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Self-Regulation Phenomena Applied to Bacterial Reaction Centers

2. Nonequilibrium Adiabatic Potential: Dark and Light Conformations Revisited

Alexander O. Goushcha^*,, Anthony J. Manzo^*, Gary W. Scott^*, Leonid N. Christophorov^,, Peter P. Knox, Yuri M. Barabash, Marina T. Kapoustina, Natalja M. Berezetska and Valery N. Kharkyanen

^* Department of Chemistry, University of California/Riverside, Riverside, California; Institute of Physics, National Academy of Science of Ukraine, Kyiv, Ukraine; Bogoliubov Institute for Theoretical Physics, National Academy of Science of Ukraine, Kyiv, Ukraine; and Lomonosov Moscow State University, Moscow, Russia

Correspondence: Address reprint requests to Gary W. Scott, E-mail: GaryScott{at}citrus.ucr.edu; or Alexander O. Goushcha, Fax: +909-787-4713; E-mail: goushcha{at}ucrac1.ucr.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION ACKNOWLEDGEMENTS REFERENCES

 
Experimental and theoretical results in support of nonlinear dynamic behavior of photosynthetic reaction centers under light-activated conditions are presented. Different conditions of light adaptation allow for preparation of reaction centers in either of two different conformational states. These states were detected both by short actinic flashes and by the switching of the actinic illumination level between different stationary state values. In the second method, the equilibration kinetics of reaction centers isolated from Rhodobacter sphaeroides were shown to be inherently biphasic. The fast and slow equilibration kinetics are shown to correspond to electron transfer (charge separation) at a fixed structure and to combined electron-conformational transitions governed by the bounded diffusion along the potential surface, respectively. The primary donor recovery kinetics after an actinic flash revealed a pronounced dependence on the time interval (t) between cessation of a lengthy preillumination of a sample and the actinic flash. A pronounced slow relaxation component with a decay half time of more than 50 s was measured for t > 10 s. This component corresponds to charge recombination in reaction centers for which light-induced structural changes have not relaxed completely before the flash. The amplitude of this component depended on the conditions of the sample preparation, specifically on the type of detergent used in the preparation. The redox potential parameters as well as the structural diffusion constants were estimated for samples prepared in different ways.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION ACKNOWLEDGEMENTS REFERENCES

 
As is well known, redox proteins have sufficient conformational flexibility to actively influence the electron transfer rate (see e.g., the recent review by Warshel and Parson, 2001.). In the early 1990s, it was proposed that regulation of elementary processes in biological systems, at the molecular level, might be dynamic and self-organizational (Chinarov et al., 1992; Christophorov et al., 1992; Gushcha et al., 1994; Tributsch and Pohlmann, 1992; Tributsch and Bogomolni, 1994), analogous to what occurs when light propagates in an active media (Haken, 1983; Nicolis and Prigogine, 1977). There are two key events here, one is the flow of charged species, i.e., many sequential, elementary reaction steps occurring in the molecule. The other is the control by slowly relaxing structural modes of the protein and cofactors. The protein assumes an active feedback role on protein structural changes caused by the flow, modifying the flow efficiency. The idea for dynamic self-organization in charge transfer biomolecules was developed recently in the literature (Tributsch and Pohlmann, 1998; Goushcha et al., 1999, 2000; Christophorov et al., 2000). A strong, charge-conformational interaction in combination with considerable flexibility of the protein matrix promotes nonequilibrium regimes involving formation of functionally important conformational states. The formalism describing this phenomenon was based on a stochastic theory of multiple, sequential electron transfer events that are correlated with slow structural motions in biological macromolecules. This formalism is very similar to the well-known approach by Agmon and Hopfield (1983) insofar as the conformational motions of protein are treated as a drift and diffusion along some single "perpendicular coordinate" (see e.g., Christophorov et al., 2000). However, the work by Agmon or other researchers, in which they explored many consecutive turnovers of the protein, does not discuss the possibility of a dynamic self-organization in the system with a threshold-like emergence of new, equilibrium functional states (see e.g., Agmon and Krissinel, 1998; Agmon, 2000; McMahon et al., 1998). Nevertheless, such an effect is virtually inevitable in nonlinear systems with external fluxes (Haken, 1983). A conventional approach (see above) uses structural potentials that correspond to different redox states of the cofactors. In contrast, for the case of slow conformational modes, the effective, adiabatic nonequilibrium potential is physically more appropriate because it accounts for the dynamics of redistribution of the cofactors' electronic state populations (see Christophorov et al., 2000; Goushcha et al., 2000 for details). Most importantly, the shape of this potential is controlled by the intensity of the photon flux, resulting in a very powerful method of (self-) regulation of the functional activity of proteins. Recent studies showed that a similar approach based on an adiabatic separation between the reaction coordinate and the remaining degrees of freedom may be very fruitful in molecular dynamic simulations of rare events in biomolecules (Rosso et al., 2002).

In Part 1 of these studies, the synergetic effects caused by light-induced structural changes in photosynthetic reaction centers (RCs) were described theoretically (Goushcha et al., 2000). In the present work, we present experimental evidence, accompanied by computer modeling, in support of this theory. The main emphasis is on changes in the effective adiabatic potential caused by a stepwise variation of the exciting light intensity. We explore the correlation between the appearance and further modification of the "light" conformational state and the kinetics of light-induced absorption changes in RCs. These correlations are well described by structural diffusion on the effective adiabatic potential.

