2006/01/29 by Radek Erban, Hans G. Othmer, Erban, Radek +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · #Biological Physics (physics.bio-ph) #Cell Behavior (q-bio.CB) #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Physical sciences #Mathematical Biology Tumor Growth #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.q-bio/0601048
openalex publication_date 2006/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical macroscopic chemotaxis equations have previously been derived from an individual-based description of the tactic response of cells that use a "run-and-tumble" strategy in response to environmental cues. Here we derive macroscopic equations for the more complex type of behavioral response characteristic of crawling cells, which detect a signal, extract directional information from a scalar concentration field, and change their motile behavior accordingly. We present several models of increasing complexity for which the derivation of population-level equations is possible, and we show how experimentally-measured statistics can be obtained from the transport equation formalism. We also show that amoeboid cells that do not adapt to constant signals can still aggregate in steady gradients, but not in response to periodic waves. This is in contrast to the case of cells that use a "run-and-tumble" strategy, where adaptation is essential.