Simulation and Modeling of the Rhodobacter sphaeroides Bacterial Reaction Center II: Primary Charge Separation

Tools for analyzing protonation states and for tracing proton transfer pathways with examples from the Rb. sphaeroides photosynthetic reaction centers

Protons participate in many reactions. In proteins, protons need paths to move in and out of buried active sites. The vectorial movement of protons coupled to electron transfer reactions establishes the transmembrane electrochemical gradient used for many reactions, including ATP synthesis. Protons move through hydrogen bonded chains of waters and hydroxy side chains via the Grotthuss mechanism and by proton binding and release from acidic and basic residues. MCCE analysis shows that proteins exist in a large number of protonation states. Knowledge of the equilibrium ensemble can provide a rational basis for setting protonation states in simulations that fix them, such as molecular dynamics (MD). The proton path into the Q_B site in the bacterial reaction centers (RCs) of Rb. sphaeroides is analyzed by MD to provide an example of the benefits of using protonation states found by the MCCE program. A tangled web of side chains and waters link the cytoplasm to Q_B. MCCE analysis of snapshots from multiple trajectories shows that changing the input protonation state of a residue in MD biases the trajectory shifting the proton affinity of that residue. However, the proton affinity of some residues is more sensitive to the input structure. The proton transfer networks derived from different trajectories are quite robust. There are some changes in connectivity that are largely restricted to the specific residues whose protonation state is changed. Trajectories with Q_B^•- are compared with earlier results obtained with Q_B [Wei et. al Photosynthesis Research volume 152, pages153-165 (2022)] showing only modest changes. While introducing new methods the study highlights the difficulty of establishing the connections between protein conformation.

Electronic Polarization Effect of the Water Environment in Charge-Separated Donor-Acceptor Systems: An Effective Fragment Potential Model Study

The electronic polarization (POL) of the surrounding environment plays a crucial role in the energetics of charge-separated systems. Here, the mechanism of POL in charge-separated systems is studied using a combined quantum mechanical and effective fragment potential (QM/EFP) method. In particular, the POL effect caused by charge separation (CS) is investigated at the atomic level by decomposition into the POL at each polarizability point. The relevance of the electric field generated by the CS is analyzed in detail. The model systems investigated are Na⁺-Cl^- and guanine-thymine solvated in water. The dominant part of the POL arises from solvent molecules close to the donor (D) and acceptor (A) units. At short D-A distances, the electric field shows both positive and negative interferences. The former case enhances the POL energy. At longer distances, the interference is weakened, and the local electric field determines the POL energy.

A Database of Force-Field Parameters, Dynamics, and Properties of Antimicrobial Compounds

We present an on-line database of all-atom force-field parameters and molecular properties of compounds with antimicrobial activity (mostly antibiotics and some beta-lactamase inhibitors). For each compound, we provide the General Amber Force Field parameters for the major species at physiological pH, together with an analysis of properties of interest as extracted from µs-long molecular dynamics simulations in explicit water solution. The properties include number and population of structural clusters, molecular flexibility, hydrophobic and hydrophilic molecular surfaces, the statistics of intraand inter-molecular H-bonds, as well as structural and dynamical properties of solvent molecules within first and second solvation shells. In addition, the database contains several key molecular parameters, such as energy of the frontier molecular orbitals, vibrational properties, rotational constants, atomic partial charges and electric dipole moment, computed by Density Functional Theory. The present database (to our knowledge the first extensive one including dynamical properties) is part of a wider project aiming to build-up a database containing structural, physico-chemical and dynamical properties of medicinal compounds using different force-field parameters with increasing level of complexity and reliability. The database is freely accessible at http://www.dsf.unica.it/translocation/db/.

