Ion transport in the simplest single file pore

Abstract

A kinetic scheme is developed to describe single-file transport through pores containing up to two ions which may be of different species. The solution for the fluxes in terms of rate constants for entry, exit, and transfer is derived without specific assumptions about symmetry or the voltage and activity dependence of the constants. For a symmetrical pore the relation between the slope conductance at zero applied potential and ion activity can have two distinct regions in which the conductance increases linearly. Zero current or reversal potentials depend on the absolute values of the activities as well as their ratios. The use of this theory to describe the cation fluxes through the pores formed by gramicidin A will be considered in a subsequent paper. Here the model is discussed for a number of more specific assumptions, most extensively the following combination: (1) while entry to a pore is less likely when the pore is already occupied at the opposite end, this entry is still rapid; (2) exit is much more rapid when the pore is occupied by two ions; and (3) transfer from one end to the other of a singly occupied pore is rapid. With these assumptions and for a range of concentrations over which the fluxes are proportional to ion activities, the model predicts a flux ratio exponent nearly equal to 2, blocking by impermeant ions, rectification due to blocking particles on one side only, relief of block by increase in the permeant ion concentration on the opposite side, and anomalous variations of the conductance and zero current potential with mole ratio when the total concentration of the two permeants is held constant.