Bacteriorhodopsin photocycle at cryogenic temperatures reveals distributed barriers of conformational substates Andrei K. Dioumaev and Janos K. Lanyi* Department of Physiology and Biophysics, University of California, Irvine, CA 92697 Communicated by Hans Frauenfelder, Los Alamos National Laboratory, Los Alamos, NM, April 26, 2007 (received for review January 24, 2007)
low-temperature kinetics 兩 distributed kinetics 兩 photointermediates 兩 infrared 兩 FTIR
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arious kinds of evidence show that macromolecules exist as populations of conformational substates (1–6). The most dramatic of these evidences is that below ⬇200 K the reactions that follow photodissociation of the CO–myoglobin complex cannot be described by conventional kinetics that would arise from a single barrier. Instead, the time course follows a nonexponential path that suggests an ensemble of barriers, and from its analysis it was concluded (6–9) that the protein, like glasses and spin glasses, assumes a large number of slightly differing conformational substates. At ambient temperature, these substates rapidly equilibrate to produce a thermally averaged homogeneous state, but at cryogenic temperatures they are distinct and noninterconvertible. More direct methods, such as x-ray scattering (7) and Mo ¨ssbauer spectroscopy (for review, see ref. 1) and spectroscopic and kinetic hole burning (10–12), have indeed detected such populations of slightly differing conformations. Conformational heterogeneity will result in nonconventional, distributed kinetics. A multibarrier ‘‘energy landscape’’ must be a property of all proteins (1–3), but its consequences for enzyme kinetics at cryogenic temperatures are difficult to explore without the technical advantages of the photodissociation and rebinding of the CO–myoglobin complex, and a few other such reactions (for reviews, see ref. 1) that can be initiated by illumination in the frozen state. The photocycle of bacteriorhodopsin, a proton pump (for reviews, see refs. 13–15), is also a light-driven reaction. It is described by the sequence, BR–h3 K 7 L 7 M1 7 M2 7 M⬘2 7 N 7 N⬘ 7 O 3 BR, containing the various spectrally identified configurational transitions of the photoisomerized 13-cis,15-anti-retinal chromophore and the www.pnas.org兾cgi兾doi兾10.1073兾pnas.0703859104
protein that recover the initial state, in ⬇10 ms. Bacteriorhodopsin would be another obvious candidate for such studies. There are several reports of the bacteriorhodopsin photocycle at cryogenic temperatures, which contain clues for the existence of conformational substates. Spectral and kinetic anomalies near 100 K had suggested the existence of multiple K photoproducts (16, 17), which come to a steady-state mixture only at temperatures above 200 K (16), in a suggested analogy with myoglobin. Similar findings were reported for the low-temperature bathoproduct of 13-cis bacteriorhodopsin (17). In a different approach, optical hole burning (18) indicated the existence of vibrational substates that give rise to inhomogeneous band broadening in this protein. We report here real-time FTIR monitoring of the K 3 L reaction at cryogenic temperatures. In this reaction, the initially twisted photoisomerized 13-cis,15-anti-retinal of the primary photoproduct relaxes and the protonated Schiff base regains its hydrogen bond to Asp-85 that was transiently lost in K (19–22). In the temperature range examined, there is also a shunt from the L state to the BR state that bypasses the normal photocycle (23), not observable at ambient temperature. Analysis of the observed kinetics according to conventional concepts, such as equilibration, branching, and parallel reactions, leads to unresolvable contradictions. Instead, the observations can be well accounted for with distributed kinetics, in which between 125 and 195 K an apparently increasing fraction of the protein undergoes reaction at increasing temperatures, reflecting the heterogeneous barriers of microscopic conformational substates. Results Blue-light (500 ⫾ 20 nm) illumination of bacteriorhodopsin films at temperatures below 155 K produces photostationary states that contain mostly the