Open Science Repository Mathematics

doi: 10.7392/openaccess.23050498


Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes


Saheed Akindeinde

Catholic University of Eastern Africa, Nairobi, Kenya


Abstract

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.



Citation: Akindeinde, S. (2014). Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes. Open Science Repository Mathematics, Online(open-access), e23050498. doi:10.7392/openaccess.23050498

Received: February 13, 2014

Published: February 22, 2014

Copyright: © 2014 Akindeinde, S. Creative Commons Attribution 3.0 Unported License.

Contact: research@open-science-repository.com



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APA

Akindeinde, S. (2014). Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes. Open Science Repository Mathematics, Online(open-access), e23050498. doi:10.7392/openaccess.23050498

MLA

Akindeinde, Saheed. “Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes.” Open Science Repository Mathematics Online.open-access (2014): e23050498.

Chicago

Akindeinde, Saheed. “Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes.” Open Science Repository Mathematics Online, no. open-access (February 22, 2014): e23050498. doi:10.7392/openaccess.23050498.

Harvard

Akindeinde, S., 2014. Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes. Open Science Repository Mathematics, Online(open-access), p.e23050498.

Science

1. S. Akindeinde, Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes, Open Sci. Repos. Math. Online, e23050498 (2014).

Nature

1. Akindeinde, S. Mathematical Modeling of Reaction-Diffusion Process in Cell Membranes. Open Sci. Repos. Math. Online, e23050498 (2014).


doi

Research registered in the DOI resolution system as: 10.7392/openaccess.23050498.


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Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 Unported License.