of all these intensities. For a black body radiator at a temperature, T, the fraction of the total number of photons with frequency (cm -1) between ~ and ~ + d~ is

! - 2 . 4 0 4 \ k T ] e x - 1 (13)

where x = hc~ / kT . To represent the absorptivity we choose a Gaussian bandshape,

a(pp) = ao'e (14)

centered at P0 with a halfwidth at half the maximum intensity of a. With this function, we can probe the ef- fectiveness of light with frequencies on the tail of this bandshape in causing photolysis. In this frequency region the absorptivity will be much less than at the maximum, so more light will penetrate the sample. However, the probability of subsequent absorption and photolysis from any single photon will be much lower. Again we shall assume that the quantum yield is one throughout the entire spectrum. Defining Do as aoIot and Ao as aoc ~, we can insert I0(D and a(D into Eq. 12 and solve for the fraction of photolyzed sample, f(Ao,Do), through numerical integration over frequency and sample thickness.

After numerical integration of Eqs. 5 and 12, we ob-

tain the results shown in Figs. 1 and 2 for photolysis resulting from monochromatic and polychromatic light sources. In Fig. 1, the fractional photolysis is plotted vs. dissociation potential at constant absorbance. Note that at sample absorbances greater than 2, the data appear to yield "saturation" curves at fractional photolysis much less than one. In Fig. 2, fractional photolysis is plotted vs. absorbance at constant dissociation potential. Com- plete photolysis requires a minimum integrated light intensity at both low and high sample absorbances. Sim- plified equations for limiting values of A and D for monochromatic light sources are given by Eqs. 7 and 11. From Eq. 7 we see that even with very small absorbances complete photolysis will not occur when the dissociation potential is small (D < 3). Most of the radiation will pass through the sample without absorption. At the op- posite extreme, at large values of absorbance, most of the radiation available for photolysis will be absorbed by the surface layers. These molecules, even though photodissociated, still contribute to the absorbance of the sample, and significantly decrease the radiation reaching those molecules below the surface. For exam- ple, from the Beer-Lambert relation (A = log(IoH)= acg), a sample with an absorbance of 3 will transmit only 10% of the incident radiation beyond the first third of sample thickness, 1% beyond the second, and 0.1% through the entire sample. For every unit increase in absorbance we need a 10-fold increase in Io to transmit the same radiation. We therefore expect that for large absorbance samples, where most of the radiation is absorbed by molecules that are photodissociated (and so does not contribute to further photolysis), the fractional photolysis will increase as (log D ) / A , as shown by Eq. 11 for monochromatic light. At constant Io, the increase in photolysis of an optically dense sample will be proportional to log(time). The fractional photolysis will be changing very slowly with time and appear to have saturated even though it may be well below the maximum, as shown in Fig. 1A.

The polychromatic curves are calculated with the assumption of black body radiation and a Gaussian line- shape for the absorptivity. Small changes in the Gaus- sian linewidth just decrease (smaller ~) or increase (larger a) the efficiency of the dissociating light. A very large linewidth produces curves similar to those of the monochromatic theory, as shown in parts A of these figures. In this case, low peak absorbance samples are more eas- ily photolyzed since more of the light is absorbed by unphotolyzed molecules. However, optically thick samples still may require prohibitive levels of radiation for photolysis since most of the light is absorbed by previously photolyzed molecules.

A xenon lamp is roughly 5 or 6 times more intense in the spectral region of interest than is a tungsten lamp, due to more efficient collecting optics and to its spectral distribution. This will result in more effective photolysis by a xenon lamp than a tungsten lamp with the same total output energy.

The next step in the mathematical progression of the theory would be to replace the absorptivity function with the actual spectral distribution of the molecules present. The absorptivities for both the ground state (g.s.) and the photo-excited state (e.s.) and the fraction of each


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F[c. 3. Log of the dissociation potent ia l vs. absorbance at cons t an t values of the fraction of the sample photolyzed for monochromat i c radiat ion. We calculated th is plot from Eq. 5 th rough numer ica l integrat ion while holding A and [ ( A , D ) fixed and i terat ing to find the corresponding value of D. T h e let ter symbols refer to the l i tera ture da ta in Table I. Errors of a factor of ten in the es t imate for the dissociation potent ia l will resul t in a d i sp lacement of one un i t along the vertical axis. The dashed lines represen t the dissociat ion potent ia l for MbCO (a~)42 = 14 m M ~ cm ~) when I W / c m ~ of 542 n m light is focused on the sample for 1 s, 1 min, and 1 h.