K intermediate because any L generated from K by a thermal reaction will be reconverted to the BR state by the blue light (24), and the temperature is too low for the L 3 M reaction (16, 25). Once the actinic light is off, the L state is built up from K through a thermal reaction. The difference FTIR spectra in Fig. 1 were measured during illumination (in red) and after 200 min (in blue) at the indicated temperatures. Fig. 1 illustrates that after blue-light illumination, virtually no K 3 L reaction is observable within 200 min at 125 K (Fig. 1a), but a partial transformation of K to L is evident at 155 K (Fig. 1b). The derived spectra of K and L shown in Fig. 2 agree with earlier published spectra for L (e.g., refs. 26 and 27) and K when measured at these temperatures (28). The characteristic changes (20, 26) are (i) in the CAO stretch region where the overlapping negative CAO stretch bands of the protonated Asp-96 and Asp-115 at ⬇1,740 cm⫺1 are shifted in L to higher and lower Author contributions: A.K.D. and J.K.L. designed research; A.K.D. performed research; A.K.D. analyzed data; and A.K.D. and J.K.L. wrote the paper. The authors declare no conflict of interest. *To whom correspondence should be addressed. E-mail:
[email protected]. © 2007 by The National Academy of Sciences of the USA
PNAS 兩 June 5, 2007 兩 vol. 104 兩 no. 23 兩 9621–9626
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The time course of thermal reactions after illumination of 100% humidified bacteriorhodopsin films was followed with FTIR spectroscopy between 125 and 195 K. We monitored the conversion of the initial photoproduct, K, to the next, L intermediate, and a shunt reaction of the L state directly back to the initial BR state. Both reactions can be described by either multiexponential kinetics, which would lead to apparent end-state mixtures that contain increasing amounts of the product, i.e., L or BR, with increasing temperature, or distributed kinetics. Conventional kinetic schemes that could account for the partial conversion require reversible reactions, branching, or parallel cycles. These possibilities were tested by producing K or L and monitoring their interconversion at a single temperature and by shifting the temperature upward or downward after an initial incubation and after their redistribution. The results are inconsistent with any conventional scheme. Instead, we attribute the partial conversions to the other alternative, distributed kinetics, observed previously in myoglobin, which arise from an ensemble of frozen conformational substates at the cryogenic temperatures. In this case, the time course of the reactions reflects the progressive depletion of distinct microscopic substates in the order of their increasing activation barriers, with a distribution width for K to L reaction of ⬇7 kJ/mol.
Fig. 1. FTIR difference spectra of bacteriorhodopsin films at different temperatures, during and after illumination. Spectra during illumination are shown in red, spectra after 200 min of subsequent thermal reaction are in blue. (a) Spectra at 125 K (blue-light illumination). (b) Spectra at 155 K (blue-light illumination). (c) Spectra at 195 K (red-light illumination).
frequencies, respectively; (ii) at the Schiff base CAN stretch band, which is at 1,609 cm⫺1 in K but shifts to a higher frequency in L similar to that in the BR state; (iii) in the ethylenic stretch region, where the 1,514 cm⫺1 band of K is up-shifted and becomes partly hidden under the amide band at ⬇1,555 cm⫺1 in L; (iv) in the fingerprint region where the ⬇1,194 cm⫺1 COC stretch band decreases in amplitude in L; and (v) in the HOOP (hydrogen-out-of-plane) region (900–1,000 cm⫺1). Fig. 2a also shows that in the temperature range examined, two K states exist. One, measured at 100 K (Fig. 2a, red) contains the well known FTIR features of ‘‘low-temperature’’ K (20, 27, 28), with large HOOP bands at 956 and 974 cm⫺1. At higher temperatures, in accord with previously published data (28–30), we find mixtures of this KLT state and another K with a characteristic HOOP band at 987 cm⫺1 in Fig. 1 a (red and blue) and b (red). However, at ⱖ135 K, the low-temperature K decays to the next K much