Dynamics of Proton Transfer in Mesoscopic Clusters

Proton transfer rates and mechanisms are studied in mesoscopic, liquid-state, molecular clusters. The proton transfer occurs in a proton-ion complex solvated by polar molecules comprising the cluster environment. The rates and mechanisms of the reaction are studied using both adiabatic and non-adiabatic molecular dynamics. For large molecular clusters, the proton-ion complex resides primarily on the surface of the cluster or one layer of solvent molecules inside the surface. The proton transfer occurs as the complex undergoes orientational fluctuations on the cluster surface or penetrates one solvent layer into the cluster leading to solvent configurations that favor the transfer. For smaller clusters the complex resides mostly on the surface of the cluster and proton transfer is observed only when the complex penetrates the cluster and solvent configurations that favor the proton transfer are achieved. Quantitative information on the cluster reaction rate constants is also presented.Comment: To appear in JCP (March). Postscript figures available on request ([email protected]

An interpretation of fluctuations in enzyme catalysis rate, spectral diffusion, and radiative component of lifetimes in terms of electric field fluctuations

Time-dependent fluctuations in the catalysis rate ({delta}k(t)) observed in single-enzyme experiments were found in a particular study to have an autocorrelation function decaying on the same time scale as that of spectral diffusion {delta}{omega}0(t). To interpret this similarity, the present analysis focuses on a factor in enzyme catalysis, the local electrostatic interaction energy (E) at the active site and its effect on the activation free energy barrier. We consider the slow fluctuations of the electrostatic interaction energy ({delta}E(t)) as a contributor to {delta}k(t) and relate the latter to {delta}{omega}0(t). The resulting relation between {delta}k(t) and {delta}{omega}0(t) is a dynamic analog of the solvatochromism used in interpreting solvent effects on organic reaction rates. The effect of the postulated {delta}E(t) on fluctuations in the radiative component ({delta}{gamma}Formula(t)) of the fluorescence decay of chromophores in proteins also is examined, and a relation between {delta}{gamma}Formula(t) and {delta}{omega}0(t) is obtained. Experimental tests will determine whether the correlation functions for {delta}k(t), {delta}{omega}0(t), and {delta}{gamma}Formula are indeed similar for any enzyme. Measurements of dielectric dispersion, {varepsilon}({omega}), for the enzyme discussed elsewhere will provide further insight into the correlation function for {delta}E(t). They also will determine whether fluctuations in the nonradiative component {gamma}Formula of the lifetime decay has a different origin, fluctuations in distance for example

How might media aid and empower young people to manage armed political conflict?

The number of children who live in conflict zones is staggering: eighty-one percent live in a conflict-ridden state –1.8 billion souls. Yet when scholars discuss children, media and conflict, they tend to focus on peace-zone children and their engagement with news about conflicts. For www.parenting.digital, Yael Warshel discusses the need to shift the focus to young people in conflict zones and recognize the important role media may play in mediating and moderating conflict zones

Equilibrium fluctuation relations for voltage coupling in membrane proteins

AbstractA general theoretical framework is developed to account for the effects of an external potential on the energetics of membrane proteins. The framework is based on the free energy relation between two (forward/backward) probability densities, which was recently generalized to non-equilibrium processes, culminating in the work-fluctuation theorem. Starting from the probability densities of the conformational states along the "voltage coupling" reaction coordinate, we investigate several interconnected free energy relations between these two conformational states, considering voltage activation of ion channels. The free energy difference between the two conformational states at zero (depolarization) membrane potential (i.e., known as the chemical component of free energy change in ion channels) is shown to be equivalent to the free energy difference between the two “equilibrium” (resting and activated) conformational states along the one-dimensional voltage couplin reaction coordinate. Furthermore, the requirement that the application of linear response approximation to the free energy functionals of voltage coupling should satisfy the general free energy relations, yields a novel closed-form expression for the gating charge in terms of other basic properties of ion channels. This connection is familiar in statistical mechanics, known as the equilibrium fluctuation-response relation. The theory is illustrated by considering the coupling of a unit charge to the external voltage in the two sites near the surface of membrane, representing the activated and resting states. This is done using a coarse-graining (CG) model of membrane proteins, which includes the membrane, the electrolytes and the electrodes. The CG model yields Marcus-type voltage dependent free energy parabolas for the response of the electrostatic environment (electrolytes etc.) to the transition from the initial to the final configuratinal states, leading to equilibrium free energy difference and free energy barrier that follow the trend of the equilibrium fluctuation relation and the Marcus theory of electron transfer. These energetics also allow for a direct estimation of the voltage dependence of channel activation (Q-V curve), offering a quantitative rationale for a correlation between the voltage dependence parabolas and the Q-V curve, upon site-directed mutagenesis or drug binding. Taken together, by introducing the voltage coupling as the energy gap reaction coordinate, our framework brings new perspectives to the thermodynamic models of voltage activation in voltage-sensitive membrane proteins, offering an a framework for a better understating of the structure-function correlations of voltage gating in ion channels as well as electrogenic phenomena in ion pumps and transporters. Significantly, this formulation also provides a powerful bridge between the CG model of voltage coupling and the conventional macroscopic treatments

