Escape from Subcellular Domains with Randomly Switching Boundaries

Abstract

Motivated by various cellular transport processes, we consider diffusion in a potential and analyze the escape time to boundaries that randomly switch between absorbing and reflecting states. Combining disparate tools from PDEs and probability theory, we study both (a) the escape to the boundary in which the entire boundary switches and (b) the escape to one of $N$ small pieces of the boundary that each randomly switch. For (a), we show how the switching boundary affects the classical rate of escape from a potential well. For (b), we significantly generalize a known result for the gated narrow escape problem and give this result an intuitive probabilistic interpretation. In both cases, our results illustrate the complementary perspectives that PDE and probabilistic methods offer escape problems.