Experimental observation of dynamic, nonequilibrium effects is often obscured by complex relaxation/dissipation processes that occur in response to the creation of a nonequilibrium state (see e.g., Carpintero and Lamela, 2000). This problem also occurs in the experimental verification of structural regulation mechanisms in proteins, in which the inherent complexity significantly complicates a direct monitoring of the protein structural relaxation in different redox states (van Mourik et al., 2001; Barabash et al., 2002). Thus, in the present work, we present experimental results that confirm the existence of the protein structural memory that lasts for a time longer than the interval between consecutive turnovers of the reaction center—a necessary condition for the nonlinear self-organization mechanisms in the ET system of an RC.

In this work, we used different detergents for RC sample preparation. Detergents are crucial for solubilization of proteins. In isolated RCs, detergent molecules are tightly bound to the protein, effectively influencing the function of biomolecules (see e.g., Feher and Okamura, 1978; Gast et al., 1996). In particular, detergents affect protein secondary structure (Ruan et al., 2000), crystallization properties of the protein (Hoff and Deisenhofer, 1997; Michel, 1991; Marone et al., 1999), the thermodynamics of quinone exchange (Shinkarev and Wraight, 1997; Agostiano et al., 1999), electron transfer kinetics (Gast et al., 1996; Tiede et al., 1996, 1998), and proton uptake (Valerio-Lepiniec et al., 1997). This work addresses, for the first time, the effects of detergents on nonlinear dynamic properties of RCs.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION ACKNOWLEDGEMENTS REFERENCES

 
Samples
In experimental studies, we used isolated RCs from photosynthetic bacteria Rhodobacter (Rb.) sphaeroides, wild-type and strain R26. These RCs were isolated and purified from photosynthetic membranes using the detergent lauryl-N,N,-dimethylamine-N-oxide (LDAO) according to the procedure described previously (Feher and Okamura, 1978; Zakharova et al., 1981). After purification in a column with oxiapatite, RCs were suspended in 10 mM Tris-HCl buffer with 0.05% LDAO, pH 7.5. Two other solutions of RCs were obtained by dialysis against an excess of two different detergents, Triton X-100 (0.05%, pH 7.5) and sodium (Na) cholate (0.1%, pH 8.0), respectively, according to conventional methods (see Zakharova and Churbanova, 2000; Lin et al., 2001 for more details about sample preparation). Note that, in contrast to LDAO, which is a zwitterionic detergent, Triton X-100 is a nonionic detergent and Na cholate is an anionic detergent. Different ionic properties of the three different detergents should affect in different ways the electrostatic environment of the protein, thereby influencing its function. The occupancy of the Q_B site after the isolation procedure was 30–90% (measured by the slow phase amplitude in the charge recombination kinetics after a saturating flash). No quinone reconstitution procedure was used. The samples were checked for the absence of cytochrome c2, assuring that each RC could undergo only one-electron photoactivation in our experiments. The absorbance ratio that characterizes the sample purity was usually 1.25–1.35.

Experimental setup
Experiments were made using an optical setup designed in our laboratory. We placed sample solutions in either a 4-mm or a 10-mm pathlength quartz cuvette. The steady-state optical absorbance of the samples was adjusted to be within the range A₈₀₀ = 0.4–0.5. The probe beam was provided either by a tungsten-halogen lamp filtered with the grating monochromator ( = 865 nm) or by a red light emitting diode (LED) with a maximum optical power centered at 835 nm. The probe beam (I_test < 0.1 µW/cm²) transmitted through the sample was filtered either with another monochromator or with band pass filters and recorded with an Si photodiode coupled to a lock-in amplifier. In the apparatus using a probe beam from a tungsten-halogen lamp, the beam was chopped at a frequency 1350 Hz. In the other apparatus, the LED provided a probe beam modulated at 50 kHz. The preamplifier bandwidth was at least 10 times larger than the frequency of modulation and the sampling rate in each experiment was at least 100 times slower than this frequency.

The pulsed photoexcitation of a sample was provided by four LEDs (_max = 835 nm) with a total maximum power at the sample of 3.5 mW/cm², well above the half-saturation limit for the bacterial RCs. The pulse duration was either 100 or 400 ms. The absorbance recovery kinetics, measured after single pulsed photoexcitation of the RCs, was exactly the same as in the case of photo-flash excitation of RCs with a single strong 2-ms light pulse.

The additional background, continuous wave (cw) excitation of the sample was provided by either a tungsten-halogen lamp filtered with red cut-off filters and an interference filter (_max = 850 nm) or by four LEDs (_max = 835 nm). The photoexcitation beam crossed the measuring light beam at an angle of either 45° or 90°. Care was taken to ensure a homogeneous excitation level across the cuvette surface. The photoexcitation intensity was adjusted using a set of neutral density filters in the case of the tungsten-halogen lamp. The irradiation intensity of the LEDs was controlled by adjusting the power supply current. The maximum excitation flux was 3.5 mW/cm².

The intensities of the probe beam and the background excitation light were monitored simultaneously as was the light that was transmitted through the sample, to account for possible instabilities in the light sources. The cuvette temperature was stabilized at either 23 ± 0.5°C or 4 ± 0.5°C. Data collection and experimental control was provided by a PC with a plug-in data acquisition board.

