Model of lipid diffusion in cytoplasmic membranes

Abstract

An analytical model of lateral lipid diffusion in heterogeneous native cytoplasmic membranes is presented. The Fourier transform method was used to solve the diffusion equation for the coordinate distribution function of lipids in a periodically inhomogeneous membrane, in which the diffusion coefficient is described by a harmonic function of the coordinates. It is shown that advection and diffusion are present in membrane. The model explains different types of lipid diffusion in membrane observed previously in experiments as a result of structural transitions of periodically located fixed protein-lipid domains associated with the spectrin-actin-ankyrin network. If these domains are the same, then super- and subdiffusion can be seen in experiments, when the mean square displacement of lipids depends non-linearly on time, and their average displacement is zero. Drift during advection was less than the chaotic Brownian displacement of lipids, advection was not observed in the experiment. When not all membrane proteins associated with the spectrin-actin-ankyrin network undergo conformational change in the same way upon ligand binding, two periodic sublattices of inhomogeneities arise in the membrane from fixed protein-lipid domains around membrane proteins associated with the cytoskeleton and nested in one another. In this case, hop diffusion can be found in experiments, when periods of nonlinear diffusion of molecules are replaced by periods of advection-diffusion, in which the average displacement of molecules is not zero. Advection is local in nature and occurs near individual protein-lipid domains. In the presented work, criteria are analytically obtained under which hop diffusion is experimentally observed in a periodically inhomogeneous membrane.