TITLE :

Discrete and hybrid modelling of gene networks, the example of the circadian
rhythm

ABSTRACT :

The qualitative modelling of biological networks is becoming increasingly
popular. In recent years, the discrete modelling of gene networks, such as the
framework initiated by René Thomas, has allowed to elucidate the functioning
of a lot of biological functions.  Formal logic and tools from computer
science can be applied within these frameworks. Temporal properties, expressed
in temporal logic, can be automatically and systematically checked against
many hypothetical models. Such approaches lead to an exhaustive
characterization of the sensible parameter values of the models.

Such modelling frameworks are mostly based on a discrete time to describe the
succession of state modifications. Consequently, they badly reflect "real
time" behaviours and they hardly treat chronometrical questions, such as
chrono-pharmacology questions. Hybrid frameworks, where one tries to define
how much time is spend within each discrete state, seem able to combine the
power of the discrete, qualitative approaches with computations on real
numbers. The difficult point is to preserve the decidability of temporal
properties.

We illustrate the evolution from purely discrete models to hybrid models via a
typical biological example: the circadian rhythm.