Emile S. Medvedev

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...

Proton Transport via the Membrane Surface

Some proton pumps, such as cytochrome c oxidase (C(c)O), translocate protons across biological membranes at a rate that considerably exceeds the rate of proton transport to the entrance of the proton-conducting channel via bulk diffusion. This effect is usually ascribed to a proton-collecting antenna surrounding the channel entrance. In this paper, we consider a realistic phenomenological model of such an antenna. In our model, a homogeneous membrane surface, which can mediate proton diffusion toward the channel entrance, is populated with protolytic groups that are in dynamic equilibrium with the solution. Equations that describe coupled surface-bulk proton diffusion are derived and analyzed. A general expression for the rate constant of proton transport via such a coupled surface-bulk diffusion mechanism is obtained. A rigorous criterion is formulated of when proton diffusion along the surface enhances the transport. The enhancement factor is found to depend on the ratio of the surface and bulk diffusional constants, pK(a) values of surface protolytic groups, and their concentration. A capture radius for a proton on the surface and an effective size of the antenna are found. The theory also predicts the effective distance that a proton can migrate on the membrane surface between a source (such as CcO) and a sink (such as ATP synthase) without fully equilibrating with the bulk. In pure aqueous solutions, protons can travel over long distances (microns). In buffered solutions, the travel distance is much shorter (nanometers); still the enhancement effect of the surface diffusion on the proton flow to a target on the surface can be tens to hundreds at physiological buffer concentrations. These results are discussed in a general context of chemiosmotic theory.

Proton transport via coupled surface and bulk diffusion

Translocation of protons across biological membranes is carried out by special membrane proteins, proton pumps. Surprisingly, the turnover rate of some proton pumps, such as cytochrome c oxidase (CcO), is higher than the bulk diffusion limit (i.e., the rate at which protons can be supplied to the entrance of the proton conducting channel via free bulk diffusion). It has been suggested that the diffusion of protons along the membrane surface that surrounds the entrance of the proton conducting channel can increase the supply of the protons and therefore explain the puzzling high turnover rates. Here we consider a phenomenological model of proton transport to a proton collecting channel. The model takes into account both the diffusion in the bulk and the coupled diffusion of protons along the membrane surface. In our model a homogeneous membrane surface, which mediates proton diffusion toward the channel entrance, is populated with protolytic groups that can exchange protons with a bulk solution. Equations which describe the coupled surface-bulk proton diffusion are derived and solved. The maximum (diffusion limited) rate at which protons can be delivered to the pump is examined. It is found that there are two regimes of surface-mediated proton transport, depending on the rate of proton exchange between the bulk and the surface. In both regimes proton transport is dominated by the contribution of surface diffusion. Due to two-dimensional character of the surface diffusion, the transport rate depends on the size of the channel entrance in a weak, logarithmic fashion. The theory also provides a simple expression for the maximum distance that a proton can migrate on the surface before it is fully equilibrated with the bulk. This result allows one to examine whether the chemiosmotic coupling between a proton source on a membrane surface, such as CcO, and a sink, such as ATP synthase, occurs via diffusion along the membrane, or involves equilibration with the bulk.

Mechanism of long-range proton translocation along biological membranes

Recent experiments suggest that protons can travel along biological membranes up to tens of micrometers, but the mechanism of transport is unknown. To explain such a long‐range proton translocation we describe a model that takes into account the coupled bulk diffusion that accompanies the migration of protons on the surface. We show that protons diffusing at or near the surface before equilibrating with the bulk desorb and re‐adsorb at the surface thousands of times, giving rise to a power‐law desorption kinetics. As a result, the decay of the surface protons occurs very slowly, allowing for establishing local gradient and local exchange, as was envisioned in the early local models of biological energy transduction.

Electrostatics of the FeS clusters in respiratory complex I

Respiratory complex I couples the transfer of electrons from NADH to ubiquinone and the translocation of protons across the mitochondrial membrane. A detailed understanding of the midpoint reduction potentials (E(m)) of each redox center and the factors which influence those potentials are critical in the elucidation of the mechanism of electron transfer in this enzyme. We present accurate electrostatic interaction energies for the iron-sulfur (FeS) clusters of complex I to facilitate the development of models and the interpretation of experiments in connection to electron transfer (ET) in this enzyme. To calculate redox titration curves for the FeS clusters it is necessary to include interactions between clusters, which in turn can be used to refine E(m) values and validate spectroscopic assignments of each cluster. Calculated titration curves for clusters N4, N5, and N6a are discussed. Furthermore, we present some initial findings on the electrostatics of the redox centers of complex I under the influence of externally applied membrane potentials. A means of determining the location of the FeS cofactors within the holo-complex based on electrostatic arguments is proposed. A simple electrostatic model of the protein/membrane system is examined to illustrate the viability of our hypothesis.

