Letter pubs.acs.org/JPCL
Coulomb Soup of Bioenergetics: Electron Transfer in a Bacterial bc1 Complex Daniel R. Martin,† David N. LeBard,‡ and Dmitry V. Matyushov*,§ †
Center for Biological Physics, Arizona State University, P.O. Box 871504, Tempe, Arizona 85287, United States Department of Chemistry, Yeshiva University, 500 West 185th St., New York, New York, 10033, United States § Center for Biological Physics, Arizona State University, P.O. Box 871504, Tempe, Arizona 85287-1504, United States ‡
S Supporting Information *
ABSTRACT: We report atomistic molecular dynamics simulations (200 ns) of the first, rate-limiting electron transfer in the electron transport chain in a bacterial bc1 complex. The dynamics of the energy gap between the donor and acceptor states include slow components, on the time-scale of tens of nanoseconds. These slow time-scales are related to large-scale elastic motions of the membrane-bound protein complex, which modulate both electrostatic and induction interactions of the electron with the protein−water−lipid thermal bath. The combined effect of these interactions is a high, ∼ 5 eV, reorganization energy of electron transfer as calculated from their variance. The reorganization energy does not reach equilibrium on the length of simulations and the system is nonergodic on this time-scale. To account for nonergodicity, two reorganization energies are required to describe the activation barrier, and their ratio is tuned by the relative time-scales of nuclear reorganization and of the reaction. SECTION: Biophysical Chemistry and Biomolecules
E
the Supporting Information (SI); we provide here only a brief overview directly relevant to the discussion of the results. The position of quinol in the active site is unknown, but the available X-ray structure identifies the position of the reaction inhibitor, stigmatellin. It was therefore assumed that quinol occupies a site close to the position of the inhibitor, and that is where it was placed in the initial configuration.5 The first electron transfer in the bc1 complex is coupled to proton transfer from QH2 to the ISP, with the overall rate of ∼103 s−1 and positive (endergonic) reaction free energy,4,6 ΔG ≃ 0.21 eV. If assigned to electron transfer, this slow rate and a relatively small donor−acceptor distance of ∼7 − 8 Å are inconsistent with the parametrization of the Marcus theory7 of protein electron transfer by Dutton and co-workers.8,9 In particular, their recipe suggests ∼0.8 eV for the electron transfer reorganization energy, while ∼2 eV is required by the Marcus theory to reproduce the experimentally observed activation enthalpy Ha ∼ 0.65 eV.10 Based on this inconsistency, a sequential mechanism of proton first-electron next was suggested.6,11 This mechanism assumes that QH2 first donates a proton to ISP’s histidine-156 (Figure 1C), thus transforming QH2 into QH−. While no direct experimental evidence of this intermediate has been reported, the corresponding pKa values for deprotonation/protonation of quinol/ISP allows one to reproduce the overall rate with commonly assumed values of
nergetic complexes of mitochondria and bacteria are among the oldest inventions of nature, and they are highly conserved in both structure and function across many species. They have been optimized to provide living organisms with chemical energy.1 The deficiencies in their functionality also largely define the rate of aging and eventually the life-span of an organism.2 The bc1 complex of plants and mitochondria is a part of Mitchell’s Q-cycle.3 It is a dimeric protein complex (Figure 1A,B) facilitating across-membrane electron transport in each of its monomers.4 The chain of redox reactions in this complex starts with the bifurcated oxidation of quinol QH2 at the Q0 site. The first electron transfer, which is also the rate-limiting step, reduces the iron−sulfur (Fe2−S2) active site of the Rieske iron−sulfur protein (ISP) (Figure 1C). The reaction produces an intermediate semiquinone, which further reduces the low potential chain including bL and bH hemes of cytochrome b. The first step in this chain of electron transfer reactions is our focus here. The goal is to obtain microscopic insights into the leading modes and time-scales of nuclear motions activating electron transfer. We present in this paper ∼200 ns atomistic molecular dynamics (MD) simulations of the forward and backward electron transfer reactions between the quinol cofactor and the ISP of the bc1 complex of Rhodobacter capsulatus. The simulation setup includes a membrane-bound protein dimer (1ZRT entry in protein data bank) combined with TIP3P waters and electrolyte ions neutralizing the system (Figure 1A). The details of the simulation protocol are given in © XXXX American Chemical Society
Received: September 5, 2013 Accepted: October 9, 2013
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Figure 1. (A) Cross-section of the MD simulation box showing the membrane-bound bc1 complex from the bacterium Rb. Capsulatus. The water is shown in blue, the 1-palmitoyl, 2-oleoyl-sn-glycero-3-phosphocholine (POPC) membrane is shown in gray, and the protein is in magenta. (B) Magnified trans-membrane protein. (C) Magnified active site for the initial charge transfer between quinol and the iron−sulfur center of the Rieske protein (ISP).
