A Hard Sphere Model for Single File Water Transport Across Biological Membranes

Abstract

AbstractWe use Gürsey’s statistical mechanics of a one-dimensional fluid to find a formula for thePf/Pdratio in the transport of hard spheres across a membrane through a narrow channel that can accommodate only single file movement.Pfis the membrane permeability for osmotic flow, andPdthe permeability for exchange across the membrane in the absence of osmotic flow. The deviation of the ratio from unity indicates the degree of cooperative transport relative to ordinary diffusion of independent isolated molecules. In contrast to an early idea thatPf/Pdmust be equal to the number of molecules in the channel, regardless of the physical nature of the interactions among the molecules, we find a functional dependence on the fractional occupancy of the length of the channel by the hard spheres. We also attempt a random walk calculation forPdindividually, which gives a result forPfas well when combined with the ratio.