How diverse forms of phenotypic variability affect microbial growth in changing environments

Numerous organisms utilize phenotypic variability to hedge their bets against unpredictable environmental changes. In microbiology, the most well-studied example of this is bacterial persistence — the phenomenon by which some fraction of the population grows relatively slowly in exchange for decreased susceptibility to antibiotics. Experimental evidence suggests a distribution of many phenotypes, not just two growth states, plays a role in bacterial growth, yet the quantitive consequences of more general forms of phenotypic variability are not well understood. Here we model various forms of phenotypic variability in changing environments, including deterministic variability arising from asymmetric segregation at cell division, to stochastic variability resulting from noisy gene expression. In our model, single-cell growth rates are functions of the phenotype and the environmental state. We derive conditions on these functions that guarantee phenotypic variability will be beneficial to a population.