Theoretical model
In modeling of the experimental results, we utilized the phenomenological theory described in detail previously (Goushcha et al., 2000; Christophorov et al., 2000). The calculation of RC absorption changes with variation of actinic light intensity were based on the forward Kolmogorov equations for a reduced two-level scheme of RC redox states:

(1)

in which and describe the time evolution of the RC distribution function over a single dimensionless structural variable x in two different redox states, (neutral state) and (charge separated state), respectively. I stands for the photoexcitation intensity, in units of the rate of a single RC photoexcitation, and is the rate of electron recombination from the primary quinone acceptor Q_A to pigment P (the photoelectron donor, which is the bacteriochlorophyll dimer). The rate of electron recombination from the secondary quinone acceptor Q_B is ; D_i is the diffusion constant; G_AB is the difference of the quasi free energies for electron localization either on Q_A or on Q_B; k_B is the Boltzmann constant; T is an absolute temperature; V_P, V_B, and x_P, x_B are the redox potentials in k_BT units and their minima positions for the charge neutral (index P) and charge-separated (index B) states of RCs, respectively.

We have shown previously that those structural rearrangements that occur more slowly than the electronic transitions that initiate them might be correctly described using a light intensity controlled, nonequilibrium adiabatic potential (see Fig. 1). This potential is determined from the equation

(2)

in which are the stationary state populations of the electronic states at a fixed value of the structural variable x and given photoexcitation intensity I. Equation 2 describes the contribution that the slow structural variable experiences from an average force arising from fast transitions of the photoactivated electron between redox cofactors. This force integrates contributions from each redox potential with the weight that corresponds to the average survival time for the photoelectron on each redox cofactor. Therefore, the motion equation for the structural variable x in the adiabatic approximation can be written as follows:

(3)

in which is the distribution function density for the structural variable. The stationary state solution of Eq. 3 reads , in which

View larger version (81K): [in this window] [in a new window]   FIGURE 1  RC effective adiabatic potential . The redox potentials were chosen in the form of Eq. 4. The model parameters were the following: xP = 2; xB = 8; kP = 10; kB = 10; P = B = 0.07; P. = B = 1.1; and kAP = 10 s-1. See text for more details.

In general, the choice of a redox potential to describe slow structural motions of a molecule is very specific for each particular molecule. In many cases, for a single well potential, the harmonic approximation suffices, thus describing an elastic restoring force. For example, the harmonic approximation was successfully applied to a description of the structural variable (perpendicular coordinate) dynamics in sorption/desorption processes of carbon monoxide in myoglobin (Agmon and Hopfield, 1983; Agmon and Krissinel, 1998). Such an approximation is clearly justified for small shifts of the structural variable from its equilibrium. In contrast, for large shifts, anharmonic processes may completely dominate system behavior.

The modeling of RC structural dynamics that accompanies photoinduced charge separation and electron transfer along the chain of cofactors that we reported recently showed that harmonic potentials do not provide a correct description of RC slow structural dynamics for any set of parameters. For example, the experimentally measured width of a hysteresis loop for the absorption changes versus actinic light intensity was always considerably larger than that calculated using a harmonic potential approach (Gushcha et al., 1994; Goushcha et al., 1997a). In several cases, the divergent or convergent behavior of RC stationary-state absorbance changes in response to a sequence of repetitive alternations of cw actinic light intensity between two levels within the bistability domain was measured (Goushcha et al., 1999). The type of absorption change behavior observed could be readily modeled using anharmonic redox potentials. In evaluating potentials of different complexity, we assumed that the restoring force might be considered as elastic (k_i—the elasticity constant) inside a certain interval of small shifts of the structural variable from its equilibrium position. Outside this interval the elastic portion of the force was assumed to vanish smoothly, preserving the overall symmetric form with respect to the equilibrium position x_i:

(4)

The width of the interval, over which the potential can be considered as harmonic, is determined by the parameter _i: for and . In the opposite case, for , the potential is anharmonic and the degree of anharmonicity is determined by the parameter _i. The anharmonic potential given by Eq. 4 allows for very good agreement between the modeling results and experiment (see e.g., Barabash et al., 2002). It describes well the bleaching and recombination kinetics of photoexcited RCs at various exposure times, enabling also determination of the parameters _i and _i.

Fig. 2 shows transmission bleaching and dark recovery kinetics for the P band of Rb. sphaeroides RCs (suspended in buffer containing 0.1% Na cholate) at 4°C measured after turning on and off a cw actinic light (3.5 mW/cm²). The exposure time was varied from 5 to 200 s. A well-defined slow relaxation component was always detected in such experiments. The dashed lines in Fig. 2 show the results of modeling the experimental curves with Eqs. 1–3 using the redox potentials in the form of Eq. 4. The method of computing the time-dependent populations of RC cofactors is given elsewhere (Barabash et al., 2002). The theoretical formalism for calculation of a generalized conformational potential at an arbitrary actinic light intensity is given in our previous work (Goushcha et al., 1997a, 2000; Abgaryan et al., 1998). The RCs transmittance at 865 nm and at photoexcitation intensity I was calculated by computing the time-dependent population of the charge-separated state n_B(t):

