Mathematical models for chemotaxis and their applications in self-organisation phenomena
arXiv:1806.08627
Abstract
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.
arXiv comment35 pages, 8 figures, Submitted to Journal of Theoretical Biology
References in corpus (10)
- Statistical physics of crime: A review
- Individual rules for trail pattern formation in Argentine ants (Linepithema humile)
- Migration of chemotactic bacteria in soft agar: role of gel concentration
- Aggregation Patterns in Stressed Bacteria
- Turing patterns from dynamics of early HIV infection over a two-dimensional surface
- Continuous macroscopic limit of a discrete stochastic model for interaction of living cells
- Stationary patterns and their selection mechanism of Urban crime models with heterogeneous near-repeat victimization effect
- Modeling ant foraging: a chemotaxis approach with pheromones and trail formation
- Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model
- The Flux Limited Keller-Segel System; Properties and Derivation from Kinetic Equations