Interaction between genes and gene products forms the basis of essential processes like signal transduction, cell metabolism or embryonic development. Recent experimental advances helped uncover the structure of many gene control and metabolic networks, creating a surge of interest in the dynamical description of gene regulation. This presentation we will explore the connections between network topology and dynamics by introducing qualitative (logical) models of the regulatory network formed by the segment polarity genes of the fruit fly Drosophila melanogaster.
We explore three modeling frameworks (synchronous Boolean, asynchronous Boolean and piecewise linear ) that span the range between discrete and continuous modeling. Our models reproduce the normal expression pattern of the segment polarity genes as well as patterns corresponding to gene mutations and over-expression experiments. The success of these models suggests that the kinetic details of the interactions can vary long as there are two separable interaction timescales and the network of interactions is unperturbed. We argue that certain topological features such as path redundancy and feedback have very strong roles in the robust dynamics of gene regulatory networks.