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