We investigate the outflux of ions through the channels in a cell membrane. The channels undergo an open/close cycle according to a periodic schedule. Our study is based both on theoretical considerations relying on homogenization theory, and on Monte Carlo numerical simulations. We examine the onset of a limiting boundary behavior characterized by a constant ratio between the outflux and the local density, in the large volume limit. The focus here is on the issue of selectivity, that is on the different behavior of the ion currents through the channel in the cases of the selected and non-selected species.
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