A Traveling-Wave Solution for Bacterial Chemotaxis with Growth

TL;DR

This paper develops an analytical framework to quantitatively understand how bacterial chemotaxis and growth drive rapid, stable population expansion, revealing how environmental factors influence expansion speed and density profiles.

Contribution

The study provides the first detailed analytical relations linking chemotaxis, growth, and environmental parameters to bacterial population expansion dynamics.

Findings

Expansion speeds increase with higher environmental chemical availability.

Analytical relations accurately predict density profiles during expansion.

Chemotaxis significantly enhances population spread under certain conditions.

Abstract

Bacterial cells navigate around their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories. However, despite numerous experimental and theoretical studies on this classical topic, chemotaxis-driven population expansion is not understood in quantitative terms. Building on recent experimental progress, we here present a detailed analytical study that provides a quantitative understanding of how chemotaxis and cell growth lead to rapid and stable expansion of bacterial populations. We provide analytical relations that accurately describe the dependence of the expansion speed and density profile of the expanding population on important molecular, cellular, and environmental parameters. In particular, expansion speeds can be boosted by orders of magnitude when the environmental availability of chemicals relative to the cellular limits of chemical sensing is high. As analytical understanding of such complex spatiotemporal dynamic processes is rare, the results derived here provide a mathematical framework for further investigations of the different roles chemotaxis plays in diverse ecological contexts.