Incorporating Protein Environments in Density Functional Theory: A Self-Consistent Reaction Field Calculation of Redox Potentials of [2Fe2S] Clusters in Ferredoxin and Phthalate Dioxygenase Reductase

Conformational coupling of redox-driven Na+-translocation in Vibrio cholerae NADH:quinone oxidoreductase

In the respiratory chain, NADH oxidation is coupled to ion translocation across the membrane to build up an electrochemical gradient. In the human pathogen Vibrio cholerae, the sodium-pumping NADH:quinone oxidoreductase (Na+-NQR) generates a sodium gradient by a so far unknown mechanism. Here we show that ion pumping in Na+-NQR is driven by large conformational changes coupling electron transfer to ion translocation. We have determined a series of cryo-EM and X-ray structures of the Na+-NQR that represent snapshots of the catalytic cycle. The six subunits NqrA, B, C, D, E, and F of Na+-NQR harbor a unique set of cofactors that shuttle the electrons from NADH twice across the membrane to quinone. The redox state of a unique intramembranous [2Fe-2S] cluster orchestrates the movements of subunit NqrC, which acts as an electron transfer switch. We propose that this switching movement controls the release of Na+ from a binding site localized in subunit NqrB.

Ionization Energies and Redox Potentials of Hydrated Transition Metal Ions: Evaluation of Domain-Based Local Pair Natural Orbital Coupled Cluster Approaches

Hydrated transition metal ions are prototypical systems that can be used to model properties of transition metals in complex chemical environments. These seemingly simple systems present challenges for computational chemistry and are thus crucial in evaluations of quantum chemical methods for spin-state and redox energetics. In this work, we explore the applicability of the domain-based pair natural orbital implementation of coupled cluster (DLPNO-CC) theory to the calculation of ionization energies and redox potentials for hydrated ions of all first transition row (3d) metals in the 2+/3+ oxidation states, in connection with various solvation approaches. In terms of model definition, we investigate the construction of a minimally explicitly hydrated quantum cluster with a first and second hydration layer. We report on the convergence with respect to the coupled cluster expansion and the PNO space, as well as on the role of perturbative triple excitations. A recent implementation of the conductor-like polarizable continuum model (CPCM) for the DLPNO-CC approach is employed to determine self-consistent redox potentials at the coupled cluster level. Our results establish conditions for the convergence of DLPNO-CCSD(T) energetics and stress the absolute necessity to explicitly consider the second solvation sphere even when CPCM is used. The achievable accuracy for redox potentials of a practical DLPNO-based approach is, on average, 0.13 V. Furthermore, multilayer approaches that combine a higher-level DLPNO-CCSD(T) description of the first solvation sphere with a lower-level description of the second solvation layer are investigated. The present work establishes optimal and transferable methodological choices for employing DLPNO-based coupled cluster theory, the associated CPCM implementation, and cost-efficient multilayer derivatives of the approach for open-shell transition metal systems in complex environments.

Theoretical Study on Redox Potential Control of Iron-Sulfur Cluster by Hydrogen Bonds: A Possibility of Redox Potential Programming

The effect of hydrogen bonds around the active site of Anabaena [2Fe-2S] ferredoxin (Fd) on a vertical ionization potential of the reduced state (IP(red)) is examined based on the density functional theory (DFT) calculations. The results indicate that a single hydrogen bond increases the relative stability of the reduced state, and shifts IP(red) to a reductive side by 0.31–0.33 eV, regardless of the attached sulfur atoms. In addition, the IP(red) value can be changed by the number of hydrogen bonds around the active site. The results also suggest that the redox potential of [2Fe-2S] Fd is controlled by the number of hydrogen bonds because IP(red) is considered to be a major factor in the redox potential. Furthermore, there is a possibility that the redox potentials of artificial iron-sulfur clusters can be finely controlled by the number of the hydrogen bonds attached to the sulfur atoms of the cluster.

Computational Biochemistry-Enzyme Mechanisms Explored

Understanding enzyme mechanisms is a major task to achieve in order to comprehend how living cells work. Recent advances in biomolecular research provide huge amount of data on enzyme kinetics and structure. The analysis of diverse experimental results and their combination into an overall picture is, however, often challenging. Microscopic details of the enzymatic processes are often anticipated based on several hints from macroscopic experimental data. Computational biochemistry aims at creation of a computational model of an enzyme in order to explain microscopic details of the catalytic process and reproduce or predict macroscopic experimental findings. Results of such computations are in part complementary to experimental data and provide an explanation of a biochemical process at the microscopic level. In order to evaluate the mechanism of an enzyme, a structural model is constructed which can be analyzed by several theoretical approaches. Several simulation methods can and should be combined to get a reliable picture of the process of interest. Furthermore, abstract models of biological systems can be constructed combining computational and experimental data. In this review, we discuss structural computational models of enzymatic systems. We first discuss various models to simulate enzyme catalysis. Furthermore, we review various approaches how to characterize the enzyme mechanism both qualitatively and quantitatively using different modeling approaches.

