Theory and simulation of proton-coupled electron transfer, hydrogen-atom transfer, and proton translocation in proteins

An electron density based analysis to establish the electronic adiabaticity of proton coupled electron transfer reactions

Electrons and protons are the main actors in play in proton coupled electron transfer (PCET) reactions, which are fundamental in many biological (i.e., photosynthesis and enzymatic reactions) and electrochemical processes. The mechanism, energetics and kinetics of PCET reactions are strongly controlled by the coupling between the transferred electrons and protons. Concerted PCET reactions are classified according to the electronical adiabaticity degree of the process. To discriminate among different mechanisms, we propose a new analysis based on the use of electron density based indexes. We choose, as test case, the 3-Methylphenoxyl/phenol system in two different conformations to show how the proposed analysis is a suitable tool to discriminate between the different degree of adiabaticity of PCET processes. The very low computational cost of this procedure is extremely promising to analyze and provide evidences of PCET mechanisms ruling the reactivity of many biological and catalytic systems.

Mechanisms for Hydrogen-Atom Abstraction by Mononuclear Copper(III) Cores: Hydrogen-Atom Transfer or Concerted Proton-Coupled Electron Transfer?

In a possibly biomimetic fashion, formally copper(III)-oxygen complexes LCu(III)-OH (1) and LCu(III)-OOCm (2) (L^2- = N,N'-bis(2,6-diisopropylphenyl)-2,6-pyridinedicarboxamide, Cm = α,α-dimethylbenzyl) have been shown to activate X-H bonds (X = C, O). Herein, we demonstrate similar X-H bond activation by a formally Cu(III) complex supported by the same dicarboxamido ligand, LCu(III)-O₂CAr¹ (3, Ar¹ = meta-chlorophenyl), and we compare its reactivity to that of 1 and 2. Kinetic measurements revealed a second order reaction with distinct differences in the rates: 1 reacts the fastest in the presence of O-H or C-H based substrates, followed by 3, which is followed by (unreactive) 2. The difference in reactivity is attributed to both a varying oxidizing ability of the studied complexes and to a variation in X-H bond functionalization mechanisms, which in these cases are characterized as either a hydrogen-atom transfer (HAT) or a concerted proton-coupled electron transfer (cPCET). Select theoretical tools have been employed to distinguish these two cases, both of which generally focus on whether the electron (e^-) and proton (H⁺) travel "together" as a true H atom, (HAT), or whether the H⁺ and e^- are transferred in concert, but travel between different donor/acceptor centers (cPCET). In this work, we reveal that both mechanisms are active for X-H bond activation by 1-3, with interesting variations as a function of substrate and copper functionality.

H2 Kinetic Isotope Fractionation Superimposed by Equilibrium Isotope Fractionation During Hydrogenase Activity of D. vulgaris Strain Miyazaki

We determined ²H stable isotope fractionation at natural abundances associated with hydrogenase activity by whole cells of Desulfovibrio vulgaris strain Miyazaki F expressing a NiFe(Se) hydrogenase. Inhibition of sulfate reduction by molybdate inhibited the overall oxidation of hydrogen but still facilitated an equilibrium isotope exchange reaction with water. The theoretical equilibrium isotope exchange δ²H-values of the chemical exchange reaction were identical to the hydrogenase reaction, as confirmed using three isotopically different waters with δ²H-values of – 62, +461, and + 1533‰. Expected kinetic isotope fractionation of hydrogen oxidation by non-inhibited cells was also superimposed by an equilibrium isotope exchange. The isotope effects were solely catalyzed biotically as hydrogen isotope signatures did not change in control experiments without cells of D. vulgaris Miyazaki.

Theoretical study of proton coupled electron transfer reaction in the light state of the AppA BLUF photoreceptor

The BLUF (blue light sensor using flavin adenine dinucleotide) domain is widely studied as a prototype for proton coupled electron transfer (PCET) reactions in biological systems. In this work, the photo-induced concerted PCET reaction from the light state of the AppA BLUF domain is investigated. To model the simultaneous transfer of two protons in the reaction, two-dimensional potential energy surfaces for the double proton transfer are first calculated for the locally excited and charge transfer states, which are then used to obtain the vibrational wave function overlaps and the vibrational energy levels. Contributions to the PCET rate constant from each pair of vibronic states are then analyzed using the theory based on the Fermi's golden rule. We show that, the recently proposed light state structure of the BLUF domain with a tautomerized Gln63 residue is consistent with the concerted transfer of one electron and two protons. It is also found that, thermal fluctuations of the protein structure, especially the proton donor-acceptor distances, play an important role in determining the PCET reaction rate. © 2018 Wiley Periodicals, Inc.

