We present multilayer gene regulatory networks (GRNs) consisting of an intercellular layer and an intracellular layer. A network in an intercellular layer represents interactions between cells, and a network in an intracellular layer indicates interactions between genes. All the nodes of an intercellular network have identical random Boolean networks (RBNs) as intracellular GRNs. We introduce genetic perturbations (e.g., mutations) to the intracellular GRNs. Varying the properties of the intracellular GRNs from ordered, through critical, to chaotic regimes, we investigate how criticality of GRNs affects the robustness and evolvability of multilayer GRNs against the genetic perturbations. We found that the robust and evolvable multilayer GRNs were generated with the highest probability when intracellular GRNs were critical. Based on our findings, we conclude that the criticality of GRNs plays an important role in determining the robustness and evolvability of multilayer GRNs at a hierarchical level.

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.

Gene regulatory network (GRN)-based morphogenetic systems have recently attracted an increasing attention in artificial life and morphogenetic engineering research. However, the relationship between microscopic properties of intracellular GRNs and collective properties of morphogenetic systems has not been fully explored yet. Thus, we propose a new GRN-based framework to elucidate how critical dynamics of GRNs in individual cells affect cell fates such as proliferation, apoptosis, and differentiation in resulting morphogenetic systems. Our model represents an aggregation of cells, where each cell has a GRN in it. We used Kauffman's NK Boolean networks for GRNs. Specifically, we randomly assigned three cell fates to the attractors. Varying the properties of GRNs from ordered, through critical, to chaotic regimes, we observed the process that cells are aggregated. We found that the criticality of a GRN made an optimal partition of basins of attraction, which led to a maximum balance between cell fates. Based on the result, we can conclude that the criticality of a GRN is an important controller to determine the frequencies of cell fates in morphogenetic systems.