Alexei A. Stuchebrukhov

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 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.

Proton pumping mechanism and catalytic cycle of cytochrome c oxidase: Coulomb pump model with kinetic gating.

Using electrostatic calculations, we have examined the dependence of the protonation state of cytochrome c oxidase from bovine heart on its redox state. Based on these calculations, we propose a possible scheme of redox‐linked proton pumping. The scheme involves His291 – one of the ligands of the CuB redox center – which plays the role of the proton loading site (PLS) of the pump. The mechanism of pumping is based on ET reaction between two hemes of the enzyme, which is coupled to a transfer of two protons. Upon ET, the first proton (fast reaction) is transferred to the PLS (His291), while subsequent transfer of the second “chemical” proton to the binuclear center (slow reaction) is accompanied by the ejection of the first (pumped) proton. Within the proposed model, we discuss the catalytic cycle of the enzyme.

Inelastic tunneling in long-distance biological electron transfer reactions

The effect of protein dynamics on the long-distance biological electron transfer reactions is discussed. Computer simulations reported recently by our group [Daizadeh, Medvedev, and Stuchebrukhov, Proc. Natl. Acad. Sci. USA 94, 3703 (1997)] have shown that in some cases a strong dynamic coupling of a tunneling electron to vibrational motions of the protein matrix can exist. This results in a modification of the conventional 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. In the present paper we study analytically the probabilities of such inelastic tunneling events and show how they affect the overall dependence of the reaction rate on the driving force, temperature, and the strength of electron–phonon coupling. Harmonic and anharmonic models are proposed for vibrational dynamics of t...

Electron tunneling in respiratory complex I

NADH:ubiquinone oxidoreductase (complex I) plays a central role in the respiratory electron transport chain by coupling the transfer of electrons from NADH to ubiquinone to the creation of the proton gradient across the membrane necessary for ATP synthesis. Here the atomistic details of electronic wiring of all Fe/S clusters in complex I are revealed by using the tunneling current theory and computer simulations; both density functional theory and semiempirical electronic structure methods were used to examine antiferromagnetically coupled spin states and corresponding tunneling wave functions. Distinct electron tunneling pathways between neighboring Fe/S clusters are identified; the pathways primarily consist of two cysteine ligands and one additional key residue. Internal water between protein subunits is identified as an essential mediator enhancing the overall electron transfer rate by almost three orders of magnitude to achieve a physiologically significant value. The identified key residues are further characterized by sensitivity of electron transfer rates to their mutations, examined in simulations, and their conservation among complex I homologues. The unusual electronic structure properties of Fe4S4 clusters in complex I explain their remarkable efficiency of electron transfer.

Computer simulation of water in cytochrome c oxidase

Statistical mechanics and molecular dynamics simulations have been carried out to study the distribution and dynamics of internal water molecules in bovine heart cytochrome c oxidase (CcO). CcO is found to be capable of holding plenty of water, which in subunit I alone amounts to about 165 molecules. The dynamic characterization of these water molecules is carried out. The nascent water molecules produced in the redox reaction at the heme a(3)-CuB binuclear site form an intriguing chain structure. The chain begins at the position of Glu242 at the end of the D channel, and has a fork structure, one branch of which leads to the binuclear center, and the other to the propionate d of heme a(3). The branch that leads to the binuclear center has dynamic access both to the site where the formation of water occurs, and to delta-nitrogen of His291. From the binuclear center, the chain continues to run into the K channel. The stability of this hydrogen bond network is examined dynamically. The catalytic site is located at the hydrophobic region, and the nascent water molecules are produced at the top of the energy hill. The energy gradient is utilized as the mechanism of water removal from the protein. The water exit channels are explored using high-temperature dynamics simulations. Two putative channels for water exit from the catalytic site have been identified. One is leading directly toward Mg(2+) site. However, this channel is only open when His291 is dissociated from CuB. If His291 is bound to CuB, the only channel for water exit is the one that originates at E242 and leads toward the middle of the membrane. This is the same channel that is presumably used for oxygen supply.

