Department of Mathematics & Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, UK; Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, Italy.
J Theor Biol. 2019 Nov 21;481:162-182. doi: 10.1016/j.jtbi.2018.06.019. Epub 2018 Jun 23.
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.
趋化作用是细胞和生物的基本导向机制，负责吸引微生物到食物、胚胎细胞到发育组织、免疫细胞到感染部位、动物到潜在配偶，以及吸引数学家进入生物学领域。Patlak-Keller-Segel（PKS）系统是数学生物学的基础部分，是建模者和分析者的首选。对于前者，它简单但能概括许多现象；后者则被这些丰富的动力学所吸引。在这里，我回顾了 PKS 系统在解释自组织过程中的应用。我考虑了它们的基础，回到了 Patlak、Keller 和 Segel 的最初努力，并简要描述了它们的模式形成特性。考虑了 PKS 系统在微生物学、发育、免疫学、癌症、生态学和犯罪等不同领域的应用。在每种情况下，都提供了有关趋化行为证据的历史观点，然后对建模工作进行了回顾；附录中包括了模型的摘要。最后，开发了一个半认真/半开玩笑的模型来解释学术界的派系是如何形成的。假设学者根据可用问题改变他们的研究方向，导致学者的聚类和“热门”研究课题的形成。