(5)

assuming that only the special pair absorbs at 865 nm. The approximate equality in Eq. 5 indicates that the right-hand side expression in Eq. 5 is valid in the adiabatic approximation. This expression allows numeric calculation of both the fast and slow components of the photoexcitation kinetics (increasing signal) in Fig. 2. In particular, the faster process with the characteristic time constant describes the kinetics of establishing quasiequilibrium electronic populations of the cofactors at a fixed value of the generalized structural variable x, whereas the slower process corresponds to the bounded diffusion of the probability density function P(t,x) on the nonequilibrium adiabatic potential as described by Eq. 3. As it is seen in Fig. 2, the increasing part of all curves has two well-defined kinetic phases as predicted by the adiabatic relationship Eq. 5. The decreasing part of all curves in Fig. 2 describes the charge recombination process and was measured upon turning off the photoactivation. This part also has two pronounced relaxation phases, but they cannot be described by an adiabatic theory because may become quite long at large x due to large light-induced deformation (structural changes). These values of may be comparable to the characteristic time of slow structural rearrangement of the macromolecule. In this case, the recombination process may be viewed as a mixed electron-conformational relaxation process wherein its biphasicity evidences the bistability in the system.

View larger version (41K): [in this window] [in a new window]   FIGURE 2  RC bleaching and recovery kinetics measured in the primary electron donor P absorption band. The actinic light intensity was 3.5 mW/cm2 and exposure time was 5 s (curve 1), 50 s (curve 2), 100 s (curve 3), and 200 s (curve 4). exc = 835 nm. The dashed lines show the modeling results. (Inset) The initial parts of the curves. Experimental conditions: 0.7 µM RC in the buffer 20 mM Tris-HCl, pH 8.0, and 0.1% Na cholate; 80% of QB-active RCs and no quinone reconstitution procedure was applied; T = 4°C.

The ability to model the experimental results was very good for short and medium exposure times (see curves 1–3 in Fig. 2), but it was not as good for long exposure times (see curve 4 in Fig. 2). Some possible reasons for this difference will be addressed in Discussion section.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION ACKNOWLEDGEMENTS REFERENCES

 
Stepwise variation of actinic light intensity. 1. Experiment
RC photobleaching and absorption recovery kinetics after a stepwise variation in the cw actinic light intensity between two levels, I₁ and I₂, always reveals an easily detectable slow relaxation phase with the time constant greater than 10 s. See e.g., results in the previous section. The amplitude of this phase exceeds half of the total bleaching/recovery amplitude if the exposure time preceding the switching event is long enough (>10 s). Several representative traces of RC absorbance changes at 865 nm, the maximum of the primary photoelectron donor absorption band, under stepwise variation of the actinic light intensity between two different levels I₁ and I₂ are shown in Fig. 3. The measurements were performed as follows. We started with the sample in the dark and applied a slow adiabatic increase of the cw actinic light intensity from I = 0 up to I = 0.5 µW/cm². Then the light intensity was rapidly increased to a slightly higher level, and the absorbance relaxation kinetics was measured. Following a waiting time to complete RC equilibration to a new quasiequilibrium level, the light intensity was again increased in a stepwise manner and the absorbance change was measured. Several more steps of a light intensity increase were applied until we reached the value of I = 0.2 mW/cm². This was followed by a stepwise decrease in I via the same set of the quasistationary state values.

View larger version (20K): [in this window] [in a new window]   FIGURE 3  RC equilibration kinetics measured at 865 nm upon stepwise variation of the actinic light intensity between the levels 0.18 mW/cm2 and 0.2 mW/cm2 (a); 0.04 mW/cm2 and 0.07 mW/cm2 (b); 0.5 µW/cm2 and 1.7 µW/cm2 (c). exc = 850 nm. Curves 1 and 2 in each graph correspond to light intensity increases and decreases, respectively. A steady-state absorbance was A800 = 0.4. Experimental conditions: 0.7 µM RC in the buffer 20mM Tris-HCl, pH 8.0, and 0.05% LDAO; 80% of QB-active RCs and no quinone reconstitution procedure was applied; T = 23°C.

RC relaxation kinetics, measured with stepwise variation of I over an interval of intermediate light intensities (0.01 mW/cm²–0.13 mW/cm²), always exhibits comparable amplitudes of fast and slow relaxation phases (Fig. 3 b). Instantaneous variation of I over a very low light intensity interval (<1.7 µW/ cm²) induces negligible amplitude of the fast relaxation component (with the time constant 1 s) and a very pronounced slow phase (Fig. 3 c).

The total time of RC equilibration depended on both the light intensity switching interval and the final value I₂. An experimental demonstration for the case of a decreasing light intensity is shown in Fig. 4, in which the traces measured at various initial I₁ and final I₂ values of the actinic light intensity are normalized and superimposed. The fastest RC recovery kinetics with the slow phase half decay time of 80 s was obtained when the final light intensity was rather high, I₂ 0.07 mW/cm² (curve 1 in Fig. 4). The equilibration kinetics slowed down when the final level I₂ was close to zero (curve 2 in Fig. 4). The slow phase half decay time was 140 s in this case. Finally, the slowest RC equilibration kinetics with _1/2 250 s was measured when I₂ value was between 0.001 mW/cm² and 0.07 mW/cm² (curve 3 in Fig. 4).

