Numerical study of the volcano e ect in chemotactic aggregation based on a kinetic transport equation with non-instantaneous tumbling

TL;DR

This study uses Monte Carlo simulations and continuum models to analyze how adaptation time and tumbling duration influence chemotactic bacterial aggregation, revealing conditions that lead to a volcano-shaped aggregation profile.

Contribution

It identifies the parameter regimes and scaling laws that produce the volcano effect in bacterial chemotaxis, highlighting the coupling of diffusion, adaptation, and tumbling duration.

Findings

Aggregation becomes steeper with increasing adaptation time at small values.

Aggregation becomes more diffusive with increasing adaptation time at large values.

The volcano-shaped aggregation profile occurs at large adaptation times with sufficient tumbling duration.

Abstract

Aggregation of chemotactic bacteria under a unimodal distribution of chemical cues was investigated by Monte Carlo (MC) simulation based on a kinetic transport equation, which considers an internal adaptation dynamics as well as a finite tumbling duration. It was found that there exist two different regimes of the adaptation time, between which the effect of the adaptation time on the aggregation behavior is reversed; that is, when the adaptation time is as small as the running duration, the aggregation becomes increasingly steeper as the adaptation time increases, while, when the adaptation time is as large as the diffusion time of the population density, the aggregation becomes more diffusive as the adaptation time increases. Moreover, the aggregation profile becomes bimodal (volcano) at the large adaptation-time regime when the tumbling duration is sufficiently large while it is always unimodal at the small adaptation-time regime. A remarkable result of this study is the identification of the parameter regime and scaling for the volcano effect. That is, by comparing the results of MC simulations to the continuum-limit models obtained at each of the small and large adaptation-time scalings, it is clarified that the volcano effect arises due to the coupling of diffusion, adaptation, and finite tumbling duration, which occurs at the large adaptation-time scaling.