Abstract

In this talk we review recent work with Sean Lawley on diffusion in randomly switching environments. One of the fundamental transport processes in biological cells is the exchange of ions, proteins and other macromolecules between subcellular domains, or between the interior and exterior of the cell, via stochastically gated membrane pores and channels. For example, the nucleus of eukaryotes is surrounded by a protective nuclear envelope within which are embedded nuclear pore complexes (NPCs). The NPCs are the sole mediators of exchange between the nucleus and cytoplasm, which requires the formation of complexes with chaperone molecules known as karyopherins. Other examples include the membrane transport of particles via voltage-gated and ligand-gated ion channels, and intercellular gap-junction coupling. One example at the more macroscopic level is the passive diffusion of oxygen during insect respiration. We show how each of these systems can be modeled in terms of diffusio n in a bounded domain with (partially) switching boundaries, and use a combination of PDE theory and probabilistic methods to determine statistical properties of the system. We highlight important differences between cases where the diffusing particles switch conformational state and cases where the boundary physically switches.