Escape from a channel

A challenge in biophysics is to devise mathematically tractable descriptions of complex processes in molecular and cellular biology. Twenty-five years ago, an elegant formalism was posited to describe channel-facilitated transport across biological membranes. This seminal work derived an effective escape rate that depends on the channel geometry and the diffusivity inside and outside of the channel. This prior escape rate formula has been used in many subsequent investigations to study a variety of biophysical systems. In this paper, we derive a new escape rate formula and rigorously show its validity in various parameter regimes. Our analysis resolves some counterintuitive predictions of the prior formula. We conclude that the prior formula is appropriate in limited biophysical circumstances.