Structure, computational and biochemical analysis of PcCel45A endoglucanase from Phanerochaete chrysosporium and catalytic mechanisms of GH45 subfamily C members

The glycoside hydrolase family 45 (GH45) of carbohydrate modifying enzymes is mostly comprised of β-1,4-endoglucanases. Significant diversity between the GH45 members has prompted the division of this family into three subfamilies: A, B and C, which may differ in terms of the mechanism, general architecture, substrate binding and cleavage. Here, we use a combination of X-ray crystallography, bioinformatics, enzymatic assays, molecular dynamics simulations and site-directed mutagenesis experiments to characterize the structure, substrate binding and enzymatic specificity of the GH45 subfamily C endoglucanase from Phanerochaete chrysosporium (PcCel45A). We investigated the role played by different residues in the binding of the enzyme to cellulose oligomers of different lengths and examined the structural characteristics and dynamics of PcCel45A that make subfamily C so dissimilar to other members of the GH45 family. Due to the structural similarity shared between PcCel45A and domain I of expansins, comparative analysis of their substrate binding was also carried out. Our bioinformatics sequence analyses revealed that the hydrolysis mechanisms in GH45 subfamily C is not restricted to use of the imidic asparagine as a general base in the "Newton's cradle" catalytic mechanism recently proposed for this subfamily.

Hydrogen Gas Ameliorates Hepatic Reperfusion Injury After Prolonged Cold Preservation in Isolated Perfused Rat Liver

Hydrogen gas reduces ischemia and reperfusion injury (IRI) in the liver and other organs. However, the precise mechanism remains elusive. We investigated whether hydrogen gas ameliorated hepatic I/R injury after cold preservation. Rat liver was subjected to 48-h cold storage in University of Wisconsin solution. The graft was reperfused with oxygenated buffer with or without hydrogen at 37° for 90 min on an isolated perfusion apparatus, comprising the H₂ (+) and H₂ (-) groups, respectively. In the control group (CT), grafts were reperfused immediately without preservation. Graft function, injury, and circulatory status were assessed throughout the perfusion. Tissue samples at the end of perfusion were collected to determine histopathology, oxidative stress, and apoptosis. In the H₂ (-) group, IRI was indicated by a higher aspartate aminotransferase (AST), alanine aminotransferase (ALT) leakage, portal resistance, 8-hydroxy-2-deoxyguanosine-positive cell rate, apoptotic index, and endothelial endothelin-1 expression, together with reduced bile production, oxygen consumption, and GSH/GSSG ratio (vs. CT). In the H₂ (+) group, these harmful changes were significantly suppressed [vs. H₂ (-)]. Hydrogen gas reduced hepatic reperfusion injury after prolonged cold preservation via the maintenance of portal flow, by protecting mitochondrial function during the early phase of reperfusion, and via the suppression of oxidative stress and inflammatory cascades thereafter.

Proton-Coupled Electron Transfer and a Tyrosine-Histidine Pair in a Photosystem II-Inspired β-Hairpin Maquette: Kinetics on the Picosecond Time Scale

Photosystem II (PSII) and ribonucleotide reductase employ oxidation and reduction of the tyrosine aromatic ring in radical transport pathways. Tyrosine-based reactions involve either proton-coupled electron transfer (PCET) or electron transfer (ET) alone, depending on the pH and the pKa of tyrosine's phenolic oxygen. In PSII, a subset of the PCET reactions are mediated by a tyrosine-histidine redox-driven proton relay, YD-His189. Peptide A is a PSII-inspired β-hairpin, which contains a single tyrosine (Y5) and histidine (H14). Previous electrochemical characterization indicated that Peptide A conducts a net PCET reaction between Y5 and H14, which have a cross-strand π-π interaction. The kinetic impact of H14 has not yet been explored. Here, we address this question through time-resolved absorption spectroscopy and 280-nm photolysis, which generates a neutral tyrosyl radical. The formation and decay of the neutral tyrosyl radical at 410 nm were monitored in Peptide A and its variant, Peptide C, in which H14 is replaced by cyclohexylalanine (Cha14). Significantly, both electron transfer (ET, pL 11, L = lyonium) and PCET (pL 9) were accelerated in Peptide A and C, compared to model tyrosinate or tyrosine at the same pL. Increased electronic coupling, mediated by the peptide backbone, can account for this rate acceleration. Deuterium exchange gave no significant solvent isotope effect in the peptides. At pL 9, but not at pL 11, the reaction rate decreased when H14 was mutated to Cha14. This decrease in rate is attributed to an increase in reorganization energy in the Cha14 mutant. The Y5-H14 mechanism in Peptide A is reminiscent of proton- and electron-transfer events involving YD-H189 in PSII. These results document a mechanism by which proton donors and acceptors can regulate the rate of PCET reactions.

