# Interactions of Solitary Pulses of E. coli in a One-Dimensional Nutrient Gradient

## TL;DR

This study investigates the unexpected reversal of E. coli pulses in a nutrient gradient, combining experiments, Keller-Segel model simulations, and a new ODE approximation to understand the underlying mechanisms.

## Contribution

It introduces a heuristic ODE model to analyze E. coli pulse interactions, providing new insights into their complex chemotactic behavior.

## Key findings

- Pulses can reverse direction and move away from nutrient sources.
- The Keller-Segel model reproduces the observed reversal behavior.
- The ODE approximation helps analyze global dynamics and parameter effects.

## Abstract

We study an anomalous behavior observed in interacting E. coli populations. When two populations of E. coli are placed on opposite ends of a long channel with a supply of nutrient between them, they will travel as pulses toward one another up the nutrient gradient. We present experimental evidence that, counterintuitively, the two pulses will in some cases change direction and be- gin moving away from each other and the nutrient back toward the end of the channel from which they originated. Simulations of the Keller-Segel chemotaxis model reproduce the experimental results. To gain better insight to the phenomenon, we introduce a heuristic approximation to the spatial profile of each population in the Keller-Segel model to derive a system of ordinary differential equations approximating the temporal dynamics of its center of mass and width. This approximate model simplifies analysis of the global dynamics of the bacterial system and allows us to efficiently explore the qualitative behavior changes across variations of parameters, and thereby provides experimentally testable hypotheses about the mechanisms behind the turnaround behavior.