Diffusion of complex objects embedded in free and supported lipid bilayer membranes: role of shape anisotropy and leaflet structure

We present a versatile numerical scheme to predict diffusion coefficients for arbitrarily shaped objects embedded in lipid bilayer membranes. Diffusion coefficients for micron-scale diamond-shaped solid domains are calculated for direct comparison to recent experiments. In supported membranes, identical objects in the distal and proximal leaflets may diffuse differently from one another; quantitative predictions for this asymmetry are provided, both for experimental systems and coarse-grained molecular simulations. We show that though recent experiments comparing the diffusion of monomeric, dimeric and trimeric protein assemblies moving over the surface of supported bilayers are inconsistent with the simplest Saffman-Delbrück model, they may be explained by a hydrodynamic model appropriate for supported membranes. We use hydrodynamic theory to numerically compute diffusion coefficients of complex objects embedded in free and supported lipid bilayer membranes.