Friction contribution to water-bond breakage kinetics

Pair-Reaction Dynamics in Water: Competition of Memory, Potential Shape, and Inertial Effects

When described by a one-dimensional reaction coordinate, pair-reaction rates in a solvent depend, in addition to the potential barrier height and the friction coefficient, on the potential shape, the effective mass, and the friction relaxation spectrum, but a rate theory that accurately accounts for all of these effects does not exist. After a review of classical reaction-rate theories, we show how to extract all parameters of the generalized Langevin equation (GLE) and, in particular, the friction memory function from molecular dynamics (MD) simulations of two prototypical pair reactions in water, the dissociation of NaCl and of two methane molecules. The memory exhibits multiple time scales and, for NaCl, pronounced oscillatory components. Simulations of the GLE by Markovian embedding techniques accurately reproduce the pair-reaction kinetics from MD simulations without any fitting parameters, which confirms the accuracy of the approximative form of the GLE and of the parameter extraction techniques. By modification of the GLE parameters, we investigate the relative importance of memory, mass, and potential shape effects. Neglect of memory slows down NaCl and methane dissociation by roughly a factor of 2; neglect of mass accelerates reactions by a similar factor, and the harmonic approximation of the potential shape gives rise to slight acceleration. This partial error cancellation explains why Kramers' theory, which neglects memory effects and treats the potential shape in harmonic approximation, describes reaction rates better than more sophisticated theories. In essence, all three effects, friction memory, inertia, and the potential shape nonharmonicity, are important to quantitatively describe pair-reaction kinetics in water.

Mean exit time and escape probability for the Ornstein-Uhlenbeck process

This paper studies the dynamics of the Ornstein-Uhlenbeck process by the deterministic quantities such as the mean exit time and escape probability. By solving the elliptic partial equations, we obtain explicit solutions to both mentioned problems using the special functions. We find that the mean exit time is longer for smaller noise, and the maximum depends on the middle of the given interval. Moreover, the likelihood that the solution orbits exiting the interval from left or right relies on the middle of the interval. The Monte Carlo simulations are carried out to support the obtained results.

Anomalous anisotropic diffusion dynamics of hydration water at lipid membranes

The diffusional water dynamics in the hydration layer of a dipalmitoylphosphatidylcholine bilayer is studied using molecular dynamics simulations. By mapping the perpendicular water motion on the ordinary diffusion equation, we disentangle free energetic and friction effects and show that perpendicular diffusion is strongly reduced. The lateral water motion exhibits anomalous diffusion up to several nanoseconds and is characterized by even further decreased diffusion coefficients, which by comparison with coarse-grained simulations are explained by the transient corrugated effective free energy landscape imposed by the lipids. This is in contrast to homogenous surfaces, where boundary hydrodynamic theory quantitatively predicts the anisotropy of water diffusion.

Conformational dynamics and internal friction in homopolymer globules: equilibrium vs. non-equilibrium simulations

We study the conformational dynamics within homopolymer globules by solvent-implicit Brownian dynamics simulations. A strong dependence of the internal chain dynamics on the Lennard-Jones cohesion strength ε and the globule size N (G) is observed. We find two distinct dynamical regimes: a liquid-like regime (for ε < ε(s) with fast internal dynamics and a solid-like regime (for ε > ε(s) with slow internal dynamics. The cohesion strength ε(s) of this freezing transition depends on N (G) . Equilibrium simulations, where we investigate the diffusional chain dynamics within the globule, are compared with non-equilibrium simulations, where we unfold the globule by pulling the chain ends with prescribed velocity (encompassing low enough velocities so that the linear-response, viscous regime is reached). From both simulation protocols we derive the internal viscosity within the globule. In the liquid-like regime the internal friction increases continuously with ε and scales extensive in N (G) . This suggests an internal friction scenario where the entire chain (or an extensive fraction thereof) takes part in conformational reorganization of the globular structure.