A pathway-based mean-field model for E. coli chemotaxis: Mathematical derivation and Keller-Segel limit

TL;DR

This paper develops a new hyperbolic moment system for E. coli chemotaxis based on pathway-based mean-field theory, deriving the Keller-Segel limit and validating it against individual-based simulations.

Contribution

It introduces a new moment system derived via kinetic theory closure, explicitly clarifies assumptions, and connects the model to the Keller-Segel limit with numerical validation.

Findings

The new moment system is hyperbolic with linear convection.

The Keller-Segel limit is obtained considering different physical time scales.

Numerical results show quantitative agreement with individual-based simulations.

Abstract

A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101]. In this paper, we derived a new moment system of PBMFT by using the moment closure technique in kinetic theory under the assumption that the methylation level is locally concentrated. The new system is hyperbolic with linear convection terms. Under certain assumptions, the new system can recover the original model. Especially the assumption on the methylation difference made there can be understood explicitly in this new moment system. We obtain the Keller-Segel limit by taking into account the different physical time scales of tumbling, adaptation and the experimental observations. We also present numerical evidence to show the quantitative agreement of the moment system with the individual based E. coli chemotaxis simulator.