Chemotaxis When Bacteria Remember: Drift versus Diffusion

TL;DR

This paper investigates bacterial chemotaxis, showing that non-adaptive responses lead to diffusion-dominated movement while adaptive responses produce biased drift and accumulation, challenging previous models that assumed memory resets.

Contribution

It provides a new analysis of chemotaxis without memory resets, introducing a biased diffusion model and contrasting adaptive versus non-adaptive bacterial responses.

Findings

Non-adaptive chemotaxis is diffusion-dominated.

Adaptive chemotaxis involves biased drift and accumulation.

New coarse-grained model of chemotaxis as biased diffusion.

Abstract

{\sl Escherichia coli} ({\sl E. coli}) bacteria govern their trajectories by switching between running and tumbling modes as a function of the nutrient concentration they experienced in the past. At short time one observes a drift of the bacterial population, while at long time one observes accumulation in high-nutrient regions. Recent work has viewed chemotaxis as a compromise between drift toward favorable regions and accumulation in favorable regions. A number of earlier studies assume that a bacterium resets its memory at tumbles -- a fact not borne out by experiment -- and make use of approximate coarse-grained descriptions. Here, we revisit the problem of chemotaxis without resorting to any memory resets. We find that when bacteria respond to the environment in a non-adaptive manner, chemotaxis is generally dominated by diffusion, whereas when bacteria respond in an adaptive manner, chemotaxis is dominated by a bias in the motion. In the adaptive case, favorable drift occurs together with favorable accumulation. We derive our results from detailed simulations and a variety of analytical arguments. In particular, we introduce a new coarse-grained description of chemotaxis as biased diffusion, and we discuss the way it departs from older coarse-grained descriptions.