ROBUSTNESS IN REGULATORY NETWORKS: A MULTI-DISCIPLINARY APPROACH J. Demongeot 1 , A. Elena 1 and S. Sen´ e 1,2 1 TIMC-IMAG, Facult´ e de M´ edecine, UJF Grenoble, 38706 La Tronche, France 2 LIP, Rhˆ one-Alpes Complex Systems Institute, 5 rue du Vercors, 69007 Lyon, France ABSTRACT We give in this paper indications about the dynamical impact (as phenotypic changes) coming from the main sources of perturbation in biological regulatory networks. First we define the boundary of the interaction graph expressing the regulations between the main elements of the network (genes, proteins, metabolites,...). Then we search what changes in the state values on the boundary could cause some changes of states in the core of the system (robustness to boundary conditions). After we analyse the role of the mode of updating (se- quential, block sequential or parallel) on the asymptotics of the network, essentially on the occurrence of limit cycles (robustness to updating methods). Finally we show the influence of some topological changes (e.g. suppression or addition of interactions) on the dynamical behavior of the system (robustness to topology perturbations). keywords: discrete dynamical systems, regulatory networks, cellular automata, robust- ness. 1 INTRODUCTION The robustness of a regulatory biological (e.g. genetic) network is its ability to present no phenotypic change after any modification of the number of its elements (e.g. genes) or of their interactions. This property can be provided by an internal redundancy, but, according to Wolfe (Wolfe, 2000), only about 3% of yeast genes with “essential” phenotypes (i.e. whose ablation is lethal), compared with about 17% of non-essential yeast genes, are homologues (i.e. formed by genome duplication). This suggests that the built-in reliability of genetic networks is not necessarily due to the physical duplication of their components. Many recent works (Borenstein and Ruppin, 2006; Elena et al., 2006; Hornstein and Shomron, 2006) are for example