A Comparison of the Inner-Sphere Reorganization Energies of Cytochromes, Iron−Sulfur Clusters, and Blue Copper Proteins

Structural Determinants of Redox Conduction Favor Robustness over Tunability in Microbial Cytochrome Nanowires

Structural determinants of a 103-fold variation in electrical conductivity for helical homopolymers of tetra-, hexa-, and octa-heme cytochromes (named Omc- E, S, and Z, respectively) from Geobacter sulfurreducens are investigated with the Pathways model for electron tunneling, classical molecular dynamics, and hybrid quantum/classical molecular mechanics. Thermally averaged electronic couplings for through-space heme-to-heme electron transfer in the "nanowires" computed with density functional theory are ≤0.015 eV. Pathways analyses also indicate that couplings match within a factor of 5 for all "nanowires", but some alternative tunneling routes are found involving covalent protein backbone bonds (Omc- S and Z) or propionic acid-ligating His H-bonds on adjacent hemes (OmcZ). Reorganization energies computed from electrostatic vertical energy gaps or a version of the Marcus continuum expression parameterized on the total (donor + acceptor) solvent-accessible surface area typically agree within 20% and fall within the range 0.48-0.98 eV. Reaction free energies in all three "nanowires" are ≤|0.28| eV, even though Coulombic interactions primarily tune the site redox energies by 0.7-1.2 eV. Given the conserved energetic parameters, redox conductivity differs by < 103-fold among the cytochrome "nanowires". Redox currents do not exceed 3.0 × 10-3 pA at a physiologically relevant 0.1 V bias, with the slowest electron transfers being on a (μs) timescale much faster than typical (ms) enzymatic turnovers. Thus, the "nanowires" are proposed to be functionally robust to variations in structure that provide a habitat-customized protein interface. The 30 pA to 30 nA variation in conductivity previously reported from atomic force microscopy experiments is not intrinsic to the structures and/or does not result from the physiologically relevant redox conduction mechanism.

Reorganization energy of electron transfer

The theory of electron transfer reactions establishes the conceptual foundation for redox solution chemistry, electrochemistry, and bioenergetics. Electron and proton transfer across the cellular membrane provide all energy of life gained through natural photosynthesis and mitochondrial respiration. Rates of biological charge transfer set kinetic bottlenecks for biological energy storage. The main system-specific parameter determining the activation barrier for a single electron-transfer hop is the reorganization energy of the medium. Both harvesting of light energy in natural and artificial photosynthesis and efficient electron transport in biological energy chains require reduction of the reorganization energy to allow fast transitions. This review article discusses mechanisms by which small values of the reorganization energy are achieved in protein electron transfer and how similar mechanisms can operate in other media, such as nonpolar and ionic liquids. One of the major mechanisms of reorganization energy reduction is through non-Gibbsian (nonergodic) sampling of the medium configurations on the reaction time. A number of alternative mechanisms, such as electrowetting of active sites of proteins, give rise to non-parabolic free energy surfaces of electron transfer. These mechanisms, and nonequilibrium population of donor-acceptor vibrations, lead to a universal phenomenology of separation between the Stokes shift and variance reorganization energies of electron transfer.

Bioinorganic Chemistry on Electrodes: Methods to Functional Modeling

One of the major goals of bioinorganic chemistry has been to mimic the function of elegant metalloenzymes. Such functional modeling has been difficult to attain in solution, in particular, for reactions that require multiple protons and multiple electrons (nH⁺/ne^-). Using a combination of heterogeneous electrochemistry, electrode and molecule design one may control both electron transfer (ET) and proton transfer (PT) of these nH⁺/ne^- reactions. Such control can allow functional modeling of hydrogenases (H⁺ + e^- → 1/2 H₂), cytochrome c oxidase (O₂ + 4 e^- + 4 H⁺ → 2 H₂O), monooxygenases (RR'CH₂ + O₂ + 2 e^- + 2 H⁺ → RR'CHOH + H₂O) and dioxygenases (S + O₂ → SO₂; S = organic substrate) in aqueous medium and at room temperatures. In addition, these heterogeneous constructs allow probing unnatural bioinspired reactions and estimation of the inner- and outer-sphere reorganization energy of small molecules and proteins.

Second Sphere Effects on Oxygen Reduction and Peroxide Activation by Mononuclear Iron Porphyrins and Related Systems

Activation and reduction of O₂ and H₂O₂ by synthetic and biosynthetic iron porphyrin models have proved to be a versatile platform for evaluating second-sphere effects deemed important in naturally occurring heme active sites. Advances in synthetic techniques have made it possible to install different functional groups around the porphyrin ligand, recreating artificial analogues of the proximal and distal sites encountered in the heme proteins. Using judicious choices of these substituents, several of the elegant second-sphere effects that are proposed to be important in the reactivity of key heme proteins have been evaluated under controlled environments, adding fundamental insight into the roles played by these weak interactions in nature. This review presents a detailed description of these efforts and how these have not only demystified these second-sphere effects but also how the knowledge obtained resulted in functional mimics of these heme enzymes.

