In a new paper stemming from a complexity class taught by Sara Walker and Hyunju Kim, we find evidence that biological networks are critically poised between order and chaos. To quantify this effect, we measure the average sensitivity of 66 gene regulatory networks from a wide variety of living systems and find that the values cluster near the critical value of one. This suggests an adaptive advantage to balancing order and chaos: Living systems must be ordered enough to preserve information and maintain regularity but not so rigid that they cannot change and evolve. The fact that this applies across a wide swath of biological processes gives further credence to the idea that there are mathematical frameworks capable of capturing features general to all life.
Biological networks are close to critical sensitivity. (A) 66 published Boolean network models of genetic regulation (red) have sensitivity near the critical value of 1. The schematic depicts the sensitivity measure, equal to the average number of nodes whose states are changed at timestep t + 1 (green) when one node’s state is changed at timestep t (light blue). Also shown are sensitivities of random ensembles preserving various aspects of the original networks. Preserving only the number of edges and mean activity bias (gray) produces much more chaotic networks. Preserving the causal structure and activity bias of each node in the network (tan) produces sensitivity generally nearer to 1, and further restricting to have the same number of canalizing functions (yellow) is closer still. This indicates that the specific structure and types of Boolean functions beyond average connectivity are important to criticality. (B) Naive random Boolean network theory does not correctly predict average sensitivity for most biological network models. Plotting average sensitivities for each network and its random ensembles separately reveals that most networks have sensitivity that is significantly different from that predicted by various random ensembles. The mean and standard deviation for each ensemble is shown for 100 samples from each ensemble.
Sara Imari Walker