Charge transfer in E. coli DNA photolyase: understanding polarization and stabilization effects via QM/MM simulations

We study fast hole transfer events in E. coli DNA photolyase, a key step in the photoactivation process, using a multiscale computational method that combines nonadiabatic propagation schemes and linear-scaling quantum chemical methods with molecular mechanics force fields. This scheme allows us to follow the time-dependent evolution of the electron hole in an unbiased fashion; that is, no assumptions about hole wave function localization, time scale separation, or adiabaticity of the process have to be made beforehand. DNA photolyase facilitates an efficient long-range charge transport between its flavin adenine dinucleotide (FAD) cofactor and the protein surface via a chain of evolutionary conserved Trp residues on the sub-nanosecond time scale despite the existence of multiple potential trap states. By including a large number of aromatic residues along the charge transfer pathway into the quantum description, we are able to identify the main pathway among alternative possible routes. The simulations show that charge transfer, which is extremely fast in this protein, occurs on the same time scale as the protein response to the electrostatic changes; that is, time-scale separation as often presupposed in charge transfer studies seems to be inappropriate for this system. Therefore, coupled equations of motion, which propagate electrons and nuclei simultaneously, appear to be necessary. The applied computational model is shown to capture the essentials of the reaction kinetics and thermodynamics while allowing direct simulations of charge transfer events on their natural time scale.

In-silico assessment of protein-protein electron transfer. a case study: cytochrome c peroxidase--cytochrome c

The fast development of software and hardware is notably helping in closing the gap between macroscopic and microscopic data. Using a novel theoretical strategy combining molecular dynamics simulations, conformational clustering, ab-initio quantum mechanics and electronic coupling calculations, we show how computational methodologies are mature enough to provide accurate atomistic details into the mechanism of electron transfer (ET) processes in complex protein systems, known to be a significant challenge. We performed a quantitative study of the ET between Cytochrome c Peroxidase and its redox partner Cytochrome c. Our results confirm the ET mechanism as hole transfer (HT) through residues Ala194, Ala193, Gly192 and Trp191 of CcP. Furthermore, our findings indicate the fine evolution of the enzyme to approach an elevated turnover rate of 5.47×10⁶ s⁻¹ for the ET between Cytc and CcP through establishment of a localized bridge state in Trp191.

We have developed a protocol capable of describing long-range electron transfer mechanisms at an atomic detailed level. We demonstrate the maturity of the computational techniques in obtaining a quantitative view of the Cytochrome c Peroxidase/Cytochrome c electron transfer process, known to be a significant challenge. In excellent agreement with experimental data, our results allow for the description of the electron transfer pathway, its mechanism and the electron transfer rate at a quantitative level. The overall protocol is free of parameterization and can be applied to any complex electron transfer process. Furthermore, the results reveal the fine enzyme evolution of this protein-protein complex to optimize its electron transfer rate by a localized bridge state.

Efficient algorithms for the simulation of non-adiabatic electron transfer in complex molecular systems: application to DNA

In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom. This allows us to perform unbiased simulations of electron transfer processes in complex media, and the computational scheme is applied to the transfer of a hole in solvated DNA. It turns out that the mean-field approach, where the wave function of the hole is driven into a superposition of adiabatic states, leads to over-delocalization of the hole charge. This problem is avoided using a surface hopping scheme, resulting in a smaller rate of hole transfer. The method is highly efficient due to the on-the-fly computation of the coarse-grained DFT Hamiltonian for the nucleobases, which is coupled to the environment using a QM/MM approach. The computational efficiency and partial parallel character of the methodology make it possible to simulate electron transfer in systems of relevant biochemical size on a nanosecond time scale. Since standard non-polarizable force fields are applied in the molecular-mechanics part of the calculation, a simple scaling scheme was introduced into the electrostatic potential in order to simulate the effect of electronic polarization. It is shown that electronic polarization has an important effect on the features of charge transfer. The methodology is applied to two kinds of DNA sequences, illustrating the features of transfer along a flat energy landscape as well as over an energy barrier. The performance and relative merit of the mean-field scheme and the surface hopping for this application are discussed.

Hopping Maps for Photosynthetic Reaction Centers()

Photosynthetic reaction centers (PRCs) employ multiple-step tunneling (hopping) to separate electrons and holes that ultimately drive the chemistry required for metabolism. We recently developed hopping maps that can be used to interpret the rates and energetics of electron/hole hopping in three-site (donor-intermediate-acceptor) tunneling reactions, including those in PRCs. Here we analyze several key ET reactions in PRCs, including forward ET in the L-branch, and hopping that could involve thermodynamically uphill intermediates in the M-branch, which is ET-inactive in vivo. We also explore charge recombination reactions, which could involve hopping. Our hopping maps support the view that electron flow in PRCs involves strong electronic coupling between cofactors and reorganization energies that are among the lowest in biology (≤ 0.4 eV).

