Structural, dynamic, and energetic aspects of long-range electron transfer in photosynthetic reaction centers

Abstract

Intramolecular electron transfer within proteins plays an essential role in biological energy transduction. Electron donor and acceptor cofactors are bound in the protein matrix at specific locations, and protein–cofactor interactions as well as protein conformational changes can markedly influence the electron transfer rates. To assess these effects, we have investigated charge recombination from the primary quinone acceptor to the special pair bacteriochlorophyll dimer in wild-type reaction centers of Rhodobacter sphaeroides and four mutants with widely modified free energy gaps. After light-induced charge separation, the recombination kinetics were measured in the light- and dark-adapted forms of the protein from 10 to 300 K. The data were analyzed by using the spin-boson model, which allowed us to self-consistently determine the electronic coupling energy, the distribution of energy gaps, the spectral density of phonons, and the reorganization energy. The analysis revealed slow changes of the energy gap after charge separation. Interesting correlations of the control parameters governing electron transfer were found and related to structural and dynamic properties of the protein.

The bioenergetic pathways of living systems involve a multitude of electron transfer (ET) reactions. Within large protein-cofactor complexes, electrons tunnel between donor and acceptor sites over substantial distances (5–30 Å). In the weak coupling regime, the ET rate coefficient is obtained from perturbation theory as (1–4)

[1]

where ℏ and V denote Planck's constant divided by 2π and the electronic coupling matrix element, respectively. The thermally averaged Franck–Condon factor, FC, represents the probability of forming a resonant complex between donor and acceptor. This quantity can be calculated in various ways, based on classical, semiclassical, or quantum-mechanical theories (4). In the celebrated classical Marcus theory (1),

[2]

with Boltzmann's constant, k_B, and absolute temperature, T. The free energy difference between the reactant and product states, ε, the nuclear reorganization energy, λ, and the electronic coupling, V, are the three system parameters that govern the ET rate. From these quantities, only the driving force, ε, is directly accessible to measurement, e.g., by delayed fluorescence (5), redox titration (6), or voltammetry (7). The other two parameters can be determined only indirectly from kinetic data and are difficult to disentangle in practice. The intrinsic flexibility of proteins adds an interesting dynamic aspect to the ET reaction. Proteins fluctuate thermally among many different conformations and respond to charge rearrangements with structural relaxations on time scales ranging from (below) picoseconds to (at least) seconds. These motions can strongly affect the ET parameters and hence the ET rates (8–10).

For studying biological ET, the photosynthetic reaction center (RC) of the purple bacterium Rhodobacter sphaeroides is a superb model system. This membrane-spanning, 120-kDa, protein–pigment complex consists of three subunits and a number of cofactors (Fig. 1A). Photon absorption causes electronic excitation of the special pair (P), and the ensuing sequence of ET steps leads to transmembrane charge separation (11–13). Here we focus on the charge recombination step , which occurs in the absence of the secondary quinone, Q_B (Fig. 1 A). This nonadiabatic ET over a distance of 25 Å is sensitive to the preillumination history and has a peculiar temperature dependence (14). Previously, we had introduced an analysis method that describes the observed nonexponential kinetics quantitatively (9, 10). In our model, the heterogeneity of proteins, conformational relaxations, and fluctuations are all mapped onto a single coordinate, the energy gap ε. Fast vibrational motions and slow diffusive conformational changes are treated separately (15), as we explain with the scheme in Fig. 2. Within the neutral (PQ_A) and charge-separated () electronic states, the RC proteins perform slow, diffusive motions on rugged, but overall parabolic, conformational free energy surfaces. Charge separation and recombination are vertical in this scheme (Condon approximation) (1). Fig. 2 shows that the energy dissipated by vibrations during the ET step, ε(q), depends on the conformational coordinate, q, because ε(q) includes the reaction free energy and reorganization energy associated with the slow degrees of freedom. Consequently, apart from the intrinsic temperature dependence of the ET rate due to a change in the thermal occupation of vibrational modes, which affects FC, there is an extrinsic temperature dependence to the ET rate caused by slow conformational motions of the RCs on the PQ_A or energy surfaces.

Fig. 1.