species need to be accounted for, such tha t a(D should be replaced by a~.~(~) • [1 - f] -F ao.~(D • [f], and a (D • ¢(~) should be replaced by ag.,.(D [1 - f]. With these substi tutions, Eq. 12 can be numerical ly integrated and solved by i terat ion for the fraction photolyzed. However, since these exper iments are normally per- formed with frozen solutions where devitrification, and hence light scattering, is a serious complication tha t is difficult to quantify, we shall not a t t empt to carry the theory any fur ther at this time. The effect of light scat-

tering would be to add a baseline tha t changes slowly relative to the spectral bands of the sample. A polychromatic source would then be expected to yield a time- dependen t fractional photolysis tha t increases more slowly than predicted by Eq. 12.

Now we shall est imate what values we can realistically expect for the dissociation potential. Le t us assume tha t the average photon from our source tha t is capable of photodissociating a heme ligand has a wavelength of 542 nm, at one of the visible peaks of MbCO. The energy per typical photon from this source is then E = h c / X =

3.66 × 10 -~9 J, so tha t per mole of 542 nm photons we have an energy of 2.21 x 10 ~ J, or 4.53 x 10 -6 mole quanta /J . Carboxymyoglobin has an absorptivi ty of 14 mM ' cm -~ at 542 nm, '° or, in terms of moles, a~42 = 1.4 × 107 mol i cm 2, and a quan tum yield of approxi- mately one. The monochromat ic photochemical dissociation potent ial will then be given by D = (1.4 × 107) • (1). (4.5 × 10 ~)q = 63q, where q is the number of Joules/ cm 2 incident on the sample. Light intensi ty of 1 W/cm 2 focused on this sample for 1 s, 1 min, and 1 h yields D = 63, 3.8 × 103, and 2.3 × 10 ~, respectively. These values of D are shown as horizontal dashed lines in Fig. 3, where log(D) is plot ted vs. absorbance at constant fractional photolysis.

Table I shows data derived from the l i terature for photolysis of some heme protein CO and NO complexes at low temperatures. Est imates of absorbance were made from the published concentrat ions, absorptivities, and sample cell characteristics. For the E P R experiments , it was assumed tha t the sample cell was cylindrical with an inside diameter of 0.3 cm, and the est imated absorbance listed in Table I refers to this maximum path length. Since actual light intensities at the sample were generally not known, they were roughly approximated for purposes of illustration. The dissociation potent ial was est imated from the published method of photolysis.

T A B L E I. Literature values of absorbance and dissociation potential for the monochromatic theory. ~

Es t im a t ed Photolyzing source c fract ion

Symbol in Exper imen ta l (electrical energy Dissociat ion photolyzed Reference Fig. 3 t echnique Sample Absorbance b input , J) potent ia l b,' ( % )

Yoshida e t al. '~ a ° E P R CcO-NO 2.5 PL (9 × 104) 5.9 x 10 ~ 100 Clore e t al . ]2 b ° E P R CcO-CO 0.74 Xe (100-200) j 4.6-9.2 97-100 Wever e t al. ':~ c ° E P R CcO-CO 2.8 PL (2.3 × 104) 2.1 x 102 95 Shaw e t al. ~4 d e E P R CcO-CO 1.5 Xe (2.7 x 10 :*) 2.5 x 10 :~ 100 Flamingo e t al. ~ e IR CcO-CO 0.58 PL (4.5 × 105) 4.4 × 10 :~ 100 Alben e t al . '~ f" IR Mb-CO 1.1-2.1 PL (3 × 10 ~) 1.9 x 103 100 Chance e t al . '~) ~7 gl E X A F S Mb-CO 5.6-28 Xe (200) 1.2 × 102 10-48 Chance e t al . 18,19 g2 E X A F S Mb-CO 5.6-14 Xe (8.0 x 103) 5.0 x 103 31-77 Spar ta l ian e t al . 20 h,.h MSssbauer Mb-CO 4.5-8.9 PL (1.8 x 104) 1.1 × 102 30-60

" D a t a f rom the l i tera ture of a few optically dense samples , where bo th the absorbance and the dissociat ion potent ia l could be es t imated , are t abu la ted here. These da ta are also p lo t ted in Fig. 3, where they can be identif ied by the let ter symbols ass igned in this table.

