Modelling the Control Mechanism of the Sodium Channel in the Apical Membrane of Tight Epithelia

The unidirectional inward Na⁺ flux, J_IN^Na, passing through the sodium channel in the apical membrane of some tight epithelia depends approximately linearly on [Na]_OUT as expected, but is also known to depend sensitively and inversely upon [Na]_IN while the ratio of the fluxes obeys the relation 4sJ_IN^Na/J_OUT^Na = [Na]_OUT/[Na]_IN. In this paper it is shown that such behaviour may be simply modelled based on the assumption of only single occupancy of the channel. With use of linear flux equations the calculated flux ratio is as measured. The additional assumption of single occupancy of the channel results in the calculated values of J_IN^Na and J_OUT^Na both being multiplied by the same factor, 1 -- P, where P is the probability that the channel is occupied by an ion. The flux ratio thus remains unchanged but J_IN^Na and J_OUT^Na may now depend inversely upon [Na⁺]_IN or [Na⁺]_OUT or both, owing to the dependence of P upon these parameters. To illustrate these general conclusions, detailed calculations are made on a particular assymetrical voltage-controlled model ion channel, based upon an ordered water structure. The results obtained are shown to simulate those found experimentally for tight epithelia.