Macroscopic limits of pathway-based kinetic models for E.coli chemotaxis in large gradient environments

TL;DR

This paper develops macroscopic models for E. coli chemotaxis that accurately reflect molecular signaling pathways, especially in large gradients where traditional models fail, validated by rigorous derivations and numerical comparisons.

Contribution

It introduces new macroscopic equations derived from pathway-based kinetic models that are valid across all gradient ranges, including large gradients, and rigorously connects molecular mechanisms to population-level behavior.

Findings

Models match agent-based simulations across gradient ranges

Provides formulas for diffusion coefficient and drift velocity from molecular data

Shows good numerical agreement with SPECS simulations

Abstract

It is of great biological interest to understand the molecular origins of chemotactic behavior of E. coli by developing population-level models based on the underlying signaling pathway dynamics. We derive macroscopic models for E.coli chemotaxis that match quantitatively with the agent-based model (SPECS) for all ranges of the spacial gradient, in particular when the chemical gradient is large such that the standard Keller-Segel model is no longer valid. These equations are derived both formally and rigorously as asymptotic limits for pathway-based kinetic equations. We also present numerical results that show good agreement between the macroscopic models and SPECS. Our work provides an answer to the question of how to determine the population-level diffusion coefficient and drift velocity from the molecular mechanisms of chemotaxis, for both shallow gradients and large gradients environments.