~' T h e absorpt ivi t ies were t aken to be 16.5 m M ' cm ~ for cy tochrome c oxidase-NO at 605 nm, 23.2 m M ~ cm- ' for cy tochrome c oxidase-CO at 605 nm, and 14 m M ' cm ~ for M bCO at 542 nm.

' Xe = Xenon arc lamp; PL = projector lamp. Projector l amps were generally focused on the sample for several minu tes , whereas xenon arc l amps were general ly f lashed for a few mil l iseconds to a few seconds.

d Arc lamps were a s s u m e d to be 1% efficient and projector lamps 0.01% efficient at conver t ing the applied power into rad ian t energy of the wavelength range required for photolysis focused onto 1 sq. cm. For purposes of i l lustration, the radia t ion was t rea ted as if it were monochromat ic at the f requency of the visible absorpt ion m a x i m u m indicated above.

o For the E P R samples it is a s s u m e d t ha t the sample cell was cylindrical with an inside d iameter of 0.3 cm. T h e es t ima ted absorbance listed above refers to this m a x i m u m pa t h length.

~ F rom the manufac tu r e r ' s e s t ima tes this l amp would have an oupu t energy of 0.1-0.2 J t ha t could be focused on the sample. These samples were photolyzed from both sides and so the effective absorbance listed above is a s sumed to be ha l f the actual absorbance.

h Scat ter ing from this sample m a y have increased the effective absorbance considerably.


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F[(~. 4. Fraction of the sample photolyzed vs. log (D~,) fbr the frequency-dependent theory. The absorbance values listed are those for the peak of the Gaussian band centered at 1.72 x 104 cm ~ (580 nm) with a half-width at half the maximum intensity of 300 cm ' (11 nm). The solid curves are calculated from Eq. 12. The experimental data points are connected by dashed lines to guide the eye. The curve labeled a is from the sperm whale MbCO sample with a measured absorbance of 1.62 at 579 nm; those labeled b and c are from the optically thick sample estimated to have an absorhance of 24 _+ 5 at 579 nm.

| l i I - ~ I r I [ [ I ~ - I - ~

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F[(~. 5. Fraction of the sample photolyzed vs. log (D,,) when the absorptivity is independent of frequency. The absorbance values are listed beside the curves which were calculated with Eq. 11. The experimental data points are connected by dashed lines to guide the eye. The curve labeled a is from the sperm whale MbCO sample with a measured absorbance of 1.62 at 579 nm; those labeled b and c are from the optically thick sample estimated to have an absorbance of 24 + 5 at 579 nm.

A xenon arc lamp is roughly 50 % efficient at converting input electrical energy into radiant light output. 21 A typical condensing lens system will collect 2.9-9.4 % of the total light output. 2I If half of this spectral output is of sufficient energy to cause photolysis, then in effect 0.7- 2.3% of the input electrical energy is converted into photolyzing light. We then assume that a typical arc lamp is 1% efficient at converting applied electrical energy into radiant photolyzing energy that can be focused onto 1 sq cm of the sample. In this laboratory, for a projector lamp with an elongated source and poorer condensing optics, and after filtering through glass and water to remove the UV and mid-infrared, we measured an efficiency of roughly 0.01%. The manufacturer's source energy output estimate was used for the data of Clore et al. 12 The quantum yield was assumed to be 1 in all cases, and relaxation of the photolyzed species was taken to be negligible (zero). No attempt was made to cor- rect the dissociation potential due to the use of other than monochromatic light. The values from Table I are also plotted on Fig. 3 for comparison with computed fractional photolysis.

EXPERIMENT

Figures 4 and 5 include infrared photolysis data from two samples of concentrated sperm whale carboxy myoglobin solution. In one sample, the water was extracted with glycerol, as detailed in "Methods." The aqueous sample had a measured absorbance of 1.62 at 579 nm and the glycerol sample had an estimated absorbance of 24 _+ 5 at 579 nm. The infrared single-beam spectra of the latter sample in the dark and after exposure to a 500 W projector lamp for 11 h (Do = 4 x 10 ~) are shown

in Fig. 6, and their absorbance difference spectrum (log Dark/Light) in Fig. 7. The FeCO absorption at 1945 cm 1 dominates all spectra, even after exhaustive photolysis, indicating that a large amount of CO remained bound to the iron. This band was so highly absorbing that it was useless for quantitative purposes. Therefore, the natural abundance of the heavy isotope bands at 1901 cm 1 (85% 1"~C160 and 15% 12ClSO), resulting from 1.31% of the total CO was used for quantitation. The absorbance difference data from this band were normalized to the Dark single-beam absorbance to obtain the fraction photolyzed and plotted in Figs. 4 and 5 for comparison with the monochromatic and polychromatic theories of photodissociation presented above. These figures also show the absorbance difference data of the 1945 cm ~ band from the less optically dense MbCO sample in frozen water.

