Web Release Date: December 11,
Lateral Diffusion of Proteins in the Plasma Membrane: Spatial Tessellation and Percolation Theory
Department of Chemistry, Sogang University, Seoul 121-742, Republic of Korea
Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706
Received: September 7, 2007
In Final Form: September 26, 2007
Abstract:
The obstructed diffusion of proteins in the plasma membrane is studied using computer simulation and an
analysis using spatial tessellation and percolation theory. The membrane is modeled as a two-dimensional
space with fixed hard disc obstacles, and the proteins are modeled as hard discs. The simulations show a
transition from normal to anomalous diffusion as the area fraction, 
m, of obstacles is increased and to confined
diffusion for area fractions above the pecolation threshold, which occurs for m = 0.22. A Voronoi tessellation
procedure is used to map the continuous space system onto an effective lattice model, with the connectivity
of bonds determined from a geometric criterion. The estimate of the percolation threshold obtained from this
lattice model is in excellent agreement with the simulation results, although the nature of the dynamics in the
continuous space model is different from lattice models. At high obstacle area fractions (but below the
percolation threshold), the primary mode of transport is a hopping motion between voids, consistent with
experiment. The simulations and analysis emphasize the importance of structural correlations between obstacles.
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