▪ Abstract Proton-coupled electron transfer (PCET) is an important mechanism for charge transfer in a wide variety of systems including biology- and materials-oriented venues. We review several are...

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Proton-Coupled Electron Transfer

Implicit Solvation Models: Equilibria, Structure, Spectra, and Dynamics.

Reversible work transition state theory: application to dissociative adsorption of hydrogen

: The unpolarized absorption and circular dichroism spectra of the fundamental vibrational transitions of the chiral molecule, 4-methyl-2-oxetanone, are calculated ab initio. Harmonic force fields are obtained using Density Functional Theory (DFT), MP2, and SCF methodologies and a 5S4P2D/3S2P (TZ2P) basis set. DFT calculations use the Local Spin Density Approximation (LSDA), BLYP, and Becke3LYP (B3LYP) density functionals. Mid-IR spectra predicted using LSDA, BLYP, and B3LYP force fields are of significantly different quality, the B3LYP force field yielding spectra in clearly superior, and overall excellent, agreement with experiment. The MP2 force field yields spectra in slightly worse agreement with experiment than the B3LYP force field. The SCF force field yields spectra in poor agreement with experiment.The basis set dependence of B3LYP force fields is also explored: the 6-31G* and TZ2P basis sets give very similar results while the 3-21G basis set yields spectra in substantially worse agreements with experiment. jg

Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields

The genetic and biochemical networks which underlie such things as homeostasis in metabolism and the developmental programs of living cells, must withstand considerable variations and random perturbations of biochemical parameters These occur as transient changes in, for example, transcription, translation, and RNA and protein degradation The intensity and duration of these perturbations differ between cells in a population The unique state of cells, and thus the diversity in a population, is owing to the different environmental stimuli the individual cells experience and the inherent stochastic nature of biochemical processes (for example, refs 5 and 6) It has been proposed, but not demonstrated, that autoregulatory, negative feedback loops in gene circuits provide stability, thereby limiting the range over which the concentrations of network components fluctuate Here we have designed and constructed simple gene circuits consisting of a regulator and transcriptional repressor modules in Escherichia coli and we show the gain of stability produced by negative feedback

Engineering stability in gene networks by autoregulation

Coupled electron and proton transfer reactions play a key role in the mechanisms of biological energy transduction.1–3 Such reactions are also fundamental for artificial energy-related systems such as fuel cells, chemical sensors, and other electrochemical devices. Biological examples include, among others, cytochrome c oxidase,4,5 bc1 complex,6,7 and photosynthetic reaction centers.8,9 In such systems, electrons tunnel between redox cofactors of an enzyme, while the coupled protons are transferred either across a single hydrogen bond or between protonatable groups along special proton-conducting channels.

In this paper general theories and models of coupled electron transfer/proton transfer (ET/PT) reactions are discussed. Pure electron transfer reactions in proteins have been thoroughly studied in the past, both experimentally10–17 and theoretically.18–25 The coupled reactions are relatively new and currently are gaining attention in the field.6,8,26–43

Two types of coupled reactions can be distinguished. In concerted electron and proton transfer reactions (denoted PCET in Refs. 29,30,43–45, although this term is also used more generally), both the ET and PT transitions occur in one step. Such concerted processes occur in reactions in which proton transfer is typically limited to one hydrogen bond; however, examples with multiple hydrogen bond rearrangements are also known.46 In sequential reactions, the transitions occur in two steps: ET/PT or PT/ET. Typically each individual step is uphill in energy, while the coupled reaction is downhill.

A sequential reaction can proceed along two parallel channels: ET then PT (EP) or PT then ET (PE). In each channel the reaction involves two sequential steps: uphill activation, and then downhill reaction to the final product state. The lifetime of the activated complex is limited by the back reaction. The general formula for the rate of such reactions can be easily developed. In the context of bioenergetics issues, however, it is interesting to analyze all of the possible cases separately because each corresponds to a different mechanism: for example, an electron can go first and pull out a proton; alternatively, a proton can go first and pull out an electron; or an electron can jump back and forth between donor and acceptor and gradually pull out a proton. In enzymes involving coupled proton and electron transport, the exact mechanism of the reaction is of prime interest.

