Biological Regulatory Networks are Minimally Frustrated*

How do biological regulatory networks differ from random networks? Multiple studies have attempted to answer this question by looking for topological features of biological networks that are absent in random networks, yielding few functional insights. Here, using a Boolean modeling framework to compare the dynamical behavior of five real biological networks to that of random networks with similar topological features, we show that biological networks possess sets of stables states that are minimally frustrated. These states exhibit gene expression patterns characteristic of canonical cell types and possess large basins of attraction due to which most cells end up in one the canonical types. The number of commonly observed cell types is thus restricted to the number of gene expression patterns in these minimally frustrated states. Random networks, with topological features similar to biological networks but with varying levels of hierarchy, do not possess such minimally frustrated stable states. Our analysis thus provides crucial insights into the design principles of biological regulatory networks.