The time dependence of single file diffusion.

The single file diffusion of particles through a narrow pore membrane separating two media is treated as a stochastic birth and death process. A set of differential-difference equations is derived to describe the probability of finding n particles in the pore at any time whose source is the left-hand medium. Explicit time-dependent solutions for an arbitary number of sites are obtained. These can be used to calculate both one-way and net flux as a function of time. Parameters are estimated from steady state permeability data, and the results of some numerical calculations are presented to illustrate the time required to approach a steady state. In many cases, significant time delays can occur.