Diffusion on Rapidly Varying Surfaces

Lateral diffusion of particles along interfaces is a frequently occurring phenomenon in cellular biology. The mobility of membrane proteins has far-reaching implications for many cellular processes, in particular protein transport, signalling and morphology, thus there has been considerable interest in measuring how the mobility of these proteins is affected by the membrane and its surrounding environment. In this talk, I will describe a multi-scale analysis approach to studying the macroscopic behaviour of passive particles diffusing laterally on such surfaces. In particular, I will demonstrate how this approach allows one to compute effective properties of the macroscopic diffusion as well as provide a means to rigorously justify a number of existing results.