Broken-Symmetry DFT Computations for the Reaction Pathway of IspH, an Iron-Sulfur Enzyme in Pathogenic Bacteria

The recently discovered methylerythritol phosphate (MEP) pathway provides new targets for the development of antibacterial and antimalarial drugs. In the final step of the MEP pathway, the [4Fe-4S] IspH protein catalyzes the 2e(-)/2H(+) reductive dehydroxylation of (E)-4-hydroxy-3-methyl-but-2-enyl diphosphate (HMBPP) to afford the isoprenoid precursors isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP). Recent experiments have attempted to elucidate the IspH catalytic mechanism to drive inhibitor development. Two competing mechanisms have recently emerged, differentiated by their proposed HMBPP binding modes upon 1e(-) reduction of the [4Fe-4S] cluster: (1) a Birch reduction mechanism, in which HMBPP remains bound to the [4Fe-4S] cluster through its terminal C4-OH group (ROH-bound) until the -OH is cleaved as water; and (2) an organometallic mechanism, in which the C4-OH group rotates away from the [4Fe-4S] cluster, allowing the HMBPP olefin group to form a metallacycle complex with the apical iron (η(2)-bound). We perform broken-symmetry density functional theory computations to assess the energies and reduction potentials associated with the ROH- and η(2)-bound states implicated by these competing mechanisms. Reduction potentials obtained for ROH-bound states are more negative (-1.4 to -1.0 V) than what is typically expected of [4Fe-4S] ferredoxin proteins. Instead, we find that η(2)-bound states are lower in energy than ROH-bound states when the [4Fe-4S] cluster is 1e(-) reduced. Furthermore, η(2)-bound states can already be generated in the oxidized state, yielding reduction potentials of ca. -700 mV when electron addition occurs after rotation of the HMBPP C4-OH group. We demonstrate that such η(2)-bound states are kinetically accessible both when the IspH [4Fe-4S] cluster is oxidized and 1e(-) reduced. The energetically preferred pathway gives 1e(-) reduction of the cluster after substrate conformational change, generating the 1e(-) reduced intermediate proposed in the organometallic mechanism.

Use of Broken-Symmetry Density Functional Theory To Characterize the IspH Oxidized State: Implications for IspH Mechanism and Inhibition

With current therapies becoming less efficacious due to increased drug resistance, new inhibitors of both bacterial and malarial targets are desperately needed. The recently discovered methylerythritol phosphate (MEP) pathway for isoprenoid synthesis provides novel targets for the development of such drugs. Particular attention has focused on the IspH protein, the final enzyme in the MEP pathway, which uses its [4Fe-4S] cluster to catalyze the formation of the isoprenoid precursors IPP and DMAPP from HMBPP. IspH catalysis is achieved via a 2e-/2H+ reductive dehydroxylation of HMBPP; the mechanism by which catalysis is achieved, however, is highly controversial. The work presented herein provides the first step in assessing different routes to catalysis by using computational methods. By performing broken-symmetry density functional theory (BS-DFT) calculations that employ both the conductor-like screening solvation model (DFT/COSMO) and a finite-difference Poisson-Boltzmann self-consistent reaction field methodology (DFT/SCRF), we evaluate geometries, energies, and Mössbauer signatures of the different protonation states that may exist in the oxidized state of the IspH catalytic cycle. From DFT/SCRF computations performed on the oxidized state, we find a state where the substrate, HMBPP, coordinates the apical iron in the [4Fe-4S] cluster as an alcohol group (ROH) to be one of two, isoenergetic, lowest-energy states. In this state, the HMBPP pyrophosphate moiety and an adjacent glutamate residue (E126) are both fully deprotonated, making the active site highly anionic. Our findings that this low-energy state also matches the experimental geometry of the active site and that its computed isomer shifts agree with experiment validate the use of the DFT/SCRF method to assess relative energies along the IspH reaction pathway. Additional studies of IspH catalytic intermediates are currently being pursued.

EPR and (57)Fe ENDOR investigation of 2Fe ferredoxins from Aquifex aeolicus

We have employed EPR and a set of recently developed electron nuclear double resonance (ENDOR) spectroscopies to characterize a suite of [2Fe-2S] ferredoxin clusters from Aquifex aeolicus (Aae Fd1, Fd4, and Fd5). Antiferromagnetic coupling between the Fe(II), S = 2, and Fe(III), S = 5/2, sites of the [2Fe-2S](+) cluster in these proteins creates an S = 1/2 ground state. A complete discussion of the spin-Hamiltonian contributions to g includes new symmetry arguments along with references to related FeS model compounds and their symmetry and EPR properties. Complete (57)Fe hyperfine coupling (hfc) tensors for each iron, with respective orientations relative to g, have been determined by the use of "stochastic" continuous wave and/or "random hopped" pulsed ENDOR, with the relative utility of the two approaches being emphasized. The reported hyperfine tensors include absolute signs determined by a modified pulsed ENDOR saturation and recovery (PESTRE) technique, RD-PESTRE-a post-processing protocol of the "raw data" that comprises an ENDOR spectrum. The (57)Fe hyperfine tensor components found by ENDOR are nicely consistent with those previously found by Mössbauer spectroscopy, while accurate tensor orientations are unique to the ENDOR approach. These measurements demonstrate the capabilities of the newly developed methods. The high-precision hfc tensors serve as a benchmark for this class of FeS proteins, while the variation in the (57)Fe hfc tensors as a function of symmetry in these small FeS clusters provides a reference for higher-nuclearity FeS clusters, such as those found in nitrogenase.

