Mathematical Modeling and Approximation of Gene Expression Patterns

This study 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 differential 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. Finally, from the considered models we derive gene regulatory networks, discuss their qualitative features and provide a basis for analyzing networks with nonlinear connections