Diffusion with periodic obstacles and applications to intracellular diffusion

An analytic expression for the effective diffusion coefficient due to periodic geometric obstacles in terms of the solution of an elliptic boundary value problem is derived by taking a probabilistic view of diffusion.; Some estimates for the effective diffusion coefficient are proven analytically. The effective diffusion coefficients for various geometric shapes and sizes of obstacles in two- and three-dimensions are evaluated by solving the elliptic boundary value problems numerically on the related fundamental domains which are determined by the shapes and sizes of the obstacles by using the finite element method. Then the Schwarz-Christoffel transformation is applied to evaluate the effective diffusion coefficient for diamond-shaped obstacles in two dimensions. There is good agreement between the results obtained by using the Schwarz-Christoffel transformation and those obtained by the finite element method.; The results are applied to interpret experimental data on the retardation of intracellular diffusion owing to cytoskeletal barriers. For the two-dimensional case, e.g., diffusion in a membrane, the results are quantitatively similar to those obtained by Saxton (25) using Monte Carlo Methods. The three-dimensional results are quantitatively similar to experimental results reported by Luby-Phelps et al. (15) for the diffusion of dextran and Ficoll particles in Swiss 3T3 cells. By accounting for geometric factors, these results allow one to assess the relative contributions of geometrical hindrance and of binding to the cytoskeletal lattice from measurements of intracellular diffusion coefficients of proteins. There is an assumption commonly made that the area (or volume) fraction of the obstacles is the primary determinant of the retardation of the diffusion. Plotting our results in terms of area (or volume) fraction suggests that this assumption is valid only for sufficiently low area fraction.