Contributions to cytochrome c inner- and outer-sphere reorganization energy

Cytochromes c are small water-soluble proteins that catalyze electron transfer in metabolism and energy conversion processes. Hydrogenobacter thermophilus cytochrome c₅₅₂ presents a curious case in displaying fluxionality of its heme axial methionine ligand; this behavior is altered by single point mutation of the Q64 residue to N64 or V64, which fixes the ligand in a single configuration. The reorganization energy (λ) of these cytochrome c₅₅₂ variants is experimentally determined using a combination of rotating disc electrochemistry, chronoamperometry and cyclic voltammetry. The differences between the λ determined from these complementary techniques helps to deconvolute the contribution of the active site and its immediate environment to the overall λ (λ_Total). The experimentally determined λ values in conjunction with DFT calculations indicate that the differences in λ among the protein variants are mainly due to the differences in contributions from the protein environment and not just inner-sphere λ. DFT calculations indicate that the position of residue 64, responsible for the orientation of the axial methionine, determines the geometric relaxation of the redox active molecular orbital (RAMO). The orientation of the RAMO with respect to the heme is key to determining electron transfer coupling (H_AB) which results in higher ET rates in the wild-type protein relative to the Q64V mutant despite a 150 mV higher λ_Total in the former.

Efficient delocalization of the redox-active molecular orbital (RAMO) in HtWT results in an increase in H_AB value which in turn accelerates the electron transfer (ET) rate in spite of the higher reorganization energy (λ) than the HtQ64V mutant.

Methemoglobin formation in mutant hemoglobin α chains: electron transfer parameters and rates

Hemoglobin-mediated transport of dioxygen (O₂) critically depends on the stability of the reduced (Fe²⁺) form of the heme cofactors. Some protein mutations stabilize the oxidized (Fe³⁺) state (methemoglobin, Hb M), causing methemoglobinemia, and can be lethal above 30%. The majority of the analyses of factors influencing Hb oxidation are retrospective and give insights only for inner-sphere mutations of heme (His58, His87). Herein, we report the first all-atom molecular dynamics simulations on both redox states and calculations of the Marcus electron transfer (ET) parameters for the α chain Hb oxidation and reduction rates for Hb M. The Hb wild-type (WT) and most of the studied α chain variants maintain globin structure except the Hb M Iwate (H87Y). The mutants forming Hb M tend to have lower redox potentials and thus stabilize the oxidized (Fe³⁺) state (in particular, the Hb Miyagi variant with K61E mutation). Solvent reorganization (λ_solv 73-96%) makes major contributions to reorganization free energy, whereas protein reorganization (λ_prot) accounts for 27-30% except for the Miyagi and J-Buda variants (λ_prot ∼4%). Analysis of heme-solvent H-bonding interactions among variants provide insights into the role of Lys61 residue in stabilizing the Fe²⁺ state. Semiclassical Marcus ET theory-based calculations predict experimental k_ET for the Cyt b5-Hb complex and provide insights into relative reduction rates for Hb M in Hb variants. Thus, our methodology provides a rationale for the effect of mutations on the structure, stability, and Hb oxidation reduction rates and has potential for identification of mutations that result in methemoglobinemia.

Why Do Most Aromatics Fail to Support Hole Hopping in the Cytochrome c Peroxidase-Cytochrome c Complex?

Electron transport through aromatic species (especially tryptophan and tyrosine) plays a central role in water splitting, redox signaling, oxidative damage protection, and bioenergetics. The cytochrome c peroxidase (CcP)-cytochrome c (Cc) complex (CcP:Cc) is used widely to study interprotein electron transfer (ET) mechanisms. Tryptophan 191 (Trp191) of CcP supports hole hopping charge recombination in the CcP:Cc complex. Experimental studies find that when Trp191 is substituted by tyrosine, phenylalanine, or redox-active aniline derivatives bound in the W191G cavity, enzymatic activity and charge recombination rates both decrease. Theoretical analysis of these CcP:Cc complexes finds that the ET kinetics depend strongly on the chemistry of the modified Trp site. The computed electronic couplings in the W191F and W191G species are orders of magnitude smaller than in the native protein, due largely to the absence of a hopping intermediate and the large tunneling distance. Small molecules bound in the W191G cavity are weakly coupled electronically to the Cc heme, and the structural disorder of the guest molecule in the binding pocket may contribute further to the lack of enzymatic activity. The couplings in W191Y are not substantially weakened compared to the native species, but the redox potential difference for tyrosine vs tryptophan oxidation accounts for the slower rate in the Tyr mutant. Thus, theoretical analysis explains why only the native Trp supports rapid hole hopping in the CcP:Cc complex. Favorable free energies and electronic couplings are essential for establishing an efficient hole hopping relay in this protein-protein complex.

