Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities

TL;DR

This paper introduces a phenotype-switching chemotaxis model demonstrating how switching rates control the formation and density of biological aggregates in multi-dimensional settings.

Contribution

It reveals that high, equal switching rates lead to unbounded aggregate densities, while bounded rates prevent such phenomena, advancing understanding of chemotactic aggregation control.

Findings

High, equal switching rates cause large aggregate densities.

Bounded switching rates prevent unbounded aggregation.

Aggregation phenomena depend critically on switching rate magnitudes.

Abstract

We consider a phenotype-switching chemotaxis model for aggregation, in which a chemotactic population is capable of switching back and forth between a chemotaxing state (performing chemotactic movement) and a secreting state (producing the attractant). We show that the switching rate provides a powerful mechanism for controlling the densities of spontaneously emerging aggregates. Specifically, in two- and three-dimensional settings it is shown that when both switching rates coincide and are suitably large, then the densities of both the chemotaxing and the secreting population will exceed any prescribed level at some points in the considered domain. This is complemented by two results asserting the absence of such aggregation phenomena in corresponding scenarios in which one of the switching rates remains within some bounded interval.