Assignment of the photoelectron spectra of FeS3(-) by density functional theory, CASPT2, and RCCSD(T) calculations

The geometric structures of FeS(3) and FeS(3)(-) with spin multiplicities ranging from singlet to octet were optimized at the B3LYP level, allowing two low-lying conformations for these clusters to be identified. The planar D(3h) conformation contains three S(2-) atomic ligands (S(3)Fe(0/-)), whereas the C(2v) structure contains, in addition to an atomic S(2-) ligand, also a S(2)(2-) ligand that is side-on-bound to the iron cation: an η(2)-S(2)FeS conformation. Subsequently, energy differences between the various states of these conformations were estimated by carrying out geometry optimizations at the multireference CASPT2 level. Several competing structures for the ground state of the anionic cluster were recognized at this level. Relative stabilities were also estimated by performing single-point RCSSD(T) calculations on the B3LYP geometries. The ground state of the neutral complex was unambiguously found to be (5)B(2). The ground state of the anion is considerably less certain. The 1(4)B(2), 2(4)B(2), (4)B(1), and (6)A(1) states were all found as low-lying η(2)-S(2)FeS(-) states. Also, (4)B(2) of S(3)Fe(-) has a comparable CASPT2 energy. In contrast, B3LYP and RCCSD(T) mutually agree that the S(3)Fe(-) state is at a much higher energy. Energetically, the bands of the photoelectron spectra of FeS(3)(-) are reproduced at the CASPT2 level as ionizations from either the (4)B(2) or (6)A(1) state of η(2)-S(2)FeS. However, the Franck-Condon factors obtained from a harmonic vibrational analysis at the B3LYP level show that only the (4)B(2)-to-(5)B(2) ionization, which preserves the η(2)-S(2)Fe-S conformation, provides the best vibrational progression match with the X band of the experimental photoelectron spectra.

Coupled electron and proton transfer reactions during the O→E transition in bovine cytochrome c oxidase

A combined DFT/electrostatic approach is employed to study the coupling of proton and electron transfer reactions in cytochrome c oxidase (CcO) and its proton pumping mechanism. The coupling of the chemical proton to the internal electron transfer within the binuclear center is examined for the O→E transition. The novel features of the His291 pumping model are proposed, which involve timely well-synchronized sequence of the proton-coupled electron transfer reactions. The obtained pK(a)s and E(m)s of the key ionizable and redox-active groups at the different stages of the O→E transition are consistent with available experimental data. The PT step from E242 to H291 is examined in detail for various redox states of the hemes and various conformations of E242 side-chain. Redox potential calculations of the successive steps in the reaction cycle during the O→E transition are able to explain a cascade of equilibria between the different intermediate states and electron redistribution between the metal centers during the course of the catalytic activity. All four electrometric phases are discussed in the light of the obtained results, providing a robust support for the His291 model of proton pumping in CcO.

Mössbauer properties of the diferric cluster and the differential iron(II)-binding affinity of the iron sites in protein R2 of class Ia Escherichia coli ribonucleotide reductase: a DFT/electrostatics study

The R2 subunit of class-Ia ribonucleotide reductase (RNR) from Escherichia coli (E. coli) contains a diiron active site. Starting from the apo-protein and Fe(II) in solution at low Fe(II)/apoR2 ratios, mononuclear Fe(II) binding is observed indicating possible different Fe(II) binding affinities for the two alternative sites. Further, based on their Mössbauer spectroscopy and two-iron-isotope reaction experiments, Bollinger et al. (J. Am. Chem. Soc., 1997, 119, 5976-5977) proposed that the site Fe1, which bonds to Asp84, should be associated with the higher observed (57)Fe Mössbauer quadrupole splitting (2.41 mm s(-1)) and lower isomer shift (0.45 mm s(-1)) in the Fe(III)Fe(III) state, site Fe2, which is further from Tyr122, should have a greater affinity for Fe(II) binding than site Fe1, and Fe(IV) in the intermediate X state should reside at site Fe2. In this paper, using density functional theory (DFT) incorporated with the conductor-like screening (COSMO) solvation model and with the finite-difference Poisson-Boltzmann self-consistent reaction field (PB-SCRF) methodologies, we have demonstrated that the observed large quadrupole splitting for the diferric state R2 does come from site Fe1(III) and it is mainly caused by the binding position of the carboxylate group of the Asp84 sidechain. Further, a series of active site clusters with mononuclear Fe(II) binding at either site Fe1 or Fe2 have been studied, which show that with a single dielectric medium outside the active site quantum region, there is no energetic preference for Fe(II) binding at one site over another. However, when including the explicit extended protein environment in the PB-SCRF model, the reaction field favors the Fe(II) binding at site Fe2 rather than at site Fe1 by ~9 kcal mol(-1). Therefore our calculations support the proposal of the previous Mössbauer spectroscopy and two-iron-isotope reaction experiments by Bollinger et al.

Geometric and electrostatic study of the [4Fe-4S] cluster of adenosine-5'-phosphosulfate reductase from broken symmetry density functional calculations and extended X-ray absorption fine structure spectroscopy

Adenosine-5'-phosphosulfate reductase (APSR) is an iron-sulfur protein that catalyzes the reduction of adenosine-5'-phosphosulfate (APS) to sulfite. APSR coordinates to a [4Fe-4S] cluster via a conserved CC-X(~80)-CXXC motif, and the cluster is essential for catalysis. Despite extensive functional, structural, and spectroscopic studies, the exact role of the iron-sulfur cluster in APS reduction remains unknown. To gain an understanding into the role of the cluster, density functional theory (DFT) analysis and extended X-ray fine structure spectroscopy (EXAFS) have been performed to reveal insights into the coordination, geometry, and electrostatics of the [4Fe-4S] cluster. X-ray absorption near-edge structure (XANES) data confirms that the cluster is in the [4Fe-4S](2+) state in both native and substrate-bound APSR while EXAFS data recorded at ~0.1 Å resolution indicates that there is no significant change in the structure of the [4Fe-4S] cluster between the native and substrate-bound forms of the protein. On the other hand, DFT calculations provide an insight into the subtle differences between the geometry of the cluster in the native and APS-bound forms of APSR. A comparison between models with and without the tandem cysteine pair coordination of the cluster suggests a role for the unique coordination in facilitating a compact geometric structure and "fine-tuning" the electronic structure to prevent reduction of the cluster. Further, calculations using models in which residue Lys144 is mutated to Ala confirm the finding that Lys144 serves as a crucial link in the interactions involving the [4Fe-4S] cluster and APS.

