Constrained Kripke structure for identifying parameters of biological models

Abstract

When modelling a complex biological system, the bottleneck of the process is the determination of parameter values that lead to model dynamics that are compatible with observations. Even for discrete modelling frameworks, this step can be limiting. Here we introduce a representation of the whole family of discrete models that can be associated to a biological system, where states are shared by all models and transitions are labelled by constraints on dynamical parameters. A model checking procedure is defined to handle this new representation. This procedure extracts the conditions on parameter settings that are compatible with a given dynamical property expressed in a temporal logic. We prove the correctness of our model checking procedure and illustrate the advantage of such an approach on some different systems of biological interest.