Dynamical disorder: Passage through a fluctuating bottleneck

Abstract

A model is proposed for a rate process that is controlled by passage through a fluctuating bottleneck. The rate of passage is proportional to the cross‐sectional area of the bottleneck. The radius of the bottleneck fluctuates in time according to a Langevin equation with a decay constant λ. Two consequences of the model are (1) decay is not exponential at short times, but changes to exponential at long times. (2) In the limit of small λ, the resulting effective rate constant at long times is proportional to λ1/2. Predictions of the model are qualitatively consistent with experimental observations on the viscosity dependence of ligand motion in myoglobin.