Modeling the MoFe nitrogenase system with broken symmetry density functional theory

Density functional theory (DFT) represents a unified framework for gaining molecular level insight into molybdenum-iron (MoFe) nitrogenase. However, accurately describing the electronic structure of the spin-polarized and spin-coupled iron-molybdenum cofactor (FeMo-co) where N(2) reduction occurs within MoFe nitrogenase is challenging. Therefore, the enhancement of DFT to include broken symmetry (BS-DFT) plus approximate spin projection has proven valuable because it provides a procedure to compute reliable geometries, energies, redox potentials, and quantities relevant to Mössbauer and ENDOR spectroscopies. After describing the theoretical tools necessary to obtain this information, we show by way of examples how BS-DFT is a very powerful partner to experiment. We expect that quantitative quantum chemical theory of this type will play an ever-increasing role in helping to decipher complex bioinorganic systems like those found in MoFe nitrogenase.

Nitrogenase structure and function relationships by density functional theory

Modern density functional theory has tremendous potential with matching popularity in metalloenzymology to reveal the unseen atomic and molecular details of structural data, spectroscopic measurements, and biochemical experiments by providing insights into unobservable structures and states, while also offering theoretical justifications for observed trends and differences. An often untapped potential of this theoretical approach is to bring together diverse experimental structural and reactivity information and allow for these to be critically evaluated at the same level. This is particularly applicable for the tantalizingly complex problem of the structure and molecular mechanism of biological nitrogen fixation. In this chapter we provide a review with extensive practical details of the compilation and evaluation of experimental data for an unbiased and systematic density functional theory analysis that can lead to remarkable new insights about the structure-function relationships of the iron-sulfur clusters of nitrogenase.

Density functional theory analysis of structure, energetics, and spectroscopy for the Mn-Fe active site of Chlamydia trachomatis ribonucleotide reductase in four oxidation states

Models for the Mn-Fe active site structure of ribonucleotide reductase (RNR) from pathogenic bacteria Chlamydia trachomatis (Ct) in different oxidation states have been studied in this paper, using broken-symmetry density functional theory (DFT) incorporated with the conductor like screening (COSMO) solvation model and also with finite-difference Poisson-Boltzmann self-consistent reaction field (PB-SCRF) calculations. The detailed structures for the reduced Mn(II)-Fe(II), the met Mn(III)-Fe(III), the oxidized Mn(IV)-Fe(III) and the superoxidized Mn(IV)-Fe(IV) states are predicted. The calculated properties, including geometries, (57)Fe Mossbauer isomer shifts and quadrupole splittings, and (57)Fe and (55)Mn electron nuclear double resonance (ENDOR) hyperfine coupling constants, are compared with the available experimental data. The Mössbauer and energetic calculations show that the (mu-oxo, mu-hydroxo) models better represent the structure of the Mn(IV)-Fe(III) state than the di-mu-oxo models. The predicted Mn(IV)-Fe(III) distances (2.95 and 2.98 A) in the (mu-oxo, mu-hydroxo) models are in agreement with the extended X-ray absorption fine structure (EXAFS) experimental value of 2.92 A (Younker et al. J. Am. Chem. Soc. 2008, 130, 15022-15027). The effect of the protein and solvent environment on the assignment of the Mn metal position is examined by comparing the relative energies of alternative mono-Mn(II) active site structures. It is proposed that if the Mn(II)-Fe(II) protein is prepared with prior addition of Mn(II) or with Mn(II) richer than Fe(II), Mn is likely positioned at metal site 2, which is further from Phe127.

Redox potential of the Rieske iron-sulfur protein quantum-chemical and electrostatic study

Quantum-chemical study of structures, energies, and effective partial charge distribution for several models of the Rieske protein redox center is performed in terms of the B3LYP density functional method in combination with the broken symmetry approach using three different atomic basis sets. The structure of the redox complex optimized in vacuum differs markedly from that inside the protein. This means that the protein matrix imposes some stress on the active site resulting in distortion of its structure. The redox potentials calculated for the real active site structure are in a substantially better agreement with the experiment than those calculated for the idealized structure. This shows an important role of the active site distortion in tuning its redox potential. The reference absolute electrode potential of the standard hydrogen electrode is used that accounts for the correction caused by the water surface potential. Electrostatic calculations are performed in the framework of the polarizable solute model. Two dielectric permittivities of the protein are employed: the optical permittivity for calculation of the intraprotein electric field, and the static permittivity for calculation of the dielectric response energy. Only this approach results in a reasonable agreement of the calculated and experimental redox potentials.

