Qualitative Petri Net Modelling of Genetic Networks

The complexity of biological regulatory networks calls for the development of proper mathematical methods to model their structures and to give insight in their dynamical behaviours. One qualitative approach consists in modelling regulatory networks in terms of logical equations (using either Boolean or multi-level discretisation). Petri Nets (PNs) offer a complementary framework to analyse large systems. In this paper, we propose to articulate the logical approach with PNs. We first revisit the definition of a rigourous and systematic mapping of multi-level logical regulatory models into specific standard PNs, called Multi-level Regulatory Petri Nets (MRPNs). In particular, we consider the case of multiple arcs representing different regulatory effects from the same source. We further propose a mapping of multi-level logical regulatory models into Coloured PNs, called Coloured Regulatory Petri Nets (CRPNs). These CRPNs provide an intuitive graphical representation of regulatory networks, relatively easy to grasp. Finally, we present the PN translation and the analysis of a multi-level logical model of the core regulatory network controlling the differentiation of T-helper lymphocytes into Th1 and Th2 types.