  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gradient is large such that the standard Keller-Segel model is no longer valid.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.