Crystal structure of Adenylylsulfate reductase from Desulfovibrio gigas suggests a potential self-regulation mechanism involving the C terminus of the beta-subunit

Adenylylsulfate reductase (adenosine 5'-phosphosulfate [APS] reductase [APSR]) plays a key role in catalyzing APS to sulfite in dissimilatory sulfate reduction. Here, we report the crystal structure of APSR from Desulfovibrio gigas at 3.1-A resolution. Different from the alpha(2)beta(2)-heterotetramer of the Archaeoglobus fulgidus, the overall structure of APSR from D. gigas comprises six alphabeta-heterodimers that form a hexameric structure. The flavin adenine dinucleotide is noncovalently attached to the alpha-subunit, and two [4Fe-4S] clusters are enveloped by cluster-binding motifs. The substrate-binding channel in D. gigas is wider than that in A. fulgidus because of shifts in the loop (amino acid 326 to 332) and the alpha-helix (amino acid 289 to 299) in the alpha-subunit. The positively charged residue Arg160 in the structure of D. gigas likely replaces the role of Arg83 in that of A. fulgidus for the recognition of substrates. The C-terminal segment of the beta-subunit wraps around the alpha-subunit to form a functional unit, with the C-terminal loop inserted into the active-site channel of the alpha-subunit from another alphabeta-heterodimer. Electrostatic interactions between the substrate-binding residue Arg282 in the alpha-subunit and Asp159 in the C terminus of the beta-subunit affect the binding of the substrate. Alignment of APSR sequences from D. gigas and A. fulgidus shows the largest differences toward the C termini of the beta-subunits, and structural comparison reveals notable differences at the C termini, activity sites, and other regions. The disulfide comprising Cys156 to Cys162 stabilizes the C-terminal loop of the beta-subunit and is crucial for oligomerization. Dynamic light scattering and ultracentrifugation measurements reveal multiple forms of APSR upon the addition of AMP, indicating that AMP binding dissociates the inactive hexamer into functional dimers, presumably by switching the C terminus of the beta-subunit away from the active site. The crystal structure of APSR, together with its oligomerization properties, suggests that APSR from sulfate-reducing bacteria might self-regulate its activity through the C terminus of the beta-subunit.

DFT calculations of comparative energetics and ENDOR/Mössbauer properties for two protonation states of the iron dimer cluster of ribonucleotide reductase intermediate X

Two models (I and II) for the active site structure of class-I ribonucleotide reductase (RNR) intermediate X in subunit R2 have been studied in this paper, using broken-symmetry density functional theory (DFT) incorporated with the conductor like screening (COSMO) solvation model and with the finite-difference Poisson-Boltzmann self-consistent reaction field (PB-SCRF) calculations. Only one of the bridging groups between the two iron centers is different between model-I and model-II. Model-I contains two mu-oxo bridges, while model-II has one bridging oxo and one bridging hydroxo. These are large active site models including up to the fourth coordination shell H-bonding residues. Mössbauer and ENDOR hyperfine property calculations show that model-I is more likely to represent the active site structure of RNR-X. However, energetically our pK(a) calculations at first highly favored the bridging oxo and hydroxo (in model-II) structure of the diiron center rather than having the di-oxo bridge (in model-I). Since the Arg236 and the nearby Lys42, which are very close to the diiron center, are on the protein surface of RNR-R2, it is highly feasible that one or two anion groups in solution would interact with the positively charged side chains of Arg236 and Lys42. The anion group(s) can be a reductant, phosphate, sulfate, nitrate, and other negatively charged groups existing in biological environments or in the buffer of the experiment. Since sulfate ions certainly exist in the buffer of the ENDOR experiment, we have examined the effect of the sulfate (SO(4)(2-), surrounded by explicit water molecules) H-bonding to the side chain of Arg236. We find that when sulfate interacts with Arg236, the carboxylate group of Asp237 tends to be protonated, and once Asp237 is protonated, the Fe(iii)Fe(iv) center in X favors the di-oxo bridge (model-I). This would explain that the ENDOR observed RNR-X active site structure is likely to be represented by model-I rather than model-II.

A computational comparison of electron transfer from reduced ferredoxin to flavin adenine dinucleotide and a gold electrode

We have carried out calculations of the electronic structure of ferredoxin and of the electronic coupling matrix element Hif for electron transfer from reduced ferredoxin to flavin adenine dinucleotide (FAD) and to cluster models of the Au111 surface and a Au111 surface with a mercaptopyridene self-assembled monolayer (SAM). We conclude, based on Hif2, that a gold electrode is approximately 14 times less efficient as an electron acceptor than FAD and that the mercaptopyridine SAM enhances electron transfer. The magnitude of Hif is large enough for these systems that the weak coupling limit approximations may no longer be valid. However, the barrier to electron transfer in the strong coupling limit is computed to be small due to minimal geometry change between oxidized and reduced ferredoxin. MD simulations of the interaction of ferredoxin and protonated pyridine within a water solvation box indicate that the protonated pyridine does strongly orient the ferredoxin, favoring electron transfer as compared to a bare gold surface, where we speculate the orientation of the ferredoxin may be more random.

Dielectric relaxation of cytochrome c oxidase: Comparison of the microscopic and continuum models

