Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures

Finding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeler that techniques like modelchecking help solving, in the qualitative but also in the quantitative case. In this article we define a continuous degree of satisfaction of temporal logic formulae with constraints. We show how such a satisfaction measure can be used as a fitness function with state-ofthe-art evolutionary optimization methods 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 temporal specification. These methods are evaluated on models of the cell cycle and of the MAPK signaling cascade.