Chemotaxis when bacteria remember: drift vs diffusion

Escherichia coli (E. coli) bacteria govern their trajectories by
switching between running and tumbling modes as a function of the
nutrient concentration they experienced in the past. In a recent
study, it has been argued, using approximate analytical treatments in
one dimension, that there is a conflict between the ability of the
bacterium to reach regions of high nutrient concentration quickly and
remaining there at long times. Here we perform numerical simulation in
one-dimension and show that there is no such conflict. To understand
these results we propose a coarse grained model which is shown to
agree well with the numerics. Importantly, the model is significantly
different from the common one used in many earlier works and which
does not capture the behavior found in our numerics. The origin of the
discrepancy is discussed.