Analysis and prediction of gene expression patterns by dynamical systems, and by a combinatorial algorithm

Taştan, Mesut
Modeling and prediction of gene-expression patterns has an important place in computational biology and bioinformatics. The measure of gene expression is determined from the genomic analysis at the mRNA level by means of microarray technologies. Thus, mRNA analysis informs us not only about genetic viewpoints of an organism but also about the dynamic changes in environment of that organism. Different mathematical methods have been developed for analyzing experimental data. In this study, we discuss the modeling approaches and the reasons why we concentrate on models derived from differential equations and improve the pioneering works in this field by including affine terms on the right-hand side of the nonlinear differential equations and by using Runge- Kutta instead of Euler discretization, especially, with Heun̕s method. Herewith, for stability analysis we apply modified Brayton and Tong algorithm to time-discrete dynamics in an extended space.


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The theory of time scales is introduced by Stefan Hilger in his PhD thesis in 1998 in order to unify continuous and discrete analysis. In our thesis, by making use of the time scale calculus we study the oscillation of nonlinear matrix differential equations of second order. the first chapter is introductory in nature and contains some basic definitions and tools of the time scales calculus, while certain well-known results have been presented with regard to oscillation of the solutions of second order matr...
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Citation Formats
M. Taştan, “Analysis and prediction of gene expression patterns by dynamical systems, and by a combinatorial algorithm,” M.S. - Master of Science, Middle East Technical University, 2005.