Regulatory interaction networks are often studied on their dynamical side (existence of attractors, study of their stability). We focus here also on their robustness, that is their ability to offer the same spatiotemporal patterns and to resist to external perturbations such as losses of nodes or edges in the networks interactions architecture, changes in their environmental boundary conditions as well as changes in the update schedule (or updating mode) of the states of their elements (e.g., if these elements are genes, their synchronous coexpression mode versus their sequential expression). We define the generic notions of boundary, core, and critical vertex or edge of the underlying interaction graph of the regulatory network, whose disappearance causes dramatic changes in the number and nature of attractors (e.g., passage from a bistable behaviour to a unique periodic regime) or in the range of their basins of stability. The dynamic transition of states will be presented in the framework of threshold Boolean automata rules. A panorama of applications at different levels will be given: brain and plant morphogenesis, bulbar cardio-respiratory regulation, glycolytic/oxidative metabolic coupling, and eventually cell cycle and feather morphogenesis genetic control.
Keywords: attractors; critical edge; critical node; interaction graph boundary; interaction graph core; microRNAs; robustness in regulatory interaction networks; updating mode.