Charge transfer in model peptides: obtaining Marcus parameters from molecular simulation

Charge transfer within and between biomolecules remains a highly active field of biophysics. Due to the complexities of real systems, model compounds are a useful alternative to study the mechanistic fundamentals of charge transfer. In recent years, such model experiments have been underpinned by molecular simulation methods as well. In this work, we study electron hole transfer in helical model peptides by means of molecular dynamics simulations. A theoretical framework to extract Marcus parameters of charge transfer from simulations is presented. We find that the peptides form stable helical structures with sequence dependent small deviations from ideal PPII helices. We identify direct exposure of charged side chains to solvent as a cause of high reorganization energies, significantly larger than typical for electron transfer in proteins. This, together with small direct couplings, makes long-range superexchange electron transport in this system very slow. In good agreement with experiment, direct transfer between the terminal amino acid side chains can be dicounted in favor of a two-step hopping process if appropriate bridging groups exist.

Kinetics of the terminal electron transfer step in cytochrome c oxidase

Cytochrome c oxidase (cco) catalyzes the oxygen reduction reaction in most aerobically respiring organisms. Decades of research have uncovered many aspects relating to structure and function of this enzyme. However, the origin of the unusually fast terminal electron transfer step from heme a to heme a(3) in cco has been the subject of intense discussions over recent years. Yet, no satisfactory consensus has been achieved. Carrying out large-scale molecular dynamics simulation of the protein embedded in a solvated membrane, we obtain a reorganization free energy λ = 0.57 eV. Evaluation of the quantized single-mode rate equation using the experimental rate and the computed reorganization free energy gives a value of 1.5 meV for the average electronic coupling (H(ab)) between heme a and heme a(3). Thus, according to our calculations, the nanosecond electron transfer (ET) is due to a small but significant activation barrier (ΔG(‡) = 0.12 eV) in combination with effective electronic coupling between the two cofactors. The activation free energy is caused predominantly by collective reorganization of protein residues. We show that our results are consistent with the weak temperature dependence observed in experiment if one allows for very minor variations in the donor-acceptor distance as the temperature changes.

Energetics of bacterial photosynthesis

We report the results of extensive numerical simulations and theoretical calculations of electronic transitions in the reaction center of Rhodobacter sphaeroides photosynthetic bacterium. The energetics and kinetics of five electronic transitions related to the kinetic scheme of primary charge separation have been analyzed and compared to experimental observations. Nonergodic formulation of the reaction kinetics is required for the calculation of the rates due to a severe breakdown of the system ergodicity on the time scale of primary charge separation, with the consequent inapplicability of the standard canonical prescription to calculate the activation barrier. Common to all reactions studied is a significant excess of the charge-transfer reorganization energy from the width of the energy gap fluctuations over that from the Stokes shift of the transition. This property of the hydrated proteins, breaking the linear response of the thermal bath, allows the reaction center to significantly reduce the reaction free energy of near-activationless electron hops and thus raise the overall energetic efficiency of the biological charge-transfer chain. The increase of the rate of primary charge separation with cooling is explained in terms of the temperature variation of induction solvation, which dominates the average donor-acceptor energy gap for all electronic transitions in the reaction center. It is also suggested that the experimentally observed break in the Arrhenius slope of the primary recombination rate, occurring near the temperature of the dynamical transition in proteins, can be traced back to a significant drop of the solvent reorganization energy close to that temperature.

Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment

Computer simulations of biological electron transfer reactions are reviewed with a focus on the calculation of reaction free energy (driving force) and reorganization free energy. Then a mixed quantum mechanical/molecular mechanical (QM/MM) approach is described which is designed for computation of these quantities for pure electron transfer reactions with large donor-acceptor separation distances. The method is applied to intra-protein electron transfer in Ru(bpy)(2)(im)His33 cytochrome c and the results compared to experimental data. Several modeling aspects which are important for successful calculation of free energies with QM/MM are discussed in detail.

Energetics and kinetics of primary charge separation in bacterial photosynthesis

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.

