Transition state and encounter complex for fast association of cytochrome c₂ with bacterial reaction center

Abstract

Electrostatic interactions strongly enhance the electron transfer reaction between cytochrome (Cyt) c₂ and reaction center (RC) from photosynthetic bacteria, yielding a second-order rate constant, k₂ ≈ 10⁹ s^-1·M^-1, close to the diffusion limit. The proposed mechanism involves an encounter complex (EC) stabilized by electrostatic interactions, followed by a transition state (TS), leading to the bound complex active in electron transfer. The effect of electrostatic interactions was previously studied by Tetreault et al. [Tetreault, M., Cusanovich, M., Meyer, T., Axelrod, H. & Okamura, M. Y. (2002) Biochemistry 41, 5807-5815] by measuring k₂ for RC and Cyt molecules with modified charged residues at the binding interface. The present work is a computational analysis of this kinetic study to determine the ensemble of configurations of the TS and EC. Changes in the TS energies due to different mutations were compared with differences in the calculated electrostatic energies for a wide range of Cyt/RC configurations. The TS ensemble, obtained from structures having the highest correlation coefficients in the comparison with experimental data, has the Cyt displaced by ≈10 Å from its position in x-ray crystal structure, close to the average position of the EC ensemble, with strong electrostatic interactions between Cyt on the M subunit side of the RC surface. The heme of the Cyt is oriented toward Tyr L162 on the RC, the tunneling contact in the bound final state on the RC. The similarity between the structures of the EC, TS, and bound state can account for the rapid rate of association responsible for fast diffusion-controlled electron transfer.

Intermolecular electron-transfer reactions play important roles in many biological processes such as photosynthesis and respiration (1). In these reactions, two electron-transfer proteins associate to form an electron donor-acceptor complex in which electron transfer occurs (2). Electrostatic interactions can greatly enhance the rate of protein association by providing long-range guidance in the association process (3). For fast processes assisted by electrostatic interactions, a two-step association mechanism has been proposed (4, 5). The first step is the formation of a loosely bound encounter complex (EC), followed by a rate-limiting process through a transition state (TS), leading to the bound active state. In this paper we examine the association process for the reaction center (RC) and cytochrome (Cyt) c₂ that are involved in the electron-transfer chain in bacterial photosynthesis by using electrostatic calculations and experimental data to obtain a molecular description of the TS and the EC. The results of these calculations describe the ensemble of states that represent a roadmap for the association process and the interactions likely to be important in the dynamics. This approach is complementary to Brownian dynamics simulations (5-7) that yield the diffusional rate constant.

The RC is the membrane protein involved in the primary light-induced electron-transfer step in bacterial photosynthesis (8, 9). Light absorbed by RC pigments activates photooxidation of the primary donor, D, a bacteriochlorophyll dimer, leading to the reduction of a quinone molecule Q, DQ → D⁺Q^-. The electron from Q^- cycles back to D⁺ through an electron-transfer chain involving the membrane-bound Cyt bc1 complex. The last step in the cycle involves a soluble Cyt c₂ molecule that shuttles the electron back to the RC to complete the cyclic electron-transfer process. This cyclic electron transfer is coupled to proton pumping across the membrane that drives ATP synthesis.

The rates of electron transfer between isolated RCs and Cyt c₂ have been measured by using laser-flash techniques and shown to be well optimized for cyclic electron transfer by using the scheme below (refs. 10-13; reviewed in ref. 14).

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Before the laser flash, the Cyt and RC (denoted DQ) are in equilibrium between a bound state and a free state with the dissociation constant K_d ≈ 10^-6 M at low ionic strength (≈5 mM) (13). After a laser flash, the observed second-order association rate constant k₂ for the reaction of the unbound Cyt has been found to be k₂ ≈ 10⁹ s^-1·M^-1, close to the diffusion limit (12, 13). The first-order electron-transfer rate constant k_e ≈ 10⁶ s^-1 (11, 13) measured for RCs having a bound Cyt is much faster than the dissociation-rate constant, k_off ≈ 10³ s^-1 (15). Because k₂ = k_ek_on/(k_off + k_e) (1), this result brings the second-order rate constant into the diffusion-limited regime where the observed second-order rate constant is approximately equal to the association rate constant k_on (k₂ ≈ k_on). Thus, the second-order rate constant measures the rate of the formation of the final bound state at which electron transfer occurs. This result is shown by the finding (16) that k₂ is independent of electron-transfer rate in the bound state, k_e. Note that the opposite fast-exchange reaction regime, k_off >> k_e, in which the second-order rate constant is given by k₂ ≈ k_e/K_d does not apply to the electrostatic mutants studied here. However, the fast-exchange regime has been observed in other cases (17, 18).