Experimental and Computational Evidence for the Reduction Mechanisms of Aromatic N-oxides by Aqueous Fe(II)-Tiron Complex

A combined experimental-theoretical approach was taken to elucidate the reduction mechanisms of five representative aromatic N-oxides (ANOs) by Fe(II)-tiron complex and to identify the rate-limiting step. Based on the possible types of complexes formed with the reductant, three groups of ANOs were studied: type I refers to those forming 5-membered ring complexes through the N and O atoms on the side chain; type II refers to those forming 6-membered ring complexes through the N-oxide O atom and the O atom on the side chain; and type III refers to complexation through the N-oxide O atom only. Density functional theory calculations suggested that the elementary reactions, including protonation, N-O bond cleavage, and the second electron transfer processes, are barrierless, indicating that the first electron transfer is rate-limiting. Consistent with the theoretical results, the experimental solvent isotope effect, KIEH, for the reduction of quinoline N-oxide (a type III ANO) was obtained to be 1.072 ± 0.025, suggesting protonation was not involved in the rate-limiting step. The measured nitrogen kinetic isotope effect, KIEN, for the reduction of pyridine N-oxide (a type III ANO) (1.022 ± 0.006) is in good agreement with the calculated KIEN for its first electron transfer (1.011-1.028), confirming that the first electron transfer is rate-limiting. Electrochemical cell experiments demonstrated that the electron transfer process can be facilitated significantly by type I complexation with FeL2(6-) (1:2 Fe(II)-tiron complex), to some extent by type II complexation with free Fe(II), but not by weak type III complexation.

A unifying neuro-fasciagenic model of somatic dysfunction - Underlying mechanisms and treatment - Part II

This paper offers an extensive review of the main fascia-mediated mechanisms underlying various therapeutic processes of clinical relevance for manual therapy. The concept of somatic dysfunction is revisited in light of the several fascial influences that may come into play during and after manual treatment. A change in perspective is thus proposed: from a nociceptive model that for decades has viewed somatic dysfunction as a neurologically-mediated phenomenon, to a unifying neuro-fascial model that integrates neural influences into a multifactorial and multidimensional interpretation of manual therapeutic effects as being partially, if not entirely, mediated by the fascia. By taking into consideration a wide spectrum of fascia-related factors - from cell-based mechanisms to cognitive and behavioural influences - a model emerges suggesting, amongst other results, a multidisciplinary-approach to the intervention of somatic dysfunction. Finally, it is proposed that a sixth osteopathic 'meta-model' - the connective tissue-fascial model - be added to the existing five models in osteopathic philosophy as the main interface between all body systems, thus providing a structural and functional framework for the body's homoeostatic potential and its inherent abilities to heal.

A unifying neuro-fasciagenic model of somatic dysfunction - underlying mechanisms and treatment - Part I

This paper offers an extensive review of the main fascia-mediated mechanisms underlying various dysfunctional and pathophysiological processes of clinical relevance for manual therapy. The concept of somatic dysfunction is revisited in light of the diverse fascial influences that may come into play in its genesis and maintenance. A change in perspective is thus proposed: from a nociceptive model that for decades has viewed somatic dysfunction as a neurologically-mediated phenomenon, to a unifying fascial model that integrates neural influences into a multifactorial and multidimensional interpretation of dysfunctional process as being partially, if not entirely, mediated by the fascia.

Hydrogen bonding networks tune proton-coupled redox steps during the enzymatic six-electron conversion of nitrite to ammonia

Multielectron multiproton reactions play an important role in both biological systems and chemical reactions involved in energy storage and manipulation. A key strategy employed by nature in achieving such complex chemistry is the use of proton-coupled redox steps. Cytochrome c nitrite reductase (ccNiR) catalyzes the six-electron seven-proton reduction of nitrite to ammonia. While a catalytic mechanism for ccNiR has been proposed on the basis of studies combining computation and crystallography, there have been few studies directly addressing the nature of the proton-coupled events that are predicted to occur along the nitrite reduction pathway. Here we use protein film voltammetry to directly interrogate the proton-coupled steps that occur during nitrite reduction by ccNiR. We find that conversion of nitrite to ammonia by ccNiR adsorbed to graphite electrodes is defined by two distinct phases; one is proton-coupled, and the other is not. Mutation of key active site residues (H257, R103, and Y206) modulates these phases and specifically alters the properties of the detected proton-dependent step but does not inhibit the ability of ccNiR to conduct the full reduction of nitrite to ammonia. We conclude that the active site residues examined are responsible for tuning the protonation steps that occur during catalysis, likely through an extensive hydrogen bonding network, but are not necessarily required for the reaction to proceed. These results provide important insight into how enzymes can specifically tune proton- and electron transfer steps to achieve high turnover numbers in a physiological pH range.

