• The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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## Section: Research Program

### Logical Paradigm for Systems Biology

Our group was among the first ones in 2002 to apply model-checking methods to systems biology in order to reason on large molecular interaction networks, such as Kohn's map of the mammalian cell cycle (800 reactions over 500 molecules) (N. Chabrier-Rivier, M. Chiaverini, V. Danos, F. Fages, V. Schächter. Modeling and querying biochemical interaction networks. Theoretical Computer Science, 325(1):25–44, 2004.). The logical paradigm for systems biology that we have subsequently developed for quantitative models can be summarized by the following identifications :

biological model = transition system $K$

dynamical behavior specification = temporal logic formula $\phi$

model validation = model-checking $\phantom{\rule{4pt}{0ex}}K,\phantom{\rule{4pt}{0ex}}s\phantom{\rule{4pt}{0ex}}\vDash ?\phantom{\rule{4pt}{0ex}}\phi$

model reduction = sub-model-checking, ${K}^{\text{'}}\subset K$ s.t. ${K}^{\text{'}}?,\phantom{\rule{4pt}{0ex}}s\phantom{\rule{4pt}{0ex}}\vDash \phantom{\rule{4pt}{0ex}}\phi$

model prediction = formula enumeration, $\phi$ s.t. $K,\phantom{\rule{4pt}{0ex}}s\phantom{\rule{4pt}{0ex}}\vDash \phantom{\rule{4pt}{0ex}}\phi ?$

static experiment design = symbolic model-checking, state $s$ s.t. $K,\phantom{\rule{4pt}{0ex}}s?\phantom{\rule{4pt}{0ex}}\vDash \phantom{\rule{4pt}{0ex}}\phi$

model synthesis = constraint solving $\phantom{\rule{4pt}{0ex}}K?,\phantom{\rule{4pt}{0ex}}s\phantom{\rule{4pt}{0ex}}\vDash \phantom{\rule{4pt}{0ex}}\phi$

dynamic experiment design = constraint solving $\phantom{\rule{4pt}{0ex}}K?,\phantom{\rule{4pt}{0ex}}s?\phantom{\rule{4pt}{0ex}}\vDash \phantom{\rule{4pt}{0ex}}\phi$

In particular, the definition of a continuous satisfaction degree for first-order temporal logic formulae with constraints over the reals, was the key to generalize this approach to quantitative models, opening up the field of model-checking to model optimization (On a continuous degree of satisfaction of temporal logic formulae with applications to systems biology A. Rizk, G. Batt, F. Fages, S. Soliman International Conference on Computational Methods in Systems Biology, 251-268) This line of research continues with the development of temporal logic patterns with efficient constraint solvers and their generalization to handle stochastic effects.