Théorique, numérique
The complexity of biological systems is partly due to the intricate structure of interactions between thousands of genes. The topology of gene networks has been under scrutiny since the emergence of systems biology, but little progress has been made to connect theoretically large-scale statistical features of networks (typically, scale-freeness) to concrete functional and evolutionary properties. Using statistical physics, we are combining analytical and computational models to unravel how natural selection shapes gene interactions and give rise to robust developmental traits. We built a statistical description for a population of individuals each described by their genes’ level of expression. In our model, the developmental dynamics of each individual were constrained by gene interactions encoded in an individual- specific matrix and included a noise source which accounted for the stochasticity inherent to developmental processes. We aimed at describing the long term population dynamics governed by the probability of each individual to survive, reproduce and mutate according to their developmental trajectories. Under reasonable assumptions, we deem it possible to derive an analytical model to obtain a reduced set of algebraic-Riccati-like equations for the developmental dynamics. This model could represent a substantial improvement in theoretical systems biology, provided that the mathematical assumptions are biologically realistic.