We have studied a charge-insertion process that models the deprotonation of a histidine side chain in the active site of cytochrome c oxidase (CcO) using both the continuum electrostatic calculations and the microscopic simulations. The group of interest is a ligand to Cu(B) center of CcO, which has been previously suggested to play the role of the proton pumping element in the enzyme; the group is located near a large internal water cavity in the protein. Using the nonpolarizable Amber-99 force field in molecular dynamics (MD) simulations, we have calculated the nuclear part of the reaction-field energy of charging of the His group and combined it with the electronic part, which we estimated in terms of the electronic continuum (EC) model, to obtain the total reaction-field energy of charging. The total free energy obtained in this MDEC approach was then compared with that calculated using pure continuum electrostatic model with variable dielectric parameters. The dielectric constant for the "dry" protein and that of the internal water cavity of CcO were determined as those parameters that provide best agreement between the continuum and microscopic MDEC model. The nuclear (MD) polarization alone (without electronic part) of a dry protein was found to correspond to an unphysically low dielectric constant of only about 1.3, whereas the inclusion of electronic polarizability increases the protein dielectric constant to 2.6-2.8. A detailed analysis is presented as to how the protein structure should be selected for the continuum calculations, as well as which probe and atomic radii should be used for cavity definition. The dielectric constant of the internal water cavity was found to be 80 or even higher using "standard" parameters of water probe radius, 1.4 A, and protein atomic radii from the MD force field for cavity description; such high values are ascribed to the fact that the standard procedure produces unphysically small cavities. Using x-ray data for internal water in CcO, we have explored optimization of the parameters and the algorithm of cavity description. For Amber radii, the optimal probe size was found to be 1.25 A; the dielectric of water cavity in this case is in the range of 10-16. The most satisfactory cavity description, however, was achieved with ProtOr atomic radii, while keeping the probe radius to be standard 1.4 A. In this case, the value of cavity dielectric constant was found to be in the range of 3-6. The obtained results are discussed in the context of recent calculations and experimental measurements of dielectric properties of proteins.

Quantum cluster size and solvent polarity effects on the geometries and Mössbauer properties of the active site model for ribonucleotide reductase intermediate X: a density functional theory study

In studying the properties of metalloproteins using ab initio quantum mechanical methods, one has to focus on the calculations on the active site. The bulk protein and solvent environment is often neglected, or is treated as a continuum dielectric medium with a certain dielectric constant. The size of the quantum cluster of the active site chosen for calculations can vary by including only the first-shell ligands which are directly bound to the metal centers, or including also the second-shell residues which are adjacent to and normally have H-bonding interactions with the first-shell ligands, or by including also further hydrogen bonding residues. It is not well understood how the size of the quantum cluster and the value of the dielectric constant chosen for the calculations will influence the calculated properties. In this paper, we have studied three models (A, B, and C) of different sizes for the active site of the ribonucleotide reductase intermediate X, using density functional theory (DFT) OPBE functional with broken-symmetry methodology. Each model is studied in gas-phase and in the conductor-like screening (COSMO) solvation model with different dielectric constants ε = 4, 10, 20, and 80, respectively. All the calculated Fe-ligand geometries, Heisenberg J coupling constants, and the Mössbauer isomer shifts, quadrupole splittings, and the (57)Fe, (1)H, and (17)O hyperfine tensors are compared. We find that the calculated isomer shifts are very stable. They are virtually unchanged with respect to the size of the cluster and the dielectric constant of the environment. On the other hand, certain Fe-ligand distances are sensitive to both the size of the cluster and the value of ε. ε = 4, which is normally used for the protein environment, appears too small when studying the diiron active site geometry with only the first-shell ligands as seen by comparisons with larger models.

Investigating the mechanisms of photosynthetic proteins using continuum electrostatics

Computational methods based on continuum electrostatics are widely used in theoretical biochemistry to analyze the function of proteins. Continuum electrostatic methods in combination with quantum chemical and molecular mechanical methods can help to analyze even very complex biochemical systems. In this article, applications of these methods to proteins involved in photosynthesis are reviewed. After giving a short introduction to the basic concepts of the continuum electrostatic model based on the Poisson-Boltzmann equation, we describe the application of this approach to the docking of electron transfer proteins, to the comparison of isofunctional proteins, to the tuning of absorption spectra, to the analysis of the coupling of electron and proton transfer, to the analysis of the effect of membrane potentials on the energetics of membrane proteins, and to the kinetics of charge transfer reactions. Simulations as those reviewed in this article help to analyze molecular mechanisms on the basis of the structure of the protein, guide new experiments, and provide a better and deeper understanding of protein functions.

Dynamical magnetostructural properties of Anabaena ferredoxin

A mixed quantum/classical investigation of the dynamical magnetostructural properties, that is, "magnetodynamics," of oxidized Anabaena PCC7119 ferredoxin is carried out at room temperature in two distinct conformational states. This protein hosts a [2Fe-2S] cluster in which two iron centers are antiferromagnetically coupled to an overall low-spin electronic ground state that has a genuine multireference character. To study the magnetodynamics of this prosthetic group, an approximate spin projection method is formulated in the framework of density functional theory that allows for multideterminant ab initio molecular dynamics simulations to be carried out efficiently. By using this scheme, the influence of both thermal fluctuations and conformational motion on the structure of the [2Fe-2S] cluster and on the dynamics of the antiferromagnetic coupling constant, J(t), has been investigated. In addition to demonstrating how sensitively the shape of the [2Fe-2S] core itself is affected by hydrogen bonding, the analyses reveal a complex dynamical coupling of J to both local vibrations and large-amplitude motion. It is shown that this interplay can be understood in terms of specific vibrational modes and distinct hydrogen-bonding patterns between the iron-sulfur cluster and the protein backbone, respectively. This implies going beyond the Goodenough-Kanamori rules for angular magnetostructural correlations of oxidized iron-sulfur prosthetic groups.

