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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 quantitatively match with the agent-based model for all ranges of the spatial gradient, in particular when the chemical gradient is large such that the standard Keller--Segel model is no longer valid.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 gradient and large gradient environments.

Macroscopic Limits of Pathway-Based Kinetic Models for E. coli Chemotaxis in Large Gradient Environments