Biomedical subjects

Raymond Kapral

Publications and source records attributed to Raymond Kapral.

At least 19 recordsLinked to original sources

PubMed2006

Solvation and proton transfer in polar molecule nanoclusters.

Proton transfer in a phenol-amine complex dissolved in polar molecule nanoclusters is investigated. The proton transfer rates and mechanisms, as well as the solvation of the complex in the cluster, are studied using both adiabatic and nonadiabatic dynamics. The phenol-amine complex exists in ionic and covalent forms and as the size of the cluster increases the ionic form gains stability at the expense of the covalent form. Both the adiabatic and nonadiabatic transfer reaction rates increase with cluster size. Given a fixed cluster size, the stability of the covalent state increases with increasing temperature. The proton transfer rates do not change monotonously with an increase in temperature. A strong correlation between the solvent polarization reaction coordinate and the location of the phenol-amine complex in the cluster is found. The ionic form of the complex strongly prefers the interior of the cluster while the covalent form prefers to lie on the cluster surface.

Journal Article↗

PubMed2006

Analysis of kinetic isotope effects for nonadiabatic reactions.

Factors influencing the rates of quantum mechanical particle transfer reactions in many-body systems are discussed. The investigations are carried out on a simple model for a proton transfer reaction that captures generic features seen in more realistic models of condensed phase systems. The model involves a bistable quantum oscillator coupled to a one-dimensional double-well reaction coordinate, which is in turn coupled to a bath of harmonic oscillators. Reactive-flux correlation functions that involve quantum-classical Liouville dynamics for chemical species operators and quantum equilibrium sampling are used to estimate the reaction rates. Approximate analytical expressions for the quantum equilibrium structure are derived. Reaction rates are shown to be influenced significantly by both the quantum equilibrium structure and nonadiabatic dynamics. Nonadiabatic dynamical effects are found to play the major role in determining the magnitude of the kinetic isotope effect for the model transfer reaction.

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PubMed2006

Mesoscopic description of solvent effects on polymer dynamics.

Solvent effects on polymer dynamics and structure are investigated using a mesoscopic solvent model that accounts for hydrodynamic interactions among the polymer beads. The simulation method combines molecular dynamics of the polymer chain, interacting with the solvent molecules through intermolecular forces, with mesoscopic multiparticle collision dynamics for the solvent molecules. Changes in the intermolecular forces between the polymer beads and mesoscopic solvent molecules are used to vary the solvent conditions from those for good to poor solvents. Polymer collapse and expansion dynamics following changes in solvent conditions are studied for homopolymer and block copolymer solutions. The frictional properties of polymers are also investigated.

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PubMed2006

Destruction of spiral waves in chaotic media.

Spiral-wave breakup in strongly chaotic media with nonphase-coherent chaotic attractors is investigated. Spiral-wave dynamics is studied for the Rössler reaction diffusion equation as the local attractor changes from a phase-coherent to a funnel form. Stable spiral waves with an Archimedean structure are observed to persist even when the local chaotic attractor has a funnel form. The destruction of funnel spiral waves in strongly chaotic media is induced by the strong phase disturbance of the local nonlinear chaotic dynamics, which breaks the stable Archimedean spiral structure and globally destroys the spatial pattern.

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PubMed2006

Nonadiabatic dynamics of condensed phase rate processes.

The study of quantum rate processes occurring in condensed phase environments is difficult because of the large number of degrees of freedom involved. Since a full quantum mechanical treatment is not computationally feasible, one is motivated to use mixed quantum-classical dynamical methods. This type of dynamics is applicable when one can single out a few degrees of freedom to be quantum in nature while treating the remainder classically. We describe a method that is based on the quantum-classical Liouville equation, which clearly prescribes the details of the coupling between the quantum and classical degrees of freedom. With the aid of this machinery, we show how to compute rate constants of reactions involving quantum particles immersed in a classical bath. We illustrate the use of this method on a model for proton transfer in a molecular complex dissolved in a polar solvent.

Computer Simulation↗

PubMed2006

Spiral wave dynamics in excitable media with spherical geometries.

We describe the spatial and temporal organization of spiral and scroll waves in spherical shells of different sizes and solid spheres. We present simulation results for the evolution of the dynamics and clustering of spiral waves as a function of the excitability of the medium. The excitability, topology, and size of the domain places restrictions on how single and multiarmed spiral waves are organized in space. The results in spherical geometries are compared with those in planar two-dimensional media. These studies are relevant to the dynamics of spiral waves in a variety of media including the heart, and chemical reactions on spherical surfaces.