Structural rigidity accelerates quantum decoherence and extends carrier lifetime in porphyrin nanoballs: a time domain atomistic simulation

Nonradiative electron-hole (e-h) recombination is the primary source of energy loss in photovoltaic cells and inevitably, it competes with the charge transfer process, leading to poor device performance. Therefore, much attention has to be paid for delaying such processes; increasing the excitonic lifetime may be a solution for this. Using the real-time, density functional tight-binding theory (DFTB) combined with nonadiabatic molecular dynamics (NAMD) simulations, we demonstrate the exciton relaxation phenomena of different metal-centered porphyrin nanoballs, which are supposed to be very important for the light-harvesting process. It has been revealed that the carrier recombination rate gradually decreases with the increase in the molecular stiffness by introducing metal-coordinating templating agents into the nanoball. Our simulation demonstrates that the lower atomic fluctuations lead to poorer electron-phonon nonadiabatic coupling in association with weak phonon modes and these as a whole are responsible for shorter quantum coherence and hence delayed recombination events. Our analysis is in good agreement with the recent experimental observation. By replacing the Zn metal center with a heavier Cd atom, a similar trend is observed; however, the rate slows down abruptly. The present simulation study provides the fundamental mechanism in detail behind the undesired energy loss during exciton recombination and suggests a rational design of impressive nanosystems for future device fabrication.

Importance of the iron-sulfur component and of the siroheme modification in the resting state of sulfite reductase

The active site of sulfite reductase (SiR) consists of an unusual siroheme-Fe₄S₄ assembly coupled via a cysteinate sulfur, and serves for multi-electron reduction reactions. Clear explanations have not been demonstrated for the reasons behind the choice of siroheme (vs. other types of heme) or for the single-atom coupling to an Fe₄S₄ center (as opposed to simple adjacency or to coupling via chains consisting of more than one atom). Possible explanations for these choices have previously been invoked, relating to the control of the spin state of the substrate-binding (siro)heme iron, modulation of the trans effect of the (Fe₄S₄-bound) cysteinate, or modulation of the redox potential. Reported here is a density functional theory (DFT) investigation of the structural interplay (in terms of geometry, molecular orbitals and magnetic interactions) between the siroheme and the Fe₄S₄ center as well as the importance of the covalent modifications within siroheme compared to the more common heme b, aiming to verify the role of the siroheme modification and of the Fe₄S₄ cluster at the SiR active site, with focus on previously-formulated hypotheses (geometrical/sterics, spin state, redox and electron-transfer control). A calibration of various DFT methods/variants for the correct description of ground state spin multiplicity is performed using a set of problematic cases of bioinorganic Fe centers; out of 11 functionals tested, M06-L and B3LYP offer the best results - though none of them correctly predict the spin state for all test cases. Upon examination of the relative energies of spin states, reduction potentials, energy decomposition (electrostatic, exchange-repulsion, orbital relaxation, correlation and dispersion interactions) and Mayer bond indices in SiR models, the following main roles of the siroheme and cubane are identified: (1) the cubane cofactor decreases the reduction potential of the siroheme and stabilizes the siroheme-cysteine bond interaction, and (2) the siroheme removes the quasi-degeneracy between the intermediate and high-spin states found in ferrous systems by preserving the latter as ground state; the higher-spin preference and the increased accessibility of multiple spin states are likely to be important in selective binding of the substrate and of the subsequent reaction intermediates, and in efficient changes in redox states throughout the catalytic cycle.

Kinetics and Energetics of Phylloquinone Reduction in Photosystem I: Insight From Modeling of the Site Directed Mutants

Two phylloquinone molecules (A ₁), one being predominantly coordinated by PsaA subunit residues (A _1A) the other by those of PsaB (A _1B), act as intermediates in the two parallel electron transfer chains of Photosystem I. The oxidation kinetics of the two phyllosemiquinones by the iron-sulfur cluster F_X differ by approximately one order of magnitude, with A 1 A - being oxidized in about 200 ns and A 1 B - in about 20 ns. These differences are generally explained in terms of asymmetries in the driving force for F_X reduction on the two electron transfer chains. Site directed mutations of conserved amino acids composing the A ₁ binding site have been engineered on both reaction center subunits, and proved to affect selectively the oxidation lifetime of either A 1 A - , for PsaA mutants, or A 1 B - , for PsaB mutants. The mutation effects are here critically reviewed, also by novel modeling simulations employing the tunneling formalism to estimate the electron transfer rates. Three main classes of mutation effects are in particular addressed: (i) those leading to an acceleration, (ii) those leading to a moderated slowing (~5-folds), and (iii) those leading to a severe slowing (>20-folds) of the kinetics. The effect of specific amino acid perturbations contributing to the poising of the phylloquinones redox potential and, in turn, to PSI functionality, is discussed.