View larger version (29K): [in this window] [in a new window]   FIGURE 4  Experimentally observed RC equilibration kinetics measured at the maximum of the primary donor absorption band at = 865 nm and after a stepwise decrease of the actinic light intensity between different levels (exc = 850 nm). Curve 1 was obtained for an I decrease between relatively high levels I1 = 0.13 mW/cm2 and I2 = 0.07 mW/cm2. A stepwise decrease of I down to the intermediate light intensity level produced a very slow equilibration kinetics, which is shown by curve 3 (I1 = 40 µW/cm2 and I2 = 14 µW/cm2). The intermediate rate of relaxation kinetics was measured after stepwise decrease of I from I1 = 4 µW/cm2 to I2 = 0 (curve 2). The sample: Rb. sphaeroides RCs isolated with 0.05% LDAO. The buffer conditions are the same as in Fig. 2. T = 23°C.

the contributions of which to the total amplitude of a signal depend on both the system parameters and experimental conditions. The fast, purely electronic relaxation component is:

(6)

The second, slow kinetic phase

(7)

corresponds to adiabatic changes in electronic populations of the cofactors, which proceed concomitantly with the structural diffusion toward a new equilibrium. See Barabash et al., 2002, for more details. Finally,

(8)

is a new stationary absorbance value that corresponds to the photoexcitation intensity I₂.

Fig. 5, a–c, shows adiabatic potentials at three pairs of levels of the initial I₁ and final I₂ light intensity, and . Note that because the light intensity varied only slightly, the difference between and is barely seen on the graphs. The corresponding kinetics of photoexcitation and recombination are shown to the right in Fig. 5, d–f. In each computational run of the photoexcitation kinetics, the excitation intensity was switched from 0 to I₁ and was held unchanged during 5000 s until complete equilibration of the system. Then the excitation intensity was increased instantaneously to I₂ followed by another 5000 s of equilibration time. The initial 1500-s time intervals are shown in Fig. 5, d–f. In calculating the recombination kinetics, the excitation intensity was first increased from 0 to I = 2 s^-1, followed by instantaneous switching down to I₁ > I₂ and then further down to I₂. Note that stationary-state absorption levels, which correspond to the same excitation levels, were always identical for increasing and decreasing excitation intensity. This was not the case for the experimental observations in Fig. 3. The reason for this divergence comes out of the limitations of the model, and will be discussed below. We used s^-1 for the excitation intensity units. For Rb. sphaeroides RCs, the excitation level of 1 s^-1 corresponds to an actinic light intensity of 0.4 1.4 mW/cm² at 865 nm (Manzo et al., unpublished). In this paper, we set 1 s^-1 as equal to 1 mW/cm².

View larger version (27K): [in this window] [in a new window]   FIGURE 5  Adiabatic potential changes induced by an instantaneous variation in photoexcitation intensity (graphs a–c). The low-intensity potential surfaces are shown with dashed lines. The curves to the right of each potential show RC equilibration kinetics calculated for the cases of increasing (dashed lines) and decreasing (solid lines) excitation intensity (see graphs d–f). The variation of excitation intensity produced very small changes in the adiabatic potential; therefore the potential surfaces corresponding to the two different values of I (these values are indicated on the graphs) are hardly distinguishable on each graph.

Fig. 6 shows the results of modeling, analogous to the experimental results presented in Fig. 4. To facilitate observation, the photoexcitation intervals were selected to be further apart from each other than were the corresponding experimental intervals in Fig. 4. The half decay time of the slow kinetic phase was 180 s for switching the excitation intensity between the levels I₁ = 5.0 s^-1 and I₂ = 4.0 s^-1 (trace 1 in Fig. 6). Switching of I between I₁ = 0.004 s^-1 and I₂ = 0.0001 produced considerably slower relaxation kinetics with the half decay time of the slow phase _1/2 250 s (trace 2 in Fig. 6). The slowest relaxation kinetics (_1/2 340 s) was calculated for the case I₁ = 0.1 s^-1 and I₂ = 0.05 s^-1 (trace 3 in Fig. 6). The value of a slow phase decay time was only slightly dependent on the initial level of photoexcitation intensity I₁, whereas the variation in the final value I₂ caused considerable changes in overall relaxation kinetics.

View larger version (26K): [in this window] [in a new window]   FIGURE 6  Calculated RC equilibration kinetics after an abrupt photoexcitation decrease between two quasistationary-state levels: from I1 = 5.0 s-1 to I2 = 4.0 s-1 (curve 1); from I1 = 0.004 s-1 to I2 = 0.0001 s-1 (curve 2); and from I1 = 0.1 s-1 to I2 = 0.05 s-1 (curve 3). The curves are normalized to unity and superimposed. The model parameters were the following: xP = 2; xB = 8; kP = 10; kB = 10; P = B = 0.07; P = B = 1.1; DP = 0.5 s-1; DB = 0.05 s-1; and = 10 s-1.

Nonequilibrium dynamic effects occurring due to accumulation of structural changes after multiple, consecutive turnovers of RCs can be revealed in the following straightforward experiment. RCs were illuminated with cw actinic light of close to saturation intensity (P_cw = 1 mW/cm², _exc = 835 nm). After cessation of the cw photoexcitation, the sample was illuminated with a sequence of short actinic pulses spaced at a variable time interval (peak intensity P_flash = 1 mW/cm², _flash = 835 nm). Fig. 7 summarizes results obtained in experiments with RCs containing three different detergents. The exposure time was 200 s, the duration of each pulse in a sequence was 0.4 s, the first pulse was triggered 5 s after cessation of the cw illumination, and the pulses spacing time was 250 s. The reference curves measured in analogous experiments but with actinic pulses blocked are also shown in each graph. The slow relaxation phase with a time constant >10 s, which was not observed in a single flash activated kinetics applied to a dark-adapted sample (not presented in this paper), was normally detected after each pulse in a sequence. The amplitude of this phase was the biggest for RCs with Triton X-100 (graph b in Fig. 7). RCs with Na cholate also showed an easily observed slow relaxation phase after each flash (graph c in Fig. 7), whereas the amplitude of this phase for RCs with LDAO was relatively small (graph a in Fig. 7). The amplitude of the slow relaxation phase was negligibly small after the first flash in a sequence for each sample. This is clearly seen in Fig. 8, in which the difference between the traces measured with actinic pulses and reference traces is shown. The amplitude of a slow relaxation phase was the highest a few minutes after cessation of cw illumination, and it diminished considerably by the end of the experiment.