more rapidly than the K 3 L transition, and its contribution need not be considered in the analysis of the latter kinetics. The time course of the K 3 L reaction can be tracked most readily with the amplitudes of the positive 1,514 cm⫺1 ethylenic stretch band for K and the negative CAO stretch band at 1,740 cm⫺1 for L. Fig. 3a shows the decay of K after the illumination at various temperatures between 135 and 155 K. Although not shown, the rise of L follows the same time course as the decay of K. The K 3 L conversion under such conditions occurs nearly quantitatively. Although the apparent amplitude of the ethylenic stretch band at 1,528 cm⫺1, which reflects BR depletion in Fig. 1b, changes somewhat, most of this change is caused by the decrease in the overlapping (positive) ethylenic stretch band of K at 1,514 cm⫺1. When decomposed (data not shown), the amplitude of the depletion at 1,528 cm⫺1 is constant within 5%, in accord with the previously proposed (31) lack of significant shunt of K to BR. Unexpectedly, the decay of K is not described by a single exponential. The K and L states appear to approach limiting mixtures that contain less K at increasing temperatures 9622 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0703859104
Fig. 2. FTIR difference spectra. (a) KLT was measured at 100 K; spectrum is shown in red. Calculated K is shown in blue. (b) Calculated L. The latter two spectra were calculated from data as in Fig. 1b measured at 135, 145, and 155 K. At each temperature, a spectrum under illumination (e.g., Fig. 1b, red) was subtracted from the spectrum at ⬇200 min (e.g., Fig. 1b) to eliminate K-specific (26) spectral features. The resulting pure but unscaled spectrum for L was subtracted from the spectrum under illumination to eliminate L-specific spectral features (26), producing a pure but unscaled K spectrum. The coefficients of these two subtractions were used for scaling K and L at 135, 145, and 155 K, which were then averaged.
(Fig. 3a). An alternative plot of the same data, with both amplitude and time on logarithmic scales, is shown in Fig. 3b. The lack of breaks or inflections agues against multiexponential kinetics as in the case of the myoglobin reaction in the same temperature range (3, 6, 9). Further, global multiexponential fits
Fig. 3. Time course of IR features from K (ethylenic stretch band), shown on a logarithmic scale vs. linear time (a) and vs. logarithmic time (b) at various temperatures, after a photostationary state containing predominantly K was created at the same temperature with blue light. (a) Fitted curves are to multicomponent exponentials. (b) For clarity, only every third data point is displayed. Fitted curves are to the empirical equation, rate ⫽ (1⫹ t/to)⫺n (6).
Dioumaev and Lanyi
with increasing numbers of exponentials did not yield additional components with different spectra. Thus, we must consider the possibility of distributed kinetics. Illumination with red light (⬎640 nm) traps a nearly pure L state in the photostationary mixtures because the primary photoproduct K is efficiently reconverted to BR by the red light (23, 32), whereas the L state accumulates slowly by the competing K 3 L thermal reaction, during the illumination. Up to 165 K, the L state appears stable within 3 h (data not shown). At temperatures between 165 and 195 K, the L state decays directly to the BR state instead of M (see Fig. 1c), as reported earlier (23). Fig. 4a contains the time course of changes in the amount
Fig. 5. Limiting amounts of the L state formed from K (open circles) and the recovered BR state from L (closed circles) that accumulate after prolonged incubation at various temperatures, as in Figs. 3 and 4. At temperatures above 165 K, the decay of the L state to BR (Fig. 4) would interfere with further monitoring of the K 3 L reaction. Likewise, the recovery of the BR state from L could not be determined at above 195 K because of interference by the L 3 M reaction. Therefore, the sigmoidal curves were calculated only from data points below 165 and 195 K for the two curves, respectively, but for clarity the lines are drawn as if at higher temperatures the L3 BR and L3 M reactions did not interfere.
