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The bacterium Escherichia coli (E. coli) moves in its natural environment ina series of straight runs, interrupted by tumbles which cause change ofdirection. It performs chemotaxis towards chemo-attractants by extending theduration of runs in the direction of the source. When there is a spatialgradient in the attractant concentration, this bias produces a drift velocitydirected towards its source, whereas in a uniform concentration, E.coli adapts,almost perfectly in case of methyl aspartate. Recently, microfluidicexperiments have measured the drift velocity of E.coli in precisely controlledattractant gradients, but no general theoretical expression for the sameexists. With this motivation, we study an analytically soluble model here,based on the Barkai-Leibler model, originally introduced to explain the perfectadaptation. Rigorous mathematical expressions are obtained for the chemotacticresponse function and the drift velocity in the limit of weak gradients andunder the assumption of completely random tumbles. The theoretical predictionscompare favorably with experimental results, especially at high concentrations.We further show that the signal transduction network weakens the dependence ofthe drift on concentration, thus enhancing the range of sensitivity.

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