(A) Cofactor arrangement in the photosynthetic reaction center (RC) of R. sphaeroides. After light excitation, an electron is ejected from the special pair (P), a bacteriochlorophyll (BChl) dimer, and transferred within 200 ps via the accessory BChl, B_A, and a bacteriopheophytin, H_A, to the primary quinone, Q_A. For this study, the secondary quinone, Q_B, was removed, so that the electron returns to P () within ≈100 ms. (B) Enlarged view of the special pair P. Also shown are key residues that were exchanged by site-directed mutagenesis [PDB ID code 1PCR (11)].

Fig. 2.

Schematic depiction of the rugged energy surfaces in the neutral (PQ_A) and charge-separated () states of RCs. The energy gap, ε, which controls the ET rates, varies as a function of the conformational coordinate, q. D and L refer to the dark- and light-adapted conformations; the probability distributions p_D and p_L represent structural heterogeneity within these states.

A special experimental protocol (9, 10) has proven useful to study the effect of protein motions on the ET kinetics: RC samples are cooled to 10 K, either in the dark, or with a strong light source switched on at select temperatures, T_L, during cooling so as to keep the RCs in the charge-separated state. After the sample has reached 10 K, light-induced ET kinetics are measured (every 5 K) while the temperature is raised to 300 K at a constant rate over several hours. Samples cooled in the dark (dark-adapted, D) are initially trapped at q = 0 (see Fig. 2). Upon light excitation to the upper surface, the RCs can relax toward the minimum during the lifetime of the charge-separated state (≈100 ms). From the analysis of the ET kinetics, the extent of relaxation before charge recombination can be obtained. Samples cooled under light from T > 250 K (light-adapted, L) are arrested at q = 1 at 10 K. As T is slowly increased, protein motions become gradually unfrozen, and the RC proteins migrate to q = 0 on the lower surface. This relaxation can also be observed by means of measurements of the ET kinetics. By measuring the temperature dependence of the ET kinetics, the relaxation dynamics and ruggedness of the energy surfaces can be studied.

The ability of our analysis to disentangle the parameters V, ε, and λ prompted us to revisit experiments in which the driving force of the step [≈500 meV in wild-type RCs at room temperature (5, 13, 16)], was varied systematically. In their pioneering study, Gunner et al. (17) replaced the native Q_A, ubiquinone-10, by quinones with different redox potentials. Lin et al. (16) changed the number of hydrogen bonds between the conjugated carbonyls of the special pair monomers and the protein matrix by modifying specific amino acid residues depicted in Fig. 1B. This modification led to large variations of the P/P⁺ midpoint potential, E_m, ranging from 410 to 765 meV. From temperature-dependent measurements of the kinetics with these modified RCs, widely differing ε, V, and λ parameters have been extracted (16–20). Here we have applied our analysis to wild-type RCs and four special pair mutants (see Table 1) to assess the effects of mutation-induced structural changes on the ET rates.

Table 1. ET parameters of wild-type and mutant RCs.

RC	nH	Em, meV	λ, meV	V0, 10-4 cm-1	γ, meV-1
HF(L168)	0	410	557	1.53	0.0019
Wild type	1	505	593	1.70	0.0027
LH(L131)	2	585	684	1.97	0.0026
FH(M197)	2	630	726	2.25	0.0023
Triple	4	765	874	3.01	0.0023

n_H is the number of hydrogen bonds to the special pair, P, and E_m values are taken from ref. 16.

Materials and Methods

RC Purification and Sample Preparation. Carotenoid containing HF(L168), LH(L131), FH(M197), and LH(L131)/LH(M160)/FH(M197) (triple) mutant RC proteins from R. sphaeroides strain ΔLM1.1 (16) as well as wild-type RCs with an engineered polyhistidine tag (poly-His RCs) (strain SMpHis, ref. 21) were used in this work. Bacterial growth, RC purification, and removal of the secondary quinone were performed as described previously (10, 21–23).

Purified, Q_B-depleted RCs were dissolved in a mixture of 75% glycerol and 25% buffer (10 mM Tris/0.1% lauryldimethylamine N-oxide, pH 8) to a final concentration of ≈15 μM and loaded into a 10 × 10 × 2.5 mm³ polymethylmethacrylate (PMMA) cuvette.

Time-Resolved Visible Spectroscopy. The cuvette containing the sample was attached to the cold finger of a closed-cycle helium refrigerator. Light-induced charge recombination kinetics were monitored in the Soret region of the BChl molecules at 436 nm, as described previously (9, 10).

