Electron transfer in a crystalline cytochrome with four hemes.

Diffusion of electrons over distances on the order of 100 µm has been observed in crystals of a small tetraheme cytochrome (STC) from Shewanella oneidensis [J. Huang et al. J. Am. Chem. Soc. 142, 10459-10467 (2020)]. Electron transfer between hemes in adjacent subunits of the crystal is slower and more strongly dependent on temperature than had been expected based on semiclassical electron-transfer theory. We here explore explanations for these findings by molecular-dynamics simulations of crystalline and monomeric STC. New procedures are developed for including time-dependent quantum mechanical energy differences in the gap between the energies of the reactant and product states and for evaluating fluctuations of the electronic-interaction matrix element that couples the two hemes. Rate constants for electron transfer are calculated from the time- and temperature-dependent energy gaps, coupling factors, and Franck-Condon-weighted densities of states using an expression with no freely adjustable parameters. Back reactions are considered, as are the effects of various protonation states of the carboxyl groups on the heme side chains. Interactions with water are found to dominate the fluctuations of the energy gap between the reactant and product states. The calculated rate constant for electron transfer from heme IV to heme Ib in a neighboring subunit at 300 K agrees well with the measured value. However, the calculated activation energy of the reaction in the crystal is considerably smaller than observed. We suggest two possible explanations for this discrepancy. The calculated rate constant for transfer from heme I to II within the same subunit of the crystal is about one-third that for monomeric STC in solution.

Calculated solvent reorganization entropies, free energies, and fluctuations of the energy gaps for intramolecular electron transfer and excitation of the solvatochromic dye B30.

Intramolecular electron transfer between two biphenyl groups linked by an androstane spacer and excitation of the pyridinium-N-phenolate betaine dye B30 to the first excited singlet state are studied by quantum/classical molecular-dynamics simulations at temperatures between 150 and 300 K in solvents with a range of polarities. Temperature dependences of the solvent reorganization energies, free energies, entropies, and the inhomogeneous broadening of B30's absorption band are examined. The variances of fluctuations of the energy gap between the reactant and product states do not have the direct proportionality to temperature that often is assumed to hold. An explanation for the observations is suggested.

Temperature-dependent solvent reorganization entropies, free energies, and transition dipole strengths for the photoexcitation of Reichardt's dye B30.

Absorption spectra of the solvatochromic dye 2,6-diphenyl-4-2,4,6-triphenyl-1-pyridinophenolate (B30) were measured in seven solvents of varying polarity over temperature ranging from each solvent's freezing point to 300 K. The excitation energies and their variances allowed calculations of the solvent reorganization energies, reorganization free energies and reorganization entropies as functions of temperature. The entropies of solvent packing around the chromophore are found to make major contributions to the reorganization free energies. The variances of the excitation energies depend only weakly on temperature, in disagreement with an expression that is often used for solvent reorganization free energies. Polar solvents reduce the transition dipole strength of B30's long-wavelength absorption band, probably because interactions with the solvent enhance the charge-transfer character of the transition. The dipole strength drops further at low temperatures.

In memory of Vladimir Anatolievich Shuvalov (1943-2022): an outstanding biophysicist.

We present here a tribute to one of the foremost biophysicists of our time, Vladimir Anatolievich Shuvalov, who made important contributions in bioenergetics, especially on the primary steps of conversion of light energy into charge-separated states in both anoxygenic and oxygenic photosynthesis. For this, he and his research team exploited pico- and femtosecond transient absorption spectroscopy, photodichroism & circular dichroism spectroscopy, light-induced FTIR (Fourier-transform infrared) spectroscopy, and hole-burning spectroscopy. We remember him for his outstanding leadership and for being a wonderful mentor to many scientists in this area. Reminiscences by many [Suleyman Allakhverdiev (Russia); Robert Blankenship (USA); Richard Cogdell (UK); Arvi Freiberg (Estonia); Govindjee Govindjee (USA); Alexander Krasnovsky, jr, (Russia); William Parson (USA); Andrei Razjivin (Russia); Jian- Ren Shen (Japan); Sergei Shuvalov (Russia); Lyudmilla Vasilieva (Russia); and Andrei Yakovlev (Russia)] have included not only his wonderful personal character, but his outstanding scientific research.

Mesoscopic to Macroscopic Electron Transfer by Hopping in a Crystal Network of Cytochromes.

