Qualitative Modelling of genetic networks using high level Petri nets

J.-P. Comet, H. Klaudel and S. Liauzu

LaMI UMR CNRS 8042, Université d'Evry Val d'Essonne Boulevard F. Mitterrand 91025 Evry Cedex

Regulatory networks are found at the core of all biological functions from bio-chemical pathways to gene regulation and cell communication processes. Because of the complexity of the interweaving retroactions, the overall behavior is difficult to grasp and the development of formal methods is needed in order to confront the supposed properties of the biological system to the model. We revisit here the tremendous work of R. Thomas in term of high-level Petri nets.

It has been already shown that the boolean approach of R. Thomas can be expressed with the formalism of standart Petri net. Here we show that the previous approach but also the multi-valuated approach of R. Thomas can be expressed with high level Petri nets. This formalism allows us to unify the modelling of both approaches, to take advantage of all results and tools in the field of high level Petri nets like the model checking tool Maria and to prevent the explosion of the number of places. Two modellings are passed in review.

The dynamical behavior of the system is based on the definition of a certain number of biological parameters which often are unknown. The analysis of functionality of circuits of the regulatory graph can reduce the total number of sets of parameter values, which have to be taken into account. The classical approach is then to generate all Petri nets corresponding to all remaining sets of parameter values and to confront each model to the available knowledge or hypothesis. By introducing another place corresponding to the possible values of parameters, it remains possible to incorporate all behaviors defined by all possible parameter values, in the same high-level Petri net.