Inter- and Intramolecular Electron Transfer in Copper Complexes: Electronic Entatic State with Redox-Active Guanidine Ligands

Fast and efficient electron transfer in blue copper proteins is realized by a structural harmonization between the Cu^I and Cu^II complex pair ("entatic state" model). Herein, we present now a Cu^I /Cu^II complex pair with redox-active guanidine ligands showing almost perfect match between both redox states. By modifying the ligand electron donor strength, the redox chemistry of the copper complex can be controlled to be either metal-centered or to cross the borderline to ligand-centered. This work is the first systematic study of complexes with redox-active ligands within the concept of the entatic state.

Theory and Electrochemistry of Cytochrome c

Extensive simulations of cytochrome c in solution are performed to address the apparent contradiction between large reorganization energies of protein electron transfer typically reported by atomistic simulations and much smaller values produced by protein electrochemistry. The two sets of data are reconciled by deriving the activation barrier for electrochemical reaction in terms of an effective reorganization energy composed of half the Stokes shift (characterizing the medium polarization in response to electron transfer) and the variance reorganization energy (characterizing the breadth of electrostatic fluctuations). This effective reorganization energy is much smaller than each of the two components contributing to it and is fully consistent with electrochemical measurements. Calculations in the range of temperatures between 280 and 360 K combine long, classical molecular dynamics simulations with quantum calculations of the protein active site. The results agree with the Arrhenius plots for the reaction rates and with cyclic voltammetry of cytochrome c immobilized on self-assembled monolayers. Small effective reorganization energy, and the resulting small activation barrier, is a general phenomenology of protein electron transfer allowing fast electron transport within biological energy chains.

Mechanism of the Primary Charge Transfer Reaction in the Cytochrome bc1 Complex

The bc₁ complex is a critical enzyme for the ATP production in photosynthesis and cellular respiration. Its biochemical function relies on the so-called Q-cycle, which is well established and operates via quinol substrates that bind inside the protein complex. Despite decades of research, the quinol-protein interaction, which initiates the Q-cycle, has not yet been completely described. Furthermore, the initial charge transfer reactions of the Q-cycle lack a physical description. The present investigation utilizes classical molecular dynamics simulations in tandem with quantum density functional theory calculations, to provide a complete and consistent quantitative description of the primary events that occur within the bc₁ complex upon quinol binding. In particular, the electron and proton transfer reactions that trigger the Q-cycle in the bc₁ complex from Rhodobacter capsulatus are studied. The coupled nature of these charge transfer reactions was revealed by obtaining the transition energy path connecting configurations of the Q_o-site prior and after the transfers. The analysis of orbitals and partial charge distribution of the different states of the Q_o-site has further supported the conclusion. Finally, key structural elements of the bc₁ complex that trigger the charge transfer reactions were established, manifesting the importance of the environment in the process, which is furthermore evidenced by free energy calculations.

Spontaneous Binding of Molecular Oxygen at the Qo-Site of the bc1 Complex Could Stimulate Superoxide Formation

A key part of the respiratory and photosynthetic pathways is the bc1 protein complex embedded in the inner membrane of mitochondria and the plasma membrane of photosynthetic bacteria. The protein complex pumps protons across the membrane to maintain an electrostatic potential, which is in turn used to drive ATP synthesis. This molecular machinery, however, is suspected to be a source of superoxide, which is toxic to the cell, even in minuscular quantities, and believed to be a factor in aging. Through molecular dynamics simulations, we investigate here the migration of molecular oxygen in the bc1 complex in order to identify possible reaction sites that could lead to superoxide formation. It is found, in particular, that oxygen penetrates spontaneously the Qo binding site of the bc1 complex in the presence of an intermediate semiquinone radical, thus making the Qo-site a strong candidate for being a center of superoxide production.

Asn47 and Phe114 modulate the inner sphere reorganization energies of type zero copper proteins

The geometric structures and electron transfer properties of type 1 Cu proteins are reasonably understood at the molecular level (E. I. Solomon and R. G. Hadt, Coord. Chem. Rev., 2011, 255, 774-789, J. J. Warren, K. M. Lancaster, J. H. Richards and H. B. Gray, J. Inorg. Biochem., 2012, 115, 119-126). Much understanding of type 1 copper electron transfer reactivity has come from site directed mutagenesis studies. For example, artificial "type zero" Cu-centres constructed in cupredoxin-azurin have showcased the capacity of outer-sphere hydrogen bonding networks to enhance Cu II/I electron transfer reactivity. In this paper, we have elaborated on earlier kinetics and electronic structural studies of type zero Cu by calculating the inner sphere reorganization energies of type 1, type 2, and type zero Cu proteins using density functional theory (DFT). Although the choice of density functionals for copper systems is not straightforward, we have benchmarked the density functionals against the recently reported ESI-PES data for two synthetic copper models (S. Niu, D.-L. Huang, P. D. Dau, H.-T. Liu, L.-S. Wang and T. J. Ichiye, Chem. Theory Comput., 2014, 10, 1283). For the Cu proteins, our calculations predict that changes in the coordination number upon metal reduction lead to large inner sphere reorganization energies for type 2 Cu sites, whereas retention in the coordination number is observed for type zero Cu sites. These variations in the coordination number are modulated by the outer-sphere coordinating residues Asn47 and Phe114, which are involved in hydrogen bonding with the Asp112 side chain.

