A Mathematical Model for Alternating Pores in Biological Membranes

We consider a mathematical model for selective permeation of chemical species through cell membranes. The mechanism relies on gating, that is on the alternate closing and opening of the pores. Firstly, we perform a preliminary analytical study of a parabolic problem set in a domain divided by a perforated interface, in the presence of periodic gating. We prove that, for vanishingly small size of the pores and time period, the interface condition prevailing in the limit is a linear relation between the flux (on either side) and the jump of the limiting solution across the interface. Note that such an interface condition only appears when the relative sizes of the relevant geometrical and temporal parameters are suitably connected. We demonstrate the appearance of a new admissible asymptotic standard with respect to the stationary version of this problem. Secondly, we investigate the issue of selection in the framework of a random walk model based on the same concepts. This study is performed through Monte Carlo numerical techniques, and is aimed at investigating how selective transport, and gating as well, can be obtained by stochastically switching the affinity of the pore for the target species. © 2011 American Institute of Physics.