Petri net modelling of biological regulatory networks

The complexity of biological regulatory networks often defies the intuition of the biologist and calls for the development of proper mathematical methods to model their structures and to give insight in their dynamical properties. One qualitative approach consists in modelling regulatory networks in terms of logical equations (using either Boolean or multi-level discretisations). The Petri Net (PN) formalism offers a complementary framework to analyse the dynamical properties of large systems, either from a qualitative or a quantitative point of view. Our proposal consists in articulating the logical approach with the PN formalism. In a previous work, we have already defined a systematic re-writing for Boolean models of regulatory networks into a standard PN formalism. In this paper, we propose a rigourous and systematic mapping of multi-level logical regulatory models into specific standard Petri nets, called Multi-level Regulatory Petri Nets (MRPN). We further propose some reduction strategies. The resulting models therefore become amenable to the algebraic and computational analyses, as well as to time extensions used by the PN community. To illustrate our approach, we apply it to a multi-level logical model of the genetic switch controlling the lysis-lysogeny decision in the bacteriophage lambda.