Modeling and simulation of genetic regulatory networks by ordinary differential equations
H. de Jong, J. Geiselmann
J. Chen, E.R. Dougherty, I. Shmulevich, Z.J. Wang (eds), Genomic Signal Processing and Statistics, Hindawi Publishing Corporation, New York, 2005, 201‑239.
A remarkable development in molecular biology has been the recent upscaling to the genomic level of its experimental methods. These methods produce, on a routine basis, enormous amounts of data on different aspects of the cell. A large part of the experimental data available today concern genetic regulatory networks underlying the functioning and differentiation of cells. In addition to high-throughput experimental methods, mathematical and computational approaches are indispensable for analyzing these networks of genes, proteins, small molecules, and their mutual interactions. In this chapter, we review methods for the modeling and simulation of genetic regulatory networks. A large number of approaches have been proposed in the literature, based on such formalisms as graphs, Boolean networks, differential equations, and stochastic master equations. We restrict the discussion here to ordinary differential equation models, which is probably the most-widely used formalism. In particular, we compare nonlinear, linear, and piecewise-linear differential equations, illustrating the application of these models by means of concrete examples taken from the literature.