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{\sl Escherichia coli} ({\sl E. coli}) bacteria govern their trajectories byswitching between running and tumbling modes as a function of the nutrientconcentration they experienced in the past. At short time one observes a driftof the bacterial population, while at long time one observes accumulation inhigh-nutrient regions. Recent work has viewed chemotaxis as a compromisebetween drift toward favorable regions and accumulation in favorable regions. Anumber of earlier studies assume that a bacterium resets its memory at tumbles-- a fact not borne out by experiment -- and make use of approximatecoarse-grained descriptions. Here, we revisit the problem of chemotaxis withoutresorting to any memory resets. We find that when bacteria respond to theenvironment in a non-adaptive manner, chemotaxis is generally dominated bydiffusion, whereas when bacteria respond in an adaptive manner, chemotaxis isdominated by a bias in the motion. In the adaptive case, favorable drift occurstogether with favorable accumulation. We derive our results from detailedsimulations and a variety of analytical arguments. In particular, we introducea new coarse-grained description of chemotaxis as biased diffusion, and wediscuss the way it departs from older coarse-grained descriptions.

Chemotaxis When Bacteria Remember: Drift versus Diffusion