Qualitative modelling and analysis of regulations in multi-cellular systems using Petri nets and topological collections

In this paper, we aim at modelling and analyzing the regulation processes in multi-cellular biological systems, in particular tissues. The modelling framework is based on interconnected logical regulatory networks (a la Rene Thomas) equipped with information about their spatial relationships. The semantics of such models is expressed through colored Petri nets to implement regulation rules, combined with topological collections to implement the spatial information. Some constraints are put on the the representation of spatial information in order to preserve the possibility of an enumerative and exhaustive state space exploration. This paper presents the modelling framework, its semantics, as well as a prototype implementation that allowed preliminary experimentation on some applications.