The structure of the Cyt/RC complex has been obtained by cocrystallizing Cyt and RC and determining the x-ray crystal structure (19). The complex is active in the crystal and has the same electron-transfer rate in the crystal as in solution, demonstrating that the complex represents the active state. In the cocrystal structure, the solvent-exposed edge of the heme cofactor of the Cyt is in contact with Tyr L162 on the RC located directly above the BChl dimer (Fig. 1). The contact between the heme edge and Tyr L162 is along the best pathway for electron transfer (20, 21). The contact region is located in a small region making short-range hydrophobic- and hydrogen-bonded contacts between the two proteins. Surrounding this contact region is a region having long-range electrostatic interactions. Positively charged residues on the Cyt are positioned opposite negatively charged residues on the RC but do not form salt bridges.

Fig. 1.

Structure of the Cyt RC complex based on the x-ray crystal structure. The groups involved in electron transfer, heme, Tyr L162, and BChl dimer, are red. The definitions of the coordinates are shown.

Electrostatic interactions have been shown to be important for the association process by the dependence of the second-order rate constant, k₂, on ionic strength (10). Changes to charge-surface groups near the binding interface by using chemical modification (22, 23) and site-directed mutagenesis (13, 24, 25) were shown to change the association rate. The role of electrostatic interactions in protein association was demonstrated by modeling studies (26-30).

In previous work (29), we analyzed the role of electrostatic interactions in the binding process of Cyt to photosynthetic RC from Rhodobacter sphaeroides, by using a simple model, in which the Cyt was displaced from the RC surface without rotation. This study yielded a distance between the Cyt and RC at the TS, corresponding to a displacement of 8 Å.

In the present study, we use a more detailed model to examine the structures of the TS and the EC for the reaction between the RC from Rb. sphaeroides and the Cyt c₂ from Rhodobacter capsulatus. The TS was studied by analyzing the extensive set of measured values for the second-order rate constants obtained by Tetreault et al. (25), similar to the approach used by Frisch et al. (31). The Cyt from Rb. capsulatus was used because of the extensive series of mutant Cyts that were available. The Cyts from Rb. sphaeroides and Rb. capsulatus have a sequence identity of 52% and display very similar structures and charge distributions (32, 33). The binding constants and electron transfer rates of Rb. sphaeroides and Rb. capsulatus Cyt with Rb. sphaeroides RCs are very similar (25). The second-order reaction rates were measured for a series of mutant RCs and Cyts having charge-reversing mutations to charged residues, six modified RCs with acid → Lys changes, and five modified Cyts with Lys → Glu changes, a total of 42 reaction combinations. By electrostatic modeling of the kinetic data, we constructed a molecular description of the TS of the binding process. The large amount of experimental data enabled us to search for the TS over a large configuration space. In addition, the EC was modeled as an ensemble of configurations stabilized by electrostatic interactions and analyzed by using a continuum electrostatic calculation for different configurations of Cyt and RC. By a comparison of the structures of the TS and EC with that of the bound state, we develop a molecular picture of the important steps in the binding process of the Cyt and RC and establish a detailed scenario of the intermolecular electron-transfer reaction.

Methods

Protein Association. In this work, we assume a two-step model involving the formation of an EC stabilized by long-range electrostatic interactions, and a TS for the association (4, 5). According to TS theory, (34) the second-order rate constant for association is related to the free-energy barrier of the TS. The change in interaction free energy of the TS, , is related to the ratio of the second-order rate constants for electron transfer.

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To determine the structure of the TS, we used the experimentally determined changes in TS free energies due to mutation of charged groups, (25), and compare them with the calculated changes in electrostatic energy for the Cyt/RC complex arranged at different docking positions. We assume that the TS ensemble for the binding process consists of a small set of closely related structures that does not change greatly by mutation, and that the change in free energy of the TS, δΔG^‡ is determined only by the electrostatic interactions between mutated charged residues. Because the separation between the mutated charged residues in the two proteins in the TS is ≈10 Å (29), van der Waals contacts are not likely to be a large part of the energy change. The energy of the EC cannot be determined from the measured binding rate, but contributes to the energy of the TS, and thus, to the value of k₂.

