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 $K,s\vDash ?\phi$

model reduction = sub-model-checking, $K^{\text{'}}\subset K$ s.t. $K^{\text{'}}?,s\vDash \phi$

model prediction = formula enumeration, $\phi$ s.t. $K,s\vDash \phi ?$

static experiment design = symbolic model-checking, state $s$ s.t. $K,s?\vDash \phi$

model synthesis = constraint solving $K?,s\vDash \phi$

dynamic experiment design = constraint solving $K?,s?\vDash \phi$

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.