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A mathematical modeling and approximation of gene expression patterns by linear and quadratic regulatory relations and analysis of gene networks

Yılmaz, Fatma Bilge
This thesis mainly concerns modeling, approximation and inference of gene regulatory dynamics on the basis of gene expression patterns. The dynamical behavior of gene expressions is represented by a system of ordinary di erential equations. We introduce a gene-interaction matrix with some nonlinear entries, in particular, quadratic polynomials of the expression levels to keep the system solvable. The model parameters are determined by using optimization. Then, we provide the time-discrete approximation of our time-continuous model. We analyze the approximating model under the aspect of stability. Finally, from the considered models we derive gene regulatory networks, discuss their qualitative features of the networks and provide a basis for analyzing networks with nonlinear connections.