Powering computational enzyme design with natural evolutionary information

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Electrostatic Contributions to Protein Stability and Folding Energy

The ability to predict the thermal stability of proteins based on their corresponding sequence is a problem of great fundamental and practical importance. Here we report an approach for calculating the electrostatic contribution to protein stability based on the use of the semimacroscopic protein dipole Langevin dipole (PDLD/S) in its linear response approximation version for self-energy with a dielectric constant, (εpεp) and an effective dielectric for charge–charge interactions (εeffεeff). The method is applied to the test cases of ubiquitin, lipase, dihydrofolate reductase and cold shock proteins with series of εpεp and εeffεeff. It is found that the optimal values of these dielectric constants lead to very promising results, both for the relative stability and the absolute folding energy. Consideration of the specific values of the optimal dielectric constants leads to an exciting conceptual description of the reorganization effect during the folding process. Although this description should be examined by further microscopic studies, the practical use of the current approach seems to offer a powerful tool for protein design and for studies of the energetics of protein folding.This work was supported by NIH Grant GM2449

Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene

Recent experiments have confirmed the importance of nuclear quantum effects even in large biomolecules at physiological temperature. Here we describe how the path integral formalism can be used to describe rigorously the nuclear quantum effects on equilibrium and kinetic properties of molecules. Specifically, we explain how path integrals can be employed to evaluate the equilibrium (EIE) and kinetic (KIE) isotope effects, and the temperature dependence of the rate constant. The methodology is applied to the [1,5] sigmatropic hydrogen shift in pentadiene. Both the KIE and the temperature dependence of the rate constant confirm the importance of tunneling and other nuclear quantum effects as well as of the anharmonicity of the potential energy surface. Moreover, previous results on the KIE were improved by using a combination of a high level electronic structure calculation within the harmonic approximation with a path integral anharmonicity correction using a lower level method.Comment: 9 pages, 4 figure

Coarse grained model for exploring voltage dependent ion channels

AbstractThe relationship between the membrane voltage and the gating of voltage activated ion channels and other systems have been a problem of great current interest. Unfortunately, reliable molecular simulations of external voltage effects present a major challenge, since meaningful converging microscopic simulations are not yet available and macroscopic treatments involve major uncertainties in terms of the dielectric used and other key features. This work extends our coarse grained (CG) model to simulations of membrane/protein systems under external potential. Special attention is devoted to a consistent modeling of the effect of external potential due to the electrodes, emphasizing semimacroscopic description of the electrolytes in the solution regions between the membranes and the electrodes, as well as the coupling between the combined potential from the electrodes plus the electrolytes and the protein ionized groups. We also provide a clear connection to microscopic treatment of the electrolytes and thus can explore possible conceptual problems that are hard to resolve by other current approaches. For example, we obtain a clear description of the charge distribution in the entire electrolyte system, including near the electrodes in membrane/electrodes systems (where continuum models do not seem to provide the relevant results). Furthermore, the present treatment provides an insight on the distribution of the electrolyte charges before and after equilibration across the membrane, and thus on the nature of the gating charge. The different aspects of the model have been carefully validated by considering problems ranging for the simple Debye–Huckel, and the Gouy–Chapman models to the evaluation of the electrolyte distribution between two electrodes, as well as the effect of extending the simulation system by periodic replicas. Overall the clear connection to microscopic descriptions combined with the power of the CG modeling seems to offer a powerful tool for exploring the balance between the protein conformational energy and the interaction with the external potential in voltage activated channels. To illustrate these features we present a preliminary study of the gating charge in the voltage activated Kv1.2 channel, using the actual change in the electrolyte charge distribution rather than the conventional macroscopic estimate. We also discuss other special features of the model, which include the ability to capture the effect of changes in the protonation states of the protein residues during the close to open voltage induced transition. This article is part of a Special Issue entitled: Membrane protein structure and function

Kinetics and mechanism of proton transport across membrane nanopores

We use computer simulations to study the kinetics and mechanism of proton passage through a narrow-pore carbon-nanotube membrane separating reservoirs of liquid water. Free energy and rate constant calculations show that protons move across the membrane diffusively in single-file chains of hydrogen-bonded water molecules. Proton passage through the membrane is opposed by a high barrier along the effective potential, reflecting the large electrostatic penalty for desolvation and reminiscent of charge exclusion in biological water channels. At neutral pH, we estimate a translocation rate of about 1 proton per hour and tube.Comment: 4 pages, 4 figure