Rapid and directed electron transfer (ET) is essential for biological processes. While the rates of ET over 1-2 nm in proteins can largely be described by simplified nonadiabatic theory, it is not known how these processes scale to microscopic distances. We generated crystalline lattices of Small Tetraheme Cytochromes (STC) forming well-defined, three-dimensional networks of closely spaced redox centers that appear to be nearly ideal for multistep ET. Electrons were injected into specific locations in the STC crystals by direct photoreduction, and their redistribution was monitored by imaging. The results demonstrate ET over mesoscopic to microscopic (∼100 µm) distances through sequential hopping in a biologically based heme network. We estimate that a hypothetical "nanowire" composed of crystalline STC with a cross-section of about 100 cytochromes could support the anaerobic respiration of a Shewanella cell. The crystalline lattice insulates mobile electrons from oxidation by O2, as compared to those in cytochromes in solution, potentially allowing for efficient delivery of current without production of reactive oxygen species. The platform allows direct tests of whether the assumptions based on short-range ET hold for sequential ET over mesoscopic distances. We estimate that the interprotein ET across 6 Å between hemes in adjacent proteins was about 105 s-1, about 100-fold slower than expectations based on simplified theory. More detailed analyses implied that additional factors, possibly contributed by the crystal lattice, may strongly impact mesoscale ET mainly by increasing the reorganizational energy of interprotein ET, which suggests design strategies for engineering improved nanowires suitable for future bioelectronic materials.

Generalizing the Marcus equation.

The Marcus equation for the rate of an electron-transfer reaction can be generalized to cover larger electronic-interaction matrix elements, irregular free-energy surfaces, and coupling to multiple vibrational modes and to recognize the different effects of vibrational relaxations and pure dephasing. Almost all the information needed to calculate the rate constant can be obtained from a quantum-classical molecular dynamics simulation of the system in the reactant state. Because the final expression for the rate constant does not depend on the reorganization energy, it is insensitive to slow relaxations that follow the reaction.

Effects of Free Energy and Solvent on Rates of Intramolecular Electron Transfer in Organic Radical Anions.

Rates of intramolecular electron transfer from a 1,1'-biphenylyl radical anion to six different acceptors on an androstane scaffold are examined with the aid of a theory that was developed recently to include effects of vibrational relaxations and dephasing. The electronic-interaction matrix element and other parameters needed for the theory are obtained by quantum-mechanical/molecular-mechanical simulations of the reactions in five solvents ranging from iso-octane to methyltetrahydrofuran. Intramolecular vibrational modes that are coupled to electron transfer are resolved in simulations in iso-octane and cyclohexane. The energies and coupling factors for these modes allow extension of the theory to incorporate transitions to and from excited vibrational levels. The calculated rates of electron transfer agree well with experimental measurements from the literature, except for reactions in which excited electronic states of the products become important.

Competition between tryptophan fluorescence and electron transfer during unfolding of the villin headpiece.

The 35-residue, C-terminal headpiece subdomain of the protein villin folds to a stable structure on a microsecond time scale and has served as a model system in numerous studies of protein folding. To obtain a convenient spectroscopic probe of the folding dynamics, Kubelka et al. introduced an ionized histidine residue at position 27, with the expectation that it would quench the fluorescence of tryptophan 23 in the folded protein by extracting an electron from the excited indole ring [Kubelka, J., et al. (2003) J. Mol. Biol. 329, 625-630]. Although the fluorescence yield decreased as anticipated when the protein folded, it was not clear that the side chains of the two residues were sufficiently close together for electron transfer to compete effectively with fluorescence. Here, hybrid classical-quantum mechanical molecular dynamics simulations are used to examine the rates of transfer of an electron from the excited tryptophan to various possible acceptors in the modified headpiece and a smaller fragment comprised of residues 21-27 (HP7). The dominant reaction is found to be transfer to the amide group on the carboxyl side of W23 (amide a24). This process is energetically favorable and has a large coupling factor in the folded protein at 280 K but becomes unfavorable as HP7 unfolds at higher temperatures. Changes in electrostatic interactions of the solvent and other parts of the protein with the indole ring and a24 contribute importantly to this change in energy.

Entropy-Enthalpy Compensation in Electron-Transfer Processes.

