Spinning proteins

Particle motility at interfaces is a fundamental aspect of many physical processes, including the mobility of proteins in fluid membranes, the kinetics of colloids on liquid droplets, and the dynamics of polymers adsorbed on a fluid membrane. In a classical paper, Saffman and Delbrück (1975) showed how to compute the hydrodynamic mobility of proteins in flat fluid membranes. Here we propose a mathematical model to tackle the rotational mobility problem for proteins embedded in a curved membrane and surrounded by two Newtonian fluids. We show that the problem can be reduced to an infinite system of ODEs, which we truncate and solve as a function of the protein size and the ratio between membrane and solvent viscosities. We show how our approach agrees with past work in two distinct limits, and explore the consequence for the mobility of finite-size proteins in vesicles.