Before revision:  We presented a mathematical explanation of phenotypic heterogeneity, stochastic phenotype switching , and bet-hedging within isogenic bacterial populations, and thus provided a theoretical framework for the analysis of experiment dataat the cellular or molecular level .
After revision:  We presented a mathematical explanation of phenotypic heterogeneity, stochastic phenotype switching , and bet-hedging within isogenic bacterial populations, and thus provided a theoretical framework for 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 .