Ordinary differential equations with applications in molecular biology.

Departament Medicină preventivă si Interdisciplinaritate, Facultatea de Medicină, Universitatea de Medicină si Farmacie "Grigore T. Popa", Iaşi.

Revista medico-chirurgicală̆ a Societă̆ţ̜ii de Medici ş̧i Naturaliş̧ti din Iaş̧i 2012 Jan-Mar

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Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

Citation

M Ilea, M Turnea, M Rotariu. Ordinary differential equations with applications in molecular biology. Revista medico-chirurgicală̆ a Societă̆ţ̜ii de Medici ş̧i Naturaliş̧ti din Iaş̧i. 2012 Jan-Mar;116(1):347-52