Stochastic Modeling and Simulation of Ion Transport through Channels

Ion channels are of major interest, and form an area of intensive research in the fields of biophysics and medicine since they control many vital physiological functions. The aim of this work is on the one hand to propose a fully stochastic and discrete model describing the main characteristics of a multiple channel system. The movement of the ions is coupled, as usual, with a Poisson equation for the electrical field; we have considered, in addition, the influence of exclusion forces. On the other hand, we have discussed the nondimensionalization of the stochastic system by using real physical parameters, all supported by numerical simulations. The specific features of both cases of micro- and nanochannels have been taken into consideration with particular attention to the latter case in order to show that it is necessary to consider a discrete and stochastic model for ions movement inside the channels.