Criticality of Gene Regulatory Networks and the Resulting Morphogenesis

We present morphogenetic systems using Kauffman's NK random Boolean network (RBN) as a gene regulatory network (GRN) and spring-mass-damper kinetics for cellular movements. We investigate what role the criticality of GRNs plays in morphogenetic pattern formation. Our model represents a cell aggregation, where all cells have identical GRNs. The properties of GRNs are varied from ordered, through critical, to chaotic by node in-degree K. For cellular behaviors, cell fates, specifically, proliferation, differentiation, apoptosis, and quiescence, are assigned to the attractors of RBNs. We obtained diverse morphologies from our morphogenetic systems. We found that nontrivial spatial patterns were generated most frequently when the GRNs were critical. Our finding indicates that the criticality of GRNs facilitates the formation of nontrivial morphologies in GRN-based morphogenetic systems.