Interactions between genes and gene products form the basis of 
essential processes like signal transduction, cell metabolism or 
embryonic development. Recent experimental advances helped uncover 
the qualitative structure of many cellular networks. Mathematical 
modeling can assist in this process by integrating the behavior of 
multiple components into a comprehensive model that goes beyond 
human intuition, and also by addressing questions that are not 
yet accessible to experimental analysis.

While chemical kinetics-based differential equations are the 
established method of describing individual interactions, the 
diversity of regulatory relationships and the sparsity of kinetic 
detail greatly hinders this type of modeling for complex regulatory 
networks. This talk will present an alternative, qualitative modeling 
paradigm that is based on the regulatory network topology and replaces 
the continuous dynamics with transitions between a set of discrete states.

We will focus on the abscisic acid signal transduction network, the 
main mechanism for minimizing water loss in plants. We synthesize 
the experimental information available about the components and 
processes involved in ABA-induced stomatal closure into a comprehensive
network, and formulate a Boolean model of the dynamical process. 
We validate the model by comparing its results with experimental 
information, and we study the resilience of the signaling network 
with respect to disruptions. Our main result is that the redundant 
network topology ensures a significant robustness, and signaling 
is completely blocked only in the case of multiple simultaneous disruptions.