Jeans type instability for a chemotactic model of cellular aggregation

TL;DR

This paper extends the Keller-Segel chemotactic model by including inertial effects, analyzes the stability of uniform cell distributions, and draws parallels with astrophysical Jeans instability, revealing new insights into cellular aggregation dynamics.

Contribution

It introduces an inertial chemotactic model, derives instability conditions considering cell inertia, and compares biological and astrophysical instability criteria.

Findings

Inertial effects influence the stability threshold of cell distributions.

Instability growth rates depend on cell density and perturbation wavelength.

An analogy is established between biological chemotactic instability and Jeans instability in astrophysics.

Abstract

We consider an inertial model of chemotactic aggregation generalizing the Keller-Segel model and we study the linear dynamical stability of an infinite and homogeneous distribution of cells (bacteria, amoebae, endothelial cells,...) when inertial effects are accounted for. These inertial terms model cells directional persistance. We determine the condition of instability and the growth rate of the perturbation as a function of the cell density and the wavelength of the perturbation. We discuss the differences between overdamped (Keller-Segel) and inertial models. Finally, we show the analogy between the instability criterion for biological populations and the Jeans instability criterion in astrophysics.