DISCRETE AND CONTINUOUS APPROACHES TO MODEL GENE REGULATORY NETWORKS G. Bernot (UNS-I3S), J.P. Comet (UNS-I3S) and J.L. Gouze (INRIA-Comore) Part 1: Discrete approaches of René Thomas to model gene networks (G. Bernot, J.-P. Comet) 1. Gene regulatory networks as directed labelled graphs 2. Discrete parameters, focal points, resource table and asynchronous state graph 3. Reverse engineering: inference of parameters 4. Classical results on positive and negative regulatory loops 5. Temporal logics applied to Thomas' networks 6. Simple example of the mucus production in P. aeruginosa 7. Singular states and applications Part 2: Continuous approaches to model gene networks (J.-L. Gouze, M. Chaves) 1. Some models of gene networks 2. Example: the bistable switch 3. Example: the negative loop, oscillators (2 and 3 genes) 4. Recalls: state space analysis for non linear ordinary differential equations 5. Asymptotic analysis (equilibriums, limit cycles), qualitative analysis 6. The continuous formalism for gene networks models 7. The Piecewise Linear formalism for gene networks models 8. Examples: study of models of the carbon starvation genetic network for E. coli. References: - R. Thomas, M. Kaufman. Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits. Chaos 11, 180-195, 2001. - G. Bernot, J-P. Comet, A. Richard, J. Guespin. Application of formal methods to biological regulatory networks: Extending Thomas' asynchronous logical approach with temporal logic. J. of Theoretical Biology (JTB), Vol.229, Issue 3, p.339-347, 2004. - E. Klipp, R. Herwig, A. Howald, C. Wierling, and H. Lehrach. Systems Biology in practice. Wiley-VCH, Weinheim, 2005.