Abstract
Persistence is a prime example of phenotypic heterogeneity, where a microbial population splits into two distinct subpopulations with different growth and survival properties as a result of reversible phenotype switching. Specifically, persister cells grow more slowly than normal cells under unstressed growth conditions, but survive longer under stress conditions such as the treatment with bactericidal antibiotics. We analyze the population dynamics of such a population for several typical experimental scenarios, namely a constant environment, shifts between growth and stress conditions, and periodically switching environments. We use an approximation scheme that allows us to map the dynamics to a logistic equation for the subpopulation ratio and derive explicit analytical expressions for observable quantities that can be used to extract underlying dynamic parameters from experimental data. Our results provide a theoretical underpinning for the study of phenotypic switching, in particular for organisms where detailed mechanistic knowledge is scarce.
Highlights
The life of microorganisms is characterized by two main tasks, rapid growth and proliferation under conditions permitting growth and survival under stressful conditions [1]
One way bacterial population cope with environmental stresses is by setting aside a small fraction of the total population, the persister cells, in a slow-growing, but stress-tolerant phenotypic state
We have analyzed a simple mathematical model to understand the dynamics of phenotype switching
Summary
The life of microorganisms is characterized by two main tasks, rapid growth and proliferation under conditions permitting growth and survival under stressful conditions [1]. [22] is based on long durations of environmental durations, such that populations structures reach their steady state before the environment changes The latter is not required in our approximation and our approach allows us to study both short and long environmental durations Rather than aiming at a general theoretical framework for phenotype switching phenomena, our goal here is to obtain simple explicit expression for measurable quantities These expressions can be used to analyze experimental data for population growth and decay to provide insights into the mechanism of persistence based on simple population-scale experiments. We will obtain approximative solutions based on the assumption that the switching rates are small compared to the growth rates, which allows us to derive relatively simple explicit expressions for observable quantities
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