imposed by the Gaussian statistics in the canonical (equilibrium thermodynamics) ensemble. The dynamics of proteins are highly dispersive,19 including transitions between substates, nominally belonging to the same folded state,20 and often occurring on the millisecond timescale.21 Under these conditions, sampling of the entire phase space available to the protein is simply not possible on the time-scale of a particular biochemical process. The canonical ensemble, while remaining a useful conceptual limit referring to an infinite observation time, becomes an unreliable tool for performing statistical averages.12,17 One can argue,12,17 as we do below, that nature has productively utilized the breakdown of the canonical description to allow the dynamical control of some parameters critical to biochemical activation. Since conformational equilibrium of a redox protein is almost never fully achieved, nonergodicity must be a part of the theoretical formalism. The first step in establishing this new formalism is to recognize the need for two reorganization energies, λSt and λvar, to account for globally nonparabolic free energy surfaces of electron transfer.12,18,17 The parameter quantifying the deviation between them, χG = λvar/λSt, is a useful indicator of the reaction occurring in the nonergodic, noncanonical regime. The next step in recognizing the importance of nonergodicity is to assign the correct value to the variance reorganization energy in the denominator in eq 1. Faster reactions will make some of the nuclear fluctuations of the system dynamically frozen on the reaction time-scale.22−25 Here again, the dispersive dynamics, specific to proteins, become a critical part of the physical picture. In order to characterize the dynamics of X, one needs to consider the time correlation functions of the energy gap, CX(t) = ⟨δX(t)δX(0)⟩. The Fourier transform of CX(t) leads to the loss function26,27 χ″(ω) = (β/2)ωCX(ω) (see SI). The results of the calculation of this function for the forward (main panel) and backward (inset) electron transfer in bc1 complex are shown in Figure 2. The peaks of the loss function define the relaxation frequencies contributing to the dynamics of X(t), and their heights specify the relative weights of these relaxation processes in CX(t). The integral of χ″(ω)/ω over the entire range of frequencies yields the thermodynamic reorganization energy λvar. The dynamical arrest of nuclear modes slower than the time-scale of the reaction τobs = k−1 requires restricting the range of frequencies affecting nuclear reorganization. The nonergodic reorganization energy25 λ(k) becomes
the electron transfer reorganization energy. Since proton transfer is endergonic, it helps to reduce the reaction Gibbs energy for the subsequent electron transfer step, which rate increases up to 1.65 × 108 s−1.4 Our simulations presented here do not support ∼0.8 eV for the electron-transfer reorganization energy, thus challenging the arguments leading to the suggested proton-first mechanism.10 However, given the presently established mechanistic framework, we set up our simulations according to the proposed mechanism assuming QH− and ISPH+ as the initial configuration for the first electron transfer. This setup allows us to critically re-examine the commonly assumed values of the reorganization energy for protein electron