Emergence of phenotype switching through continuous and discontinuous evolutionary transitions

Bacterial persistence (phenotypic tolerance to antibiotics) provides a prime example of bet-hedging, where normally growing cells generate slow-growing but antibiotic-tolerant persister cells to survive through periods of exposure to antibiotics. The population dynamics of persistence is explained by a phenotype switching mechanism that allows individual cells to switch between these different cellular states with different environmental sensitivities. Here, we perform a theoretical study based on an exact solution for the case of a periodic variation of the environment to address how phenotype switching emerges and under what conditions switching is or is not beneficial for long-time growth. Specifically we report a bifurcation through which a fitness maximum and minimum emerge above a threshold in the duration of exposure to the antibiotic. Only above this threshold, the optimal phenotype switching rates are adjusted to the time scales of the environment, as emphasized by previous theoretical studies, while below the threshold a non-switching population is fitter than a switching one. The bifurcation can be of different type, depending on how the phenotype switching rates are allowed to vary. If the switching rates for both directions of the switch are coupled, the transition is discontinuous and results in evolutionary hysteresis, which we confirm with a stochastic simulation. If the switching rates vary individually, a continuous transition is obtained and no hysteresis is found. We discuss how both scenarios can be linked to changes in the underlying molecular networks.