Biophysics↗

PubMed2006

Progress in the theory of mixed quantum-classical dynamics.

Quantum-classical Liouville dynamics can be used to study the properties of open quantum systems that are coupled to bath or environmental degrees of freedom whose dynamics can be approximated by classical equations of motion. In contrast to many open quantum system approaches, quantum-classical dynamics provides a detailed description of the bath molecules. Such a description is especially appropriate for the study of quantum rate processes, such as proton and electron transport, where the detailed dynamics of the bath has a strong influence on the quantum rate. The quantum-classical Liouville equation can also serve as a starting point for the derivation of reduced descriptions where all or some of the bath degrees of freedom are projected out. Quantum-classical Liouville dynamics can be simulated in terms of an ensemble of surface-hopping trajectories whose character differs from that in other surface-hopping schemes. The results of studies of proton transfer in condensed phase and reactive dynamics in a dissipative environment are presented to illustrate applications of the formalism.

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PubMed2005

Mesoscopic multiparticle collision dynamics of reaction-diffusion fronts.

A mesoscopic multiparticle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion dynamics of complex reactive systems. The method is illustrated by a study of cubic autocatalytic fronts. The mesoscopic scheme is able to reproduce the results of reaction-diffusion descriptions under conditions where the mean field equations are valid. The model is also able to incorporate the effects of molecular fluctuations on the reactive dynamics.

Journal Article↗

PubMed2005

Nonadiabatic quantum-classical reaction rates with quantum equilibrium structure.

Time correlation function expressions for quantum reaction-rate coefficients are computed in a quantum-classical limit. This form for the correlation function retains the full quantum equilibrium structure of the system in the spectral density function but approximates the time evolution of the operator by quantum-classical Liouville dynamics. Approximate analytical expressions for the spectral density function, which incorporate quantum effects in the many-body environment and reaction coordinate, are derived. The results of numerical simulations of the reaction rate are presented for a reaction model in which a two-level system is coupled to a bistable oscillator which is, in turn, coupled to a bath of harmonic oscillators. The nonadiabatic quantum-classical dynamics is simulated in terms of an ensemble of surface-hopping trajectories and the effects of the quantum equilibrium structure on the reaction rate are discussed.

Journal Article↗

PubMed2005

Model for line defects in complex-oscillatory spiral waves.

Spiral waves in period-doubled and other complex-oscillatory media possess line defects across which the phase of the oscillation changes by multiples of 2pi. For such systems, the concept of a splay state, introduced for coupled oscillator systems, is generalized to an Archimedean spiral splay field. In this splay field a spiral wave in a two dimensional space is considered to be a special splay state where spatial points having identical phase space orbits take phases determined by the Archimedean spiral on which they lie. Using the Archimedean spiral splay field, an equation that determines the shape of the line defect is derived.

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PubMed2005

Front explosion in a periodically forced surface reaction.

Resonantly forced oscillatory reaction-diffusion systems can exhibit fronts with complicated interfacial structure separating phase-locked homogeneous states. For values of the forcing amplitude below a critical value the front "explodes" and the width of the interfacial zone grows without bound. Such front explosion phenomena are investigated for a realistic model of catalytic CO oxidation on a Pt(110) surface in the 2:1 and 3:1 resonantly forced regimes. In the 2:1 regime, the fronts are stationary and the front explosion leads to a defect-mediated turbulent state. In the 3:1 resonantly forced system, the fronts propagate. The front velocity tends to zero as the front explosion point is reached and the final asymptotic state is a 2:1 resonantly locked labyrinthine pattern. The front dynamics described here should be observable in experiment since the model has been shown to capture essential features of the CO oxidation reaction.

Journal Article↗

PubMed2005

Blue moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics.

We give a new formula expressing the components of the mean force in terms of a conditional expectation which can be computed by Blue Moon sampling. This generalizes to the vectorial case a formula first derived by Ruiz-Montero et al. for a scalar reaction coordinate. We also discuss how to compute this conditional average by means of constrained stochastic dynamics which, unlike the usual constrained molecular dynamics, introduces no bias. Finally, we give a new perspective on bias removal by using constrained molecular dynamics.

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PubMed2005

Quantum-classical Liouville dynamics of nonadiabatic proton transfer.

