Dipole Moment and Binding Energy of Water in Proteins from Crystallographic Analysis.

The energetics of water molecules in proteins is studied using the water placement software Dowser. We compared the water position predictions for 14 high-resolution crystal structures of oligopeptide-binding protein (OppA) containing a large number of resolved internal water molecules. From the analysis of the outputs of Dowser with variable parameters and comparison with experimental X-ray data, we derived an estimate of the average dipole moment of water molecules located in the internal cavities of the protein and their binding energies. The water parameters thus obtained from the experimental data are then analyzed within the framework of charge-scaling theory developed recently by this group; the parameters are shown to be in good agreement with the predictions that the theory makes for the dipole moment in a protein environment. The water dipole in the protein environment is found to be much different from that in the bulk and in such models as SPC or TIPnP. The role of charge scaling due to electronic polarizability of the protein is discussed.

Similarity of cytochrome c oxidases in different organisms.

Most of biological oxygen reduction is catalyzed by the heme-copper oxygen reductases. These enzymes are redox-driven proton pumps that take part in generating the proton gradient in both prokaryotes and mitochondria that drives synthesis of ATP. The enzymes have been divided into three evolutionarily-related groups: the A-, B-, and C-families. Recent comparative studies suggest that all oxygen reductases perform the same chemistry for oxygen reduction and comprise the same essential elements of the proton pumping mechanism, such as the proton loading and kinetic gating sites, which, however, appear to be different in different families. All species of the A-family, however, demonstrate remarkable similarity of the central processing unit of the enzyme, as revealed by their recent crystal structures. Here we demonstrate that cytochrome c oxidases (CcO) of such diverse organisms as a mammal (bovine heart mitochondrial CcO), photosynthetic bacteria (Rhodobacter sphaeroides CcO), and soil bacteria (Paracoccus denitrificans CcO) are not only structurally similar, but almost identical in microscopic electrostatics and thermodynamics properties of their key amino-acids. By using pK(a) calculations of some of the key residues of the catalytic site, D- and K- proton input, and putative proton output channels of these three different enzymes, we demonstrate that the microscopic properties of key residues are almost identical, which strongly suggests the same mechanism in these species. The quantitative precision with which the microscopic physical properties of these enzymes have remained constant despite different evolutionary routes undertaken is striking.

Electronic continuum model for molecular dynamics simulations of biological molecules.

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.

Electronic Polarizability and the Effective Pair Potentials of Water.

Employing the continuum dielectric model for electronic polarizability, we have developed a new consistent procedure for parameterization of the effective nonpolarizable potential of liquid water. The model explains the striking difference between the value of water dipole moment 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 consistency of the parameterization scheme can be achieved if the magnitude of the effective dipole of water is understood as a scaled value [Formula: see text], where εel =1.78 is the electronic (high-frequency) dielectric constant of water, and a new electronic polarization energy term, missing in the previous theories, is included. The new term is evaluated by using Kirkwood - Onsager theory. The new scheme is fully consistent with experimental data on enthalpy of vaporization, density, diffusion coefficient, and static dielectric constant. The new 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.

Electronic continuum model for molecular dynamics simulations.

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.

Dielectric relaxation of cytochrome c oxidase: Comparison of the microscopic and continuum models.

We have studied a charge-insertion process that models the deprotonation of a histidine side chain in the active site of cytochrome c oxidase (CcO) using both the continuum electrostatic calculations and the microscopic simulations. The group of interest is a ligand to Cu(B) center of CcO, which has been previously suggested to play the role of the proton pumping element in the enzyme; the group is located near a large internal water cavity in the protein. Using the nonpolarizable Amber-99 force field in molecular dynamics (MD) simulations, we have calculated the nuclear part of the reaction-field energy of charging of the His group and combined it with the electronic part, which we estimated in terms of the electronic continuum (EC) model, to obtain the total reaction-field energy of charging. The total free energy obtained in this MDEC approach was then compared with that calculated using pure continuum electrostatic model with variable dielectric parameters. The dielectric constant for the "dry" protein and that of the internal water cavity of CcO were determined as those parameters that provide best agreement between the continuum and microscopic MDEC model. The nuclear (MD) polarization alone (without electronic part) of a dry protein was found to correspond to an unphysically low dielectric constant of only about 1.3, whereas the inclusion of electronic polarizability increases the protein dielectric constant to 2.6-2.8. A detailed analysis is presented as to how the protein structure should be selected for the continuum calculations, as well as which probe and atomic radii should be used for cavity definition. The dielectric constant of the internal water cavity was found to be 80 or even higher using "standard" parameters of water probe radius, 1.4 A, and protein atomic radii from the MD force field for cavity description; such high values are ascribed to the fact that the standard procedure produces unphysically small cavities. Using x-ray data for internal water in CcO, we have explored optimization of the parameters and the algorithm of cavity description. For Amber radii, the optimal probe size was found to be 1.25 A; the dielectric of water cavity in this case is in the range of 10-16. The most satisfactory cavity description, however, was achieved with ProtOr atomic radii, while keeping the probe radius to be standard 1.4 A. In this case, the value of cavity dielectric constant was found to be in the range of 3-6. The obtained results are discussed in the context of recent calculations and experimental measurements of dielectric properties of proteins.