Stereoelectronic effects of porphyrin ligand on the oxygen transfer efficiency of high valent manganese-oxo porphyrin species: A DFT study

The structure and properties of the N[Formula: see text]–Mn–O bonds of high valent manganese-oxo of the second and third generation porphyrins in the presence of imidazole have been studied by means of density functional (DFT) method with 6-31G* basis set in the gas phase as well as water solution. The geometric structures, frontier molecular orbitals, thermodynamic parameters, aromaticity indices and physical properties such as chemical potential and chemical hardness of [(TPP)(ImH)MnO][Formula: see text] and its derivatives were calculated. The obtained results showed that [(TPP)(ImH)MnO][Formula: see text] bearing halogen atoms at the [Formula: see text]-pyrrole positions had a saddle conformation with low Mn–O strength. The electron density ([Formula: see text] and Laplacian ([Formula: see text] properties at critical points of the N[Formula: see text]–Mn–O bonds, estimated by AIM calculations, indicate that Mn–O bonds in third generation porphyrins have lower [Formula: see text] and Mn–N[Formula: see text] distances have higher [Formula: see text] than the second generation ones. The calculations of aromaticity indices for chelated rings at the porphyrin center show that HOMA and NICS in third generation porphyrins are generally lower than that of second ones which is in agreement with their saddle conformation. These results are supported by natural bond orbital (NBO) analysis.

Rates and Routes of Electron Transfer of [NiFe]-Hydrogenase in an Enzymatic Fuel Cell

Hydrogenase enzymes are being used in enzymatic fuel cells immobilized on a graphite or carbon electrode surface, for example. The enzyme is used for the anodic oxidation of molecular hydrogen (H2) to produce protons and electrons. The association and orientation of the enzyme at the anode electrode for a direct electron transfer is not completely resolved. The distal FeS-cluster in [NiFe]-hydrogenases contains a histidine residue which is known to play a critical role in the intermolecular electron transfer between the enzyme and the electrode surface. The [NiFe]-hydrogenase graphite electrode association was investigated using Brownian Dynamics simulations. Residues that were shown to be in proximity to the electrode surface were identified (His184, Ser196, Glu461, Glu464), and electron transfer routes connecting the distal FeS-cluster with the surface residues were investigated. Several possible pathways for electron transfer between the distal FeS-cluster and the terminal amino acid residues were probed in terms of their rates of electron transfer using DFT methods. The reorganization energies λ of the distal iron-sulfur cluster and coronene as a molecular model for graphite were calculated. The reorganization energy of the distal (His)(Cys)3 cluster was found to be not very different from that of a standard cubane clusters with a (Cys)4 coordination. Electronic coupling matrix elements and rates of electron transfer for the different pathways were calculated according to the Marcus equation. The rates for glutamate-mediated electrode binding were found to be incompatible with experimental data. A direct electron transfer from the histidine ligand of the distal FeS-cluster to the electrode yielded rates of electron transfer in excellent agreement with experiment. A second pathway, however, from the distal FeS-cluster to the Ser196 residue was found to be equally efficient and feasible.

The Importance of the MM Environment and the Selection of the QM Method in QM/MM Calculations: Applications to Enzymatic Reactions

In this chapter, we discuss the influence of an anisotropic protein environment on the reaction mechanisms of saccharopine reductase and uroporphyrinogen decarboxylase, respectively, via the use of a quantum mechanical and molecular mechanical (QM/MM) approach. In addition, we discuss the importance of selecting a suitable DFT functional to be used in a QM/MM study of a key intermediate in the mechanism of 8R-lipoxygenase, a nonheme iron enzyme. In the case of saccharopine reductase, while the enzyme utilizes a substrate-assisted catalytic pathway, it was found that only through treating the polarizing effect of the active site, via the use of an electronic embedding formalism, was agreement with experimental kinetic data obtained. Similarly, in the case of uroporphyrinogen decarboxylase, the effect of the protein environment on the catalytic mechanism was found to be such that the calculated rate-limiting barrier is in good agreement with related experimentally determined values for the first decarboxylation of the substrate. For 8R-lipoxygenase, it was found that the geometries and energies of the multicentered open-shell intermediate complexes formed during the mechanism are quite sensitive to the choice of the density functional theory method. Thus, while density functional theory has become the method of choice in QM/MM studies, care must be taken in the selection of a particular high-level method.