For complete or partial light adaptation of the RCs, light from a 250-W tungsten lamp (Oriel, Stratford, CT) was passed through a heat filter and a long pass filter (RG645, Schott, Mainz, Germany). Illumination was switched on at selected temperatures during cooling to 10 K. With this illumination, RC molecules were kept in the charge-separated state for ≥95% of the time during cooling (9, 10). After arrival at 10 K, samples were warmed in the dark with a ramp rate of 4.7 mK/s for both dark- and light-adapted samples. ET kinetics after flash excitation were measured every 5 K between 10 and 300 K; at least five traces were averaged at each temperature.

Numerical Computations. Data analysis was performed on PC workstations using pv-wave (Visual Numerics, Boulder, CO), except for FC calculations with the spin-boson model (SBM). These were implemented on a Sun UltraSPARC-III architecture at the computer facility of the University of Ulm, by using functions of the NAG C library (Mark 6, NAG, Oxford).

Experimental Results

Distributions of Rate Coefficients. Measurement of the charge recombination kinetics yields the survival probability of the charge-separated state, N(t), which can be expressed by a distribution of rate coefficients, f(log k) (9, 10, 24),

[3]

Fig. 3 shows contour plots of rate distributions, obtained from maximum entropy analyses (24), of charge recombination kinetics in HF(L168) (A and B) and LH(L131) mutant RCs (C and D) after cooling in the dark (A and C) and under continuous illumination from 280 K (B and D). The distributions of rate coefficients can be characterized by a logarithmically averaged rate and standard deviation,

[4]

[5]

The temperature dependencies of both parameters after cooling under different illumination conditions are plotted in Fig. 4 for HF(L168), LH(L131), and FH(M197) RCs. For comparison, wild-type data are also included.

Fig. 3.

Contour plots of the distributions of rate coefficients for the mutants HF(L168) (A and B) and LH(L131) (C and D), obtained for samples cooled in the dark (A and C) and under illumination from 280 K (B and D).

Fig. 4.

Temperature dependence of logarithmically averaged charge recombination rates, log k_ET (Upper) and widths σ_ET (Lower) of the distributions of rate coefficients for HF(L168) (A), LH(L131) (B), FH(M197) (C), and wild-type (D) RCs.

All mutant samples exhibit qualitatively the same behavior as observed earlier with wild-type RCs (9, 10). The distributed kinetics arise from conformational heterogeneity in the ensemble. Dark-cooled samples exhibit a pronounced step in k_ET between 160 and 220 K, accompanied by a broadening of f(log k). Both of these effects are caused by conformational relaxation during the 100-ms lifetime of the charge-separated state. The change is largest for HF(L168) (≈10-fold) and decreases with increasing midpoint potential. For the triple mutant LH(L131)/LH(M160)/FH(M197), only a factor of ≈2 is observed.

For all samples except HF(L168), cooling under illumination from 280 K yields similar k_ET values at 10 and 300 K. This behavior is expected from our model, because relaxation on the () surface is complete within 100 ms at 300 K, so that charge recombination takes place from the light-adapted conformation at q = 1 (Fig. 2). (The change due to the intrinsic temperature dependence of the ET is small, as shown below.) Note that the widths of the rate distributions of the light-adapted form are much larger than those of the dark-adapted form at low temperature; both merge, however, around 200 K.

The data on the light-adapted conformation of mutant HF(L168) differ from those of the other samples. It has a markedly broader rate distribution, and k_ET is ≈4-fold smaller at 10 K than at 300 K (Fig. 4).

Quantitative Analysis

ET Model. In the analysis, the energy gap, ε, was singled out as the key parameter that depends on the RC conformation. Thus, a distribution of energy gaps, g(ε), represents conformational heterogeneity, and slow diffusive motions affect the position and width of this distribution. For calculating ET rates as a function of ε and T, we used the SBM, a quantum-mechanical description of ET coupled to a bath of harmonic oscillators that is characterized by a spectral density, J(ω) (25–28). Fig. 5 shows how the resulting k(ε, T) curves enable us to map f(log k) onto g(ε),

[6]

With this relation, Eq. 3 can be recast into

[7]

Fig. 5.