Dioumaev and Lanyi
Fig. 6. Tests of the reversibility of the K 3 L reaction. Filled circles represent the time course when the K state was created by blue illumination and its decay was followed at either 135 or 155 K (as in Fig. 3a). Open circles are data from separate experiments, with K created and its dynamics monitored for the first 180 min at 135 K, followed by shift of the temperature to 155 K (a) or created and monitored for the first 140 min at155 K, and then the temperature was shifted to 135 K (b). In both cases, the time course of the temperatureinduced changes was monitored after the temperature jump, but no data were collected during the reequilibration of the temperature, for periods of 130 min (a) and 40 min (b). (a) The dashed line is the estimate of the further progress of the K 3 L reaction at the higher temperature. (b) The dashed line illustrates what would be expected (approximately) if the L 3 K back-reaction occurred.
of the L state after red illumination at various temperatures. As for the K 3 L reaction (Fig. 3a), the time course deviates from a single exponential, and the extent of the decay seems to reach limiting values that increase with increasing temperatures. Again, the alternative plots, with logarithmic scales for both amplitude and time, are shown in Fig. 4b. As in Fig. 3b, their shapes suggest distributed kinetics. A minor amount of M might be present at higher temperatures (e.g., at 195 K in Fig. 1c), but the spectra in Fig. 1c before and after incubation are fully scalable, indicating a decay of L back to BR rather than an L-to-M redistribution. In conventional kinetics (Fig. 3a), it appears that the K 3 L reaction proceeds to limiting mixtures that contain more product at higher temperatures, and the same is true for the L 3 BR reaction (Fig. 4a). In Fig. 5, the apparent final amounts of the L and BR states, extrapolated from the first 200 min after illumination, are shown as functions of temperature. In both cases, the assumption of conventional kinetics with distinct kinetic components yields accumulations of the product of the thermal reaction that are strongly temperature-dependent, with midpoints of 143 and 195 K for the K 3 L and L 3 BR reactions, respectively. The reversibility of the K 3 L reaction was tested in two ways. First, the thermal reaction after blue-light illumination, as in Fig. 3, was allowed to proceed to near apparent completion, and the temperature was then either raised or lowered. Fig. 6 a and b shows, respectively, incubation at 135 K followed by a shift to 155 K and in another experiment, illumination and incubation at 155 K followed by a shift to 135 K. If K and L were in a thermally controlled equilibrium, the two experiments should yield mixtures that depend solely on the final temperature. However, the PNAS 兩 June 5, 2007 兩 vol. 104 兩 no. 23 兩 9623
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Fig. 4. Time course of the decay of IR features from L (CAO stretch band), illustrating the decay of L to BR (Fig. 1c) at various temperatures, after a photostationary state containing virtually only L was created at the same temperature with red light. The data and the fitted curves are as in Fig. 3 a and b. (b) For clarity, only every third data point is displayed.
half-maximum in Fig. 7b) around the mean activation energy, a value comparable with that for myoglobin (6).
Fig. 7. Calculation of activation energy spectra for the K 3 L reaction from the fits in Fig. 3b, as described in ref. 6 and the text. (a) Test of the applicability of the method in ref. 6 and estimation of the activation energy at the peak of the distribution curve and the preexponential factor. The mean activation enthalpy is 41 kJ/mol, and the preexponential factor, A, is ⬇10⫺11 s⫺1. (b) Calculated energy spectrum. The spectrum in bold is the average of the curves calculated at 135, 140, 145, and 155 K; the shaded area corresponds to ⫾1 SD. The full-width at half-maximum of the distribution function is ⬇7 kJ/mol.