View larger version (21K): [in this window] [in a new window]   FIGURE 7  RC transmittance changes (at 835 nm) after a stepwise variation of actinic light intensity. The cw actinic light (I = 1 mW/cm2, exc = 835 nm) was turned on at the instant t = 5 s and was off at t = 205 s. A train of actinic flashes spaced at 250 s time intervals was applied 5 s after turning off a cw actinic light. Transmittance changes after the first flash are not resolved on the graphs. The reference signals measured in separate runs with actinic flashes blocked are also shown on the graphs.

View larger version (20K): [in this window] [in a new window]   FIGURE 8  The difference between the traces recorded with applied actinic flashes and reference traces. Note the absence of the slow relaxation component after the first pulse on each graph.

View larger version (23K): [in this window] [in a new window]   FIGURE 9  Comparison of RC response to each of the actinic flashes in a train. The 10-s duration traces were cut from the corresponding curves in Fig. 5, then normalized to unity and superimposed.

Fig. 10 shows the results of computer simulations for RCs with LDAO (graph a) and for those with either Na cholate or Triton X-100 (graph b). The amplitude of a slow relaxation phase (with the time constant >200 s) was significant for the set of parameters characteristic for RCs with either Na cholate or for those with Triton X-100 after the second and several subsequent pulses. See graph a in Fig. 11, in which the difference between the two traces of each graph in Fig. 10 is presented. For the case of RCs with LDAO, only a slightly noticeable "accumulation" of the slow relaxation component was obtained after each pulse in a train (graph b in Fig. 11). The amplitude of a slow relaxation component after the first pulse was always negligibly small for each system.

View larger version (23K): [in this window] [in a new window]   FIGURE 10  Results of modeling of RC response to 200-s duration cw actinic light followed by photoexcitation with a sequence of pulses. Each graph shows also a result of a separate run without generating photoexciting pulses (a reference trace). The first pulse in a sequence (not resolved on the graphs) was generated 5 s after cessation of cw photoexcitation. The parameters of the model for the traces on the graph (a) were as follows: xP = 2; xB = 8; kP = 10; kB = 10; P = B = 0.07; P. = B = 1.1; DP = 0.5 s-1; DB = 0.05 s-1; and = 10 s-1. The traces on the graph (b) were obtained for the same set of parameters as above except of kB = 5; DP = DB = 0.025 s-1.

View larger version (23K): [in this window] [in a new window]   FIGURE 11  The difference between traces calculated with photoexciting pulses on and reference traces. Note the absence of the slow relaxation component after the first pulse on each graph (compare with corresponding experimental graphs in Fig. 6).

View larger version (25K): [in this window] [in a new window]   FIGURE 12  Comparison of pulses in sequences shown in Fig. 8. The 10-s duration traces were cut from the corresponding curves in Fig. 8, normalized to unity, and superimposed. The initial five pulses for each system are shown.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSION ACKNOWLEDGEMENTS REFERENCES

Qualitatively let us consider the charge separation process upon continuous photoactivation at intensity I. Initially, at the instant of switching on a continuous actinic light, all RCs are in a state with the electron localized on the donor and with the value of the structural variable x close to the dark value x_P. After the actinic light is switched on, charge separation proceeds and the quasistationary state distribution of RCs over the states with the electron localized either on the donor or on the acceptor is reached after the characteristic time interval :

(9)

RCs with separated charges gradually begin to undergo conformational changes (on the time scale ) that can be modeled as movement (diffusion) of the RC distribution along the upper potential surface (see Fig. 13) toward its minimum x_B, corresponding to the light-adapted conformational state.

View larger version (27K): [in this window] [in a new window]   FIGURE 13  Simplified qualitative description of electronic and conformational transitions during the charge separation and recombination in RC. The lower potential surface represents the redox potential of the charge-neutral state, whereas the upper potential describes the charge-separated state. The fast charge-separation (bleaching) phase corresponds to electronic transitions "up" at different but fixed values of the structural variable x. The fast recombination phase appears due to electronic transitions "down" (charge recombination) around x = 2 only. The slow phase of structural relaxation in the charge-separated state appears due to the bounded diffusion along the upper potential surface to the right and causes the slow photobleaching phase in Fig. 2. The slow recombination phase arises due to both the charge recombination in the highly deformed state (around x = 8) and electron-conformational transitions governed by the diffusion/drift along the potential surfaces to the left. See text for more details.

