Lev I. Krishtalik

The mechanism of the proton transfer: an outline

A brief summary of the principal notions of the quantum-mechanical theory of the charge transfer reactions has been presented. In the framework of this theory, the mechanism of the proton transfer consists in the classical medium reorganization that equalizes the proton energy levels in the initial and final states, and a consequent proton transfer via a quantum-mechanical underbarrier transition. On the basis of this mechanism, factors influencing the proton transfer probability, and hence kinetic isotope effect, have been discussed; among them are the optimum tunneling distance, the involvement of the excited vibrational states, etc. Semi-classical and quantum-mechanical treatments of the Swain-Schaad relations have been compared. Some applications to enzymatic proton-transfer reactions have been described.

Energetics of multielectron reactions. Photosynthetic oxygen evolution

Abstract In examining the energetics of the elementary act of reactions, involving a change in the number of particles, one has to consider not the standard free reaction energy, or the free energy at given reagent concentrations, but only the configurational component of the free energy. It is this quantity, independent of the reagents concentration, which affects directly the probability of the elementary act of the reaction. Using this approach it is shown that the oxygen-evolution reaction from water corresponds to the configurational redox potential about + 1.4 V, i.e., to a higher one than the redox potential of the primary acceptor of Photosystem II-oxidized P-680. The subdivision of the overall reaction into steps cannot eliminate this energy deficiency. It is shown that the potential in question can be considerably decreased if protons detached from water during the elementary act undergo immediate binding with sufficiently strong bases. An increase in the pH value of these bases upon reduction of manganese as well as the ionization of water molecules preceding their oxidation favours the reaction. The favourable energetics of the process in the form of a single four-electron or of two two-electron elementary acts are pointed out.

ELECTROSTATIC ION-SOLVENT INTERACTION

Abstract A new method is described for determination of the electrostatic component of the free energy of ion transfer from one solvent to another. The method is based on the compensation of the solvophobic effects in the difference of the redox potentials of two oxidation steps of large compact particles. Corresponding measurements have been made for the cobaltocene and dicarbollylnickel systems. On this basis, scales of ion transfer energies and electrode potentials in different solvents have been developed. It has been shown that the transfer energy of large ions in aprotic solvents obeys the Born equation. This implies two consequences. First, it is necessary to revise the existing version of the non-local electrostatics theory which overestimates the effect of the space correlation of polarization. Second, our results provide sufficient justification for the use of the Marcus equation for calculation of the reorganization energy of the reactions of large ions and, hence, the validity of the conclusions drawn with its use (in particular, on the influence of the time of longitudinal dielectric relaxation of the medium on the electron transfer kinetics).

Electrostatics of proteins: Description in terms of two dielectric constants simultaneously

In the semi‐continuum treatment of the energetics of charge formation (or transfer) inside a protein, two components of the energy are inevitably present: the energy of interaction of the ion with the pre‐existing intraprotein electric field, and the energy due to polarization of the medium by the newly formed charge. The pre‐existing field is set up by charges (partial or full) of the protein atoms fixed in a definite structure. The calculation of this field involves only the electronic polarization (the optical dielectric constant ϵo) of the protein because the polarization due to shifts of heavy atoms has already been accounted for by their equilibrium coordinates. At the same time, the aqueous surroundings should be described by the static constant ϵsw, as the positions of water molecules are not fixed. The formation of a new charge, absent in the equilibrium X‐ray structure, results in shifts of electrons and polar atoms, i.e., it involves all kinds of medium polarization described by the static dielectric constant of protein ϵs. Thus, in calculations of the total energy, two different dielectric constants of the protein are operative simultaneously. This differs from a widely used algorithm employing one effective dielectric constant for both components of the ions energy. Proteins: 28:174–182, 1997.

Photosynthetic electron transfer controlled by protein relaxation: analysis by Langevin stochastic approach.