transfer. The results reaffirm our previously accumulated experience that these common values have little support from atomistic simulations.12 The mechanistic description of protein electron transfer starts with defining the reaction coordinate. The instantaneous energy gap between the acceptor and donor electronic states X = ΔE(Q), fluctuating due to thermal motions of the nuclear coordinates Q, has been adopted as the reaction coordinate in modern formulations of the theory.13 Since many nuclear modes affect the statistics of the collective coordinate ΔE(Q), the statistics of X in each redox state is typically Gaussian.13,14 The free energy surfaces as functions of X are then parabolas Fi(X ) = F0i + (X − Xi)2 /(4λ var)
(1)
In this equation, F0i is the free energy at the minimum Xi = ⟨ΔE(Q)⟩i; ⟨...⟩i denotes the statistical average in state i. The denominator in eq 1 denotes the variance reorganization energy defined, in the thermodynamic limit, through the 2 variance of X: λvar i = β⟨(δX) ⟩i/2, β = 1/(kBT). The conditions to be of thermodynamic consistency14,15 also require λvar i var var independent of the state, λvar 1 = λ2 = λ , and, additionally, to be equal to the Stokes shift reorganization energy λSt = (X1 − X2)/2. While deviations from both relations have been observed, the first condition is often found to be much better satisfied than the second.12 We will therefore assign one single value to λvar, while the dramatic violation of the second thermodynamic condition,16 λvar = λSt, is our main focus here. The reason behind this violation is the inability to reach the thermodynamic equilibrium and to establish canonical ensemble on the time of simulation or on the reaction time.12,17 The breakdown of the equality between the two routes to the reorganization energy implies that free energy surfaces in eq 1 are globally non-Gaussian, even though locally parabolic.18 The parameters defining each Fi(X) separately do not satisfy global requirements of consistency, such as λvar = λSt, 3603
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substantially to the overall λvar (note the ω−1 scaling in the frequency integral in eq 2) and produce a nearly continuous growth of λ(k) when the rate gets slower (Figure 3). The instantaneous energy gap between the donor and acceptor electronic states ΔE(Q) combines the nonpolar induction, ΔE ind (Q), and Coulomb, ΔE C (Q), components.25,28,29 The total average energy gap Xi in eq 1 is a sum of the gas-phase part X0 and the solvent-induced shift ⟨X⟩i listed in Table 1. The average induction gap Xind i is a large part of ⟨X⟩i Table 1. Energy Parameters of the Forward (1→2) and Backward (2→1) Electron Transfer in the bc1 Complexa Figure 2. Loss spectrum of the energy gap fluctuations for the forward (1→2) and backward (2→1, inset) electron transfer. The overall loss spectrum (blue) is separated into the Coulomb (red) and induction (green) contributions.
∫k
Xind i
λp
λw
λvar
λC
λind
1→2 2→1
−2.0 −6.7
−1.9 −1.7
2.9 3.3
5.8 6.4
5.1 5.0
2.3 2.3
1.1 1.1
All values (in eV) are obtained from averages on 200 ns long MD trajectories; λp and λw refer to the protein and water components of the reorganization energy, respectively. bThe difference between the average values ⟨X⟩i defines the Stokes sift and the corresponding reorganization energy λSt = (⟨X⟩1 − ⟨X⟩2)/2 = 2.4 eV.
