The switch-like character of the dynamics of genetic regulatory
networks has attracted much attention from mathematical biologists and
researchers on hybrid systems alike. We extend our previous work on a
method for the qualitative analysis of hybrid models of genetic regulatory
networks, based on a class of piecewise-affine differential equation (PADE)
models, in two directions. First, we present a refinement of the method
using a discrete or qualitative abstraction that preserves stronger
properties of the dynamics of the PA systems, in particular the sign
patterns of the derivatives of the concentration variables. The discrete
transition system resulting from the abstraction is a conservative
approximation of the dynamics of the PA system and can be computed
symbolically. Second, we apply the refined method to a regulatory system
whose functioning is not yet well-understood by biologists, the
nutritional stress response in the bacterium Escherichia
coli.
