Analysis of Single Bacterium Dynamics in a Stochastic Model of Toxin-Producing Bacteria

Abstract

We stochastically model two bacterial populations which can produce toxins. We propose to analyse this biological system by following the dynamics of a single bacterium during its lifetime, as well as its progeny. We study the lifespan of a single bacterium, the number of divisions that this bacterium undergoes, and the number of toxin molecules that it produces during its lifetime. We also compute the mean number of bacteria in the genealogy of the original bacterium and the number of toxin molecules produced by its genealogy. We illustrate the applicability of our methods by considering the bacteria Bacillus anthracis and antibiotic treatment, making use of in vitro experimental data. We quantify, for the first time, bacterial toxin production by exploiting an in vitro assay for the A16R strain, and make use of the resulting parameterised model to illustrate our techniques.