Optimality and adaptation of phenotypically switching cells in fluctuating environments

Stochastic switching between alternative phenotypic states is a common cellular survival strategy during unforeseen environmental fluctuations. Cells can switch between different subpopulations that proliferate at different rates in different environments. Optimal population growth is typically assumed to occur when phenotypic switching rates match environmental switching rates. However, it is not well understood how this optimum behaves as a function of the growth rates of phenotypically different cells. In this study, we use mathematical and computational models to test how the actual parameters associated with optimal population growth differ from those assumed to be optimal. We find that the predicted optimum is practically always valid if the environmental durations are long. However, the regime of validity narrows as environmental durations shorten, especially if subpopulation growth rate differences differ from each other (are asymmetric) in two environments. Furthermore, we study the fate of mutants with switching rates previously predicted to be optimal. We find that mutants which match their phenotypic switching rates with the environmental ones can only sweep the population if the assumed optimum is valid, but not otherwise.