Translational diffusion in lipid membranes beyond the Saffman-Delbruck approximation

The Saffman-Delbrück approximation is commonly used in biophysics to relate the membrane inclusion size to its translational diffusion coefficient and membrane viscosity. However, this approximation has a restricted validity range, and its application to determination of inclusion sizes from diffusion data may in certain cases lead to unreliable results. At the same time, the model by Hughes et al. (Hughes, B. D., B. A. Pailthorpe, and C. R. White. 1981. J. Fluid Mech. 110:349-372.), providing diffusion coefficients of membrane inclusions for arbitrary inclusion sizes and viscosities of the membrane and surrounding fluids, involves substantial computational efforts, which prevents its use in practical data analysis. We develop a simple and accurate analytical approximation to the Hughes et al. model and demonstrate its performance and utility by applying it to the recently published experimental data on translational diffusion of micrometer-sized membrane domains.