Boolean Networks with Intricate Updating Mode: Application to Genetic Regulatory Networks Involved in Familial Diseases

(1) Background: Many familial diseases are caused by genetic accidents, which affect both the genome and its epigenetic environment, expressed as an interaction graph between the genes. We wish to show the existence of a form of robustness for such interaction networks in the case of three familial diseases: Familial angioedema; Osteogenesis imperfecta; Biliary atresia; (2) Methods: The update of the gene states at the vertices of the interaction graph (1 if a gene is activated, 0 if it is inhibited) can be done in multiple ways, well studied over the last 20 years: parallel, block-parallel, sequential, block-sequential, random, etc. (3) Results: We study three particular interaction graphs, linked to the familial diseases chosen as examples. They have in common a subgraph that is activated in an intricate manner, a new update mode, of which we study the robustness; (4) Conclusions: Comparison of the interaction modes of the three familial diseases studied, which are of different etiology, shows visible common points in the regulatory graphs of the genes involved, in particular a structural robustness with respect to their expression clock.