Calculation of Electrostatic Energies. The structures of the native RC (19) and Cyt (33) were obtained from the crystallographic coordinates [Protein Data Bank (PDB) ID codes 1L9B and 1C2R]. Mutant structures were obtained by manually modeling the modified residues into the protein structure by using the program swiss pdb viewer (35) followed by an energy-minimization procedure using the amber potential. The structures of the RC and Cyt in the complex are relatively unchanged from that in the isolated state, justifying the use of a rigid-body conformational search. Larger conformational changes would have required a more extensive fitting (36). In this study, two different methods were used to calculate the electrostatic energy, a full-continuum calculation and a Coulomb's law calculation. A full-continuum electrostatics calculation using the dielectric-continuum model was used to calculate energies of the EC for native Cyt and RC as described (29). In the dielectric-continuum model, the protein molecules are treated as point charges within a region having a dielectric constant ε_in surrounded by solvent with a dielectric constant ε_ext = 80, and electrostatic energy can be obtained by solving the Poisson-Boltzmann equation (37). The choice of the protein dielectric constant, ε_in, varies depending on the system (38), and requires calibration for each problem. We used ε_in = 10 throughout this study because it reproduced the effect of mutation on the binding free energy in the previous study (29). From energy difference between the bound structure and the unbound structure, the electrostatic binding energy is obtained as . It consists of two types of interactions (37), ΔG_elec = ΔG_coul (ε_in) + ΔG_solv(ε_in, ε_ext), where ΔG_coul(ε_in) is change in the pairwise Coulomb energy calculated between charges on different proteins, using ε_in and ΔG_solv(ε_in, ε_ext) is the desolvation energy, the change in the electrostatic contribution to the solvation energy. An effect of mutation on the electrostatic interaction energy is also defined accordingly, δΔG_elec = δΔG_coul + δΔG_solv.

One drawback of the dielectric-continuum model is that it is too time-consuming to perform the calculations for each mutation in a large configurational space (≈15 min for one binding energy calculation). Therefore, a Coulomb's law calculation was used to calculate the electrostatic energy of the Cyt/RC complex in the TS,

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where i and j refer to charges on RC and Cyt. In a previous study of the bound complex, we observed that the mutational changes in the total electrostatic energy, δΔG_elec, are approximately proportional to the changes in the Coulombic energy, δΔG_coul (29). In this study, we found that such a linear relationship exists for the other configurations as well and justifies the use of the Coulomb equation (see Supporting Text and Fig. 7, which are published as supporting information on the PNAS web site).

Determining the TS Ensemble by Using the Correlation Coefficient. For each Cyt/RC configuration, the effects of mutating charged residues on the Coulombic energy, δΔG_coul, were calculated by using ε = 10. These free-energy changes were compared with the experimental changes in free energy, . The differences between the calculated and experimental values were not directly compared because these differences would depend on the absolute values of the calculated energies, which are difficult to obtain precisely, because of uncertainties in the dielectric constant. Instead, we compared the correlation coefficient, R, between calculated data and the experimental data as the measure of the likelihood that a structure corresponds to the TS. The correlation coefficient is a measure of the linear relationship between two variables independent of the slope (39). This coefficient is expected to be independent of the absolute value of the ε but would be sensitive to the relative distances between charged residues of the Cyt and RC in the TS. From the linear relationship between δΔG_coul and δΔG_elec discussed above, the Coulombic calculation should be sufficient to evaluate the correlation between calculated and experimental energies.

Monte Carlo Sampling of the TS and EC Ensembles. The configuration space was sampled by using the Metropolis Monte Carlo algorithm (40). The coordinate axes were based on the x-ray cocrystal structure of Cyt and RC from Rb. sphaeroides obtained by Axelrod et al. (19). Fig. 1 shows schematic representation of the x, y, and z axes and the rotation angles φ, θ, and ψ. In plotting energies as a function of the angular coordinates, the parameters θ and φ are replaced by the defined parameters, u = sin θ cos φ, v = sin θ sin φ (see Fig. 1). For the sampling of the TS ensemble, the acceptance ratio was taken to be exp(-ΔR/T_R), where the correlation coefficient, R, is the effective energy parameter, and T_R is an effective dimensionless temperature. For the sampling of the EC, the electrostatic interaction energy, ΔG_elec, calculated from the dielectric-continuum model is used to define the acceptance ratio, i.e., exp(-ΔG_elec/k_BT). See Supporting Text for details.

