Text S 1 Paul François

Genetic networks are evolved by repeated rounds of selection, growth and mutation. Typically 40 networks are followed in parallel. At each step of the algorithm, equations corresponding to the networks are integrated, and a ” fitness” or ” scoring” function is computed. Networks are then ranked according to this fitness; the best half is retained, then each network kept is copied and mutated. Mutations are of two types : mutations changing the kinetic constants within the networks or mutations changing the topology of the network, i.e. adding/removing new proteins or interactions. At each generation, a given mutation has a pre-determined probability to happen. Mutations changing kinetic parameters in the network are assumed to have a higher probability of occurrence than mutations changing network topologies, and among the latter, the probability of removing existing interactions is higher than probability of adding new interactions. This choice of probabilities corresponds to a biologically realistic limit for which the most probable evolutionary event is to modify existing interactions, the second most probable event being to delete interactions and creating new ones is the least probable. Results of evolution described in this chapter are largely independent of the precise choice of mutation rates as long as simulations are run in this limit. After the mutation step, the entire process is iterated. A “generation” is one iteration of this selection/growth/mutation process, and corresponds to many generations in a real organism since we are only concerned with mutations in the one network under study. This procedure favours the evolution with time of network topologies and parameters satisfying the fitness function.