Solvent reorganization energies, free energies, and entropies are obtained for photoexcitation of three molecules that exhibit strong solvatochromism [Nile red, 5-(dimethylamino)-5'-nitro-2,2-bisthiophene, and Reichardt's dye B30] by measuring their optical absorption spectra at temperatures between 150 and 300 K in solvents with a range of polarities. Energies, free energies, and entropies of solvent reorganization are also obtained from computer simulations of three intramolecular electron-transfer reactions (charge separation and recombination in Zn-porphyrin-quinone cyclophane and charge transfer in a bis-biphenylandrostane radical anion). Entropy-enthalpy compensation in the solvent reorganization free energy for photoexcitation or electron transfer is found to be essentially complete (having nearly equal and opposite contributions from entropic and enthalpic effects) for all of the processes with solvent reorganization energies less than about 0.1 eV. Compensation becomes less complete as the reorganization energy becomes larger. A semiclassical treatment of the solvent reorganization entropy can rationalize these results.

A temperature-dependent conformational change of NADH oxidase from Thermus thermophilus HB8.

Using molecular dynamics simulations and steady-state fluorescence spectroscopy, we have identified a conformational change in the active site of a thermophilic flavoenzyme, NADH oxidase from Thermus thermophilus HB8 (NOX). The enzyme's far-UV circular dichroism spectrum, intrinsic tryptophan fluorescence, and apparent molecular weight measured by dynamic light scattering varied little between 25 and 75°C. However, the fluorescence of the tightly bound FAD cofactor increased approximately fourfold over this temperature range. This effect appears not to be due to aggregation, unfolding, cofactor dissociation, or changes in quaternary structure. We therefore attribute the change in flavin fluorescence to a temperature-dependent conformational change involving the NOX active site. Molecular dynamics simulations and the effects of mutating aromatic residues near the flavin suggest that the change in fluorescence results from a decrease in quenching by electron transfer from tyrosine 137 to the flavin.

Reorganization Energies, Entropies, and Free Energy Surfaces for Electron Transfer.

Reorganization energies for an intramolecular self-exchange electron-transfer reaction are calculated by quantum-classical molecular dynamics simulations in four solvents with varying polarity and at temperatures ranging from 250 to 350 K. The reorganization free energies for polar solvents decrease systematically with increasing temperature, indicating that they include substantial contributions from entropy changes. The variances of the energy gap between the reactant and product states have a major component that is relatively insensitive to temperature. Explanations are suggested for these observations, which appear to necessitate rethinking the free energy functions of a distributed coordinate that frequently are used in discussions of reaction dynamics.

Dynamics of the Excited State in Photosynthetic Bacterial Reaction Centers.

In the initial charge-separation reaction of photosynthetic bacterial reaction centers, a dimer of strongly interacting bacteriochlorophylls (P) transfers an electron to a third bacteriochlorophyll (BL). It has been suggested that light first generates an exciton state of the dimer and that an electron then moves from one bacteriochlorophyll to the other within P to form a charge-transfer state (PL+PM-), which passes an electron to BL. This scheme, however, is at odds with the most economical analysis of the spectroscopic properties of the reaction center and particularly with the unusual temperature dependence of the long-wavelength absorption band. The present paper explores this conflict with the aid of a simple model in which exciton and charge-transfer states are coupled to three vibrational modes. It then uses a similar model to show that the main experimental evidence suggesting the formation of PL+PM- as an intermediate could reflect pure dephasing of vibrational modes that modulate stimulated emission.

Entropy production and the Second Law in photosynthesis.

An assertion that the primary photochemistry of photosynthesis can violate the Second Law of thermodynamics in certain efficient systems has been put forward by Jennings et al., who maintain their position strongly despite an argument to the contrary by Lavergne. We identify a specific omission in the calculation of Jennings et al. and show that no violation of the Second Law occurs, regardless of the photosynthetic efficiency.

Temperature Dependence of the Rate of Intramolecular Electron Transfer.

Quantum mechanical/molecular mechanical simulations are used to explore the temperature dependence of intramolecular electron-transfer rates in systems that represent both the "normal" and the "inverted" regions of the Marcus curve. The treatment uses an approach that includes effects of vibrational relaxations and dephasing and is largely free of adjustable parameters. Effects of temperature on the distribution of the energy gap between the reactant and product ( P( xo)), the electronic-interaction matrix element, and the rates of dephasing and vibrational relaxations are considered. The simulations reproduce the measured rate constant and temperature dependence well for photochemical charge separation in a porphyrin-benzoquinone cyclophane and for a ground-state charge-shift reaction in a biphenylyl-androstane-naphthylyl radical. They overestimate the rate of the charge-shift reaction in a biphenylyl-androstane-benzoquinone adduct but are in accordance with the observation that this reaction is almost independent of temperature. Arrhenius plots of rate constants calculated with various P( xo) distributions show that the apparent activation enthalpy depends on whether or not P( xo) shifts with temperature.

