A dynamic lattice Monte Carlo model of ion transport in inhomogeneous dielectric environments: Method and implementation

A dynamic lattice Monte Carlo (DLMC) simulation approach to the description of ion transport in dielectric environments is presented. Conventional app roaches using periodic boundary conditions are inefficient for nonequilibri um situations in inhomogeneous systems. Instead, the simulated system is em bedded in a bigger system that determines the average electrostatic potenti al and the ionic concentrations at its boundaries. Two issues are of specia l importance: implementing the given boundary conditions in the treatment o f dynamical processes at and near the boundaries, and efficient evaluation of ion-ion interaction in the heterogeneous dielectric medium during the Mo nte Carlo simulation. The performance of the method is checked by comparing numerical results to exact solutions for simple geometries, and to mean fi eld (Poisson-Nernst-Planck, PNP) theory in a system where the latter should provide a reasonable description. Other examples in which the PNP theory f ails in various degrees are shown and discussed. In particular, PNP results deviate considerably from the DLMC dynamics for ion transport through rigi d narrow membrane channels with large disparity between the dielectric cons tants of the protein and the water environments.