Sommaire:

We are interested in proving the possibility and, more importantly, the impossibility of behaviours within large-scale models of biological networks. The presented results apply in the scope of qualitative models of biological networks, where each interacting component (gene, protein, ...) is represented by a variable varying within a finite (small) set of qualitative levels. These sets typically result from a quantization of the population of the species. We first introduce the Process Hitting formal language for the qualitative modelling of biological networks. The Process Hitting allows to specify the local interactions between components with various degrees of precision for the involved cooperations. Thanks to the particular structure of Process Hitting models, we show how to extract events that are necessary for activating a component of interest. Such a causality analysis actually results in a very compact abstract representation of the model dynamics, and can be used to prove the existence or absence of some reachability properties. Finally, we discuss how our method can be used to extract sets of components playing a crucial role for achieving a given reachability property, suggesting potential therapeutic targets. We illustrate our results with applications to boolean models of signalling and regulatory pathways, ranging from 100 to more than 9000 interacting components.

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