Electron-Transfer Dynamics in a Zn-Porphyrin-Quinone Cyclophane: Effects of Solvent, Vibrational Relaxations, and Conical Intersections.

Rate constants for photochemical charge separation and recombination in a zinc-porphyrin-benzoquinone cyclophane are calculated by an approach that was developed recently to include effects of vibrational dephasing and relaxation and to reduce the dependence on freely adjustable parameters. The theory is extended to treat the rate of vibrational relaxation individually for each vibrational sublevel of the initial charge-transfer product. Quantum-mechanical/molecular-mechanical simulations of the reactions in iso-octane, toluene, dichloromethane, and acetonitrile suggest that charge separation occurs at conical intersections in the two more polar solvents, but at avoided crossings in the nonpolar solvents. In agreement with experimental measurements, however, the calculated rate constants for charge separation are similar in polar and nonpolar solvents. Charge recombination to the ground state is found to have electronic coupling factors smaller than that of charge separation and to be affected more strongly by interactions with the solvent.

Modeling electrostatic effects in proteins.

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

Vibrational Relaxations and Dephasing in Electron-Transfer Reactions.

The rates of nonadiabatic electron-transfer reactions depend on four main factors: the probability of finding the system in a conformation in which the reactant and product states have the same energy, the electronic coupling that drives oscillations between the two diabatic states, the dephasing that damps these oscillations, and the vibrational or electronic relaxations that trap the product state by transferring energy to the surroundings. This paper develops a simple expression that combines these factors in a relatively realistic manner. Values for all the parameters in the expression can be obtained from microscopic quantum-mechanical/molecular-mechanical simulations. The theory is tested by calculations of the rates of electron transfer from excited indole rings to a variety of acceptors in peptides and indole-acrylamide compounds. For the systems that are studied, the theory gives considerably better agreement with experiment than expressions that do not consider the rates of vibrational relaxations and dephasing.

Electron donors and acceptors in the initial steps of photosynthesis in purple bacteria: a personal account.

The discovery by Louis N. M. Duysens in the 1950s that illumination of photosynthetic purple bacteria can cause oxidation of either a bacteriochlorophyll complex (P) or a cytochrome was followed by an extended period of uncertainty as to which of these processes was the 'primary' photochemical reaction. Similar questions arose later about the roles of bacteriopheophytin (BPh) and quinones as the initial electron acceptor. This is a personal account of kinetic measurements that showed that electron transfer from P to BPh occurs in the initial step, and that the oxidized bacteriochlorophyll complex (P(+)) then oxidizes the cytochrome while the reduced BPh transfers an electron to a quinone.

Fluorescence of tryptophan in designed hairpin and Trp-cage miniproteins: measurements of fluorescence yields and calculations by quantum mechanical molecular dynamics simulations.

The quantum yield of tryptophan (Trp) fluorescence was measured in 30 designed miniproteins (17 ß-hairpins and 13 Trp-cage peptides), each containing a single Trp residue. Measurements were made in D(2)O and H(2)O to distinguish between fluorescence quenching mechanisms involving electron and proton transfer in the hairpin peptides, and at two temperatures to check for effects of partial unfolding of the Trp-cage peptides. The extent of folding of all the peptides also was measured by NMR. The fluorescence yields ranged from 0.01 in some of the Trp-cage peptides to 0.27 in some hairpins. Fluorescence quenching was found to occur by electron transfer from the excited indole ring of the Trp to a backbone amide group or the protonated side chain of a nearby histidine, glutamate, aspartate, tyrosine, or cysteine residue. Ionized tyrosine side chains quenched strongly by resonance energy transfer or electron transfer to the excited indole ring. Hybrid classical/quantum mechanical molecular dynamics simulations were performed by a method that optimized induced electric dipoles separately for the ground and excited states in multiple π-π* and charge-transfer (CT) excitations. Twenty 0.5 ns trajectories in the tryptophan's lowest excited singlet π-π* state were run for each peptide, beginning by projections from trajectories in the ground state. Fluorescence quenching was correlated with the availability of a CT or exciton state that was strongly coupled to the π-π* state and that matched or fell below the π-π* state in energy. The fluorescence yields predicted by summing the calculated rates of charge and energy transfer are in good accord with the measured yields.