Microscopic rate coefficients k(ε, T) (wild-type RCs) as a function of ε, calculated with the SBM. The arrows illustrate schematically the connection between the experimentally determined rate distributions, f(log k), and the energy gap distributions, g(ε). The g(ε) distributions governing ET at 50 K < T < 120 K are shown for samples cooled in the dark (solid line) and under illumination from 280 K (dashed line).

On general grounds, we would expect that V and λ are also distributed parameters. However, it is clearly not reasonable to model the experimental f(log k) data with more than one independent distribution. Therefore, two simplifying assumptions were introduced in the analysis: (i) The logarithm of V was taken to depend linearly on the energy gap ε,

[8]

with parameters γ, V₀ = V(300 K), and ε₀ = ε(300 K). This functional dependence can be motivated by the semiclassical tunneling model (9). Note that Eq. 8 introduces a distribution in log V that is correlated with g(ε). (ii) In the SBM, the spectral density of harmonic oscillators, J(ω), was treated as a smooth function, independent of temperature and conformation. Consequently, the model does not attribute heterogeneity to the reorganization energy (28). With these simplifying assumptions, the model precisely describes the temperature dependence of the nonexponential ET kinetics for all samples examined here with a minimal set of parameters. Moreover, it self-consistently explains a variety of phenomena associated with conformational heterogeneity and dynamics.

Self-Consistent Determination of Model Parameters. The SBM analysis affords a self-consistent determination of the parameters governing ET from the experimental data (10). The procedure is based on the absence of conformational changes affecting the ET reaction between 50 and 120 K. This is evident from the fact that, after cooling under illumination from 180 or 280 K, all samples showed a constant k_ET below 120 K (Fig. 4), reflecting the inability of the RCs to diffuse on the PQ_A surface in Fig. 2. Moreover, starting illumination at 110 K during cooling yields k_ET data essentially identical to that for cooling in the dark, confirming that slow conformational motions that affect the ET kinetics are frozen out. Thus, between 50 and 120 K, the T dependence of ET derives exclusively from the variation of k(ε, T), as described by the SBM, and not from protein motions affecting g(ε). Fig. 5 shows that the temperature dependence of the ET rate of a particular molecule within the heterogeneous ensemble of RCs depends strongly on its energy gap, ε. To quantify this variation, we have added the differences between all pairs of kinetic traces taken between 50 and 120 K (altogether n data sets),

[9]

For cooling under illumination from 280 K, the Δ_p(t) data in Fig. 6 are negative at short times (large k) and show a crossover to positive values at long times (small k). This behavior is easily understood from the T dependence of k(ε, T) in Fig. 5. For small ε, ET rates are small and increase with T. At ≈450 meV, there is a crossing point above which ET rates are larger and decrease with T. At this isokinetic point, Δ_p(t) = 0. Of course, the transition between negative and positive Δ_p(t) values can appear only if the isokinetic point is within the range of ε values covered by the g(ε) distribution (Fig. 5), which is the case for all light-adapted samples. Fig. 6 reveals that the g(ε) distributions are centered to the right of the isokinetic point, except for HF(L168), whose g(ε) is located in the steep part of the k(ε, T) curves. By contrast, the dark-cooled samples show only negative excursions, which places their g(ε) distributions to the right of the isokinetic point. The analogous behavior of the various samples is quite remarkable, considering the widely differing driving forces.

Fig. 6.

Sum of pair differences, Δ_p(t), characterizing the dispersion of ET rates with T between 50 and 120 K for HF(L168) (A), LH(L131) (B), FH(M197) (C), and wild-type (D) RCs. Solid lines, simulated sums of pair differences with the optimal ET parameter set (for samples cooled under light from 280 K).

For determining the model parameters, the driving force at 300 K was set equal to the P/P⁺ midpoint potential, E_m, for the light-adapted sample, as suggested from the dynamic model (Fig. 2). Mutation-induced changes in the potential can be neglected (16). The other relevant ET control parameters (V₀, γ, J(ω)/ω) were then varied until the time-dependent behavior of Δ_p(t) was reproduced (solid lines in Fig. 6). This procedure also gives an estimate of the spectral density of phonons coupled to the ET, as J(ω) governs the shape of k(ε, T) and thus Δ_p(t). Calculations with a variety of distribution functions for J(ω)/ω showed that best agreement with the Δ_p(t) data were obtained by using a Lorentzian centered at 0 cm^–1 with a width (full width at half maximum) of 60 cm^–1. For some mutants, Gaussians at ≈120 cm^–1 were added to accurately reproduce the dispersion. It also became apparent that localized high-frequency modes contribute definitely less than 10% to the total reorganization energy.

