A mutation-selection paradigm for the dynamics of biological networks*

The developmental trajectory of biological systems results from the interplay between the need to explore the state space and to select optimal (functional) configurations. This is strictly true in the case of Darwinian evolution, in the simplest case driven by mutations and population selection. We assume that the same paradigm can model the short-term dynamics of biological networks.  We develop a formal framework based on the existence of a fitness function to maximize and a master equation encoding the dynamics. We find analytical and/or numerical solutions in simple cases – single fitness maximum, 2* fitness landscape. We develop a pipeline that allows to model experimental data. We show how parsimonious fitness functions are able to predict the large-scale dynamics for the development of the C.elegans brain networks, from hatching to adult age. Our framework can be used to model a variety of dynamical processes in biology, e.g. the brain network reorganization following a brain injury or the development of insect colonies.