Self-Diffusion in Cell Membranes in the Long Time Regime

We consider the process of self-diffusion in the cellular structure in the presence of permeable barriers in long time regime. Based on the most general concepts of the translation mobility and geometry of a heterogeneous system, an expression for the self-diffusion coefficient of liquid molecules in such a medium in a long time regime was derived. We have shown that the value of the self-diffusion coefficient in the long-time limit is determined by the probability of interaction of the diffusant molecule with an obstacle. We obtained an expression for the probability of such interaction as a function of the surface-to-volume ratio (S/V). Comparing the obtained analytical expression with the results of computer simulation was performed. Shown the exponential dependence of the self-diffusion coefficient on the barrier pinning density