Features of Gene Regulatory Dynamics on Minimally Frustrated Topologies

The dynamics of biological networks exhibit many features that differentiate them from random networks: robustness to node and edge deletion, sloppy parameter sensitivities, and conserved functionality across scales. Understanding the inter-dependence of these behaviors could shed light on the evolution of biological networks that exhibit all of the above mentioned features. We have previously shown that biological regulatory networks have minimally frustrated topologies, a feature not seen in random networks. Here, we analyze the ODEs-based dynamics of gene regulation on networks with minimally frustrated topologies and find that they exhibit stable states that vary mostly along a single principal component, a property that is key to establishing and maintaining cell types. This behavior is robust to node and edge deletion, and is preserved under network coarse graining. We further show that selection for the minimally frustrated property is sufficient to evolve networks that exhibit many of the well-known features of biological dynamics. Our analysis provides useful insights into the design principles of biological networks regulating cell fate and the evolutionary pressures that have shaped them.