up-shift and down-shift of the temperature yield different results. The amount of the K state decreases further when the temperature is raised from 135 to 155 K, to the level reached when both illumination and incubation are at 155 K. Importantly, however, the amount of K does not increase when the temperature is shifted from 155 to 135 K, even though the test is carried out as long as the reaction requires at 135 K. Second, the time courses of thermal reactions at 155–165 K are different after blue-light and red-light illumination. If the mixture produced by the illumination contains mainly K, the K 3 L thermal reaction is observable (Figs. 1b and 3), but if the mixture contains mainly L, the reverse L 3 K reaction is absent (Figs. 1c and 4). Thus, both sets of experiments demonstrate that L is produced from K by an irreversible reaction. The L 3 BR thermal reaction is obviously irreversible, but a change in the yield of the BR state was determined in a temperature up-shift experiment as in Fig. 6a (data not shown). At 175 K, the limiting extent of conversion of L to the BR state is ⬇8%, but raising the temperature to 195 K produces further conversion, to a total of ⬇43%, consistent with the limiting yields of BR at these temperatures in Fig. 4a. For distributed kinetics, it is possible to calculate the activation energy spectrum (6) from the fits in Fig. 3b. The data for the L 3 BR reaction (Fig. 4b) was not suited for such a plot because we are restricted to a narrow temperature range where it can be examined without interference (see legend to Fig. 5). By using the approach to this calculation in ref. 6, Fig. 7a shows a plot of RT䡠ln(n/to) vs. temperature for the K 3 L reaction, where n and to are parameters in the fits to the kinetics (see legend to Fig. 3b). It is linear, as expected (6). The intercept on the ordinate gives the activation enthalpy at the peak of the distribution curve, and it is 41 kJ/mol, in accord with the Eyring activation enthalpy, 41 ⫾ 1 kJ/mol, at ambient temperatures (33). Fig. 7b shows the energy spectrum, calculated as in ref. 6. The curves from the fits at different temperatures are nearly superimposable (data not shown), and in Fig. 7b we give their average. The distribution spectrum indicates that the deviations from a single exponential in Fig. 3a are accounted for by a spread of ⬇7 kJ/mol (full-width at 9624 兩 www.pnas.org兾cgi兾doi兾10.1073兾pnas.0703859104
Discussion The need to postulate conformational substates for myoglobin arose from the nonexponential time course of the geminate rebinding that follows photodissociation of its CO complex (1, 6, 9). Unlike this reaction, the bacteriorhodopsin photocycle is a cascade of numerous consecutive reactions, which severely limits the temperature range in which individual reactions can be examined. With many intermediate states, it is particularly difficult to distinguish between conventional but multiexponential kinetics and distributed kinetics. In conventional kinetics, the thermal reaction after blue-light illumination (Fig. 3a) is a reequilibration of mixtures that contain initially mostly K to produce mixtures that contain much increased amounts of L. For example, at 155 K, the initial mixture (at the end of the illumination) contains ⬎93% K and ⬍7% L, and extrapolation to infinite time yields a mixture containing ⬇23% K and ⬇77% L. This treatment of the data at different temperatures between 135 K and 155 K produces a set of extrapolated mixtures of K and L, in which the higher the temperature, the more L is found in the final mixture (Figs. 3a and 5). The simplest explanation would be a reversible K 7 L reaction with a temperature-dependent K/L equilibrium. To distinguish between a complex kinetic scheme with multiple, distinct, but closely lying time constants and a simple K 3 L reaction with a continuous distribution of time constants, we used perturbation experiments. When the dynamics is probed in this way, the scheme BR -hv 3 K 7 L and its simple variants, as suggested for ambient temperatures (34–37), lead to inconsistencies. When the reaction is allowed to come to a steady state at 135 K (Fig. 6a) and the temperature is increased to 155 K, the amount of L increases, and the composition of the sample shifts to what would be reached when illuminated and allowed to react thermally further at the higher temperature. On the other hand, when the initial equilibration is at 155 K, decreasing the temperature to 135 K does not result in a decrease in the amount of L (Fig. 6b). Similarly, two different illumination regimes at a single fixed temperature produce seemingly inconsistent results: illumination with blue light, which produces mostly K, leads to a thermal reaction producing L, but illumination with red light, which produces mostly L, is not followed by a thermal reaction leading