Hybrid Model of gene regulatory networks, the case of the lac-operon

The study of genetic regulatory networks has become an important field of research in biomathematics and biocomputing. With the early progresses made in biotechnology, there will be more and more data available concerning the expression of genes ; the understanding of such complex systems will then become crucial. However, even though several serious models have been proposed ([3], [1]), these systems still raise some challenging questions, from both qualitative and quantitative points of view. What we propose in this paper, after a brief description of the well-known lac-operon, is a hybrid model of the regulatory mechanism responsible for the treatment of lactose by the bacterium e-coli.