  Whereas the relationship between criticality of gene regulatory networks
(GRNs) and dynamics of GRNs at a single cell level has been vigorously studied,
the relationship between the criticality of GRNs and system properties at a
higher level has remained unexplored. Here we aim at revealing a potential role
of criticality of GRNs at a multicellular level which are hard to uncover
through the single-cell-level studies, especially from an evolutionary
viewpoint. Our model simulated the growth of a cell population from a single
seed cell. All the cells were assumed to have identical GRNs. We induced
genetic perturbations to the GRN of the seed cell by adding, deleting, or
switching a regulatory link between a pair of genes. From numerical
simulations, we found that the criticality of GRNs facilitated the formation of
nontrivial morphologies when the GRNs were critical in the presence of the
evolutionary perturbations. Moreover, the criticality of GRNs produced
topologically homogenous cell clusters by adjusting the spatial arrangements of
cells, which led to the formation of nontrivial morphogenetic patterns. Our
findings corresponded to an epigenetic viewpoint that heterogeneous and complex
features emerge from homogeneous and less complex components through the
interactions among them. Thus, our results imply that highly structured tissues
or organs in morphogenesis of multicellular organisms might stem from the
criticality of GRNs.
