## Section: New Results

### Model Reductions by Graph Transformations

Participants : François Fages, Steven Gay, Sylvain Soliman, Denis Thieffry.

Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also more and more employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and positive/negative influence graphs. The analysis of circuits in the influence graphs has been introduced by René Thomas in the late 70's with necessary conditions for oscillations (homeostasie) and multistability (cell differentiation).

In [19] , model reduction techniques preserving the circuits in the influence graph are investigated and evaluated on a gene regulatory network responsible for segment polarity in Drosophilia. In [34] , general structural model reduction techniques based on graph edition operations are investigated and evaluated on models of cell signalling. The perspective of these preliminary studies is to relate models at different levels of details by formal graph transformation operations, and design systematic model reduction/expansion strategies.

In [38] , an extension of the syntax of reaction rules with antagonists is proposed for SBML and BIOCHAM in order to make visible in the rules the inhibitors of a reaction that are often hidden in the kinetic expression. This extension allows us to efficiently compute the influence graph of a reaction model and to compare models at different levels of details.