(10)

Such an increase of the portion of RCs with separated charges corresponds to the slow phase of bleaching kinetics in Fig. 2 because these phase kinetics are determined by the rate of RC conformational change at a constant photoexcitation intensity. See also the slow (structural) relaxation phase in the charge separated state, Fig. 13. However, at "low" photoexcitation intensity, the RC, after charge recombination, has enough time to return back to the minimum x_P of the dark (charge-neutral) potential. This sequence of electronic transitions and structural rearrangements corresponds to cycle 1 in Fig. 13. Therefore, under "low" actinic light intensity, the RC will accumulate only a slight conformational change with a coordinate x that is close to the dark-adapted value of the structural variable x_P.

At high photoactivation intensities, a slight conformational change during the first charge separation event of the RC does not have enough time before the next charge separation event to fully relax back along the lower potential surface (the slow (structural) relaxation phase in the charge-neutral state, Fig. 13) to the initial, dark-adapted state (). The next photoactivation of the RC and following charge separation occurs with the macromolecule already in a slightly changed conformational state. This ratcheting of the conformation is a key feature of the model because the effects of accumulated structural changes and self-regulation could only become possible under the condition of noticeable structural memory in the system (see also Barabash et al., 2002). The ratcheting process repeats after each charge recombination event and the conformational change increases. As a result, under continuous wave photoexcitation, the RC gradually undergoes conformational change until it attains the minimum of the potential surface of the light adapted state x_B. A high photoexcitation frequency does not allow the RC to fully return to the point x = x_P, and the RC conformational coordinate now fluctuates around the structural variable value x_B. See cycle 2 in Fig. 13.

The most interesting effects occur at intermediate light intensities. In this case, cycle 1 and cycle 2 may coexist. I.e., if the initial conformational change of the RC was relatively slight, the system fluctuates according to cycle 1; if, alternatively, the initial change was larger than some specific value , then the system behavior is described by cycle 2. This effect is related to the charge recombination rate dependence on the structural variable value. This qualitative analysis of kinetics of electronic transitions and associated conformational changes in RCs is rigorously described by the nonequilibrium effective adiabatic potential , which was defined in Eq. 2 (see Goushcha et al., 2000, part 1; Christophorov, et al., 2000). The second term in Eq. 2 accounts for the force that causes the conformational change in an RC with separated charges. This term depends on both the curvature of the potential surface of RC in the charge-separated state and the survival time in this state. The latter is determined by the relationship between the rate constants of photoexcitation and recombination, to be precise by the value . The form of the first term in Eq. 2 is analogous to that of the second term, and it determines the force acting on the structural variable after the charge recombination is complete. This force drives the structure back toward the dark-adapted state (the dark value of the structural variable). As shown in Fig. 14, the effective potential has a single minimum at either x = x_P at low photoexcitation intensities or x = x_B at high photoexcitation levels. At intermediate levels of cw actinic light, the structural variable effective potential has two minima and exhibits properties of a photoinduced bistability. The potential maximum corresponds to the critical deformation that divides the two structural states, and the depths of potential minima depend on the actinic light intensity. This is a remarkable property of the effective potential that allows its application for the description of RC thermodynamic properties in light-induced structural transitions.

View larger version (21K): [in this window] [in a new window]   FIGURE 14  Possible cases for the effective potential shape change at various light intensities (graph a—increasing light intensity I, graph b—decreasing I). The initial state is represented with potential curve 4 on each graph. Three possible cases of the final state are represented with the potential surfaces 1 (low excitation intensity), 2 (medium excitation intensity), and 3 (high excitation intensity). The dotted line shows the distribution function at the initial excitation intensity and arrows indicate schematically the direction of electronic transitions.

Practically any process of RC photoexcitation or recombination, except maybe in the case of charge recombination in an experiment when lengthy and intensive actinic illumination to a sample is turned off completely, can be effectively described using the formalism of a nonequilibrium adiabatic potential. In other words, this formalism is applied if, at a final light intensity I₂, the value remains small enough for the adiabatic approximation to hold true.

Under continuous photoexcitation and applying adiabatic elimination of the fast electronic transitions, i.e., by reduction of Eq. 1 to Eq. 3, the redox potentials are not suitable for describing the structural state of the RC. Conversely, the nonequilibrium effective adiabatic potential gives an adequate description. The shape of depends both on the redox potentials and on the photoactivation intensity, I. Note that the initial redox potentials were chosen as single valley potentials (see Fig. 13 and Eq. 4). Conversely, the effective potential has two minima within the bistability domain (i.e., over a specific interval of I only) independently of the location of the electron. Due to fast electron transitions, in the adiabatic approximation, the structure senses only the time-averaged electron density.

Fig. 14 describes qualitatively three possible characteristic cases of the shape of the effective potential. Corresponding changes in the distribution function over the structural variable are described by Eq. 3 and can be revealed in slow components of the equilibration kinetics when diffusion along the structural variable proceeds while overcoming a noticeable barrier of . For the case of photoexcitation (bleaching), we chose I₁ = 0, whereas the three different I₂ levels were chosen in the way that the corresponding adiabatic potentials describe three possible cases:

1. Low excitation intensity. Charge photoseparation leads to a weak structural deformation, which is not strong enough for bistability to occur. The adiabatic potential has only one, "dark" minimum. The second, "light" minimum does not appear. See curve 1 in Fig. 14 a. The equilibration kinetics will not exhibit a very slow equilibration component.
   
2. Medium excitation intensity. The excitation intensity is strong enough for the bistability to occur. The depths of the "dark" and "light" conformational valleys are approximately equal (curve 2 in Fig. 14 a) and the probabilities for each of the two possible conformational states are approximately equal. The equilibration (bleaching) kinetics will be biphasic with comparable amplitudes of both phases. The relaxation time constant of the slow equilibration component will be much longer than in case 1).
   
