Spatial information to restrict the dynamics of genetic regulatory networks

In the course of understanding the functioning of cellular processes, modelling frameworks for biological networks are mandatory in order to reason on the models and their properties. One of the main problems with such modelling framework is to determine the dynamics of gene regulatory networks (GRN). Formal techniques, most of them based on model checking, have been applied to select valid dynamics, that is dynamics consistant with biological experiments expressed by temporal properties. The problem is that these formal techniques rapidly become intractable because dynamics associated to the GRN are most of the time very numerous. Recently, it has been observed in in vivo experiments and in genomic and transcriptomic studies, that spatial informations are necessary to better understand both the mechanisms and the dynamics of GRN. In this paper we propose to extend the modelling framework of R. Thomas in order to introduce such spatial information between genes. We will show how these further informations allow us to restrict dynamics of GRN. We will illustrate our approach on two classical models of GRN: the mucus production in Pseudomonas aeruginosa and the lytic/lysogenic switch in the lambda phage.