Anomalous phospholipid subdiffusion in compartmentalized cell membrane and the mathematical model of the time-dependent diffusion coefficient

Abstract

Recent experimental data on an anomalous diffusion of phospholipids in compartmentalized cell membrane are analysed. A new mathematical model of passive transport with the time-dependent diffusion coefficient is proposed. The model with the step-type asymptotical dependence of the diffusion coefficient is applied to a concrete example, and a correspondence between the experimental and theoretical results is shown. The random distribution of immobilized obstructions as well as the membrane skeleton meshwork offer a theoretical basis for modifying the available models of transport and thus for refining the diffusion model. The experimentally obtained time-dependend coefficient of diffusion is shown to agree with the proposed theoretical model. Keywords: passive transport, the first Fick’s law, mathematical modeling