Results

TS Configurations. Approximately 70,000 configurations were sampled with the Monte Carlo procedure, including configurations rejected by the Metropolis criteria. In total, ≈27,000 configurations have correlation coefficients >0.8, and the maximum is 0.894. The distribution shows rather simple behavior with a single peak in R as a function of each of the six coordinates (see Supporting Text and Fig. 8, which are published as supporting information on PNAS web site). Thus, it is reasonable to assume that the average of the TS ensemble represent the structure of the TS that best fits the experimental data and that the measured-rate constant k₂ represents an average over the different structures in the TS ensemble.

The ensemble of structures with high correlation coefficients was analyzed to obtain a description of the average values of the coordinates. Average values were computed by taking into account the volume in phase space, i.e. w(θ_i) ∞ sin θ_i, but without Boltzmann weighting. Table 1 shows the average values obtained from the sets consisting of the best 1% and 5% configurations having the highest correlation coefficients. The x, y, and z coordinates show a displacement of the Cyt in the TS away from its position in the bound state. The Cyt is displaced by z ≈ 5 Å from the RC surface and x ≈ 9 Å toward the M subunit side of the surface. The Cyt is tilted by an angle θ = 24°. The angle φ ≈ 180° indicates that the tilt is in the -x direction. In the following discussion, we define the TS ensemble to be the best 1% of states with the highest correlation coefficient.

Table 1. TS and EC ensembles.

Ensemble	Cutoff	No. of states	x	y	z	u	v	ψ
TS	−1%	750	−9.0 ± 2.3	−4.1 ± 2.8	5.2 ± 1.3	−0.40 ± 0.13	−0.00 ± 0.06	350 ± 9
TS	−5%	14,332	−8.3 ± 5.1	−4.0 ± 4.2	6.0 ± 2.5	−0.32 ± 0.26	−0.01 ± 0.13	350 ± 14
EC	+1 kBT	51	−6.4 ± 5.3	4.2 ± 3.2	5.0 ± 1.3	−0.05 ± 0.25	0.07 ± 0.15	27 ± 68
EC	+2 kBT	769	−5.0 ± 5.0	2.7 ± 4.1	5.2 ± 1.4	−0.06 ± 0.22	0.04 ± 0.17	24 ± 64

Average ± SD, u = sin θ cos φ, v = sin θ cos φ, distances are in angstroms, angles are in degrees.

A test of the TS ensemble was made by comparing the value of with the value of δΔG_elec calculated as the Boltzmann-weighted average of free-energy changes for different mutants over the TS ensemble,

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where i is the index of the configuration in the TS ensemble and the summations are done for entire TS ensembles weighted by the phase space volume. The calculated and experimental values showed good quantitative agreement, (R = 0.89, slope = 1.12) (Fig. 2). The Boltzmann weighting accounts for a shift in the average configuration of the TS in different mutants and improves the fit compared with the unweighted average (R = 0.88, slope = 1.17, data not shown).

Fig. 2.

Changes in free energy due to mutations, δΔG_calc, calculated as the Boltzmann-weighted average for the TS ensemble, compared with the experimental free energy changes, δΔG_exp. R = 0.89. The line represents a fit y = 1.56 + 1.12x.

Comparison of the TS with the EC. A simple model for the EC is the ensemble of configurations stabilized by electrostatic interactions before formation of short-range interactions necessary for stabilization of the final bound complex. This electrostatically stabilized ensemble of states was generated by a standard Metropolis Monte Carlo algorithm, using the calculated values of δΔG_elec for different configurations of native Cyt and RC. The position and orientation of the EC is similar to that of the TS (Table 1), with the Cyt located over the M subunit side of the RC surface. However, the EC distribution is broader, more delocalized than that for the TS (Fig. 3). Thus, the TS ensemble represents a small subset of the EC ensemble. The electrostatic energy profile of the EC is similar to that previously found in studies of the Cyt and RC from Rb. sphaeroides (29). The minimum electrostatic energy is at a position of the Cyt at a solvent-separated distance above the RC surface, biased toward the M subunit side of the RC with orientation close to that of the Cyt in the bound state. The average values for the TS coordinates are similar to that of the EC, except that the values for y and u are offset from the average values in the EC.

Fig. 3.

Distribution of the electrostatic interaction energies for different configurations in the EC calculated with the continuum model. The black dots represent energies of the sampled structure projected onto translational coordinates, x, y, and z, and the rotational coordinates, u, v, and ψ, where u = sin θ cos φ, u = sin θ sin φ. Negative values of u correspond to structures that are tilted toward unit M side. The energies of the TS ensemble (750 structures) are shown superimposed as blue circles, and the position of the average TS is shown as a red circle. The origin represents the bound-state structure.