Inner reorganization limiting electron transfer controlled hydrogen bonding: intra- vs. intermolecular effects

In this work, experimental evidence of the influence of the electron transfer kinetics during electron transfer controlled hydrogen bonding between anion radicals of metronidazole and ornidazole, derivatives of 5-nitro-imidazole, and 1,3-diethylurea as the hydrogen bond donor, is presented. Analysis of the variations of voltammetric EpIcvs. log KB[DH], where KB is the binding constant, allowed us to determine the values of the binding constant and also the electron transfer rate k, confirmed by experiments obtained at different scan rates. Electronic structure calculations at the BHandHLYP/6-311++G(2d,2p) level for metronidazole, including the solvent effect by the Cramer/Truhlar model, suggested that the minimum energy conformer is stabilized by intramolecular hydrogen bonding. In this structure, the inner reorganization energy, λi,j, contributes significantly (0.5 eV) to the total reorganization energy of electron transfer, thus leading to a diminishment of the experimental k.

Concerted proton-electron transfers: fundamentals and recent developments

Proton-coupled electron transfers (PCET) are ubiquitous in natural and synthetic processes. This review focuses on reactions where the two events are concerted. Semiclassical models of such reactions allow their kinetic characterization through activation versus driving force relationships, estimates of reorganization energies, effects of the nature of the proton acceptor, and H/D kinetic isotope effect as well as their discrimination from stepwise pathways. Several homogeneous reactions (through stopped-flow and laser flash-quench techniques) and electrochemical processes are discussed in this framework. Once the way has been rid of the improper notion of pH-dependent driving force, water appears as a remarkable proton acceptor in terms of reorganization energy and pre-exponential factor, thanks to its H-bonded and H-bonding properties, similarly to purposely synthesized "H-bond train" molecules. The most recent developments are in modeling and description of emblematic concerted proton-electron transfer (CPET) reactions associated with the breaking of a heavy-atom bond in an all-concerted process.

Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation

Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Role of the -PEWY-glutamate in catalysis at the Q(o)-site of the Cyt bc(1) complex

We re-examine the pH dependence of partial processes of ubihydroquinone (QH(2)) turnover in Glu-295 mutants in Rhodobacter sphaeroides to clarify the mechanistic role. In more crippled mutants, the bell-shaped pH profile of wildtype was replaced by dependence on a single pK at ~8.5 favoring electron transfer. Loss of the pK at 6.5 reflects a change in the rate-limiting step from the first to the second electron transfer. Over the range of pH 6-8, no major pH dependence of formation of the initial reaction complex was seen, and the rates of bypass reactions were similar to the wildtype. Occupancy of the Q(o)-site by semiquinone (SQ) was similar in the wildtype and the Glu→Trp mutant. Since heme b(L) is initially oxidized in the latter, the bifurcated reaction can still occur, allowing estimation of an empirical rate constant <10(3)s(-1) for reduction of heme b(L) by SQ from the domain distal from heme b(L), a value 1000-fold smaller than that expected from distance. If the pK ~8.5 in mutant strains is due to deprotonation of the neutral semiquinone, with Q(•-) as electron donor to heme b(L), then in wildtype this low value would preclude mechanisms for normal flux in which semiquinone is constrained to this domain. A kinetic model in which Glu-295 catalyzes H(+) transfer from QH•, and delivery of the H(+) to exit channel(s) by rotational displacement, and facilitates rapid electron transfer from SQ to heme b(L) by allowing Q(•-) to move closer to the heme, accounts well for the observations.