back to K. Thus, the limiting mixtures K and L that develop at these temperatures are not temperature-dependent equilibria because they can be shifted from K toward L but not from L toward K, and all models that include a back-reaction from L to K are excluded. Kinetic schemes alternative to those with reversible reactions, as have been proposed and long argued over for the ambient-temperature photocycle (for review, see 14), contain either parallel reaction sequences from several alternative initial BR states, or branching. The reason for heterogeneity or branching would be, for example, partial protonation states of critical residues depending on the pH (38), nonequivalence of the monomers in the bacteriorhodopsin trimer (39), or a neighbor/cooperativity effect of photocycling molecules on one another in the membrane (40, 41). However, the temperature up-shift experiment (Fig. 6a) rules out both parallel and branching cycles, as a group. Without a reversible step, all such models lead to end-state mixtures of K and L (of necessity, multiple K and/or L states), whose compositions are fully determined by (i) the initial heterogeneity of the sample in all models with parallel photocycles, and (ii) the ratio of rates at the branching point in all branching models. Without an L 3 K back-reaction (and it is excluded), once the final compositions are reached in these models, there is no possibility of further change. Yet the amount of L in the final mixtures is not fixed Dioumaev and Lanyi
Dioumaev and Lanyi
of the changed geometry around the retinal (21) to give a more BR-like structure in L at low temperatures than at ambient temperature, would account for both of these differences. However, the L intermediate produced at low temperature is capable of entering the next photocycle step. Warming of illuminated bacteriorhodopsin that contains the trapped L state, from ⬇170 K to above 200 K, yields the M state (16, 23, 48), as it would in the normal photocycle sequence. On the other hand, a shunt reaction had been suggested to uncouple transport from the photochemical cycle when the pump generates excessive proton gradient across the membrane and therefore increased proton back-pressure (49, 50). Thus, an alternative explanation for the L 3 BR shunt, at least, would be that it occurs in the ambient-temperature photocycle also, under some conditions. This possibility remains open because the photocycle has been studied mostly in the absence of control by the proton potential it produces. Materials and Methods Purple membrane containing wild-type bacteriorhodopsin was isolated according to a standard procedure (51). The membranes were washed with 0.5–1 mM [bis(2-hydroxyethyl)amino]tris(hydroxymethyl)methane buffer, pH 7.0, and deposited on a 13-mm CaF2 IR window (Harrick, Ossining, NY) followed by drying under mild vacuum and rehumidification for ⬎3 weeks at 100% humidity. The films were covered by a second CaF2 window (separated from the first by a 0.8-mm Teflon spacer) and sealed with vacuum grease. The films had optical densities of ⬇0.5 at 570 nm. After humidification, the samples developed a ⬇0.64 OD absorption in the water band at ⬇3,300 cm⫺1. This procedure produced samples capable of a normal photocycle. The sample holder was placed in an Optistat DM cryostat, equipped with an ITC 601 temperature controller (both by Oxford Instruments, Abingdon, U.K.) that provided temperature stability within 0.1 K. A heavy (⬇100 g) homemade cold block for holding the sample was mounted on the tip of the standard sample holder. Temperature was monitored with a K-type thermocouple and an HH 81 digital thermometer (both by Omega Engineering, Stamford, CT), attached directly to the cold block. An equilibration time of ⬇60 min was allowed for each temperature change. The IR measurements were performed with a Bruker IFS66/s FTIR spectrometer, equipped with a photovoltaic MCT detector (model KMPV11-1-LJ2/239; Kolmar Technologies, Congers, GA), at 2 cm⫺1 resolution. Data were collected for the 0 –5,250 cm⫺1 range in the rapid-scan mode with averaging on a quasi-logarithmic time scale (33 points per decade). Preillumination spectra (6,196 scans) were always collected at the same temperature, before the time-resolved measurements. The sample chamber was separated from the rest of the spectrometer with two germanium cut-off filters with antiref lection coating, which provided transmission in the range of 830 –3,900 cm⫺1 (Janos Technology, Keene, NH), but blocked stray visible light, including that of the IR globar and the spectrometer He-Ne laser. The germanium filter closer to the detector was tilted by 45° and used also as a mirror for illumination with the excitation visible light along the geometric axis of the measurement. Excitation light was provided by a 175-W Cermax xenon lamp (ILC Technology, Sunnyvale, CA) through a 5-mm diameter liquid light guide and either a 500 ⫾ 20-nm interference filter (blue light, ⬇30 mW/cm2 for 480–520 nm) or a high-pass filter ⬎640 nm (red light, ⬇60 mW/cm2 for 640–680 nm). The samples were routinely light-adapted at 280 K with blue light for 10 min before cooling the sample to the desired temperature. We thank H. Frauenfelder for valuable discussions. This work was supported in part by National Institutes of Health Grant R01-GM29498 and Department of Energy Grant DEFG03-86ER13525 (to J.K.L.). PNAS 兩 June 5, 2007 兩 vol. 104 兩 no. 23 兩 9625