A DFT investigation of axial N-donor ligands effects on the high valent manganese-oxo meso-tetraphenyl porphyrin

The effect of different electronic and structural nitrogen donors (L) on the N ( ax )- Mn - O properties in the high valent manganese-oxo meso-tetraphenylporphyrin intermediate is investigated by the density functional B3LYP method with 6-31g* basis set. The geometric structures, frontier molecular orbitals, thermodynamic parameters and physical properties such as chemical potential and chemical hardness of [( TPP )( L ) MnO ]+ complexes in the gas phase as well as water solution are calculated. Our theoretical results confirm that the Mn - O distances in [( TPP )( L ) MnO ]+ species decrease by replacing imidazoles with pyridines, amins as well as electron-poor and hindered nitrogen donors resulting from extending the Mn – N ( ax ) bonds. These results are supported by vibrational frequencies, atoms in molecules (AIM) and natural bond orbital (NBO) analysis. It is worth mentioning that the co-catalytic activity trend of different nitrogen donors observed experimentally in the presence of title Mn porphyrin is consistent with the calculated Mn – N ( ax ) and Mn – O bond lengths in this work.

Mechanism of primary and secondary ion-radical pair formation in photosystem I complexes

The mechanisms of the ultrafast charge separation in reaction centers of photosystem I (PS I) complexes are discussed. A kinetic model of the primary reactions in PS I complexes is presented. The model takes into account previously calculated values of redox potentials of cofactors, reorganization energies of the primary P700(+)A0(-) and secondary P700(+)A1(-) ion-radical pairs formation, and the possibility of electron transfer via both symmetric branches A and B of redox-cofactors. The model assumes that the primary electron acceptor A0 in PS I is represented by a dimer of chlorophyll molecules Chl2A/Chl3A and Chl2B/Chl3B in branches A and B of the cofactors. The characteristic times of formation of P700(+)A0(-) and P700(+)A1(-) calculated on the basis of the model are close to the experimental values obtained by pump-probe femtosecond absorption spectroscopy. It is demonstrated that a small difference in the values of redox potentials between the primary electron acceptors A0A and A0B in branches A and B leads to asymmetry of the electron transfer in a ratio of 70 : 30 in favor of branch A. The secondary charge separation is thermodynamically irreversible in the submicrosecond range and is accompanied by additional increase in asymmetry between the branches of cofactors of PS I.

Identification of ubiquinol binding motifs at the Qo-site of the cytochrome bc1 complex

Enzymes of the bc₁ complex family power the biosphere through their central role in respiration and photosynthesis. These enzymes couple the oxidation of quinol molecules by cytochrome c to the transfer of protons across the membrane, to generate a proton-motive force that drives ATP synthesis. Key for the function of the bc₁ complex is the initial redox process that involves a bifurcated electron transfer in which the two electrons from a quinol substrate are passed to different electron acceptors in the bc₁ complex. The electron transfer is coupled to proton transfer. The overall mechanism of quinol oxidation by the bc₁ complex is well enough characterized to allow exploration at the atomistic level, but details are still highly controversial. The controversy stems from the uncertain binding motifs of quinol at the so-called Q_o active site of the bc₁ complex. Here we employ a combination of classical all atom molecular dynamics and quantum chemical calculations to reveal the binding modes of quinol at the Q_o-site of the bc₁ complex from Rhodobacter capsulatus. The calculations suggest a novel configuration of amino acid residues responsible for quinol binding and support a mechanism for proton-coupled electron transfer from quinol to iron–sulfur cluster through a bridging hydrogen bond from histidine that stabilizes the reaction complex.

Importance of polarization effect in the study of metalloproteins: application of polarized protein specific charge scheme in predicting the reduction potential of azurin

Molecular dynamics (MD) simulation is commonly used in the study of protein dynamics, and in recent years, the extension of MD simulation to the study of metalloproteins is gaining much interest. Choice of force field is crucial in MD studies, and the inclusion of metal centers complicates the process of accurately describing the electrostatic environment that surrounds the redox centre. Herein, we would like to explore the importance of including electrostatic contribution from both protein and solvent in the study of metalloproteins. MD simulations with the implementation of thermodynamic integration will be conducted to model the reduction process of azurin from Pseudomonas aeruginosa. Three charge schemes will be used to derive the partial charges of azurin. These charge schemes differ in terms of the amount of immediate environment, respective to copper, considered during charge fitting, which ranges from the inclusion of copper and residues in the first coordination sphere during density functional theory charge fitting to the comprehensive inclusion of protein and solvent effect surrounding the metal centre using polarized protein-specific charge scheme. From the simulations conducted, the relative reduction potential of the mutated azurins respective to that of wild-type azurin (ΔEcal) were calculated and compared with experimental values. The ΔEcal approached experimental value with increasing consideration of environmental effect hence substantiating the importance of polarization effect in the study of metalloproteins. This study also attests the practicality of polarized protein-specific charge as a computational tool capable of incorporating both protein environment and solvent effect into MD simulations.

