Quasi-two-dimensional diffusion of interacting globular proteins*

Diffusion of proteins along lipid membranes plays a vital role in cell signaling processes. How the collective and self-diffusion of proteins are affected by direct and hydrodynamic interactions is relevant, e.g., for protein clustering and oligomerization of receptor protein subunits. Using mesoscale hydrodynamic simulations, the dynamic predictions by a minimalistic protein-membrane-cytosol model are explored. The model describes globular proteins as Brownian spheres, confined to lateral motion in a planar monolayer embedded in a three-dimensional viscous fluid. The proteins are assumed to interact pairwisely either via a hard-core potential or a soft potential consisting of competing short-range attractive and long-range repulsive parts. We analyze spatio-temporal correlations from short times where inertial motion is resolved up to long times where the solvent-mediated hydrodynamic interactions between proteins are fully developed. In this context, we investigate the short-time buildup of inter-protein hydrodynamic interactions by multiple scattering of sound and vorticity diffusion, and long-time anomalous enhancement of collective diffusion, in their dependence on protein concentration.