Section: New Results

Inferring Reaction Rule Models from Ordinary Differential Equations

Participants : François Fages, Steven Gay, Sylvain Soliman.

Many models in Systems Biology are described as Ordinary Differential Equations (ODEs), which allow for numerical integration, bifurcation analyses, parameter sensitivity analyses, etc. However, before fixing the kinetics and parameter values and going to simulations, various analyses can be performed based only on the structure of the model. This approach has rapidly developed in Systems Biology in the last decade, with for instance, the analyses of structural invariants in Petri net representation, model reductions by subgraph epimorphims, qualitative attractors in logical dynamics or temporal logic properties by analogy to circuit and program verification. These complementary analysis tools do not rely on kinetic information, but on the structure of the model with reactions.

In [8] , [19] , we present a symbolic computation algorithm for inferring a reaction model from an ODE system, based a general compatibility condition between the kinetic expression and the structure of a reaction, and report on its use for automatically curating the writing in SBML of the models in the respository biomodels.net. SBML is now a standard for sharing and publishing reaction models. However, since SBML does not enforce any coherence between the structure and the kinetics of a reaction, an ODE model can be transcribed in SBML without reflecting the real structure of the reactions, hereby invalidating many structural analyses. We show that the automatic writing in SBML of the models of biomodels.net allows us to reduce the percentage of models with a non well-formed reaction from 66% to 28%.