A proton transfer reaction in a linear hydrogen-bonded complex dissolved in a polar solvent is studied using mixed quantum-classical Liouville dynamics. In this system, the proton is treated quantum mechanically and the remainder of the degrees of freedom is treated classically. The rates and mechanisms of the reaction are investigated using both adiabatic and nonadiabatic molecular dynamics. We use a nonadiabatic dynamics algorithm which allows the system to evolve on single adiabatic surfaces and on coherently coupled pairs of adiabatic surfaces. Reactive-flux correlation function expressions are used to compute the rate coefficients and the role of the dynamics on the coherently coupled surfaces is elucidated.

Journal Article↗

PubMed2005

Two-particle friction in a mesoscopic solvent.

The effects of hydrodynamic interactions on the friction tensors for two particles in solution are studied. The particles have linear dimensions on nanometer scales and are either simple spherical particles interacting with the solvent through repulsive Lennard-Jones forces or are composite cluster particles whose atomic components interact with the solvent through repulsive Lennard-Jones forces. The solvent dynamics is modeled at a mesoscopic level through multiparticle collisions that conserve mass, momentum, and energy. The dependence of the two-particle relative friction tensors on the interparticle separation indicates the importance of hydrodynamic interactions for these nanoparticles.

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PubMed2005

Transport properties of quantum-classical systems.

Correlation function expressions for calculating transport coefficients for quantum-classical systems are derived. The results are obtained by starting with quantum transport coefficient expressions and replacing the quantum time evolution with quantum-classical Liouville evolution, while retaining the full quantum equilibrium structure through the spectral density function. The method provides a variety of routes for simulating transport coefficients of mixed quantum-classical systems, composed of a quantum subsystem and a classical bath, by selecting different but equivalent time evolution schemes of any operator or the spectral density. The structure of the spectral density is examined for a single harmonic oscillator where exact analytical results can be obtained. The utility of the formulation is illustrated by considering the rate constant of an activated quantum transfer process that can be described by a many-body bath reaction coordinate.

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PubMed2004

Friction and diffusion of a Brownian particle in a mesoscopic solvent.

The friction and diffusion coefficients of a massive Brownian particle in a mesoscopic solvent are computed from the force and the velocity autocorrelation functions. The mesoscopic solvent is described in terms of free streaming of the solvent molecules, interrupted at discrete time intervals by multiparticle collisions that conserve mass, momentum, and energy. The Brownian particle interacts with the solvent molecules through repulsive Lennard-Jones forces. The decays of the force and velocity autocorrelation functions are analyzed in the microcanonical ensemble as a function of the number N of solvent molecules and Brownian particle mass and diameter. The simulations are carried out for large system sizes and long times to assess the N dependence of the friction coefficient. The decay rates of these correlations are confirmed to vary as N(-1) in accord with earlier predictions. Hydrodynamic effects on the velocity autocorrelation function and diffusion coefficient are studied as a function of Brownian particle mass and diameter.

Journal Article↗

PubMed2004

Topological constraints on spiral wave dynamics in spherical geometries with inhomogeneous excitability.

We analyze the way topological constraints and inhomogeneity in the excitability influence the dynamics of spiral waves on spheres and punctured spheres of excitable media. We generalize the definition of an index such that it characterizes not only each spiral but also each hole in punctured, oriented, compact, two-dimensional differentiable manifolds and show that the sum of the indices is conserved and zero. We also show that heterogeneity and geometry are responsible for the formation of various spiral-wave attractors, in particular pairs of spirals in which one spiral acts as a source and a second as a sink--the latter similar to an antispiral. The results provide a basis for the analysis of the propagation of waves in heterogeneous excitable media in physical and biological systems.

Journal Article↗

PubMed2004

Quantum-classical limit of quantum correlation functions.

A quantum-classical limit of the canonical equilibrium time correlation function for a quantum system is derived. The quantum-classical limit for the dynamics is obtained for quantum systems comprising a subsystem of light particles in a bath of heavy quantum particles. In this limit the time evolution of operators is determined by a quantum-classical Liouville operator, but the full equilibrium canonical statistical description of the initial condition is retained. The quantum-classical correlation function expressions derived here provide a way to simulate the transport properties of quantum systems using quantum-classical surface-hopping dynamics combined with sampling schemes for the quantum equilibrium structure of both the subsystem of interest and its environment

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