  The main difficulty when modelling gene networks is the identification of the
parameters that govern their dynamics. It is particularly difficult for models
in which time is continuous: parameters have real values which cannot be
enumerated. The widespread idea is to infer new constraints that reduce the
range of possible values. Here we present a new work based on a particular
class of Hybrid automata (inspired by Thomas discrete models) where discrete
parameters are replaced by signed celerities. We propose a new approach
involving Hoare logic and weakest precondition calculus (a la Dijkstra) that
generates constraints on the parameter values. Indeed, once proper
specifications are extracted from biological traces with duration information
(found in the literature or biological experiments), they play a role similar
to imperative programs in the classical Hoare logic. We illustrate our hybrid
Hoare logic on a small model controlling the lacI repressor of the lactose
operon.