3. High excitation intensity. Photoexcitation leads to strong light-induced structural changes resulting in disappearance of the "dark" conformational state and creation of the "light" conformational state. The adiabatic potential is again monostable, although a slightly pronounced shoulder around small values of x evidences the influence of the potential of the charge-neutral redox state (curve 3 in Fig. 14 a). The photoexcitation (bleaching) equilibration kinetics will be generally biphasic but the slow phase will not be as grossly delayed as in case 2).
   

For the recombination process, the schematic representation of the initial and final adiabatic potentials is reversed with respect to the case of photoexcitation (bleaching). See Fig. 14 b. The initial excitation intensity I₁ was chosen to be high enough to produce a monostable adiabatic potential with the "light" conformational state only. The three final values I₂ were chosen in the way that corresponding adiabatic potentials described three possible cases like we made above for the case of photoexcitation (bleaching). The recombination equilibration kinetics in any of the three cases is generally biphasic. The equilibration time should be expected to be the slowest for the case of intermediate values of I₂.

The above features of RCs equilibration kinetics were observed experimentally (Figs. 3 and 4) and modeled theoretically (Figs. 5 and 6). In the case of the lowest light intensities I₁ and I₂, when the potential barrier that separates the two stable states is either relatively low or completely vanishes (see e.g., Fig. 5 a), the time constant of the slow component of equilibration kinetics is 200 s or smaller. See experimental results in Fig. 3 c and curve 2 in Fig. 4 and corresponding results of modeling in Fig. 5 d and curve 2, Fig. 6. The amplitude of the fast equilibration component is very small in this case mainly due to the small factor in the expression for the fast relaxation component (see Eq. 6). Upon increasing the light intensities I₁ and I₂, the amplitude of the fast relaxation component increases monotonically. At intermediate light intensities, when the depths of potential minimums are almost equal, the potential maximum reaches its maximum height (see e.g., Fig. 5 b) and the time constant of the slow equilibration component becomes very long (300 s or longer). See experimental results in Fig. 3 b and curve 3 in Fig. 4 and corresponding results of modeling in Fig. 5 e and curve 3, Fig. 6. A further increase in the photoexcitation intensities I₁ and I₂ leads to a decrease of the potential barrier height (see Fig. 5 c) that results in corresponding acceleration of the equilibration kinetics. See experimental results in Fig. 3 a and curve 1 in Fig. 4 and corresponding results of modeling in Fig. 5 f and curve 1, Fig. 6.

A pronounced asymmetry in the slow equilibration phases of photoexcitation (bleaching) and relaxation process essentially distinguishes experimentally measured kinetics (Fig. 3) from the calculated dependencies (Fig. 5). One possible reason for this difference could be a significant obstacle to the thermally assisted transitions over the potential barrier due to roughness in the potential surface, which has not been taken into account in calculations (Frauenfelder et al., 1991). Experimentally, this phenomenon results in a significant delay in equilibration of the true stationary state at a particular light intensity within the bistability domain. As a result, the measured absorbance can be slightly lower than the true stationary-state value for the increasing excitation intensity, whereas this value for the case of a decreasing excitation intensity can be higher than the real stationary-state value. Unfortunately, it is usually very difficult to detect a true stationary state in a real experiment. Note that accounting for such effects could only slightly modify the modeling results obtained here (see e.g., Fig. 5), making them closer to the experimentally measured kinetic dependences (Fig. 3).

Note also that an asymmetry of RC photoexcitation (bleaching) and recombination kinetics is an inherent property that could be observed any time the exciting light intensity is switched between two quite different levels. For example, if one light intensity level is very high and a corresponding adiabatic conformational potential has a single, "light" valley and the other light intensity level corresponds to the adiabatic potential with the two approximately equal valleys, then the instantaneous decrease in the actinic light intensity between these two levels will cause a very long equilibration phase. In contrast, the disappearance of the barrier upon rapidly increasing light intensity up will result in a very fast equilibration of the system (see Fig. 15).

View larger version (19K): [in this window] [in a new window]   FIGURE 15  RC photoexcitation (bleaching) (dashed curve 1) and recombination (solid curve 2) kinetics calculated using Eq. 5 for the excitation switching "up" and "down" between the levels 0.028 s-1 and 5.0 s-1. The parameters of the model were as follows: xP = 2; xB = 8; kP = 10; kB = 10; P = B = 0.07; P = B = 1.1; DP = 0.5 s-1; DB = 0.05 s-1; and kAP = 10 s-1.

At the instant of the second flash, a significant amount of RCs with the deformed structure has accumulated in the ground state, producing a pronounced retardation of relaxation after a flash. The third, fourth, and fifth flashes also result in significant amplitudes of the slow relaxation phase, although these amplitudes decrease gradually with flash number (see graphs b and c in Fig. 8). Such a dependence of the amplitude of the slow relaxation phase is determined by the competition between the charge recombination process that enriched the population of the "light" conformational state with charge-neutral molecules, and diffusion/drift of this pool of population toward the equilibrium in the "dark" potential valley. The latter process defines the diffusion constant D_P and controls the relaxation time of the structure to a dark-adapted state. See Fig. 13, a slow (structural) relaxation phase in the charge-neutral redox state. Obviously this competition is advantageous for RC accumulat