Composition and abstraction of logical regulatory modules: application to multicellular systems
Motivation: Logical (Boolean or multi-valued) modelling is widely employed to study regulatory or signalling networks. Even though these discrete models constitute a coarse, yet useful, abstraction of reality, the analysis of large networks faces a classical combinatorial problem. Here, we propose to take advantage of the intrinsic modularity of inter-cellular networks to set up a compositional procedure that enables a significant reduction of the dynamics, yet preserving the reachability of stable states. To that end, we rely on process algebras, a well-established computational technique for the specification and verification of interacting systems. Results: We develop a novel compositional approach to support the logical modelling of interconnected cellular networks. First, we formalise the concept of logical regulatory modules and their composition. Then, we make this framework operational by transposing the composition of logical modules into a process algebra framework. Importantly, the combination of incremental composition, abstraction and minimisation using an appropriate equivalence relation (here the safety equivalence) yields huge reductions of the dynamics. We illustrate the potential of this approach with two case-studies: the Segment-Polarity and the Delta-Notch modules.