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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 μ(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 μ(eff) = μ/√ε(el), where ε(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.

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.

Cytochrome c oxidase (CcO) is the terminal enzyme of the cell respiratory chain in mitochondria and aerobic bacteria. It catalyzes the reduction of oxygen to water and utilizes the free energy of the reduction reaction for proton pumping across the inner-mitochondrial membrane, a process that results in a membrane electrochemical proton gradient. Although the structure of the enzyme has been solved for several organisms, the molecular mechanism of proton pumping remains unknown. In the present paper, continuum electrostatic calculations were employed to evaluate the electrostatic potential, energies, and protonation state of bovine heart cytochrome c oxidase for different redox states of the enzyme along its catalytic cycle. Three different computational models of the enzyme were employed to test the stability of the results. The energetics and pH dependence of the P-->F, F-->O, and O-->E steps of the cycle have been investigated. On the basis of electrostatic calculations, two possible schemes of redox-linked proton pumping are discussed. The first scheme involves His291 as a pump element, whereas the second scheme involves a group linked to propionate D of heme a(3). In both schemes, loading of the pump site is coupled to ET between the two hemes of the enzyme, while transfer of a chemical proton is accompanied by ejection of the pumped H(+). The two models, as well as the energetics results are compared with recent experimental kinetic data. The proton pumping across the membrane is an endergonic process, which requires a sufficient amount of energy to be provided by the chemical reaction in the active site. In our calculations, the conversion of OH(-) to H(2)O provides 520 meV of energy to displace pump protons from a loading site and overall about 635 meV for each electron passing through the system. Assuming that the two charges are translocated per electron against the membrane potential of 200 meV, the model predicts an overall efficiency of 63%.

Photolyase is an enzyme that catalyzes photorepair of thymine dimers in UV damaged DNA by electron-transfer reaction. We docked a thymine dimer to photolyase catalytic site, using crystal structure coordinates of the substrate-free enzyme from Escherichia coli, studied molecular dynamics of the system, and calculated the electron-transfer matrix element between the lowest unoccupied molecular orbitals of flavin and the dimer. We find that the rms transfer matrix element along the dynamic trajectory is about 6 cm -1 , which is consistent with the experimentally determined rate of transfer. In the average configuration the docked thymine dimer is sitting deep in the catalytic site, and approaches the adenine of FAD with the C4dO4 carbonyl groups. The average distance between the flavin and the base pair is less than 3 Å. The electron-transfer mechanism utilizes the unusual conformation of FAD in photolyases, in which the isoalloxazine ring of the flavin and the adenine are in close proximity, and the peculiar features of the docked orientation of the dimer. The calculations show that despite the short distance between the donor and acceptor complexes, the electrontransfer mechanism between the flavin and the thymine bases is not direct, but indirect, with the adenine acting as an intermediate.

Electronic polarizability is an important factor in molecular interactions. In the conventional force fields such as AMBER or CHARMM, however, there is inconsistency in how the effect of electronic dielectric screening of Coulombic interactions, inherent for the condensed phase media, is treated. Namely, the screening appears to be accounted for via effective charges only for neutral moieties, whereas the charged residues are treated as if they were in vacuum. As a result, the electrostatic interactions between ionized groups are exaggerated in molecular simulations by the factor of about 2. The discussed here MDEC (Molecular Dynamics in Electronic Continuum) model provides a theoretical framework for modification of the standard non-polarizable force fields to make them consistent with the idea of uniform electronic screening of partial atomic charges. The present theory states that the charges of ionized groups and ions should be scaled; i.e. reduced by a factor of about 0.7. In several examples, including the interaction between Na+ ions, which is of interest for ion-channel simulations, and the dynamics of an important salt-bride in Cytochrome c Oxidase, we compared the standard non-polarizable MD simulations with MDEC simulations, and demonstrated that MDEC charge scaling procedure results in more accurate interactions. 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 fields simulations.

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Computer simulations of the effect of protein dynamics on the long distance tunneling mediated by the protein matrix have been carried out for a Ru-modified (His 126) azurin molecule. We find that the tunneling matrix element is a sensitive function of the atomic configuration of the part of the protein matrix in which tunneling currents (pathways) are localized. Molecular dynamics simulations show that f luctuations of the matrix element can occur on a time scale as short as 10 fs. These short time f luctuations are an indication of a strong dynamic coupling of a tunneling electron to vibrational motions of the protein nuclear coordinates. The latter results in a modification of the conventional Marcus picture of electron transfer in proteins. The new element in the modified theory is that the tunneling electron is capable of emitting or absorbing vibrational energy (phonons) from the medium. As a result, some biological reactions may occur in an activationless fashion. An analytical theoretical model is proposed to account for thermal f luctuations of the medium in long distance electron transfer reactions. The model shows that, at long distances, the phonon-modified inelastic tunneling always dominates over the conventional elastic tunneling.Electron transfer is an integral part of many biological processes, such as photosynthesis and respiration. Much effort, therefore, has been directed toward understanding transport properties of various biological materials. In particular, recent experimental studies have provided information on the distance and structural dependence of electron transfer rates in various natural and modified proteins (1-4). In these systems, electron transfer typically occurs over distances of 10-30 Å and is due to tunneling mediated by the intervening medium between donor and acceptor.It is commonly believed that fundamental principles of long distance electron transfer are essentially the same as those of any other electron transfer reaction (5). The only difference seems to be in the nature of electronic coupling; in short distance reactions, electronic orbitals of donor and acceptor directly overlap whereas in long distance reactions this coupling is indirect because of sequential overlaps of atomic orbitals of the donor, the intervening medium (bridge), and the orbitals of the acceptor. These sequential overlaps give rise to the concept of superexchange. It is assumed that all states in the bridging medium are virtual, i.e., there are no other resonant states in the system but those of donor and acceptor. The resonance between donor and acceptor occurs in the course of thermal fluctuations of the polar environment. The absence of real intermediate states and direct coupling physically means that electron transfer occurs via tunneling. In this picture, the overall rate of electron transfer is proportional to the frequency at which donor and acceptor states come to resonance and the probability to transfer an electron between donor and acceptor states at the transition state (i...