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  to propose a fully stochastic  model describing the main characteristics of a multiple channel system , in which ion movement is coupled with a Poisson--Nernst--Planck equation . Exclusion forces are considered and different nondimensionalization procedure, supported by numerical simulation, are discussed. Both cases of nano and micro channels are considered .
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 nano channels have been have been taken in due consideration with particular attention to the latter case in order to show that it is necessary to consider inside the channels a discrete and stochastic model for ions movement .
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on one hand
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and discrete
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, in which ion movement is coupled with a Poisson--Nernst--Planck equation . Exclusion forces are considered and different nondimensionalization procedure,
. 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
R
simulation, are discussed. Both cases of nano and micro channels are considered
simulations. The specific features of both cases of micro and nano channels have been have been taken in due consideration with particular attention to the latter case in order to show that it is necessary to consider inside the channels a discrete and stochastic model for ions movement