(Table 1), as found for all electron-transfer proteins for which this analysis has been performed.29,30 Coulomb contributions to ⟨X⟩i from water and protein are also large, but, in contrast to the induction interactions, they tend to cancel in the total ⟨X⟩i. This comes from opposite signs (screening) of electrostatic potentials created by charged surface residues and by hydration water polarized by them.31 The same cancellation occurs in the variance reorganization energy, where the total λvar is typically below the simple addition of the protein and water parts due to a typically negative cross protein-water term λpw (not listed in Table 1).31 In contrast to a large magnitude of the average induction gap, ind Xind is typically i , the corresponding reorganization energy λ 25,29,30 small. This is because the fluctuations of ΔEind(Q), producing a nonzero λind, are driven by density fluctuations of the medium, which are restricted in dense, closely packed media. The ability to describe Lennard-Jones systems by meanfield theories, and the related small entropy of their thermodynamics,32 has the same origin of restricted density fluctuations affecting the nonpolar interaction energies. However, in the case of bc1 electron transfer, λind is unusually large (Table 1). This is because of significant density rearrangements in the system from large amplitude conformational motions of the ISP protein33 (see SI). We indeed observe a major conformational change of the entire complex caused by the forward electron transfer and resulting in nearly doubling of the donor−acceptor (QH to Fe2S2) distance from ∼8 Å to ∼15 Å (see Figure S4 in SI). In contrast to the cancellation between the protein and water Coulomb contributions to λvar (λp+λw>λvar), this cancellation does not occur between the Coulomb and induction components of the reorganization energy (λC+λind < λvar, Table 1). As a result, the overall variance reorganization energy λvar is very large, ≃ 5 eV. The Stokes-shift reorganization energy λSt is much smaller, resulting in χG ≃ 2. The system is nonergodic, and a large χG lowers the otherwise high activation barrier of electron transfer (see below). The essential role of nonergodicity in protein electron transfer is that it allows lower activation barriers without requiring more negative reaction free energy ΔG to achieve that purpose. Reaction times that are short compared to the time required to sample the landscape of
∞
χ ′′(ω)(dω/ω)
⟨X⟩ib
a
Figure 3. Upper panel: Reorganization energies of the forward (1→2) and backward (2→1) reactions vs the reaction rate k. Also shown are the Coulomb (red) and induction (green) components of the forward reorganization energy. Lower panel: Reorganization energy of water. The shaded areas show the contributions from different Debye relaxation processes to λw(k).
λ (k ) ∝
reaction
(2)
This function of the reaction rate k calculated for the bc1 complex is shown in Figure 3 The theory of nonergodic protein electron transfer outlined above necessitates the knowledge of the loss function χ″(ω), which needs to be equilibrated on the simulation time τsim much longer than the reaction time τobs. If the reaction is dominated by low population of the protonated ISP, the estimated reaction rate4 kexp ≃ 108 s−1 falls in the range of timescales accessible by MD. Alternatively, if the reaction occurs with the slow uphill electron transfer on the millisecond timescale, our present simulations cannot provide a full analysis of this mechanism since the reorganization energy as a function of the observation window does not plateau on 200 ns of simulations (Figure 3). This observation suggests the existence of slow relaxation processes not presently resolved by simulations. Slow relaxation of the protein indeed affects the dynamics of X(t) (see SI). These slow motions contribute 3604
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conformational states of the protein prevent the system from being trapped in the equilibrium state with high λSt and a corresponding high activation barrier. The water component of the reorganization energy λw significantly exceeds ∼1 eV typically reported for redox pairs (Table 1). 24,34 Even though the protein−water crosscorrelations reduce the total reorganization energy (λpw < 0), the reason for a large λw is puzzling. The separation of the overall λw into three relaxation components used to fit the corresponding time relaxation function is shown in the lower panel of Figure 3. The reorganization energy of ∼2 eV is reached on the time-scale of ∼10 ps of dielectric relaxation of water. It further nearly doubles at ∼1 ns relaxation time and adds yet additional 2 eV from a ∼ 10 ns relaxation component. Bulk water obviously lacks these slow relaxation processes. However, the protein reorganization energy follows a very similar pattern, which strongly suggests that the long-time relaxation components in λw(k) arise from collective motions of the protein−water interface. The slow dynamics of the interfacial water are therefore driven by the corresponding slow dynamics of the protein.31,35,36 Have our simulations completely clarified the mechanism of first electron transfer in the bc1 complex? The answer is in the negative for now. We have resolved the puzzle of earlier studies suggesting the need for a large reorganization energy to explain the slow rate.6,10 The reorganization energy is indeed much higher than usually anticipated, and two reorganization energies are in fact required to determine the activation barrier. The reorganization energy as a function of the rate does not saturate (Figure 3) and, therefore, one cannot extrapolate λvar obtained for a 200 ns trajectory to the millisecond time-scale of the electron-first mechanism. Since this time-scale is not attainable by our computational resources, we have not simulated the QH2/ISP configuration for the direct electron transfer. We also currently are not in the position to definitively decide whether proton transfer precedes electron transfer. Despite these concerns, our present results are fairly consistent with the idea of direct electron transfer from quinol to the ISP, without the first step of proton transfer. Our perspective on protein electron transfer, requiring two reorganization energies, can be recast in the form of a model with three independent parameters: λvar, ΔG, and χG. The free energy surfaces of electron transfer in eq 1 can be rewritten in the form (see SI for the derivation) F1(X ) = F2(X ) =
Figure 4. Fi(X) for the forward (i = 1) and backward (i = 2) electron transfer (eq 3) with ΔG = 0.21 eV, λvar = 5 eV, and χG = 2.
