## Section: New Results

### Parameter Search and Robustness Analysis w.r.t. Temporal Logic Properties

Participants : Grégory Batt, François Fages, Sylvain Soliman, Aurélien Rizk.

Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a central task of the modeller that techniques like model-checking help solving, in the qualitative but also in the quantitative case. In [22] , we show how the previous method for QFLTL(R) constraint solving can be used to define a continuous degree of satisfaction of LTL(R) formulae in a given trace. We then show how such a satisfaction measure can be used as a fitness function with state-of-the-art search methods (namely the Covariance Matrix Adaptation Evolutionary Strategy CMAES of Nikolaus Hansen from the TAO project-team.)in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some specification. These novel methods are evaluated on models of the cell cycle and of the MAPK signalling cascade. In [26] , [27] , they are used to analyze a gene activation cascade in synthetic biology.