Stochastic Receptor Expression Allows Sensitive Bacteria to Evade Phage Attack. Part II: Theoretical Analyses

Stochastic gene expression in bacteria can create a diverse protein distribution. Most of the current studies have focused on fluctuations around the mean, which constitutes the majority of a bacterial population. However, when the bacterial population is subject to a severe selection pressure, it is the properties of the minority cells that determine the fate of the population. The central question is whether phenotype heterogeneity, such as a spread in the expression level of a critical protein, is sufficient to account for the persistence of the bacteria under the selection. A related question is how long such persistence can last before genetic mutation becomes significant. In this work, survival statistics of a bacterial population with a diverse phage-receptor number distribution is theoretically investigated when the cells are subject to phage pressures. The calculations are compared with our experimental observations presented in Part I in this issue. The fundamental basis of our analysis is the Berg-Purcell theoretical result for the reaction rate between a phage particle and a bacterium with a discrete number of receptors, and the observation that most phage-resistant mutants isolated in laboratory cultures are defective in phage binding. It is shown that a heterogeneous bacterial population is significantly more fit compared to a homogeneous population when confronting a phage attack.