Dielectric relaxation in proteins: the computational perspective

In photoexcitation and electron transfer, a new dipole or charge is introduced, and the structure is adjusted. This adjustment represents dielectric relaxation, which is the focus of this review. We concentrate on a few selected topics. We discuss linear response theory, as a unifying framework and a tool to describe non-equilibrium states. We review recent, molecular dynamics simulation studies that illustrate the calculation of dynamic and thermodynamic properties, such as Stokes shifts or reorganization free energies. We then turn to the macroscopic, continuum electrostatic view. We recall the physical definition of a dielectric constant and revisit the decomposition of the free energy into a reorganization and a static term. We review some illustrative continuum studies and discuss some difficulties that can arise with the continuum approach. In conclusion, we consider recent developments that will increase the accuracy and broaden the scope of all these methods.

Reorganization free energies for long-range electron transfer in a porphyrin-binding four-helix bundle protein

To explore the possibility of electron transport in a recently designed four-helix bundle protein (Cochran, F. V.; et al. J. Am. Chem. Soc. 2005, 127, 1346), we have computed the reorganization free energy for (i) oxidation of a single Ru-porphyrin cofactor and (ii) electron self-exchange between two Ru-porphyrin cofactors binding to the solvated protein. Sampling the classical electrostatic energy gap for 20 ns, we find that the fluctuations are well described by Gaussian statistics and obtain reorganization free energies of 0.90 +/- 0.04 eV for oxidation and 1.36 +/- 0.08 eV for self-exchange. The latter is 0.1-0.2 eV higher than the experimental estimate for interprotein electron self-exchange in cytochrome b5. As in natural electron carriers, inner-sphere reorganization is very small, 88 meV for self-exchange between two model cofactors computed at the density functional level of theory. Decomposing the outer-sphere reorganization free energy, we find that the solvent (aqueous ionic solution) is the primary outer-sphere medium for oxidation, contributing 0.60 eV (69%). The protein contributes only 0.27 eV (31%). For self-exchange, the solvent contribution, 0.68 eV (54%), and the protein contribution, 0.59 eV (46%), are almost equally important. The large solvent contribution is due to the slow decay of dipole reorientation of the solvent as a function of distance to the cofactor, implying that the change in the electric field upon electron transfer is not as effectively screened by the four-helix bundle protein. However, ranking the residues according to their free energy contributions, it is suggested that the reorganization free energy can be decreased by about 0.2 eV if two glutamine residues in the vicinity of the cofactor are mutated into less polar amino acids.

Modeling electrostatic effects in proteins

Electrostatic energies provide what is perhaps the most effective tool for structure-function correlation of biological molecules. This review considers the current state of simulations of electrostatic energies in macromolecules as well as the early developments of this field. We focus on the relationship between microscopic and macroscopic models, considering the convergence problems of the microscopic models and the fact that the dielectric 'constants' in semimacroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering a wide range of functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding and protein stability. We conclude by pointing out that, despite the current problems and the significant misunderstandings in the field, there is an overall progress that should lead eventually to quantitative descriptions of electrostatic effects in proteins and thus to quantitative descriptions of the function of proteins.

Rewiring photosynthesis: engineering wrong-way electron transfer in the purple bacterial reaction centre

The purple bacterial reaction centre uses light energy to separate charge across the cytoplasmic membrane, reducing ubiquinone and oxidizing a c-type cytochrome. The protein possesses a macroscopic structural two-fold symmetry but displays a strong functional asymmetry, with only one of two available membrane-spanning branches of cofactors (the so-called A-branch) being used to catalyse photochemical charge separation. The factors underlying this functional asymmetry have been the subject of study for many years but are still not fully understood. Site-directed mutagenesis has been partially successful in rerouting electron transfer along the normally inactive B-branch, allowing comparison of the kinetics of equivalent electron transfer reactions on the two branches. Both the primary and secondary electron transfer steps on the B-branch appear to be considerably slower than their A-branch counterparts. The effectiveness of different mutations in rerouting electron transfer along the B-branch of cofactors is discussed.