Discussion

In this work, a set of TS structures for the formation of the active Cyt/RC complex was obtained by fitting experimental kinetic data over a wide range of protein-protein configurations. In addition, the structures of the ECs formed between the two proteins were delineated by calculating the energies of the protein configurations stabilized by electrostatic interactions.

The results found in this study are in agreement with the fast-reaction model shown schematically in Fig. 4. The EC starts to form when the electrostatic interaction between Cyt and RC overcomes the entropic cost due to the loss of rotational and translational degrees of freedom, and the interacting proteins enter a “steering region” where the electrostatic interaction > k_BT (41). In our calculations, this boundary occurs at z > 20 Å (see z plot in Fig. 3), much farther than the distance z ≈ 5 Å for the TS obtained in this study. Thus, our results support the model in which electrostatic docking leads to the formation of an EC followed by the TS for formation of short-range interactions leading to the bound state. This scenario is similar to that proposed for fast reactions assisted by electrostatic interactions (3, 5, 41-43).

Fig. 4.

The reaction coordinate diagram showing the EC, TS, and bound state. The dashed line represents the reaction of modified protein, resulting in changes in binding energy, δΔG, and TS energy, δΔG^‡.

The ensemble of structures obtained for the EC and TS are shown compared with the structure of the bound state in Fig. 5. The EC is represented by the ensemble of states with 2k_BT of the minimum electrostatic energy. The TS ensemble is qualitatively represented by the best 1% of states having the highest correlation coefficient. The EC and TS ensembles are represented by structures of the Cyt at the average positions.

Fig. 5.

Representations of the EC (a), the TS (b), and the bound state (c) for the reaction between the Cyt and RC. The average structures are green, and the heme, Tyr L162, and BChl dimer are orange. The blue envelope represents the region occupied by C^α atoms of the Cyt in the ensemble. The blue circle shows the CBC methyl group of the heme in the average structure. The red circles show representative positions of the CBC methyl group in the ensemble. Shown are the progression of the Cyt from a delocalized distribution in the EC (a) through a more localized position in the TS (b), in which the heme CBC methyl group points toward Tyr L162 to the bound state (c), in which the CBC methyl group is in contact with the Tyr L162 for electron transfer.

Several features of these structures are apparent. The Cyt in the EC (Fig. 5a) is located on the M subunit side of the RC surface, optimizing strong electrostatic interactions as suggested by docking studies (26-29). The Cyt is not well localized in the EC but can assume a wide range of positions. The TS (Fig. 5b) is also situated over the M subunit side of the RC surface. The average position of the TS is close to the average position of the EC and is stabilized by electrostatic interactions. However, the Cyt in the TS is rotated so that the CBC methyl group of the heme is localized, pointed toward Tyr L162 on the RC surface, in position for the formation of short-range van der Waals contacts for binding and strong tunneling interactions for rapid electron transfer. Thus, the TS found here represents a structure intermediate between that of the EC localized on the M subunit side of the RC surface and that of the final bound state located at the center of the RC surface. The relatively long distance between heme edge and Tyr L162 in the TS explains the observation that mutations to hydrophobic residues in the binding interface have a negligible effect on k_on (18).

The role of specific charge-charge interactions in the association process is shown in Fig. 6. Fig. 6a is a plot of the distances between specific charged residues in the EC, TS, and bound state. The distances between the most strongly interacting residues in the EC and TS are very similar, although the rms deviations of the distances are much larger in the EC. An interesting feature of these data in Fig. 6a is the movement of some distances in the EC to values in the TS close to those found in the bound state. Most notable is the distance between M95 and C99, which has the same distance in the TS as in the bound state. The distances between M184:C99, M292:C8, and M184:C93 are also closer to their values in the bound state. This result suggests a role of these interactions in nucleating the TS; i.e., these interactions form first and lead to the final bound state. Another feature of the plot in Fig. 6a is that the rms deviations of some distances in the EC ensemble appear to be smaller than others. In particular, the rms deviations of the distances between M184:C99, M184:C93, and M184:C54 are smaller than average. This result is likely a reflection of the central position of these interactions in the EC. The positions of some of these critical residues in the EC and TS are shown in Fig. 6 b and c. These residues are found on the Cyt surface near C99, C93, and C54 in the center of the positively charged region of the Cyt that interacts with the center of the negatively charged cluster of residues centered around M184, M95, and M292 (25). These interactions help to guide the Cyt to its position in the bound active state. In contrast, some interacting residues, e.g., L155:C32 and M292:C8, that are relatively close in the bound state are relatively far apart in the TS (Fig. 6 a and c). This result suggests that these interactions form later as the Cyt rotates into position for making short-range contacts. The TS interactions in the association process depicted above are generally in agreement with the scenario proposed in the double-mutant study of Tetreault et al. (25). However, the computational analysis in the present study allows the properties of the EC and TS ensembles to be described in greater detail.