First we will consider a simple four-state model of reactions where the proton moves across a single hydrogen bond; both concerted and sequential reactions will be treated. Then we will consider models for long-distance proton transfer, also denoted proton transport or proton translocation. Typically, electron transfer coupled to proton translocation in proteins involves an electron tunneling over a long distance between two redox cofactors, coupled to a proton moving along a proton conducting channel in a classical, diffusion-like random walk fashion. Again, separately the electron and proton transfer reactions are typically uphill, while the coupled reaction is downhill in energy. The schematics of this process is shown in Fig. 1. The kinetics of such reactions can be much different from those involving proton transfer across a single hydrogen bond. In this paper, we will discuss the specifics of such long-distance proton-coupled reactions.



Fig. 1

Schematics of the electron transfer reaction coupled to proton translocation. In the reaction, an electron is tunneling over a long distance between two redox cofactors, O and R, and a coupled proton is transferred over a proton conducting channel. The ...



Following the review of theoretical concepts, a few applications will be discussed. First the phenoxyl/phenol and benzyl/toluene self-exchange reactions will be examined. The phenoxyl/phenol reaction involves electronically nonadiabatic proton transfer and corresponds to a proton-coupled electron transfer (PCET) mechanism, whereas the benzyl/toluene reaction involves electronically adiabatic proton transfer and corresponds to a hydrogen atom transfer (HAT) mechanism. Comparison of these two systems provides insight into fundamental aspects of electron-proton interactions in these types of systems. Next a series of theoretical calculations on experimentally studied PCET reactions in solution and enzymes will be summarized, along with general predictions concerning the dependence of rates and kinetic isotope effects (the ratio of the rate constants for hydrogen and deuterium transfer) on system properties such as temperature and driving force. The final application that will be discussed is cytochrome c oxidase (CcO). CcO is the terminal component of the electron transport chain of the respiratory system in mitochondria and is one of the key enzymes responsible for energy generation in cells. The intricate correlation between the electron and proton transport via electrostatic interactions, as well as the kinetics of the coupled transitions, appear to be the basis of the pumping mechanism in this enzyme.

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Theory of Coupled Electron and Proton Transfer Reactions

The issues of electronic polarizability in molecular dynamics simulations are discussed. We argue that the charges of ionized groups in proteins, and charges of ions in conventional non-polarizable force fields such as CHARMM, AMBER, GROMOS, etc should be scaled by a factor about 0.7. Our model explains why a neglect of electronic solvation energy, which typically amounts to about a half of total solvation energy, in non-polarizable simulations with un-scaled charges can produce a correct result; however, the correct solvation energy of ions does not guarantee the correctness of ion–ion pair interactions in many non-polarizable simulations. The inclusion of electronic screening for charged moieties is shown to result in significant changes in protein dynamics and can give rise to new qualitative results compared with the traditional non-polarizable force field simulations. The model also explains the striking difference between the value of water dipole μ ∼ 3D reported in recent ab initio and experimental studies with the value μeff ∼ 2.3D typically used in the empirical potentials, such as TIP3P or SPC/E. It is shown that the effective dipole of water can be understood as a scaled value μeff = μ/√eel, where eel = 1.78 is the electronic (high-frequency) dielectric constant of water. This simple theoretical framework provides important insights into the nature of the effective parameters, which is crucial when the computational models of liquid water are used for simulations in different environments, such as proteins, or for interaction with solutes.