Relaxation processes in proteins range in time from picoseconds to seconds. Correspondingly, biological electron transfer (ET) could be controlled by slow protein relaxation. We used the Langevin stochastic approach to describe this type of ET dynamics. Two different types of kinetic behavior were revealed, namely: oscillating ET (that could occur at picoseconds) and monotonically relaxing ET. On a longer time scale, the ET dynamics can include two different kinetic components. The faster one reflects the initial, nonadiabatic ET, whereas the slower one is governed by the medium relaxation. We derived a simple relation between the relative extents of these components, the change in the free energy (DeltaG), and the energy of the slow reorganization Lambda. The rate of ET was found to be determined by slow relaxation at -DeltaG < or = Lambda. The application of the developed approach to experimental data on ET in the bacterial photosynthetic reaction centers allowed a quantitative description of the oscillating features in the primary charge separation and yielded values of Lambda for the slower low-exothermic ET reactions. In all cases but one, the obtained estimates of Lambda varied in the range of 70-100 meV. Because the vast majority of the biological ET reactions are only slightly exothermic (DeltaG > or = -100 meV), the relaxationally controlled ET is likely to prevail in proteins.

pH-dependent redox potential: how to use it correctly in the activation energy analysis.

The activation barrier (the activation free energy) for the reactions elementary act proper does not depend on the presence of reactants outside the reaction complex. The barrier is determined directly by the concentration-independent configurational free energy. In the case of redox reactants with pH-dependent redox potential, only the pH-independent quantity, the configurational redox potential enters immediately into expression for activation energy. Some typical cases of such reactions have been discussed (e.g., simultaneous proton and electron detachment, acid dissociation followed by oxidation, dissociation after oxidation, and others). For these mechanisms, the algorithms for calculation of the configurational redox potential from the experimentally determined redox potentials have been described both for the data related to a dissolved reactant or to a prosthetic group of an enzyme. Some examples of pH-dependent enzymatic redox reactions, in particular for the Rieske iron-sulfur protein, have been discussed.

Electrochemistry of solvated electrons

Over the past 10–15 years a new trend has been developed in theoretical electrochemistry: the electrochemistry of solvated electrons. In this review theoretical concepts of the electrochemical properties of solvated electrons and the results of experimental studies are considered from a unified position. Also discussed are: energy levels of localized (solvated) and delocalized electrons in solutions and methods for their determination; conditions of electrochemical formation of solvated electrons and properties of these solutions; equilibrium on an “electron electrode”. The kinetics and mechanisms of cathodic generation of solvated electrons and of their anodic “oxidation” are discussed in detail. In the last sections participation of solvated electrons in “ordinary” electrode reactions is discussed, and the possibilities of cathodic electrosyntheses utilizing solvated electrons are considered.

Intramembrane electron transfer: processes in the photosynthetic reaction center

Abstract The intramembrane charge transfer has been analyzed in the framework of the ‘fixed-charge-density’ formalism. For a three-layer model of membrane, the expressions for the reorganization energy have been derived. In the case of very fast reactions, the time-evolution of the dielectric response of a protein should be taken into account. This has been described phenomenologically in terms of a set of effective dielectric constants, e τ , operative in different time intervals. For the charge separation process, the effects of the variable e τ on the reaction free energy and on the medium reorganization energy are equal and opposite in sign, and hence compensate each other. As a result, the photosynthetic primary charge separation proves to be activationless, irrespective of the value of e τ . On the basis of the existing experimental data, the semiquantitative estimates of e τ at different times were given. With these values of e τ , the activation energy close to zero was calculated for the reactions of electron transfer from bacteriopheophytin to quinone, of recombination of the primary radical-ion pair with formation of a neutral triplet, and of recombination of the special pair cation with quinone anion.

Activationless electron transfer in the reaction centre of photosynthesis

The reorganization energies of the medium and the activation energies of electron transfer in the photosynthetic reaction centre have been calculated (the geometric parameters are assumed in accordance with the X-ray crystallographic analysis data for Rhodopseudomonas viridis ). Due to the low reorganization energy of the protein medium and the optimum relations of the effective dimensions of reagents, for each step of the main electron transfer path, the corresponding reorganization energy and the free energy of reaction (difference of redox potentials) are similar. As a result, the activation energy of each of these electron transfer steps is negligible. The electron back-transfer from the primary acceptor to the primary donor, though strongly advantageous thermodynamically, is hindered by high activation energy.

Determination of the surface potentials of solvents

Abstract A method for evaluation of the surface potential at the solvent-gas interface has been developed. It is based on the validity of the Born equation for the electrostatic part of the Gibbs solvation energy of large symmetric compact ions such as metallocenes, a result which was obtained earlier. The surface potential was found as the difference of the real solvation energy of the ferricinium cation and its chemical solvation energy calculated according to the Born equation. The values of surface potentials for six different solvents were obtained, and the data are compared with the results of other methods described in the literature.