Identification of Dynamic Parameters for Gene Networks

The study of gene networks allows us to better understand some biological processes such as the adaptation of the organism to a disturbance of the environment. In a discrete modelling framework of gene networks, it has been shown that the Hoare logic can help the modeller to identify the parameters of the model, so that the latter exhibits the observed biological traces. In this paper we present a hybrid modelling of gene networks which pays particular attention to the time spent in each state and we introduce an extension of the Hoare logic in this hybrid framework. The weakest precondition calculus associated with this modified Hoare logic makes it possible to determine the minimal constraints on the dynamic parameters of a gene network from an observed biological trace. These constraints form a continuous CSP that can be solved using the AbSolute continuous solver. The first experimental results show that the obtained solutions are in agreement with the specification of the Hoare triple coming from biological expertise.