The concentration estimates of the aqueous sample from the 579-nm peak height (a = 12.2 mM-lcm I at room temperature; Ref. 10) and from the integrated intensity of the FeCO vibrational absorbance envelope (B = 30.4 ± 0.2 mM ~cm-2; Ref. 22) were the same within experimental error at 14 _+ 1 mM. The absorbance enhancement factor, the ratio of the absorbance of the frozen sample at low temperature with the solution absorbance at room temperature, 7 must then be either uni- ty or some nonunity value that is the same at both wavelengths. Since there is a nine-fold difference in wavelength between 579 nm and 1945 cm I (5140 nm), even a very weak wavelength-dependence from light scattering would be observable. The absorptivity of the near-infrared band at 766 nm is then 0.37 _+ 0.03 mM 1 cm l measured at 12 K, but extrapolated to liquid conditions by the visible and infrared band absorption.


r r

14 K

~o

E

q )

c A o

Dark

A, I I I I I I I

1 8 0 0 1 9 0 0 2 0 0 0 2 1 0 0 2 2 0 0 2 3 0 0 2 4 0 0

F r e q u e n c y ( c m - I )

FIe. 6. Mid- inf rared s ingle-beam spect ra of optically th ick MbCO. The bo t tom spec t rum was t aken in the Dark at 13 K after re laxat ion at 180 K. The top spec t rum (Light) was taken a t 14-15 K after 11 h of i l luminat ion (Do = 4 x 10 ~,) following the Dark da ta collection. Fe'~C"~O absorbs at 1945 cm ' with a shoulder at 1927 cm ~ and a minor band at 1969 cm '. These are marked A1, A2, and A,, respectively, following the des ignat ion of Alben et alp T he heavy isotopes (Fe"~C'"O and Fe'~C'aO) absorb at 1901 cm ~, as indicated by the arrow. T h e photolyzed '2C'"O (band B, of Alben et alP) absorbs a t 2131 cm ' in the Light spec t rum.

For the optically thick protein sample in glycerol (see Figs. 6 and 7) the concentration of the photolyzed species at 2131 cm ' could be estimated from its integrated intensity (B = 1.4 ± 0.1 mM ' cm-2; Ref. 5). We calculated the final fractional photolysis from the absorbances of the 1901 cm ' band estimated from the single-beam Light and Dark spectra shown in Fig. 6 by interpolating a baseline and calculating the absorbance of the bands. The original MbCO concentration could then be estimated to be 53 ± 10 mM, so that the absorbance at 579 nm would be expected to be 24 ± 5.

The dissociation potential for the experimental data in Figs. 4 and 5 is approximated from the measured total radiant energy reaching the sample and the characteristics of a black body source. From the ratio of the energy density (U) and the photon density (N) resulting from a black body, we determine the average energy per mole of quanta to be ( E ) = U ( N o / N ) = 7.40 x 104 J/mol, where No is Avogadro's number and the black body temperature is 3300 K, the approximate temperature of the tungsten lamp employed for photolysis. From this and the absorptivity at 579 nm (ao = 12.2 mM 1 cm-') we estimate the dissociation potential to be Do = ( a o / ( E ) ) q =

165q, where q is the number of Joules per cm 2 striking the sample. We choose to use the modified dissociation potential, Do, defined as if the sample had constant absorptivity equal to the band maximum and a quantum yield of 1, rather than the integrated dissociation potential, because experimentally the latter is not directly available. It requires a detailed knowledge of the absorptivity, the number of photons, and the quantum yield as a function of frequency. Do, however, can be readily estimated for both theory and experiment.

The optically thick sample was allowed to relax at 180

0

E (:D

_Z::i

0

09

_C:i

<~

I

Fe, C,,O e'2ClsO

l I

1900

I

II.

