Probabilistic Gene Network

In this article we present a modelling framework that links the well known modelling framework of gene network introduced by R. Thomas and Markov chains. In a first development we introduce a Markov chain having as state space the set of all possible states of the R. Thomas models: we generate the transition probabilities by examining all the possible parameterizations of the interaction graph. The second development focuses on a stochastic framework where several parameterizations of a same qualitative gene interaction graph are considered and transition probabilities allow one to jump from a state to another one which can potentially be in another parameterized model. The idea is to consider only parameterized qualitative models of R. Thomas which abstract biological knowledge, and to use transition probabilities to allow to jump from one to another, if information coming from biological experiments reinforces the belief in a particular model.