Robustness analysis of a model of gene regulatory network with memory

The response to different kinds of perturbations of a discrete model of gene regulatory network, which is a generalization of the random Boolean network model (RBN), is extensively discussed. The model includes memory effects and the analysis pays particular attention to the influence on the system stability of a parameter (i.e. the decay time of the gene products) that determines the duration of the memory effects. It is shown that this parameter deeply affects the overall behaviour of the system, with special regard to the dynamical regimes and the sensitivity. Furthermore, a noteworthy difference in the response of systems characterized by different memory lengths in presence of either temporary or permanent damages is highlighted, as well as a substantial difference, with respect to classical RBNs, concerning the relationship between the specific dynamical regime and the landscape of the attractors.