Multiple-site concerted proton-electron transfer reactions of hydrogen-bonded phenols are nonadiabatic and well described by semiclassical Marcus theory

Photo-oxidations of hydrogen-bonded phenols using excited-state polyarenes are described to derive fundamental understanding of multiple-site concerted proton-electron transfer reactions (MS-CPET). Experiments have examined phenol bases having -CPh(2)NH(2), -Py, and -CH(2)Py groups ortho to the phenol hydroxyl group and tert-butyl groups in the 4,6-positions for stability (HOAr-NH(2), HOAr-Py, and HOAr-CH(2)Py, respectively; Py = pyridyl; Ph = phenyl). The photo-oxidations proceed by intramolecular proton transfer from the phenol to the pendent base concerted with electron transfer to the excited polyarene. For comparison, 2,4,6-(t)Bu(3)C(6)H(2)OH, a phenol without a pendent base and tert-butyl groups in the 2,4,6-positions, has also been examined. Many of these bimolecular reactions are fast, with rate constants near the diffusion limit. Combining the photochemical k(CPET) values with those from prior thermal stopped-flow kinetic studies gives data sets for the oxidations of HOAr-NH(2) and HOAr-CH(2)Py that span over 10(7) in k(CPET) and nearly 0.9 eV in driving force (ΔG(o)'). Plots of log(k(CPET)) vs ΔG(o)', including both excited-state anthracenes and ground state aminium radical cations, define a single Marcus parabola in each case. These two data sets are thus well described by semiclassical Marcus theory, providing a strong validation of the use of this theory for MS-CPET. The parabolas give λ(CPET) ≅ 1.15-1.2 eV and H(ab) ≅ 20-30 cm(-1). These experiments represent the most direct measurements of H(ab) for MS-CPET reactions to date. Although rate constants are available only up to the diffusion limit, the parabolas clearly peak well below the adiabatic limit of ca. 6 × 10(12) s(-1). Thus, this is a very clear demonstration that the reactions are nonadiabatic. The nonadiabatic character slows the reactions by a factor of ~45. Results for the oxidation of HOAr-Py, in which the phenol and base are conjugated, and for oxidation of 2,4,6-(t)Bu(3)C(6)H(2)OH, which lacks a base, show that both have substantially lower λ and larger pre-exponential terms. The implications of these results for MS-CPET reactions are discussed.

Quantum dynamics in continuum for proton transport--generalized correlation

As a key process of many biological reactions such as biological energy transduction or human sensory systems, proton transport has attracted much research attention in biological, biophysical, and mathematical fields. A quantum dynamics in continuum framework has been proposed to study proton permeation through membrane proteins in our earlier work and the present work focuses on the generalized correlation of protons with their environment. Being complementary to electrostatic potentials, generalized correlations consist of proton-proton, proton-ion, proton-protein, and proton-water interactions. In our approach, protons are treated as quantum particles while other components of generalized correlations are described classically and in different levels of approximations upon simulation feasibility and difficulty. Specifically, the membrane protein is modeled as a group of discrete atoms, while ion densities are approximated by Boltzmann distributions, and water molecules are represented as a dielectric continuum. These proton-environment interactions are formulated as convolutions between number densities of species and their corresponding interaction kernels, in which parameters are obtained from experimental data. In the present formulation, generalized correlations are important components in the total Hamiltonian of protons, and thus is seamlessly embedded in the multiscale/multiphysics total variational model of the system. It takes care of non-electrostatic interactions, including the finite size effect, the geometry confinement induced channel barriers, dehydration and hydrogen bond effects, etc. The variational principle or the Euler-Lagrange equation is utilized to minimize the total energy functional, which includes the total Hamiltonian of protons, and obtain a new version of generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation and generalized Kohn-Sham equation. A set of numerical algorithms, such as the matched interface and boundary method, the Dirichlet to Neumann mapping, Gummel iteration, and Krylov space techniques, is employed to improve the accuracy, efficiency, and robustness of model simulations. Finally, comparisons between the present model predictions and experimental data of current-voltage curves, as well as current-concentration curves of the Gramicidin A channel, verify our new model.

Energy transfer mediated by asymmetric hydrogen-bonded interfaces

Amidine-appended ferrocene derivatives form a supramolecular assembly with Ru(ii)(bpy-COOH) (L)22+ complexes (bpy-COOH is 4-CO2H-4'-CH3-bpy and L = bpy, 2,2'-bipyridine or btfmbpy, 4,4'-bis (trifluoromethyl)-2,2'-bipyridine). Steady-state, time-resolved spectroscopy and kinetic isotope effects establish that the metal-to-ligand charge transfer excited states of the Ru(ii) complexes are quenched by proton-coupled energy transfer (PCEnT). These results show that proton motion can be effective in mediating not only electron transfer (ET) but energy transfer (EnT) as well.

Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface

Proton transport plays an important role in biological energy transduction and sensory systems. Therefore, it has attracted much attention in biological science and biomedical engineering in the past few decades. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The density of all other ions in the solvent is assumed to obey the Boltzmann distribution in a dynamic manner. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic scale. A variational solute-solvent interface is designed to separate the explicit molecule and implicit solvent regions. We formulate a total free-energy functional to put proton kinetic and potential energies, the free energy of all other ions, and the polar and nonpolar energies of the whole system on an equal footing. The variational principle is employed to derive coupled governing equations for the proton transport system. Generalized Laplace-Beltrami equation, generalized Poisson-Boltzmann equation, and generalized Kohn-Sham equation are obtained from the present variational framework. The variational solvent-solute interface is generated and visualized to facilitate the multiscale discrete/continuum/quantum descriptions. Theoretical formulations for the proton density and conductance are constructed based on fundamental laws of physics. A number of mathematical algorithms, including the Dirichlet-to-Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The gramicidin A channel is used to validate the performance of the proposed proton transport model and demonstrate the efficiency of the proposed mathematical algorithms. The proton channel conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and confirms the proposed model.

Proton coupled electron transfer and redox active tyrosines in Photosystem II

In this article, progress in understanding proton coupled electron transfer (PCET) in Photosystem II is reviewed. Changes in acidity/basicity may accompany oxidation/reduction reactions in biological catalysis. Alterations in the proton transfer pathway can then be used to alter the rates of the electron transfer reactions. Studies of the bioenergetic complexes have played a central role in advancing our understanding of PCET. Because oxidation of the tyrosine results in deprotonation of the phenolic oxygen, redox active tyrosines are involved in PCET reactions in several enzymes. This review focuses on PCET involving the redox active tyrosines in Photosystem II. Photosystem II catalyzes the light-driven oxidation of water and reduction of plastoquinone. Photosystem II provides a paradigm for the study of redox active tyrosines, because this photosynthetic reaction center contains two tyrosines with different roles in catalysis. The tyrosines, YZ and YD, exhibit differences in kinetics and midpoint potentials, and these differences may be due to noncovalent interactions with the protein environment. Here, studies of YD and YZ and relevant model compounds are described.

Partial steps of charge translocation in the nonpumping N139L mutant of Rhodobacter sphaeroides cytochrome c oxidase with a blocked D-channel

The N139L substitution in the D-channel of cytochrome oxidase from Rhodobacter sphaeroides results in an approximately 15-fold decrease in the turnover number and a loss of proton pumping. Time-resolved absorption and electrometric assays of the F --> O transition in the N139L mutant oxidase result in three major findings. (1) Oxidation of the reduced enzyme by O(2) shows approximately 200-fold inhibition of the F --> O step (k approximately 2 s(-1) at pH 8) which is not compatible with enzyme turnover ( approximately 30 s(-1)). Presumably, an abnormal intermediate F(deprotonated) is formed under these conditions, one proton-deficient relative to a normal F state. In contrast, the F --> O transition in N139L oxidase induced by single-electron photoreduction of intermediate F, generated by reaction of the oxidized enzyme with H(2)O(2), decelerates to an extent compatible with enzyme turnover. (2) In the N139L mutant, the protonic phase of Deltapsi generation coupled to the flash-induced F --> O transition greatly decreases in rate and magnitude and can be assigned to the movement of a proton from E286 to the binuclear site, required for reduction of heme a(3) from the Fe(4+) horizontal lineO(2-) state to the Fe(3+)-OH(-) state. Electrogenic reprotonation of E286 from the inner aqueous phase is missing from the F --> O step in the mutant. (3) In the N139L mutant, the KCN-insensitive rapid electrogenic phase may be composed of two components with lifetimes of approximately 10 and approximately 40 mus and a magnitude ratio of approximately 3:2. The 10 mus phase matches vectorial electron transfer from Cu(A) to heme a, whereas the 40 mus component is assigned to intraprotein proton displacement across approximately 20% of the membrane dielectric thickness. This proton displacement might be triggered by rotation of the charged K362 side chain coupled to heme a reduction. The two components of the rapid electrogenic phase have been resolved subsequently with other D-channel mutants as well as with cyanide-inhibited wild-type oxidase. The finding helps to reconcile the unusually high relative contribution of the microsecond electrogenic phase in the bacterial enzyme ( approximately 30%) with the net electrogenicity of the F --> O transition coupled to transmembrane transfer of two charges per electron.

