Hierarchical analysis of piecewise affine models of gene regulatory networks |
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Authors: | Laurent Tournier Jean-Luc Gouzé |
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Institution: | (1) INRIA COMORE, 2004 route des lucioles, 06902 Sophia-Antipolis, France |
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Abstract: | A key point in the analysis of dynamical models of biological systems is to handle systems of relatively high dimensions.
In the present paper we propose a method to hierarchically organize a certain type of piecewise affine (PWA) differential
systems. This specific class of systems has been extensively studied for the past few years, as it provides a good framework
to model gene regulatory networks. The method, shown on several examples, allows a qualitative analysis of the asymptotic
behavior of a PWA system, decomposing it into several smaller subsystems. This technique, based on the well-known strongly
connected components decomposition, is not new. However, its adaptation to the non-smooth PWA differential equations turns
out to be quite relevant because of the strong discrete structure underlying these equations. Its biological relevance is
shown on a 7-dimensional PWA system modeling the gene network responsible for the carbon starvation response in Escherichia coli.
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