The ET parameters of all mutants are compiled in Table 1. The scaling factor γ is similar for all mutants (Table 1), with an average of 0.0024 meV^–1. Fig. 7 shows the systematic variation of V₀ and λ with E_m and thus the driving force ε. To a good approximation, the logarithm of the electronic coupling varies linearly with E_m, with a slope κ = 0.00085 meV^–1. This dependence is similar to the one introduced in Eq. 8. Whereas Eq. 8 describes the variation of V and ε within a given sample, κ describes the change of V with ε between different samples. The pronounced increase of the reorganization energy, λ, in Fig. 7B is also roughly linear in E_m.

Fig. 7.

Dependence of the ET parameters on the P/P⁺ midpoint potential. (A) Electronic coupling matrix element V₀. Solid line, linear fit. (B) Reorganization energy λ (♦). Also shown: difference in the peak of g(ε) between the light- and dark-adapted conformation, Δε, at 50 K (○).

Fit Results. Conformational relaxation on the PQ and energy surfaces in Fig. 2 affects the positions and the widths of the g(ε) distributions. Therefore, these two parameters were varied to fit the ET kinetics at all temperatures with Eq. 7. Fig. 8 shows the temperature dependencies of the mean, 〈ε〉, and the width, σ_ε, of the Gaussian distributions. They look qualitatively similar to the f(log k) parameters in Fig. 4. In Fig. 7B, we have also plotted the separation between the peaks of the dark-adapted and light-adapted g(ε) distributions, Δε = 〈ε(D)〉 – 〈ε(L)〉 at 50 K. It decreases monotonically with E_m, from 190 meV for HF(L168) to less than 50 meV for the triple mutant.

Fig. 8.

Parameters characterizing the g(ε) distributions of mutant and wild-type RCs as obtained from the fits. Note the different 〈ε〉 axis range for each mutant.

The HF(L168) mutant has the lowest mean energy gap in the dark- and light-adapted forms. This observation pushes the analysis into a much steeper k(ε, T) range than for the other RCs (Fig. 5), so that minor changes of ε are translated into large alterations of the ET rate coefficient. However, the general features of the dynamic ET model are also reproduced for this mutant.

Above 270 K, ET rates are seen to increase slightly, likely because of temperature-dependent protonation of residues close to the special pair (29, 30). These effects are outside of the scope of the model presented here, and consequently, data above 270 K were omitted from the fits.

Discussion and Conclusions

The microscopic parameters governing long-range ET, V, ε, and λ, are difficult to disentangle from experimental data. We have extracted these parameters for the reaction from an analysis of the detailed shapes of the rate distributions and their temperature variations by using the SBM model for a set of special pair mutants with widely varying driving forces. When the ET rate was mapped onto a single conformational coordinate, dynamic effects became apparent that are caused by protein motions in response to the altered charge distribution (9, 10). Analysis of the detailed temperature dependence of the ET provides insights into the barriers opposing conformational change. Here we will focus on the comparison of the mutants to examine the effects of local structural changes on the ET parameters.

Electronic Coupling. The data in Table 1 show a clear correlation of the electronic coupling parameter V₀ with the number of hydrogen bonds, n_H, and concomitantly, the energy gap. The coupling is controlled by (i) the nature of the electronic energy eigenstates of donor and acceptor, and (ii) the properties of the intervening medium.

Experimental (31, 32) and theoretical (33, 34) studies have given evidence that alterations of the hydrogen bonds to the protein matrix cause slight structural rearrangements of the special pair. Stark effect spectroscopy (35), photochemically induced dynamic nuclear polarization (photo-CIDNP), ¹³C solid-state NMR (36), EPR, ENDOR (electron–nuclear double resonance), and TRIPLE (electron–nuclear–nuclear triple resonance) studies (37, 38) all have shown asymmetric electron distributions in the ground, excited, and ionized states of the special pair in wild-type RCs, and addition or removal of hydrogen bonds between the special pair and the protein matrix affects the spin distribution between the P_L and P_M BChl monomers (37).