Determination of the intrinsic redox potentials of FeS centers of respiratory complex I from experimental titration curves.

Recently, Euro et al. [Biochem. 47, 3185 (2008) ] have reported titration data for seven of nine FeS redox centers of complex I from Escherichiacoli. There is a significant uncertainty in the assignment of the titration data. Four of the titration curves were assigned to N1a, N1b, N6b, and N2 centers; one curve either to N3 or N7; one more either to N4 or N5; and the last one denoted Nx could not be assigned at all. In addition, the assignment of the titration data to the N6b/N6a pair is also uncertain. In this paper, using our calculated interaction energies [Couch et al. BBA 1787, 1266 (2009)], we perform statistical analysis of these data, considering a variety of possible assignments, find the best fit, and determine the intrinsic redox potentials of the centers. The intrinsic potentials could be determined with an uncertainty of less than +/-10 mV at a 95% confidence level for best fit assignments. We also find that the best agreement between theoretical and experimental titration curves is obtained with the N6b-N2 interaction equal to 71+/-14 or 96+/-26 mV depending on the N6b/N6a titration data assignment, which is stronger than was expected and may indicate a close distance of the N2 center to the membrane surface.

Fast and slow fluorescence decays in pyrazine under nanosecond excitation conditions: A resolution of the enigma

We study the fluorescence decay behavior of the S1(1B3u) electronic state of pyrazine following its excitation from the ground S0(1A1g) electronic state with a few nanoseconds light pulse. Our probe of the dynamics is the time‐dependent Schrodinger equation. We form superpositions of the eight strongest S1 molecular eigenstates (MEs) of pyrazine with the light pulse, and then compute the total spontaneous emission as a function of time using the known optical properties of the MEs. Both coherent and incoherent contributions to the fluorescence decay have been observed. We find that single exponential decays exist at selected frequencies in the spectrum, corresponding to exact ME resonances. However, most decays are biexponential owing to the off‐resonant excitation of many nearby MEs. Even resonant excitation decays become biexponential at high power. Thus, the ‘‘enigma’’ is apparently resolved; the fast component (and its J dependence) in the nanosecond excited fluorescence decay of pyrazine has its orig...

CORRELATION BETWEEN THE INTENSITIES OF VIBRATIONAL OVERTONE TRANSITIONS AND THE REPULSIVE BRANCH OF THE MOLECULAR POTENTIAL

Energy levels en and n←0 vibrational overtone transition intensities for a distorted Morse potential (DMP) and a linear dipole moment function are calculated, and then are treated as “observed” quantities. The values of (en−e0)/n vs n fall on a straight line very closely. A linear least-squares fit provides an effective anharmonicity parameter (xe)eff which is then used to construct an “effective” Morse potential (EMP). The EMP closely follows the DMP near equilibrium but declines in the far repulsive and attractive regions. The intensities calculated for the EMP systematically overestimate or underestimate the DMP intensities, depending on whether the repulsive branch of the EMP above the dissociation limit runs over or under that of the DMP, respectively, and the discrepancies rapidly increase with the overtone number. This effect of the repulsive branch is further investigated quantitatively by comparing the steepness of the repulsive potential β calculated directly from the potential curve with its va...

Intensity anomalies in the rotational and ro-vibrational spectra of diatomic molecules

We study the anomalies in the distributions of intensities of transitions in the purely rotational bands and the rotational branches of the vibrational bands within the unperturbed ground electronic states in spectra of diatomic molecules. While normally these distributions follow smooth patterns, sudden drops in intensity values are often observed. We analyze the origin of these anomalies in HF, DF, and CO and find that they are predominantly associated with specific forms of the dipole-moment functions (DMFs). The rotational transitions at which these anomalies occur and their severity are very sensitive to these forms, which makes them a promising tool for refining the empirical DMFs.

Hund’s Case (a)-case (b) transition in the singlet-triplet absorption spectrum of pyrazine in a supersonic jet

An analytic expression is derived for calculating the intensities of individual spin-rovibronic lines in the fully resolved gas phase electronic spectrum of a polyatomic molecule, in which one of the zero-order electronic states is a triplet state. The expression is employed to calculate the effect of fine structure splitting on the singlet-triplet absorption spectrum of pyrazine using the parameters available from experiment. A transition from Hund’s coupling Case (a) to Case (b) on going from low J to high J rotational levels is predicted to occur at a moderate resolution of a few hundred MHz. The effect is more pronounced in pyrazine-d4 and the pyrazine-argon van der Waals complex owing to their larger mass.