Comparative PCET study of a donor-acceptor pair linked by ionized and nonionized asymmetric hydrogen-bonded interfaces

A Zn(II) amidinium porphyrin is the excited-state electron donor (D) to a naphthalene diimide acceptor (A) appended with either a carboxylate or sulfonate functionality. The two-point hydrogen bond (...[H(+)]...) formed between the amidinium and carboxylate or sulfonate functionalities establishes a proton-coupled electron transfer (PCET) pathway for charge transfer. The two D...[H(+)]...A assemblies differ only by the proton configuration within the hydrogen-bonding interface. Specifically, the amidinium ion transfers a proton to the carboxylate to form a nonionized amidine-carboxylic acid two-point hydrogen network, whereas the amidinium retains both protons when bound to the sulfonate functionality, forming an ionized amidinium-sulfonate two-point hydrogen bond network. These two interface configurations within the dyads thus allow for a direct comparison of the PCET kinetics for the same donor and acceptor juxtaposed by ionized and nonionized hydrogen-bonded interfaces. Analysis of the PCET kinetics ascertained from transient absorption and transient emission spectroscopy reveals that the ionized interface is more strongly impacted by the local solvent environment, thus establishing that the initial static configuration of the proton interface is a critical determinant in the kinetics of PCET.

Demonstration of proton-coupled electron transfer in the copper-containing nitrite reductases

The reduction of nitrite (NO2-) into nitric oxide (NO), catalyzed by nitrite reductase, is an important reaction in the denitrification pathway. In this study, the catalytic mechanism of the copper-containing nitrite reductase from Alcaligenes xylosoxidans (AxNiR) has been studied using single and multiple turnover experiments at pH 7.0 and is shown to involve two protons. A novel steady-state assay was developed, in which deoxyhemoglobin was employed as an NO scavenger. A moderate solvent kinetic isotope effect (SKIE) of 1.3 +/- 0.1 indicated the involvement of one protonation to the rate-limiting catalytic step. Laser photoexcitation experiments have been used to obtain single turnover data in H2O and D2O, which report on steps kinetically linked to inter-copper electron transfer (ET). In the absence of nitrite, a normal SKIE of approximately 1.33 +/- 0.05 was obtained, suggesting a protonation event that is kinetically linked to ET in substrate-free AxNiR. A nitrite titration gave a normal hyperbolic behavior for the deuterated sample. However, in H2O an unusual decrease in rate was observed at low nitrite concentrations followed by a subsequent acceleration in rate at nitrite concentrations of >10 mM. As a consequence, the observed ET process was faster in D2O than in H2O above 0.1 mM nitrite, resulting in an inverted SKIE, which featured a significant dependence on the substrate concentration with a minimum value of approximately 0.61 +/- 0.02 between 3 and 10 mM. Our work provides the first experimental demonstration of proton-coupled electron transfer in both the resting and substrate-bound AxNiR, and two protons were found to be involved in turnover.

Theoretical Studies of Proton-Coupled Electron Transfer: Models and Concepts Relevant to Bioenergetics

Theoretical studies of proton-coupled electron transfer (PCET) reactions for model systems provide insight into fundamental concepts relevant to bioenergetics. A dynamical theoretical formulation for vibronically nonadiabatic PCET reactions has been developed. This theory enables the calculation of rates and kinetic isotope effects, as well as the pH and temperature dependences, of PCET reactions. Methods for calculating the vibronic couplings for PCET systems have also been developed and implemented. These theoretical approaches have been applied to a wide range of PCET reactions, including tyrosyl radical generation in a tyrosine-bound rhenium polypyridyl complex, phenoxyl/phenol and benzyl/toluene self-exchange reactions, and hydrogen abstraction catalyzed by the enzyme lipoxygenase. These applications have elucidated some of the key underlying physical principles of PCET reactions. The tools and concepts derived from these theoretical studies provide the foundation for future theoretical studies of PCET in more complex bioenergetic systems such as Photosystem II.

Adiabatic and Non-adiabatic Concerted Proton−Electron Transfers. Temperature Effects in the Oxidation of Intramolecularly Hydrogen-Bonded Phenols

The one-electron electrochemical and homogeneous oxidations of two closely similar aminophenols that undergo a concerted proton-electron transfer reaction, in which the phenolic proton is transferred to the nitrogen atom in concert with electron transfer, are taken as examples to test procedures that allow the separate determination of the degree of adiabaticity and the reorganization energy of the reaction. The Marcus (or Marcus-Hush-Levich) formalism is applicable in both cases, but not necessarily in its adiabatic version. Linearization of the activation-driving force laws simplifies the treatment of the kinetic data, notably allowing the use of Arrhenius plots to treat the temperature dependence of the rate constant. A correct estimation of the adiabaticity and reorganization energy requires the determination of the variation of the driving force with temperature. Application of these procedures led to the conclusion that, unlike previous reports, the homogeneous reaction is non-adiabatic, with a transmission coefficient of the order of 0.005, and that the self-exchange reorganization energy is about 1 eV lower than previously estimated. With such systems, the intramolecular reorganization energy, although sizable, is in fact rather modest, being only slightly larger than that for the outer-sphere electron transfer that produced the cation radical. The electrochemical reaction is, in contrast, adiabatic, as revealed by the temperature dependence of its standard rate constant obtained from cyclic voltammetric experiments. This difference in behavior is deemed to derive from the effect of the strong electric field within which the electrochemical reaction takes place, stabilizing a zwitterionic form of the reactant (in which the proton has been transferred from oxygen to nitrogen). Taking this difference in adiabaticity into account, the magnitudes of the reorganization energies of the two reactions appear to be quite compatible with one another, as revealed by an analysis of the solvent and intramolecular contributions in both cases.

