Boolean Networks with Classic and New Updating Modes Applied to Genetic Regulation in Some Familial Diseases

Many familial diseases are caused by genetic accidents, which affect the genome and its epigenetic environment, summarized as an interaction network between genes. We wish to study the existence or absence of robustness for such genetic interaction networks centered on the gene SP1 and involved in three familial diseases: familial angioedema, osteogenesis imperfecta, and biliary atresia. The updating of gene states at the vertices of the interaction graph of the genetic network (1 if a gene is activated, 0 if it is inhibited) can be performed in multiple ways that have been well-studied over the last 20 years: parallel, block-parallel, sequential, block-sequential, random, etc. We add to these classic updating modes two new ones, the intricate and the state-dependent. We have studied the robustness of three particular interaction graphs related to the familial diseases chosen as examples. The comparison of the interaction graphs and dynamics of the chosen familial diseases of different etiology shows common points in their interaction graphs and similarities in their dynamics according to their expression clock.