Model of Lipid Diffusion in Cytoplasmic Membranes

Abstract

An analytical model was developed to describe lateral lipid diffusion in heterogeneous native cytoplasmic membranes. The Fourier transform was used to solve the diffusion equation for a coordinate distribution function of lipids in a periodically inhomogeneous membrane, in which the diffusion coefficient is described by a harmonic function of coordinates. Advection and diffusion were shown to occur in the membrane. According to the model, various types of lipid diffusion observed experimentally in the membrane result from structural transitions arising in periodically arranged, fixed protein–lipid domains associated with the spectrin–actin–ankyrin network. If the domains are the same, superdiffusion and subdiffusion can be observed in experiments; i.e., the mean square displacement of lipids depends nonlinearly on time and their average displacement is zero. Drift during advection was lower than the chaotic Brownian displacement of lipids, advection was not observed in the experiment. When membrane proteins associated with the spectrin–actin–ankyrin network do not all undergo similar conformational changes 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 are nested in one another. In this case, hop diffusion can be found in experiments; i.e., periods of nonlinear diffusion of molecules are replaced by periods of advection–diffusion, in which the average displacement of molecules is nonzero. Advection is local in nature and occurs near individual protein–lipid domains. Criteria for hop diffusion to be experimentally observed in a periodically inhomogeneous membrane were obtained analytically.