  Fluctuating environments pose tremendous challenges to bacterial populations.
It is observed in numerous bacterial species that individual cells can
stochastically switch among multiple phenotypes for the population to survive
in rapidly changing environments. This kind of phenotypic heterogeneity with
stochastic phenotype switching is generally understood to be an adaptive
bet-hedging strategy. Mathematical models are essential to gain a deeper
insight into the principle behind bet-hedging and the pattern behind
experimental data. Traditional deterministic models cannot provide a correct
description of stochastic phenotype switching and bet-hedging, and traditional
Markov chain models at the cellular level fail to explain their underlying
molecular mechanisms. In this paper, we propose a nonlinear stochastic model of
multistable bacterial systems at the molecular level. It turns out that our
model not only provides a clear description of stochastic phenotype switching
and bet-hedging within isogenic bacterial populations, but also provides a
deeper insight into the analysis of multidimensional experimental data.
Moreover, we use some deep mathematical theories to show that our stochastic
model and traditional Markov chain models are essentially consistent and
reflect the dynamic behavior of the bacterial system at two different time
scales. In addition, we provide a quantitative characterization of the critical
state of multistable bacterial systems and develop an effective data-driven
method to identify the critical state without resorting to specific
mathematical models.
