Run and tumble chemotaxis in a shear flow: the effect of temporal comparisons and other complications

Escherichia coli is a motile bacterium that moves up a chemoattractant gradient by performing a biased random walk composed of alternating runs and tumbles. This paper presents calculations of the chemotactic drift velocity vd (the mean velocity up the chemoattractant gradient) of an E. coli cell performing chemotaxis in a uniform, steady shear flow, with a weak chemoattractant gradient at right angles to the flow. Extending earlier models, a combined analytic and numerical approach is used to assess the effect of several complications, namely (i) a cell cannot detect a chemoattractant gradient directly but rather makes temporal comparisons of chemoattractant concentration, (ii) the tumbles exhibit persistence of direction, meaning that the swimming directions before and after a tumble are correlated, (iii) the cell suffers random re-orientations due to rotational Brownian motion, and (iv) the non-spherical shape of the cell affects the way that it is rotated by the shear flow. These complications influence the dependence of vd on the shear rate gamma. When they are all included, it is found that (a) shear disrupts chemotaxis and shear rates beyond gamma = 2/second cause the cell to swim down the chemoattractant gradient rather than up it, (b) in terms of maximising drift velocity, persistence of direction is advantageous in a quiescent fluid but disadvantageous in a shear flow, and (c) a more elongated body shape is advantageous in performing chemotaxis in a strong shear flow.