Accounting for electronic polarization in non-polarizable force fields

The issues of electronic polarizability in molecular dynamics simulations are discussed. We argue that the charges of ionized groups in proteins, and charges of ions in conventional non-polarizable force fields such as CHARMM, AMBER, GROMOS, etc should be scaled by a factor about 0.7. Our model explains why a neglect of electronic solvation energy, which typically amounts to about a half of total solvation energy, in non-polarizable simulations with un-scaled charges can produce a correct result; however, the correct solvation energy of ions does not guarantee the correctness of ion-ion pair interactions in many non-polarizable simulations. The inclusion of electronic screening for charged moieties is shown to result in significant changes in protein dynamics and can give rise to new qualitative results compared with the traditional non-polarizable force field simulations. The model also explains the striking difference between the value of water dipole $\mu$~3D reported in recent ab initio and experimental studies with the value $\mu_{eff}$~2.3D typically used in the empirical potentials, such as TIP3P or SPC/E. It is shown that the effective dipole of water can be understood as a scaled value $\mu_{eff}=\mu/\sqrt{\epsilon_{el}}$, where $\epsilon_{el}$=1.78 is the electronic (high-frequency) dielectric constant of water. This simple theoretical framework provides important insights into the nature of the effective parameters, which is crucial when the computational models of liquid water are used for simulations in different environments, such as proteins, or for interaction with solutes.

Accounting for electronic polarization in nonpolarizable force fields

Quantum calculations are reported for the intramolecular vibrational energy redistribution and absorption spectra of the first two excited states of the acetylenic CH stretch vibration in the polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si. Using approximate potential energy surfaces, comparison is made with the corresponding recent experimental spectra. It is found that a model of intramolecular vibrational relaxation based on the assumption of sequential off-resonance transitions via third and fourth order vibrational couplings (as opposed to direct high order couplings) is in agreement with experimental results on spectral linewidths. In a semiclassical limit this type of relaxation corresponds to a dynamic tunneling in phase space. It is shown that the local density of resonances of third and fourth order, rather than the total density of states, plays a central role for the relaxation. It is found that in the Si molecule an accidental absence of appropriate resonances results in a bottleneck in the initial stages of relaxation. As a result, an almost complete localization of the initially prepared excitation occurs. It is shown that an increase of the mass alone of the central atom from C to Si cannot explain the observed difference in the C and Si molecules. The spectral linewidths were calculated with the Golden Rule formula after prediagonalization of the relevant vibrational states which are coupled in the molecule to the CH vibration, directly or indirectly. For the spectral calculations, in addition to the direct diagonalization, a modified recursive residue generation method was used, allowing one to avoid diagonalization of the transformed Lanczos Hamiltonian. With this method up to 30 000 coupled states could be analyzed on a computer with relatively small memory. The efficiency of C programming language for the problem is discussed.

Theoretical study of intramolecular vibrational relaxation of acetylenic CH vibration for v=1 and 2 in large polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si

A simple model for accounting for electronic polarization in molecular dynamics (MD) simulations is discussed. In this model, called molecular dynamics electronic continuum (MDEC), the electronic polarization is treated explicitly in terms of the electronic continuum (EC) approximation, while the nuclear dynamics is described with a fixed-charge force field. In such a force-field all atomic charges are scaled to reflect the screening effect by the electronic continuum. The MDEC model is rather similar but not equivalent to the standard nonpolarizable force-fields; the differences are discussed. Of our particular interest is the calculation of the electrostatic part of solvation energy using standard nonpolarizable MD simulations. In a low-dielectric environment, such as protein, the standard MD approach produces qualitatively wrong results. The difficulty is in mistreatment of the electronic polarizability. We show how the results can be much improved using the MDEC approach. We also show how the dielectric constant of the medium obtained in a MD simulation with nonpolarizable force-field is related to the static (total) dielectric constant, which includes both the nuclear and electronic relaxation effects. Using the MDEC model, we discuss recent calculations of dielectric constants of alcohols and alkanes, and show that the MDEC results are comparable with those obtained with the polarizable Drude oscillator model. The applicability of the method to calculations of dielectric properties of proteins is discussed.

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Alexei A. Stuchebrukhov

Papers

Theory of Coupled Electron and Proton Transfer Reactions

Accounting for electronic polarization in non-polarizable force fields

Accounting for electronic polarization in nonpolarizable force fields

Theoretical study of intramolecular vibrational relaxation of acetylenic CH vibration for v=1 and 2 in large polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si

Electronic continuum model for molecular dynamics simulations