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Microscopic Simulation of Membrane Molecule Diffusion on Corralled Membrane Surfaces

Anne Marie S. Niehaus ^*, Dionisios G. Vlachos ^*, Jeremy S. Edwards , Petr Plechac  and Roger Tribe 

^* Department of Chemical Engineering, University of Delaware, Newark, Delaware; Molecular Genetics and Microbiology, Cancer Research and Treatment Center, University of New Mexico Health Sciences Center, and Chemical and Nuclear Engineering, University of New Mexico, Albuquerque, New Mexico; Department of Mathematics, University of Tennessee, Knoxville, Tennessee; and Mathematics Institute, University of Warwick, Coventry, United Kingdom

Correspondence: Address reprint requests to Dionisios G. Vlachos, Dept. of Chemical Engineering, University of Delaware, Newark, DE 19716. E-mail: vlachos{at}che.udel.edu.

The current understanding of how receptors diffuse and cluster in the plasma membrane is limited. Data from single-particle tracking and laser tweezer experiments have suggested that membrane molecule diffusion is affected by the presence of barriers dividing the membrane into corrals. Here, we have developed a stochastic spatial model to simulate the effect of corrals on the diffusion of molecules in the plasma membrane. The results of this simulation confirm that a fence barrier (the ratio of the transition probability for diffusion across a boundary to that within a corral) on the order of 10³–10⁴ recreates the experimentally measured difference in diffusivity between artificial and natural plasma membranes. An expression for the macroscopic diffusivity of receptors on corralled membranes is derived to analyze the effects of the corral parameters on diffusion rate. We also examine whether the lattice model is an appropriate description of the plasma membrane and look at three different sets of boundary conditions that describe diffusion over the barriers and whether diffusion events on the plasma membrane may occur with a physically relevant length scale. Finally, we show that to observe anomalous (two-timescale) diffusion, one needs high temporal (microsecond) resolution along with sufficiently long (more than milliseconds) trajectories.