Mathematical models for chemotaxis and their applications in self-organisation phenomena

Kevin J. Painter

Research output: Contribution to journalArticlepeer-review

66 Citations (Scopus)
62 Downloads (Pure)


Chemotaxis is a fundamental guidance mechanism of cells and organisms, responsible for attracting microbes to food, embryonic cells into developing tissues, immune cells to infection sites, animals towards potential mates, and mathematicians into biology. The Patlak–Keller–Segel (PKS) system forms part of the bedrock of mathematical biology, a go-to-choice for modellers and analysts alike. For the former it is simple yet recapitulates numerous phenomena; the latter are attracted to these rich dynamics. Here I review the adoption of PKS systems when explaining self-organisation processes. I consider their foundation, returning to the initial efforts of Patlak and Keller and Segel, and briefly describe their patterning properties. Applications of PKS systems are considered in their diverse areas, including microbiology, development, immunology, cancer, ecology and crime. In each case a historical perspective is provided on the evidence for chemotactic behaviour, followed by a review of modelling efforts; a compendium of the models is included as an Appendix. Finally, a half-serious/half-tongue-in-cheek model is developed to explain how cliques form in academia. Assumptions in which scholars alter their research line according to available problems leads to clustering of academics and the formation of “hot” research topics.

Original languageEnglish
Pages (from-to)162-182
Number of pages21
JournalJournal of Theoretical Biology
Early online date23 Jun 2018
Publication statusPublished - 21 Nov 2019


  • Bacteria
  • Development
  • Ecology
  • Pathology
  • Patlak–Keller–Segel
  • Pattern formation
  • Slime molds
  • Social clique formation
  • Social sciences

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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