Stochastical Langevin-Lorentz-Poisson modelling of Ion Flow through membrane ionic channels

In this paper a stochastical Langevin-Lorentz-Poisson modelling of ion flow through membrane ionic channels is presented. In the model the spatial charge effects are modelled assuming stationary conditions and the spatial ionic distributions is described by a coupled system of equations, a dynamic Langevin-Lorentz equation and a Poisson equation. The numerical solution of the coupled problem is performed by using an iterative method. The ion displacements are determined by time integrating the Langevin-Lorentz equation in the absence of the thermal noise, obtaining the deterministic ion position and velocity. A Fokker-Planck analysis is then performed in order to estimate the effective ion position and velocity. A typical Ca++ channel is examined and the simulation results are expressed in terms of number ion exits from the channel versus the transmembrane potential.