Theoretical results for chemotactic response and drift of E. coli in a weak attractant gradient

TL;DR

This paper develops an analytical model for E. coli chemotaxis in weak attractant gradients, deriving explicit expressions for response and drift velocity, and compares predictions with experimental data, revealing network effects on sensitivity.

Contribution

It provides the first analytical expressions for E. coli chemotactic response and drift velocity in weak gradients based on the Barkai-Leibler model, extending understanding of bacterial chemotaxis.

Findings

Theoretical predictions match experimental drift velocities at high concentrations.

Signal transduction reduces drift dependence on attractant concentration.

Analytical model captures chemotactic response in weak gradients.

Abstract

The bacterium Escherichia coli (E. coli) moves in its natural environment in a series of straight runs, interrupted by tumbles which cause change of direction. It performs chemotaxis towards chemo-attractants by extending the duration of runs in the direction of the source. When there is a spatial gradient in the attractant concentration, this bias produces a drift velocity directed towards its source, whereas in a uniform concentration, E.coli adapts, almost perfectly in case of methyl aspartate. Recently, microfluidic experiments have measured the drift velocity of E.coli in precisely controlled attractant gradients, but no general theoretical expression for the same exists. With this motivation, we study an analytically soluble model here, based on the Barkai-Leibler model, originally introduced to explain the perfect adaptation. Rigorous mathematical expressions are obtained for the chemotactic response function and the drift velocity in the limit of weak gradients and under the assumption of completely random tumbles. The theoretical predictions compare favorably with experimental results, especially at high concentrations. We further show that the signal transduction network weakens the dependence of the drift on concentration, thus enhancing the range of sensitivity.