Author summary

Bacteria grow exponentially consuming nutrients, and then starve until the next nutrient is added. During the starvation, the cells enter dormancy and the cells become tolerant not only to starvation but also to other stressors. When nutrients are given to the starved cells, it takes some time before the cells fully "wake-up" and proliferate again. At first sight, it appears that the shorter this lag time the better for the bacteria. However, if the environment may contain another deadly stressor such as antibiotics, it may be better to "over-sleep" until the stressor is gone. Thus, they need to evolve to optimize their waking up strategy in the fluctuating environment. Here we have developed a theory for the optimal strategy for the repeated grow-and-starvation cycles with a fluctuating application of antibiotics. The optimal lag time exhibits a steep transition from immediate wake-up to over-sleep when the severeness of the antibiotics exceeds the threshold. The proposed general framework provides a way to predict the optimal distribution of lag time for various environmental fluctuation, and it may open for possible applications in administrating drug usage for interventions of pathogenic bacteria as well as cancer therapies where drug tolerance of dormant cells are observed.

Prolonged lag time can be induced by starvation contributing to the antibiotic tolerance of bacteria. We analyze the optimal lag time to survive and grow the iterative and stochastic application of antibiotics. A simple model shows that the optimal lag time can exhibit a discontinuous transition when the severeness of the antibiotic application, such as the probability to be exposed the antibiotic, the death rate under the exposure, and the duration of the exposure, is increased. This suggests the possibility of reducing tolerant bacteria by controlled usage of antibiotics application. When the bacterial populations are able to have two phenotypes with different lag times, the fraction of the second phenotype that has different lag time shows a continuous transition. We then present a generic framework to investigate the optimal lag time distribution for total population fitness for a given distribution of the antibiotic application duration. The obtained optimal distributions have multiple peaks for a wide range of the antibiotic application duration distributions, including the case where the latter is monotonically decreasing. The analysis supports the advantage in evolving multiple, possibly discrete phenotypes in lag time for bacterial long-term fitness.