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but can be increased by increasing the temperature (Fig. 6a). We conclude that the limiting K plus L mixtures are neither thermal equilibria nor true end states, even though the conversion is partial and depends on temperature. The same arguments apply to the L 3 BR reaction. Conventional kinetic analyses thus lead to irresolvable contradictions, but the results are consistent with kinetics determined by microscopic conformational substates (Figs. 3b and 4b). In this kind of a model, the time course of the thermal reactions reflects the sampling of numerous separate substates, frozen and not interconvertible at cryogenic temperatures (1). The observed time progression of the conversion of distinct protein substates is in the order of their increasing barrier size. In this case, the apparent rate constant is time variable, and extrapolation to infinite time is in principle not possible. The suggested empirical equation (6) for distributed kinetics fits the data well, as shown on double-logarithmic plots (Figs. 3b and 4b). With distributed kinetics, what appears to be a final fraction of reaction product will be the population with impediments to the reaction too high to overcome with a reasonable probability on the time scale of the experiment. Depending on the distribution of barrier magnitudes in the energy landscape of the protein, the fraction of the readily reactive population may be steeply dependent on temperature, as found (Fig. 5). The temperature dependence of the yields of the product is then not from the enthalpy change in the overall reaction. Rather, it gives an indirect description of the distribution of the barriers. The result of the explicit calculation of the barrier distribution according to ref. 6. is given in Fig. 7b. This interpretation of the reaction at cryogenic temperatures precludes conventional kinetic and thermodynamic analyses, but some concepts remain valid. The barriers to the back-reaction from L, however numerous, must be higher than for the forward reaction, i.e., the K 3 L reaction will be irreversible under these conditions because the tests of the reversibility were on the same time scale as the rise of L and did not produce K from L (Fig. 6b). The L 3 BR reaction is inherently irreversible because otherwise it would be possible to enter the photocycle without illumination. Further, if based not on kinetic but other spectral evidence, alternative substates for the intermediates cannot be excluded. Indeed, for K, we detect some of the differing HOOP bands reported earlier (28). Although not immediately evident, the possibility of alternative L substates remains. The results raise a number of questions. Might ambienttemperature kinetics reflect heterogeneous barriers from conformational substates also? There is evidence from neutron scattering that the average internal motion in bacteriorhodopsin begins to increase sharply at a critical temperature between 150 and 200 K (42, 43), as in other proteins, although the retinal region is more rigid than the rest of the protein (44). The results suggest that rapid protein motions, allowing thermal averaging of substates on the time scale of the photocycle reactions, do become possible at ambient temperature, and one would predict therefore conventional kinetics. Attempts have been made to account for experimental discrepancies from simple models with distributed kinetics (45, 46); however, although they gave better fits, the validity of this approach (vs. more complex conventional kinetic schemes) remains an open question. Apart from the presence of distinct substates, the lowtemperature photocycle differs from the ambient-temperature cycle in at least two respects. First, the K 3 L reaction that leads to a transient mixture of K and L during the photocycle and had suggested K 7 L equilibration at ambient temperature (34 –37) is unidirectional at low temperatures. Second, the L 3 BR shunt reaction (23), which we confirm here, is not evident at ambient temperature. The difference between a low-temperature and a high-temperature L state noted earlier by FTIR spectroscopy (27, 47), perhaps from greater recovery
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