Stochastic Receptor Expression Allows Sensitive Bacteria to Evade Phage Attack. Part II: Theoretical Analyses
Emily Chapman-McQuiston 1 and X.L. Wu 1*
1 University of Pittsburgh
* To whom correspondence should be addressed. E-mail: xlwu{at}pitt.edu.
Submitted on September 12, 2007
Revised on November 2, 2007
Accepted on 14 January 2008
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Abstract |
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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. 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.
Key Words:
bacteria, ecology, lambda phage, modeling, persistence