The Possible Role of Proton-Coupled Electron Transfer (PCET) in Water Oxidation by Photosystem II

All higher life forms use oxygen and respiration as their primary energy source. The oxygen comes from water by solar-energy conversion in photosynthetic membranes. In green plants, light absorption in photosystem II (PSII) drives electron-transfer activation of the oxygen-evolving complex (OEC). The mechanism of water oxidation by the OEC has long been a subject of great interest to biologists and chemists. With the availability of new molecular-level protein structures from X-ray crystallography and EXAFS, as well as the accumulated results from numerous experiments and theoretical studies, it is possible to suggest how water may be oxidized at the OEC. An integrated sequence of light-driven reactions that exploit coupled electron-proton transfer (EPT) could be the key to water oxidation. When these reactions are combined with long-range proton transfer (by sequential local proton transfers), it may be possible to view the OEC as an intricate structure that is "wired for protons".

Ab initio calculation of proton-coupled electron transfer rates using the external-potential representation: A ubiquinol complex in solution

In quantum-mechanical/molecular-mechanical (QM/MM) treatment of chemical reactions in condensed phases, one solves the electronic Schrodinger equation for the solute (or an active site) under the electrostatic field from the environment. This Schrodinger equation depends parametrically on the solute nuclear coordinates R and the external electrostatic potential V. This fact suggests that one may use R and V as natural collective coordinates for describing the entire system, where V plays the role of collective solvent variables. In this paper such an (R,V) representation of the QM/MM canonical ensemble is described, with particular focus on how to treat charge transfer processes in this representation. As an example, the above method is applied to the proton-coupled electron transfer of a ubiquinol analog with phenoxyl radical in acetonitrile solvent. Ab initio free-energy surfaces are calculated as functions of R and V using the reference interaction site model self-consistent field method, the equilibrium points and the minimum free-energy crossing point are located in the (R,V) space, and then the kinetic isotope effects (KIEs) are evaluated approximately. The results suggest that a stiffer proton potential at the transition state may be responsible for unusual KIEs observed experimentally for related systems.

Minimum Energy Pathways for Proton Transfer between Adjacent Sites Exposed to Water

The capacity to transfer protons between surface groups is an innate property of many proteins. The transfer of a proton between donor and acceptor, located as far as 6-7 A apart, necessitates the participation of water molecules in the process. In a previous study we investigated the mechanism of proton transfer (PT) between bulk exposed sites, a few ångströms apart, using as a model the proton exchange between the proton-binding sites of the fluorescein molecule in dilute aqueous solution.1 The present study expands the understanding of PT reactions between adjacent sites exposed to water through the calculation the minimum energy pathways (MEPs) by the conjugate peak refinement algorithm2 and a quantum-mechanical potential. The PT reaction trajectories were calculated for the fluorescein system with an increasing number of water molecules. The MEP calculations reveal that the transition state is highly strained and involves a supramolecular structure in which fluorescein and the interconnecting water molecules are covalently bonded together and the protons are shared between neighboring oxygens. These findings are in accord with the high activation energy, as measured for the reaction, and indicate that PT reactions on the surface proceed by a semi- or fully concerted rather than stepwise mechanism. A similar mechanism is assumed to be operative on the surface of proteins and renders water-mediated PT reactions as highly efficient as they are.

Design principles of proton-pumping haem-copper oxidases

Transmembrane electrochemical proton gradients are used to store free energy in biological systems, and to drive the synthesis of biomolecules and transmembrane transport. These gradients are maintained by membrane-bound proton transporters that employ free energy provided by, for example, electron transfer or light. In recent years, the structures of several membrane proteins involved in proton translocation have been determined, and indicate that both protein-bound water molecules and protonatable amino acid residues play central roles in transmembrane proton conduction. From these structures, in combination with functional studies, have emerged general principles of proton transfer across membranes and control mechanisms for such reactions, in particular with regard to the electron-transfer-driven proton pump cytochrome c oxidase.