A tridiagonal patch model of bacteria inhabiting a nanofabricated landscape

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Abstract

In this paper we employ a discrete-diflusion modeling framework to examine a system inspired by the nano-ecology experiments on the bac- terium Escherichia coli reported upon in Keymer et al. (2006). In these experiments, the bacteria inhabit a linear array of 85 \microhabitat patches (MHP's)", linked by comparatively thinner corridors through which bacteria may pass between adjacent MHP's. Each MHP is connected to its own source of nutrient substrate, which ows into the MHP at a rate that can be con- trolled in the experiment. Logistic dynamics are assumed within each MHP, and nutrient substrate ow determines the prediction of the within MHP dy- namics in the absence of bacteria dispersal between patches. Patches where the substrate ow rate is sufficiently high sustain the bacteria in the absence of between patch movement and may be regarded as sources, while those with insufficient substrate ow lead to the extinction of the bacteria in the within patch environment and may be regarded as sinks. We examine the role of dis- persal in determining the predictions of the model under source-sink dynamics.

Original languageEnglish (US)
Pages (from-to)953-973
Number of pages21
JournalMathematical Biosciences and Engineering
Volume14
Issue number4
DOIs
StatePublished - Aug 2017

Keywords

  • Discrete-diflusion model
  • Gener- alized tridiagonal system
  • Micro-habitat patches
  • Nano-ecology
  • Persistence theory
  • Source-sink dynamics

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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