Computational simulation of a new system modelling ions electromigration through biological membranes
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RESEARCH
Open Access
Computational simulation of a new system modelling ions electromigration through biological membranes Noureddine Alaa* and Hamid Lefraich *Correspondence: [email protected] Department of Mathematics, Laboratory of Applied Mathematics and Computer Science (LAMAI), Faculty of Science and Technology, Cadi Ayaad University, Abdelkarim Elkhattabi Avenue, Marrakech, Morocco
Abstract Background: The interest in cell membrane has grown drastically for their important role as controllers of biological functions in health and illness. In fact most important physiological processes are intimately related to the transport ability of the membrane, such as cell adhesion, cell signaling and immune defense. Furthermore, ion migration is connected with life-threatening pathologies such as metastases and atherosclerosis. Consequently, a large amount of research is consecrated to this topic. To better understand cell membranes, more accurate models of ionic flux are required and also their computational simulations. Results: This paper is presenting the numerical simulation of a more general system modelling ion migration through biological membranes. The model includes both the effects of biochemical reaction between ions and fixed charges. The model is a nonlinear coupled system. In the first we describe the mathematical model. To realize the numerical simulation of our model, we proceed by a finite element discretisation and then by choosing an appropriate resolution algorithm to the nonlinearities. Conclusions: We give numerical simulations obtained for different popular models of enzymatic reaction which were compared to those obtained in literature on systems of ordinary differential equations. The results obtained show a complete agreement between the two modellings. Furthermore, various numerical experiments are presented to confirm the accuracy, efficiency and stability of the proposed method. In particular, we show that the scheme is unconditionally stable and second-order accurate in space. Keywords: Reaction-diffusion system, Electromigration, Nonlinear coupled system, Finite element method, Nernst-Planck equations, Numerical analysis, Enzyme kinetics, Substrate suicide, Cooperative phenomena, Computational simulation
Background Cell membrane is the biological membrane separating the intracellular environment from the extracellular one. The cell membrane surrounds all cells and it’s selectively permeable, permitting the free passage of some substances and restricting the passage of others, thus controlling the flux of substances in and out of the cell. All diseases are problems of regulating the passage of materials at the level of the cell. Consequently, to understand the cause of a disease, we need to understand the alterations that take place at the cellular © 2013 Alaa and Lefraich; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribu
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