Investigation of B-branch electron transfer by femtosecond time resolved spectroscopy in a Rhodobacter sphaeroides reaction centre that lacks the QA ubiquinone

The dynamics of electron transfer in a membrane-bound Rhodobacter sphaeroides reaction centre containing a combination of four mutations were investigated by transient absorption spectroscopy. The reaction centre, named WAAH, has a mutation that causes the reaction centre to assemble without a Q(A) ubiquinone (Ala M260 to Trp), a mutation that causes the replacement of the H(A) bacteriopheophytin with a bacteriochlorophyll (Leu M214 to His) and two mutations that remove acidic groups close to the Q(B) ubiquinone (Glu L212 to Ala and Asp L213 to Ala). Previous work has shown that the Q(B) ubiquinone is reduced by electron transfer along the so-called inactive cofactor branch (B-branch) in the WAAH reaction centre (M.C. Wakeham, M.G. Goodwin, C. McKibbin, M.R. Jones, Photo-accumulation of the P(+)Q(B)(-) radical pair state in purple bacterial reaction centres that lack the Q(A) ubiquinone, FEBS Letters 540 (2003) 234-240). In the present study the dynamics of electron transfer in the membrane-bound WAAH reaction centre were studied by femtosecond transient absorption spectroscopy, and the data analysed using a compartmental model. The analysis indicates that the yield of Q(B) reduction via the B-branch is approximately 8% in the WAAH reaction centre, consistent with results from millisecond time-scale kinetic spectroscopy. Possible contributions to this yield of the constituent mutations in the WAAH reaction centre and the membrane environment of the complex are discussed.

A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region

A phenomenological model of electron transfer reactions in solvents undergoing glass transition is discussed. The reaction constant cuts off slow polarization modes from the spectrum of nuclear thermal motions active on the observation time scale. The arrest of nuclear solvation in turn affects the reaction activation barrier making it dependent on the rate. The resultant rate constant is sought from a self-consistent equation. The model describes well the sharp change in the solvent Stokes shift of optical lines in the glass-transition region. It is also applied to describe the temperature dependence of primary charge separation and reduction of primary pair in photosynthetic reaction centers. The model shows that a weak dependence of the primary charge separation rate on temperature can be explained by dynamical arrest of nuclear solvation on the picosecond time scale of electron transfer. For reduction of primary pair by cytochrome, the model yields a sharp turnover of the reaction kinetics at the transition temperature when nuclear solvation freezes in.

Theoretical Investigation of the “CO in”−“CO out” Isomerization in a [2Fe−2S] Ferredoxin: Free Energy Profiles and Redox States

This paper reports on extensive molecular dynamics simulations (about 40 ns in total) in both the reduced and the oxidized states of Ferredoxin from Cyanobacterium Anabaena PCC7119. These calculations have provided us with the free energy profile of the phi(47) backbone angle which controls the "CO in" to "CO out" transition of Cys46 in the reduced and oxidized Fd7119. Our main motivation has been to identify the time scales involved in the reduction of Fd and single out the amino acid residues crucially affecting the conformational change and, thus, electron transfer. The free energy profiles obtained in this study are relevant to electron transfers in the PSI/Fd7119 and Fd7119/FNR complexes. Our findings based on hydrated ferredoxin simulations are that activated processes are to occur in the protein during electron transfer to and from ferredoxin. The relative stability and the activation barrier of the "CO in" to "CO out" transition can be modulated by the distance between the Ser47 and the Glu94 residues. In our calculations, for short distances, the "CO in" state is favored in the reduced form, whereas for large distances, the "CO out" state becomes increasingly favored. Accordingly, conformational changes in Fd7119 when bound to PSI or FNR can have crucial effects on the kinetics of the electron transfer. Our simulations also show that the hydrogen bond between between Ser47(OG) and Cys46(O) is essential to lock in the "CO out" state. This finding explains why only the Ser47Thr Fd7119 mutant sustains electron transfer activity, as only residues serine and threonine can form a specific hydrogen bond with Cys46(O). Finally, our simulations predict that Phe65 has a large probability of being in close contact with the Cys46(O) at the top of the conformational free energy barrier. This carbonyl/phenyl ring interaction can then facilitate the de-localization of the Fd's electron toward the Pi orbitals of Phe65 aromatic ring which is thought to be crucial to the Fd7119/FNR electron transfer