A Two-Dimensional Model of Potassium Signaling and Oscillatory Growth in a Biofilm

Noah Ford*, Garth Fisher, Arthur Prindle, David Chopp

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Biofilms are complex communities of bacteria that exhibit a variety of collective behaviors. These behaviors improve their ability to survive in many different environments. One of these collective behaviors seen in Bacillus subtilis is the ability for starving cells to stop the growth of other cells using potassium signaling and voltage changes. This signaling produces an oscillatory growth pattern so that during periods of low growth the nutrients diffuse deeper into the biofilm and reach the nutrient-starved, interior regions of the biomass. In this paper, we develop a mathematical model to describe this oscillatory behavior, and we use this model to develop a two-dimensional simulation that reproduces many of the important features seen in the experimental data. This simulation allows us to examine the spatial patterning of the oscillatory behavior to better understand the relationships between the various regions of the biofilm. Studying the spatial components of the metabolic and voltage oscillations could allow for the development of new control techniques for biofilms with complex shapes.

Original languageEnglish (US)
Article number60
JournalBulletin of Mathematical Biology
Issue number5
StatePublished - May 2021


  • Biofilms
  • Mathematical modeling
  • Oscillatory behavior

ASJC Scopus subject areas

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics


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