New York University
Phase transitions in the evolution of phenotypic memory
The role of gene regulatory networks is to respond to environmental conditions and optimize growth of the cell. A typical example is found in bacteria, where metabolitic genes are activated in response to nutrient availability, and are subsequently turned off to conserve energy when their specific substrates are depleted. However, in fluctuating environmental conditions, regulatory networks could experience strong evolutionary pressures not only to turn the right genes on and off, but also to respond optimally under a wide spectrum of fluctuation timescales. It remains unclear how these networks have evolved.
Here we present a method to compute memory-based adaptive strategies in fluctuating environments for a simple 2-phenotype model. We find that optimal strategies correspond to distinct regions in phase space, with crossovers given by first and second order phase transitions. The mean-field formulation is used to infer the nature of evolution that has taken place: either through change of the structure of the network, or through modifying the interactions between its components.
Furthermore, we formulate a theory that allows us to compute observables to arbitrary precision, by perturbatively treating cell's environmental history. More generally, our findings point towards a microscopic model of phenotypic switches in the space of histories similar to disordered spin chains.