0.5, is consistent with typical reorganization and activation entropies observed experimentally and in computer simulations.37 The endergonic ΔG puts the backward reaction in the microseconds range. However, according to our simulations, this reaction is prevented by a faster, on the time-scale of ≃20 ns (see Figure S7 in SI), conformational transition of the complex, which nearly doubles the distance between QH and Fe2S2 (see SI). We note that back electron transfer on the nanoseconds time-scale, as suggested in the proton-first mechanism,4 would compete with this conformational transition. The back electron transfer should therefore be sufficiently slow to allow the conformational transition to occur. To summarize, membrane-bound protein complexes present a “Coulomb soup” physically distinct from common redox systems made of rigid donor−acceptor molecules and studied by solution redox chemistry.24 A large number of charged/polar surface residues, complex surface topology,38 and surface waters polarized by water-exposed charges create conditions for highamplitide electrostatic fluctuations. These also include strong modulation of the induction interactions in flexible complexes, such as the bc1 complex studied here. The reorganization energy λvar quantifies the statistical spread of electrostatic fluctuations projected on the electron transfer reaction coordinate. The dynamics of these fluctuations are highly dispersive, leaving some of the nuclear relaxation processes dynamically frozen on time-scales of many biologically significant processes. The inability to establish an equilibrium canonical ensemble requires at least two modifications to traditional theories of electron transfer: (i) two separate reorganization energies (or a combination of one reorganization energy and the parameter χG, eq 3) and (ii) dynamical restrictions imposed on the effective reorganization energy entering the rates, eq 2. The evolutionary optimization of the bc1 complex, and, potentially, of the entire biological energy chain,1 has taken advantage of static and dynamical controls provided by the proposed picture of protein electron transfer. While the breadth of fluctuations can be controlled by the distribution of the protein surface charge, determined by the sequence, the dynamical control of the activation barrier is achieved by tuning the rate of nuclear reorganization to the rate of the reaction.
(X − λ var /χG − χG ΔG)2 4λ var (X + λ var /χG − χG ΔG)2 4λ var
+ ΔG
(3)
The crossing F1(0) = F2(0) at X = 0 defines the activation barriers for the forward and backward reactions shown in Figure 4. The free energy of activation is unknown experimentally since only the activation enthalpy of Ha ≃ 0.65 eV has been reported.10 However, our simulation parameters directly yield the experimental rate constant4,6 of ∼103 s−1 without further adjustments when Dutton’s parametrization for the electron-transfer tunneling probability8,9 is applied (see SI). The activation free energy of the forward reaction Fa = F1(0) = 0.43 eV can be combined with the experimental enthalpy to give the activation entropy of TSa = 0.22 eV. This value, and more specifically the ratio TSa/Fa ≃
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ASSOCIATED CONTENT
S Supporting Information *
Simulation protocols and calculation procedures for the reaction rates. This material is available free of charge via the Internet at http://pubs.acs.org. 3605
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
This research was supported by the National Science Foundation (MCB-1157788) and by startup funding from Yeshiva University (DNL). CPU time was provided by the National Science Foundation through XSEDE resources (TGMCB080116N and TG-MCB120160). We are grateful to Anthony Crofts for comments on the manuscript.
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