Anomalous Diffusion of Proteins Coupled to Membrane Thickness, Height, and Lipid Order

Abstract

Diffusion of proteins in lipid membranes has traditionally been described by a hydrodynamic model that treats the membrane as a two-dimensional fluid surrounded by a less viscous outer fluid. As a result, the diffusion coefficient of proteins in a membrane is predicted to have a weak (logarithmic) dependence on the protein size. This result has been experimentally confirmed for micron-scale objects in membranes and related systems such as thin smectic-A films, but the evidence for the size-dependence of protein diffusion coefficients is mixed, with some groups observing a much stronger, 1/R dependence on protein radius. This has led to speculation that the primary source of drag on a protein is not viscous, but comes from coupling to other fields, such as lipid ordering. We discuss simple continuum models of the dynamics of proteins with hydrophobic mismatch, spontaneous curvature, active protein-membrane interactions, and coupling to lipid chain order. We show that these coupling mechanisms will generically create diffusion that is anomalous at short times, which may lead to the observation of differing diffusion coefficients by different techniques.