Molecular dynamics study of the primary charge separation reactions in Photosystem I: effect of the replacement of the axial ligands to the electron acceptor A₀

Molecular dynamics (MD) calculations, a semi-continuum (SC) approach, and quantum chemistry (QC) calculations were employed together to investigate the molecular mechanics of ultrafast charge separation reactions in Photosystem I (PS I) of Thermosynechococcus elongatus. A molecular model of PS I was developed with the aim to relate the atomic structure with electron transfer events in the two branches of cofactors. A structural flexibility map of PS I was constructed based on MD simulations, which demonstrated its rigid hydrophobic core and more flexible peripheral regions. The MD model permitted the study of atomic movements (dielectric polarization) in response to primary and secondary charge separations, while QC calculations were used to estimate the direct chemical effect of the A(0A)/A(0B) ligands (Met or Asn in the 688/668 position) on the redox potential of chlorophylls A(0A)/A(0B) and phylloquinones A(1A)/A(1B). A combination of MD and SC approaches was used to estimate reorganization energies λ of the primary (λ₁) and secondary (λ₂ ) charge separation reactions, which were found to be independent of the active branch of electron transfer; in PS I from the wild type, λ₁ was estimated to be 390 ± 20mV, while λ₂ was estimated to be higher at 445 ± 15mV. MD and QC approaches were used to describe the effect of substituting Met688(PsaA)/Met668(PsaB) by Asn688(PsaA)/Asn668(PsaB) on the energetics of electron transfer. Unlike Met, which has limited degrees of freedom in the site, Asn was found to switch between two relatively stable conformations depending on cofactor charge. The introduction of Asn and its conformation flexibility significantly affected the reorganization energy of charge separation and the redox potentials of chlorophylls A(0A)/A(0B) and phylloquinones A(1A)/A(1B), which may explain the experimentally observed slowdown of secondary electron transfer in the M688N(PsaA) variant. This article is part of a special issue entitled: photosynthesis research for sustainability: keys to produce clean energy.

The role of protein dynamics and thermal fluctuations in regulating cytochrome c/cytochrome c oxidase electron transfer

In this overview we present recent combined electrochemical, spectroelectrochemical, spectroscopic and computational studies from our group on the electron transfer reactions of cytochrome c and of the primary electron acceptor of cytochrome c oxidase, the CuA site, in biomimetic complexes. Based on these results, we discuss how protein dynamics and thermal fluctuations may impact on protein ET reactions, comment on the possible physiological relevance of these results, and finally propose a regulatory mechanism that may operate in the Cyt/CcO electron transfer reaction in vivo. This article is part of a Special Issue entitled: 18th European Bioenergetic Conference.

Comparative analysis of the performance of commonly available density functionals in the determination of geometrical parameters for copper complexes

In this study, a set of 50 transition-metal complexes of Cu(I) and Cu(II), were used in the evaluation of 18 density functionals in geometry determination. In addition, 14 different basis sets were considered, including four commonly used Pople's all-electron basis sets; four basis sets including popular types of effective-core potentials: Los Alamos, Steven-Basch-Krauss, and Stuttgart-Dresden; and six triple-ζ basis sets. The results illustrate the performance of different methodological alternatives for the treatment of geometrical properties in relevant copper complexes, pointing out Double-Hybrid (DH) and Long-range Correction (LC) Generalized Gradient Approximation (GGA) methods as better descriptors of the geometry of the evaluated systems. These however, are associated with a computational cost several times higher than some of the other methods employed, such as the M06 functional, which has also demonstrated a comparable performance. Regarding the basis sets, 6-31+G(d) and 6-31+G(d,p) were the best performing approaches. In addition, the results show that the use of effective-core potentials has a limited impact, in terms of the accuracy in the determination of metal-ligand bond-lengths and angles in our dataset of copper complexes. Hence, these could become a good alternative for the geometrical description of these systems, particularly CEP-121G and SDD basis sets, if one is considering larger copper complexes where the computational cost could be an issue.

Fast electron transfer through a single molecule natively structured redox protein

The electron transfer properties of proteins are normally measured as molecularly averaged ensembles. Through these and related measurements, proteins are widely regarded as macroscopically insulating materials. Using scanning tunnelling microscopy (STM), we present new measurements of the conductance through single-molecules of the electron transfer protein cytochrome b(562) in its native conformation, under pseudo-physiological conditions. This is achieved by thiol (SH) linker pairs at opposite ends of the molecule through protein engineering, resulting in defined covalent contact between a gold surface and a platinum-iridium STM tip. Two different orientations of the linkers were examined: a long-axis configuration (SH-LA) and a short-axis configuration (SH-SA). In each case, the molecular conductance could be 'gated' through electrochemical control of the heme redox state. Reproducible and remarkably high conductance was observed in this relatively complex electron transfer system, with single-molecule conductance values peaking around 18 nS and 12 nS for the SH-SA and SH-LA cytochrome b(562) molecules near zero electrochemical overpotential. This strongly points to the important role of the heme co-factor bound to the natively structured protein. We suggest that the two-step model of protein electron transfer in the STM geometry requires a multi-electron transfer to explain such a high conductance. The model also yields a low value for the reorganisation energy, implying that solvent reorganisation is largely absent.

