A Stochastic Intracellular Model of Anthrax Infection With Spore Germination Heterogeneity

Bevelynn Williams, Martín López-García*, Joseph J. Gillard, Thomas R. Laws, Grant Lythe, Jonathan Carruthers, Thomas Finnie, Carmen Molina-París

*Corresponding author for this work

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We present a stochastic mathematical model of the intracellular infection dynamics of Bacillus anthracis in macrophages. Following inhalation of B. anthracis spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of B. anthracis. The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from in vitro infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of B. anthracis. The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.

Original languageEnglish
Article number688257
Number of pages23
JournalFrontiers in Immunology
Publication statusPublished - 23 Aug 2021

Bibliographical note

Funding Information: BW is supported by an EPSRC CASE studentship, project reference 2345914, in partnership with Dstl under contract number DSTLX-1000142022.

Open Access: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is
cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Publisher Copyright: © Copyright © 2021 Williams, López-García, Gillard, Laws, Lythe, Carruthers, Finnie and Molina-París.

Citation: Williams, Bevelynn, et al. "A stochastic intracellular model of anthrax infection with spore germination heterogeneity." Frontiers in immunology (2021): 2865.

DOI: https://doi.org/10.3389/fimmu.2021.688257


  • Bacillus anthracis
  • Markov process
  • approximate Bayesian computation
  • dose-response
  • intracellular model
  • rupture size distribution
  • spore germination
  • time to macrophage rupture


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