Section: New Results

Petri Net Representation of Biological Networks

Participants : François Fages, Faten Nabli, Sylvain Soliman, Denis Thieffry.

In [20] , we present a way to compute the minimal semi-positive invariants of a Petri net representing a biological reaction system, as a Constraint Satisfaction Problem (CSP). The use of Petri-nets to manipulate reaction models,and make available a variety of tools is quite old, and recently analyses based on invariant computation for biological models have become more and more frequent, especially in the context of module decomposition. In our case, this analysis brings both qualitative and quantitative information on the models, in the form of conservation laws and consistency checking, thanks to finite domain constraint programming. It is noticeable that some of the most recent optimizations of standard invariant computation techniques in Petri-nets correspond to well-known techniques in CSPs, like symmetry-breaking. A simple prototype based on GNU-Prolog's FD solver, and including symmetry detection and breaking, was incorporated into the BIOCHAM modelling environment.

Other uses of Petri Nets structural properties computation were investigated in [35] , and most notably an incomplete symbolic search for steady states based on T-invariants computation and other structural properties.

These developments are focused on the applications of the CALAMAR ANR project, where large models of the E2F/RB pathway and of other cancer-related processes are studied. This project also dwelves, on the formal side, on relationships between different formalisms, whether BIOCHAM-like reaction-centered, or regulation-centered like logical models [1] [6] , the Petri Net level being common to both frameworks.