Robustness analysis of a Boolean 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 (RBN) model, is 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 behavior of the system, with special regard to the dynamical regimes and the sensitivity. Furthermore, a noteworthy divergence in the response of systems characterized by different memory lengths in the presence of either temporary or permanent damages is highlighted, as is the substantial difference, with respect to classical RBNs, between the specific dynamical regime and the landscape of the attractors.