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Escherichia coli is a motile bacterium that moves up a chemoattractantgradient by performing a biased random walk composed of alternating runs andtumbles. Previous models of run and tumble chemotaxis neglect one or morefeatures of the motion, namely (i) a cell cannot directly detect achemoattractant gradient but rather makes temporal comparisons ofchemoattractant concentration, (ii) rather than being entirely random, tumblesexhibit persistence of direction, meaning that the new direction after a tumbleis more likely to be in the forward hemisphere, and (iii) rotational Brownianmotion makes it impossible for an E. coli cell to swim in a straight lineduring a run. This paper presents an analytic calculation of the chemotacticdrift velocity taking account of (i), (ii) and (iii), for weak chemotaxis. Theanalytic results are verified by Monte Carlo simulation. The results reveal asynergy between temporal comparisons and persistence that enhances the driftvelocity, while rotational Brownian motion reduces the drift velocity.

Persistence of direction increases the drift velocity of run and tumble chemotaxis