Fe t2C 16 0

,it

I I

F AA =o.I

_1_

14 K

I I I 2000 2100 2200

F r e q u e n c y ( c m - I )

FIG. 7. M b C O - M b * C O mid- inf ra red absorbance difference. Shown here is the negat ive logar i thm of the ratio of the s ingle-beam spect ra of Fig. 6 (Dark/Light) .

K for about 30 min between two sets of photolysis experiments (curves b and c of Figs. 4 and 5). In the first experiment, the sample was only 76 ± 8% photolyzed after 11 h in front of the projector lamp (curve b), even though a bright red image of the lamp was transmitted through the sample. The second experiment showed only about half this fractional photolysis (curve c, 39 ± 5 % photolyzed) after a similar amount of time. Several more cycles through temperature, including one overnight relaxation at 180 K, succeeded in making the sample near- ly opaque to infrared light. This probably represented increased light scattering due to the formation of micro- crystals during devitrification of the solvent. Such phe- nomena have been described previously2 ,s,9

DISCUSSION AND CONCLUSION

The frequency-independent theory predicts that it will be extremely difficult, if not impossible, to completely photodissociate optically dense heme-ligand solutions. When the frequency-dependence of the absorptivity and the light intensity are included, even very highly absorbing samples may have a region at the tail of their absorption band that is transparent enough for the photolyzing radiation to adequately penetrate the sample, yet absorbing enough to cause efficient photolysis. The experimental results with MbCO fall somewhere between these extremes. The theory is incomplete in several respects, and analysis of these may help to explain the discrepancy. First, it was assumed that the absorptivity was the same before and after photolysis. While this is a reasonable approximation at the absorption peaks it can be very poor at the tail. If the photodissociated form absorbs more strongly on the long wavelength tail than does the ligated form, as in the case of MbCO, it will have an increased shielding effect, making


it more difficult to photolyze the remainder. Second, scattering from micro-crystalline surfaces within the sample may severely decrease the sample penetration of radiation at all frequencies. In the extreme case, reflec- tions at the incident surface will result in increased exposure and complete photodissociation of the initial layers, whereas the bulk of the sample will remain essentially unphotolyzed. Third, the presence of other forms of the protein, such as deoxy-Mb or met-Mb, will increase the optical density of the sample without con- tributing to the photodissociated species. Fourth, relaxation of the photolyzed species through molecular tunneling of the CO back to the iron will decrease the expected fractional photolysis if the rate of relaxation is not small compared to the rate of photolysis, as might be the case for thick samples. These four effects will all contribute towards making the experimental data behave somewhere in between predictions from the frequency-independent and the frequency-dependent theories.

While most of the experimental conditions cited in Table I have resulted in complete photolysis under the monochromatic theory, two clearly have not. The spectra of the photolyzed system of Spartalian e t al . 2° were obviously a composite of the ligated and photodissociated species and were analyzed by the authors with this realization. Their frozen solution showed visible signs of devitrification, and they estimated their samples to be 64-65% photolyzed, slightly greater than predicted by the monochromatic theory. The EXAFS sample conditions of Chance and coworkers 1~-1' would also be predicted by the monochromatic model to result in incomplete photodissociation of the MbCO. The interpretation of their data is based in part upon the observation of negligible change in the population of the photolyzed species after repeated light flashes. As we have shown (Fig. 1), this condition should not by itself be construed as proof of complete photolysis.

These examples serve to illustrate the need to determine whether experimental conditions are sufficient to achieve a required degree of photolysis. This may be done by measurement before and during or after photolysis in order to directly obtain the fraction photolyzed. The infrared measurements described in this paper show how the heme-carboxy and photolyzed *CO may both be quantitated from the same spectrum. The relations between sample thickness, light intensity, and fractional photolysis described in this paper may help

to guide investigators in their experimental design. However, it should be noted that this description ne- glects molecular tunneling and applies only to the limiting condition of zero relaxation that is approached (but not reached) at temperatures below 10 K for most heme proteins.

ACKNOWLEDGMENTS

This work was supported in part by grants from the National Insti- tutes of Health (HL-17839 and HL-28144). Computer time was fur- nished without charge by the Instruction and Research Computer Cen- ter at Ohio State University.

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photochemical dissociation in optically dense solutions: applications to photolyzed carboxymyoglobin...

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