Tunneling currents in electron transfer reactions in proteins

A new theoretical method for the analysis of the superexchange coupling and localization of electron tunneling pathways in long distance electron transfer reactions is introduced. The new method allows one to examine spatial distribution of microscopic quantum mechanical tunneling currents flowing through individual atoms, or to evaluate the relative probability that the tunneling electron will pass through an individual atom, in the intervening medium between donor and acceptor in the course of an electron transfer reaction. It is shown how the interatomic tunneling currents introduced in this paper can be calculated using methods of quantum chemistry. The method provides a rigorous theoretical framework for the description of the tunneling process in long‐range electron transfer reactions in proteins. The relation of the present theory of tunneling currents to the theory of pathways of Beratan and Onuchic is discussed.

TUNNELING CURRENTS IN ELECTRON TRANSFER REACTION IN PROTEINS. II. CALCULATION OF ELECTRONIC SUPEREXCHANGE MATRIX ELEMENT AND TUNNELING CURRENTS USING NONORTHOGONAL BASIS SETS

In this paper we further develop the concept of interatomic tunneling currents [A.A. Stuchebrukhov, J. Chem. Phys. 104, 8424 (1996)] for the description of long‐range electron tunneling in proteins. Here we discuss a formulation of the theory for the case when nonorthogonality of the atomic basis set of the medium propagating electron is explicitly taken into account. This method provides an effective computational scheme for an exact, i.e., nonperturbative, evaluation (in one‐electron approximation) of the superexchange electron tunneling matrix element, and allows one to determine which regions in the protein matrix are important for the tunneling process. The theory is applied for calculation of tunneling currents and the electronic matrix element in His126‐Ru‐modified blue copper protein azurin from a recent experimental work of Gray and co‐workers. Analysis of interatomic currents reveals a nontrivial structure of the tunneling flow between donor and acceptor in the intervening protein medium in this...

Concerted electron and proton transfer: Transition from nonadiabatic to adiabatic proton tunneling

A concerted electron–proton transfer reaction is discussed, in which proton tunneling occurs simultaneously with electronic transition. It is assumed that the potential in which the proton moves is formed by two electronic states, which in the absence of their interaction would cross in the region between the two minima of the proton adiabatic potential. The proton tunneling between the two wells is, therefore, coupled to a switch between the two electronic states. The later occurs only when the proton is in the tunneling region under the barrier. A simple analytical expression for the tunneling matrix element TDA is derived, which is uniformly correct for small and large values of the electronic coupling. For small electronic coupling our expression coincides with that obtained in the nonadiabatic theory of proton-coupled electron transfer reactions. For large electronic coupling the expression is reduced to that obtained in the Born–Oppenheimer approximation. The transition from nonadiabatic to adiabati...

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.

Tunneling matrix element in Ru-modified blue copper proteins: Pruning the protein in search of electron transfer pathways

We investigate with semi-empirical extended Huckel theory calculations the tunneling matrix element for electron transfer in three ruthenium-modified blue copper azurin molecules from the bacterium Pseudomonas aeruginosa which have been recently synthesized and studied experimentally by Gray and co-workers. All of the atoms in the protein can be included in the calculations with the method of transition amplitudes that has been developed recently. Our particular focus here, however, is to develop procedures that create a truncated protein much smaller than the initial 2000 atom one, the aim being to retain only those amino acids that are important to the electron tunneling mechanism. Such a procedure, which we refer to as ‘pruning’, is useful, first because it reduces the size of the problem, perhaps allowing for more accurate techniques to be used on the truncated protein, and second because it allows for the identification of the regions in the protein in which the tunneling electron is localized. The pruning procedures enable us to reduce the number of atoms required in an extended Huckel theory analysis of the tunneling mechanism by approximately a factor of 10 over that in the original protein.