DFT/electrostatic calculations of pK(a) values in cytochrome c oxidase

Using classical electrostatic calculations, earlier we examined the dependence of the protonation state of bovine cytochrome c oxidase (CcO) on its redox state. Based on these calculations, we have proposed a model of CcO proton pumping that involves His291, one of the Cu(B) histidine ligands, which was found to respond to redox changes of the enzyme Fe(a)(3)-Cu(B) catalytic center. In this work, we employ combined density functional and continuum electrostatic calculations to evaluate the pK(a)() values of His291 and Glu242, two key residues of the model. The pK(a) values are calculated for different redox states of the enzyme, and the influence of different factors on the pK(a)'s is analyzed in detail. The calculated pK(a)() values of Glu242 are between 9.4 and 12.0, depending on the redox state of the protein, which is in excellent agreement with recent experimental measurements. Assuming the reduced state of heme a(3), His291 of the oxidized Cu(B) center possesses a pK(a)() between 2.1 and 4.0, while His291 of the reduced Cu(B) center has a pK(a) above 17. The obtained results support the proposal that the His291 ligand of the Cu(B) center in CcO is a proton pump element.

Combined DFT and electrostatics study of the proton pumping mechanism in cytochrome c oxidase

Cytochrome c oxidase is a redox-driven proton pump which converts atmospheric oxygen to water and couples the oxygen reduction reaction to the creation of a membrane proton gradient. The structure of the enzyme has been solved; however, the mechanism of proton pumping is still poorly understood. Recent calculations from this group indicate that one of the histidine ligands of enzyme's CuB center, His291, may play the role of the pumping element. In this paper, we report on the results of calculations that combined first principles DFT and continuum electrostatics to evaluate the energetics of the key energy generating step of the model-the transfer of the chemical proton to the binuclear center of the enzyme, where the hydroxyl group is converted to water, and the concerted expulsion of the proton from delta-nitrogen of His291 ligand of CuB center. We show that the energy generated in this step is sufficient to push a proton against an electrochemical membrane gradient of about 200 mV. We have also re-calculated the pKa of His291 for an extended model in which the whole Fe(a3)-CuB center with their ligands is treated by DFT. Two different DFT functionals (B3LYP and PBE0), and various dielectric models of the protein have been used in an attempt to estimate potential errors of the calculations. Although current methods of calculations do not allow unambiguous predictions of energetics in proteins within few pKa units, as required in this case, the present calculation provides further support for the proposed His291 model of CcO pump and makes a specific prediction that could be targeted in the experimental test.

Structure, redox, pK a, spin. A golden tetrad for understanding metalloenzyme energetics and reaction pathways

After a review of the current status of density functional theory (DFT) for spin-polarized and spin-coupled systems, we focus on the resting states and intermediates of redox-active metalloenzymes and electron transfer proteins, showing how comparisons of DFT-calculated spectroscopic parameters with experiment and evaluation of related energies and geometries provide important information. The topics we examine include (1) models for the active-site structure of methane monooxygenase intermediate Q and ribonucleotide reductase intermediate X; (2) the coupling of electron transfer to proton transfer in manganese superoxide dismutase, with implications for reaction kinetics; (3) redox, pK(a), and electronic structure issues in the Rieske iron-sulfur protein, including their connection to coupled electron/proton transfer, and an analysis of how partial electron delocalization strongly alters the electron paramagnetic resonance spectrum; (4) the connection between protein-induced structural distortion and the electronic structure of oxidized high-potential 4Fe4S proteins with implications for cluster reactivity; (5) an analysis of cluster assembly and central-atom insertion into the FeMo cofactor center of nitrogenase based on DFT structural and redox potential calculations.

Improved Density Functional Theory/Electrostatic Calculation of the His291 Protonation State in Cytochrome c Oxidase: Self-Consistent Charges for Solvation Energy Calculation

The protonation state of His291 in cytochrome c oxidase (CcO), a ligand to the Cu(B) center of the enzyme, has been recently studied in this group by using combined density functional theory (DFT)/electrostatic (QM/MM) calculations. On the basis of these calculations, a model of the proton pumping mechanism of CcO has been proposed. Due to certain technical difficulties, the procedure used in the previous calculation to find partial atomic charges of the QM system for the solvation energy evaluation was not entirely satisfactory; i.e., it was not self-consistent. Here, we describe a procedure that resolves the problem and report on the improved calculations of the protonation state of the His residue. The new procedure fits the protein and reaction field potentials in the region of the QM system with artificial point charges placed on a surface of a sphere surrounding the QM system and a few charges inside the sphere and allows one to perform DFT calculations that involve an inhomogeneous dielectric environment in a self-consistent way. The procedure improves the accuracy of calculations in comparison with previous work. The improved results show, however, that although the absolute energies change significantly the relative energies of the protonated and deprotonated states of His291 remain close to the previously reported ones and therefore do not change significantly the pK(a) values reported earlier. Therefore, our new improved calculations support for the proposed His291 model of the CcO pump.

Two conformational states of Glu242 and pKas in bovine cytochrome c oxidase

Cytochrome c oxidase (CcO) is the terminal enzyme in the respiratory electron transport chain of aerobic organisms. It catalyses the reduction of atmospheric oxygen to water, and couples this reaction to proton pumping across the membrane; this process generates the electrochemical gradient that subsequently drives the synthesis of ATP. The molecular details of the mechanism by which electron transfer is coupled to proton pumping in CcO is poorly understood. Recent calculations from our group indicate that His291, a ligand of the Cu(B) center of the enzyme, may play the role of the pumping element. In this paper we describe calculations in which a DFT/continuum electrostatic method is used to explore the coupling of the conformational changes of Glu242 residue, the main proton donor of both chemical and pump protons, to its pKa, and the pKa of His291, a putative proton loading site of our pumping model. The computations are done for several redox states of metal centers, different protonation states of Glu242 and His291, and two well-defined conformations of the Glu242 side chain. Thus, in addition to equilibrium redox/protonation states of the catalytic cycle, we also examine the transient and intermediate states. Different dielectric models are employed to investigate the robustness of the results, and their viability in the light of the proposed proton pumping mechanism of CcO. The main results are in agreement with the experimental measurements and support the proposed pumping mechanism. Additionally, the present calculations indicate a possibility of gating through conformational changes of Glu242; namely, in the pumping step, we find that Glu242 needs to be reprotonated before His291 can eject a proton to the P-site of membrane. As a result, the reprotonation of Glu can control proton release from the proton loading site.

