Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes

by Open Science Repository Mathematics
(February 2014)


In this paper, we discuss the mathematical modeling and numerical implementation of reaction-diffusion processes inside a cell nucleus where the diffusion of nuclear materials is restricted by its membrane. Viewing the two-specie interaction between the chemical composition of the cell and its membrane as an enzyme-substrate process we modeled the reaction-diffusion in the cell membrane under quasi-steady state equilibrium assumption. The pure diffusion process inside the three-dimensional cell depends on the solution of a two-dimensional reaction-diffusion process on the interface on its cell membrane. Through adaptive nite element discretization, we solve the three-dimensional pure diff usion problem using the solution of the two-dimensional problem on the membrane as a Dirichlet data. The paper is complemented with numerical results.

Keywords: mathematical modeling, reaction, diffusion, finite element, discretization, cell membrane.

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Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes

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