  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 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 about 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 in due 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.
