Effects of internal dynamics on chemotactic aggregation of bacteria

TL;DR

This study explores how internal adaptation dynamics influence bacterial chemotactic aggregation, revealing nonmonotonic aggregation behavior and unique trapezoidal profiles through simulations and asymptotic analysis.

Contribution

It introduces a novel asymptotic equation for large adaptation times and links it to observed aggregation patterns, advancing understanding of bacterial chemotaxis models.

Findings

Aggregation peaks when adaptation time matches bacterial run time.

Large adaptation times lead to trapezoidal aggregation profiles.

Asymptotic equations accurately describe different aggregation regimes.

Abstract

The effects of internal adaptation dynamics on the self-organized aggregation of chemotactic bacteria are investigated by Monte Carlo (MC) simulations based on a two-stream kinetic transport equation coupled with a reaction-diffusion equation of the chemoattractant that bacteria produce. A remarkable finding is a nonmonotonic behavior of the peak aggregation density with respect to the adaptation time; more specifically, aggregation is the most enhanced when the adaptation time is comparable to or moderately larger than the mean run time of bacteria. Another curious observation is the formation of a trapezoidal aggregation profile occurring at a very large adaptation time, where the biased motion of individual cells is rather hindered at the plateau regimes due to the boundedness of the tumbling frequency modulation. Asymptotic analysis of the kinetic transport system is also carried out, and a novel asymptotic equation is obtained at the large adaptation-time regime while the Keller-Segel type equations are obtained when the adaptation time is moderate. Numerical comparison of the asymptotic equations with MC results clarifies that trapezoidal aggregation is well described by the novel asymptotic equation, and the nonmonotonic behavior of the peak aggregation density is interpreted as the transient of the asymptotic solutions between different adaptation time regimes.