Molecular level approaches for investigation of electron transfer in nonpolar solvents.

The authors extend their previous work published in Leontyev and TachiyaJ. Chem. Phys. 123, 224502 (2005) and study not only forward but also reverse electron transfer between pyrene and dimethylaniline in a nonpolar solvent, n-hexane. The distribution function methodology and molecular dynamics technique adopted in their previous work are used. Two algorithms (I and II) are formulated for obtaining the reorganization energy and the solvation free energy difference in the linear response approximation. The two algorithms are combined with different cutoff schemes and tested for polarizable and nonpolarizable solvent models. Agreement between the results obtained by the two algorithms was achieved only for simulations employing the particle mesh Ewald treatment. It is concluded that algorithm I provides a reliable scheme for evaluation of the reorganization energy and the solvation free energy difference. Moreover, a new algorithm referred to as the G-function algorithm is formulated which does not assume the linear response approximation, and is tested on evaluation of the solvation free energy difference. Agreement between the results from the G-function algorithm and those from algorithms I and II is fairly good, although it depends on the degree of statistical consistency of the simulations. In the case of nonpolar solvents the G-function method has practical importance because, unlike the conventional thermodynamic integration approach, it requires equilibrium molecular configuration ensembles only for the initial and final states of the system.

The reorganization energy of electron transfer in nonpolar solvents: molecular level treatment of the solvent.

The intermolecular electron transfer in a solute pair consisting of pyrene and dimethylaniline is investigated in a nonpolar solvent, n-hexane. The earlier elaborated approach [M. Tachiya, J. Phys Chem. 97, 5911 (1993)] is used; this method provides a physically relevant background for separating inertial and inertialess polarization responses for both nonpolarizable and polarizable molecular level simulations. The molecular-dynamics technique was implemented for obtaining the equilibrium ensemble of solvent configurations. The nonpolar solvent, n-hexane, was treated in terms of OPLS-AA parametrization. Solute Lennard-Jones parameters were taken from the same parametrization. Solute charge distributions of the initial and final states were determined using ab initio level [HF/6-31G(d,p)] quantum-chemical calculations. Configuration analysis was performed explicitly taking into account the anisotropic polarizability of n-hexane. It is shown that the Gaussian law well describes calculated distribution functions of the solvent coordinate, therefore, the rate constant of the ET reaction can be characterized by the reorganization energy. Evaluated values of the reorganization energies are in a range of 0.03-0.11 eV and significant contribution (more then 40% of magnitude) comes from anisotropic polarizability. Investigation of the reorganization energy lambda dependence on the solute pair separation distance d revealed unexpected behavior. The dependence has a very sharp peak at the distance d=7 A where solvent molecules are able to penetrate into the intermediate space between the solute pair. The reason for such behavior is clarified. This new effect has a purely molecular origin and cannot be described within conventional continuum solvent models.

Excluded volume effect for large and small solutes in water.

The cavitation effect, i.e., the process of the creation of a void of excluded volume in bulk solvent (a cavity), is considered. The cavitation free energy is treated in terms of the information theory (IT) approach [Hummer, G.; Garde, S.; Garcia, A. E.; Paulaitis, M. E.; Pratt, L. R. J. Phys. Chem. B 1998, 102, 10469]. The binomial cell model suggested earlier is applied as the IT default distribution p(m) for the number m of solute (water) particles occupying a cavity of given size and shape. In the present work, this model is extended to cover the entire range of cavity size between small ordinary molecular solutes and bulky biomolecular structures. The resulting distribution consists of two binomial peaks responsible for producing the free energy contributions, which are proportional respectively to the volume and to the surface area of a cavity. The surface peak dominates in the large cavity limit, when the two peaks are well separated. The volume effects become decisive in the opposite limit of small cavities, when the two peaks reduce to a single-peak distribution as considered in our earlier work. With a proper interpolation procedure connecting these two regimes, the MC simulation results for model spherical solutes with radii increasing up to R = 10 A [Huang, D. H.; Geissler, P. L.; Chandler, D. J. Phys. Chem. B 2001, 105, 6704] are well reproduced. The large cavity limit conforms to macroscopic properties of bulk water solvent, such as surface tension, isothermal compressibility and Tolman length. The computations are extended to include nonspherical solutes (hydrocarbons C1-C6).