Modeling and computations of the intramolecular electron transfer process in the two-heme protein cytochrome c(4)

The di-heme protein Pseudomonas stutzeri cytochrome c(4) (cyt c(4)) has emerged as a useful model for studying long-range protein electron transfer (ET). Recent experimental observations have shown a dramatically different pattern of intramolecular ET between the two heme groups in different local environments. Intramolecular ET in homogeneous solution is too slow (>10 s) to be detected but fast (ms-μs) intramolecular ET in an electrochemical environment has recently been achieved by controlling the molecular orientation of the protein assembled on a gold electrode surface. In this work we have performed computational modeling of the intramolecular ET process by a combination of density functional theory (DFT) and quantum mechanical charge transfer theory to disclose reasons for this difference. We first address the electronic structures of the model heme core with histidine and methionine axial ligands in both low- and high-spin states by structure-optimized DFT. The computations enable estimating the intramolecular reorganization energy of the ET process for different combinations of low- and high-spin heme couples. Environmental reorganization free energies, work terms ("gating") and driving force were determined using dielectric continuum models. We then calculated the electronic transmission coefficient of the intramolecular ET rate using perturbation theory combined with the electronic wave functions determined by the DFT calculations for different heme group orientations and Fe-Fe separations. The reactivity of low- and high-spin heme groups was notably different. The ET rate is exceedingly low for the crystallographic equilibrium orientation but increases by several orders of magnitude for thermally accessible non-equilibrium configurations. Deprotonation of the propionate carboxyl group was also found to enhance the ET rate significantly. The results are discussed in relation to the observed surface immobilization effect and support the notion of conformationally gated ET.

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.

Comparison of chemical properties of iron, cobalt, and nickel porphyrins, corrins, and hydrocorphins

Density functional calculations have been used to compare the geometric, electronic, and functional properties of the three important tetrapyrrole systems in biology, heme, coenzyme B 12, and coenzyme F430, formed from iron porphyrin ( Por ), cobalt corrin ( Cor ), and nickel hydrocorphin ( Hcor ). The results show that the flexibility of the ring systems follows the trend Hcor > Cor > Por and that the size of the central cavity follows the trend Cor < Por < Hcor . Therefore, low-spin Co I, Co II, and Co III fit well into the Cor ring, whereas Por seems to be more ideal for the higher spin states of iron, and the cavity in Hcor is tailored for the larger Ni ion, especially in the high-spin Ni II state. This is confirmed by the thermodynamic stabilities of the various combinations of metals and ring systems. Reduction potentials indicate that the +I and +III states are less stable for Ni than for the other metal ions. Moreover, Ni – C bonds are appreciably less stable than Co - C bonds. However, it is still possible that a Ni – CH 3 bond is formed in F 430 by a heterolytic methyl transfer reaction, provided that the donor is appropriate, e.g. if coenzyme M is protonated. This can be facilitated by the adjacent SO 3− group in this coenzyme and by the axial glutamine ligand, which stabilizes the Ni III state. Our results also show that a Ni III– CH 3 complex is readily hydrolysed to form a methane molecule and that the Ni III hydrolysis product can oxidize coenzyme B and M to a heterodisulphide in the reaction mechanism of methyl coenzyme M reductase.

Reorganization energy for internal electron transfer in multicopper oxidases

We have calculated the reorganization energy for the intramolecular electron transfer between the reduced type 1 copper site and the peroxy intermediate of the trinuclear cluster in the multicopper oxidase CueO. The calculations are performed at the combined quantum mechanics and molecular mechanics (QM/MM) level, based on molecular dynamics simulations with tailored potentials for the two copper sites. We obtain a reorganization energy of 91-133 kJ/mol, depending on the theoretical treatment. The two Cu sites contribute by 12 and 22 kJ/mol to this energy, whereas the solvent contribution is 34 kJ/mol. The rest comes from the protein, involving small contributions from many residues. We have also estimated the energy difference between the two electron-transfer states and show that the reduction of the peroxy intermediate is exergonic by 43-87 kJ/mol, depending on the theoretical method. Both the solvent and the protein contribute to this energy difference, especially charged residues close to the two Cu sites. We compare these estimates with energies obtained from QM/MM optimizations and QM calculations in a vacuum and discuss differences between the results obtained at various levels of theory.