Fig. 6.

Distances between charged residues in the Cyt RC reaction. (a) Plot of the average distance between charges in the EC (blue triangles), TS (red dots), and bound state (black squares). Some distances in the TS are similar to that of the bound state. (e.g., M95:C99, M184:C93, and M184:C99), suggesting a role of these interactions in the TS. The error bars represent the rms deviation of the distances. Smaller rms deviations are observed for some residues in the EC, indicating a central position in the average structure. Average structures of the EC (b) and TS (c), colored according to the rms deviation of the Cyt position. Dark blue regions centered near the positively charged residues Lys C54, C93, C99, and heme are relatively restricted compared with the peripheral Lys residues C8 and C32.

The positioning of the Cyt with its positively charged residues in the negative potential energy surface on the M side of the RC was suggested by previous electrostatic modeling studies (26-28). Three models for the structure of the Cyt/RC complex resulted from these studies. Interestingly, these models roughly correspond to the three different states of the system discussed here. The model of Allen et al. (27), with the Cyt centrally located with heme directly above Tyr L162, corresponds to the bound state; the Tiede and Chang model (26), which has strong electrostatic interactions but has the heme pointing toward Tyr L162, corresponds to the TS; and the model of Adir et al. (28), which has the strongest electrostatic binding, corresponds to the EC. The diffuse electrostatic interaction between the Cyt and RC pointed out by Tiede et al. (30) is relevant to the EC. The different results of these modeling studies depended on the relative weights given to electrostatic energy and electron transfer tunneling interaction.

A second important feature of the TS is the position of the Cyt with the exposed heme edge directed toward Tyr L162. The Cyt in this orientation is in position to make short-range van der Waals contacts necessary for binding and electron transfer. However, the distance between putative electron tunneling contact surfaces in the TS is ≈10 Å greater than in the bound state, similar to the distance proposed in previous studies (13, 29). Because the electron transfer rate decreases exponentially with distance, the electron transfer rate between the Cyt and RC in the TS is expected to be much slower than in the bound state. For a 10-Å-longer tunneling distance, when using tunneling decay factor β = 1.61 - 1.75 Å^-1 for transfer through an aqueous interface (44), electron transfer times in the TS of 10-40 s are expected. These long times preclude a mechanism in which electron transfer occurs at the TS. The structure of the TS is consistent with the mechanism in which the next step in the reaction is the formation of short-range contacts and electron transfer from the bound state.

To what is the TS barrier due? The average coordinates of the TS appear to be quite similar to average coordinates of the EC as shown in Fig. 5 and Table 1. A key difference between the TS and the EC is the smaller range of TS distances and angular coordinates; i.e., the TS represents a smaller volume in configuration space. Thus, the TS represents an entropy barrier to the formation of the bound complex. A rough estimate of the entropy barrier, based on calculating the relative volumes in configuration space for the TS and EC shown in Table 1, is that the TS occupancy is reduced by approximately a factor of 100 relative to the EC. In addition, the translational rotational entropy barrier, other nonelectrostatic contributions such as desolvation processes, or loss of side-chain entropy before the formation of van der Waals contacts may be present (45).

The close resemblance between the minimum energy configuration of the EC and the TS shown in Fig. 3 is an important feature that helps to increase the rate process for protein association. The energies of the TS ensemble are within 2k_BT of the minimum EC coordinates, allowing easy access to the TS configuration. The association process resembles a binding funnel, in which a smaller number of lower energy configurations are brought close to the target configuration of the final state (46). An important feature of the smooth-binding funnel is the absence of trapped states that could impede the search for the bound state. Electrostatic calculations indicate that trapped states due to formation of salt bridges between charged residues on the Cyt and RC do not form as the result of the high energy for desolvation of the protein surface (29). This desolvation penalty is responsible for the relatively large distances (≈10 Å) between charged residues in the EC and TS (Fig. 6a). In addition, the relatively small number of hydrophobic residues in the short-range binding domain (19) may be important in ensuring that when short-range van der Waals contacts do form, they lead to the bound state rather than to a trapped state. The processes that are important in the final steps of protein association and electron transfer are not well understood and require further study.