  The complex dynamics of gene expression in living cells can be
well-approximated using Boolean networks. The average sensitivity is a natural
measure of stability in these systems: values below one indicate typically
stable dynamics associated with an ordered phase, whereas values above one
indicate chaotic dynamics. This yields a theoretically motivated adaptive
advantage to being near the critical value of one, at the boundary between
order and chaos. Here, we measure average sensitivity for 66 publicly available
Boolean network models describing the function of gene regulatory circuits
across diverse living processes. We find the average sensitivity values for
these networks are clustered around unity, indicating they are near critical.
In many types of random networks, mean connectivity <K> and the average
activity bias of the logic functions <p> have been found to be the most
important network properties in determining average sensitivity, and by
extension a network's criticality. Surprisingly, many of these gene regulatory
networks achieve the near-critical state with <K> and <p> far from that
predicted for critical systems: randomized networks sharing the local causal
structure and local logic of biological networks better reproduce their
critical behavior than controlling for macroscale properties such as <K> and
<p> alone. This suggests the local properties of genes interacting within
regulatory networks are selected to collectively be near-critical, and this
non-local property of gene regulatory network dynamics cannot be predicted
using the density of interactions alone.