Theoretical Study on Electronic and Spin Structures of [Fe2S2]2+,+ Cluster: Reference Interaction Site Model Self-Consistent Field (RISM-SCF) and Multireference Second-Order Møller−Plesset Perturbation Theory (MRMP) Approach

Electronic structures of [Fe(2)S(2)(SCH(3))(4)](2-,3-) in DMSO solution are calculated using reference interaction site model complete active space self-consistent field (RISM-CASSCF)/multireference second-order Møller-Plesset perturbation theory (MRMP) method. For the reduced state, we obtain both the low-spin Fe(3+)Fe(2+) localized and high-spin Fe(2.5+)Fe(2.5+) delocalized forms, which are very close in energy. The spin interaction constants obtained from the energies of states with various spin multiplicities are in good agreement with the available experimental estimates both for the oxidized and for the reduced states. The dynamic electron correlation effect is found to be important in estimating the spin interaction between the Fe ions. The redox potentials are calculated to be 2.87 and 2.78 eV for the localized and delocalized reduced states, respectively, which are close to the experimental values. We devise a simple model for calculating the free energy curves of the reduction process based on the RISM-SCF theory. The activation barrier height is calculated to be 7.4 kcal/mol at the equilibrium geometry of oxidized state, indicating that the reduction reaction will occur efficiently in DMSO solvent. The effect of solvent fluctuation on the free energy profiles is discussed on the basis of the present calculations.

Probing the Electronic Structure of [2Fe-2S] Clusters with Three Coordinate Iron Sites by Use of Photoelectron Spectroscopy

Five series of [2Fe-2S] complexes, [Fe(2)S(2)Cl(2)(-)(x)(CN)(x)](-), [Fe(2)S(2)(SEt)(2)(-)(x)Cl(x)](-), [Fe(2)S(2)(SEt)(2)(-)(x)(CN)(x)](-), [Fe(2)S(2)Cl(2)(-)(x)(OAc)(x)](-) (OAc = acetate), and [Fe(2)S(2)(SEt)(2)(-)(x)(OPr)(x)](-) (OPr = propionate) (x = 0-2), were produced by collision-induced dissociation of the corresponding [4Fe-4S] complexes, and their electronic structures were studied by photoelectron spectroscopy. All the [2Fe-2S] complexes contain a [Fe(2)S(2)](+) core similar to that in reduced [2Fe] ferredoxins but with different coordination geometries. For the first three series, which only involve tricoordinated Fe sites, a linear relationship between the measured binding energies and the substitution number (x) was observed, revealing the independent ligand contributions to the total electron binding energies. The effect of the ligand increases in the order SEt --> Cl --> CN, conforming to their electron-withdrawing ability in the same order. The carboxylate ligands in the [Fe(2)S(2)Cl(2)(-)(x)(OAc)(x)](-) and [Fe(2)S(2)(SEt)(2)(-)(x)(OPr)(x)](-) complexes were observed to act as bidentate ligands, giving rise to tetracoordinated iron sites. This is different from their monodentate coordination behavior in the [4Fe-4S] cubane complexes, reflecting the high reactivity of the unsatisfied three-coordinate iron site in the [2Fe-2S] complexes. The [2Fe-2S] complexes with tetracoordinated iron sites exhibit lower electron binding energies, that is, higher reductive activity than the all tricoordinate planar clusters. The electronic structures of all the [2Fe-2S] complexes were shown to conform to the "inverted energy level scheme".

Electronic Structure and Intrinsic Redox Properties of [2Fe−2S]+ Clusters with Tri- and Tetracoordinate Iron Sites

Using potentially bidentate ligands (-SC2H4NH2), we produced [2Fe-2S]+ species of different coordination geometries by fission of [4Fe-4S]2+ complexes. Even though the ligands are monodentate in the cubane complexes, both mono- and bidentate complexes were observed in the [2Fe] fission products through self-assembly because of the high reactivity of the tricoordinate iron sites. The electronic structure of the [2Fe] species was probed using photoelectron spectroscopy and density functional calculations. It was found that tetracoordination significantly decreases the electron binding energies of the [2Fe] complexes, thus increasing the reducing capability of the [2Fe-2S]+ clusters.

Molecular dynamics simulation of truncated bovine adrenodoxin

The 128 amino acid long soluble protein adrenodoxin (Adx) is a typical member of the ferredoxin protein family that are electron carrier proteins with an iron-sulfur cofactor. Adx carries electrons from adrenodoxin reductase (AdR) to cytochrome P450s. Its binding modes to these proteins were previously characterized by site-directed mutagenesis, by X-ray crystallography for the complex Adx:AdR, and by NMR. However, no clear evidence has been provided for the driving force that promotes Adx detachment from AdR upon reduction. Here, we characterized the conformational dynamics of unbound Adx in the oxidized and reduced forms using 2-20 ns long molecular dynamics simulations. The most noticeable difference between both forms is the enhanced flexibility of the loop (47-51) surrounding the iron-sulfur cluster in the reduced form. Together with several structural displacements at the binding interface, this increased flexibility may be the key factor promoting unbinding of reduced Adx from AdR. This points to an intrinsic property of reduced Adx that drives dissociation.