The protein matrix connecting donor and acceptor provides a variety of pathways for electron tunneling, consisting of through-space and through-bond segments (39). Quantum interference among individual pathways can lead to a pronounced sensitivity of the electronic coupling to slight structural modifications (8). The observed correlation between V and n_H is in good agreement with the expectation that hydrogen bonds are excellent tunneling mediators (39, 40). Our results thus strongly suggest that the additional hydrogen bonds to the special pair facilitate electron tunneling in the reaction.

Reorganization Energy and Spectral Density of Phonons. Our analysis reveals a substantial increase of λ with the P/P⁺ midpoint potential of the mutant RCs (Table 1 and Fig. 7B). Allen and coworkers (41) reported a linear correlation between the change in E_m and the number, and thus the cumulative enthalpies, of hydrogen bonds between histidine side chains and the C2 and C9 carbonyl groups. Hydrogen bond formation, however, does not appear to be the sole physical mechanism responsible for the change in E_m because the change of the P/P⁺ midpoint potential scales with the change of the side-chain permanent dipole moment in a series of mutations at the L168 and M197 positions (42). Tyrosine and histidine both donate hydrogen bonds of similar strength to P; yet, the effect of tyrosine on E_m is much weaker. Histidine side chains, however, have a strong dipole moment and thus may raise E_m by charge–dipole interaction (38, 42). The increased polarity in the environment of the cofactor is also expected to lead to an increase of λ, as seen in Fig. 7B.

Within our SBM analysis, the multitude of vibrational modes coupled to charge recombination was modeled as a smooth function involving exclusively low-frequency vibrations (ω ≤ 300 cm^–1). For all samples, the shape of J(ω)/ω was predominantly a Lorentzian centered at 0, which represents a Debye relaxation. Determination of the spectral density within our analysis should be treated with caution, however, because it involves inversion of a complex integral representing FC. Moreover, structural heterogeneity, modeled by the g(ε) distribution, causes blurring of sharp features of J(ω). Yet, the spectral density that best fits the kinetics coincides nicely with results from MD simulations of primary charge separation (27, 28) or path integral simulations (43). Evidence of the predominant involvement of low-frequency modes was also provided by femtosecond spectroscopy of the first excited singlet state, P* (44, 45) and the subsequent formation of charge-separated states (46). Both processes were shown to couple to vibrations below ≈300 cm^–1. The low-frequency spectrum of modes coupled to the P → P* transition is affected by modification of hydrogen bonds to the special pair (44, 45). This effect implies that protein–cofactor interactions are significantly modified in the special pair mutants. In proteins, many delocalized (global) low-frequency modes are present, in which large parts of the protein vibrate in a concerted fashion (47). Our results suggest that the additional hydrogen bonds introduced by mutation provide a more rigid suspension of the special pair cofactors within the protein, which improves the coupling to the global low-frequency modes. However, there are also localized low-frequency vibrations, as inferred from resonance Raman spectroscopy (48) and density functional normal mode calculations of the BChl cofactors (49) that may contribute to J(ω).

Conformational Relaxation. The separation between the peaks of the dark-adapted and light-adapted g(ε) distributions, Δε at 50 K, and thus the total extent of energy gap relaxation after a change of the electronic state decreases markedly with increasing E_m (Figs. 7B and 8). Apparently, the more tightly the BChl cofactors of P are coupled to the protein matrix, the smaller the relaxation step. This observation suggests that conformational relaxation is associated with subtle rearrangements of the cofactors within their cavities. The effect is particularly pronounced for HF(L168), which has no hydrogen bonds to the C2 and C9 carbonyl groups, giving rise to a huge Δε = 190 meV.

A final remark concerns the temperature dependence of the relaxation features of the parameters g(ε) distribution, 〈ε〉, and σ_ε in Fig. 8. For the dark-adapted sample, the relaxation step due to protein motions (on the ≈100-ms time scale) is seen between 170 and 250 K. For the light-cooled samples, conformational changes (on the ≈10⁴-s time scale) start already at 120 K. These broad temperature intervals reflect the ruggedness of the conformational energy landscape. As a consequence, conformational dynamics at room temperature occurs on essentially all time scales, from picoseconds to beyond milliseconds (9).