Power-law tail in lag time distribution underlies bacterial persistence

Genetically identical microbial cells respond to stress heterogeneously, and this phenotypic heterogeneity contributes to population survival. Quantitative analysis of phenotypic heterogeneity can reveal dynamic features of stochastic mechanisms that generate heterogeneity. Additionally, it can enable a priori prediction of population dynamics, elucidating microbial survival strategies. Here, we quantitatively analyzed the persistence of an Escherichia coli population. When a population is confronted with antibiotics, a majority of cells is killed but a subpopulation called persisters survives the treatment. Previous studies have found that persisters survive antibiotic treatment by maintaining a long period of lag phase. When we quantified the lag time distribution of E. coli cells in a large dynamic range, we found that normal cells rejuvenated with a lag time distribution that is well captured by an exponential decay [exp(-kt)], agreeing with previous studies. This exponential decay indicates that their rejuvenation is governed by a single rate constant kinetics (i.e., k is constant). Interestingly, the lag time distribution of persisters exhibited a long tail captured by a power-law decay. Using a simple quantitative argument, we demonstrated that this power-law decay can be explained by a wide variation of the rate constant k. Additionally, by developing a mathematical model based on this biphasic lag time distribution, we quantitatively explained the complex population dynamics of persistence without any ad hoc parameters. The quantitative features of persistence demonstrated in our work shed insights into molecular mechanisms of persistence and advance our knowledge of how a microbial population evades antibiotic treatment.