  Chemotaxis of the bacterium Escherichia coli is well understood in shallow
chemical gradients, but its swimming behavior remains difficult to interpret in
steep gradients. By focusing on single-cell trajectories from simulations, we
investigated the dependence of the chemotactic drift velocity on attractant
concentration in an exponential gradient. While maxima of the average drift
velocity can be interpreted within analytical linear-response theory of
chemotaxis in shallow gradients, limits in drift due to steep gradients and
finite number of receptor-methylation sites for adaptation go beyond
perturbation theory. For instance, we found a surprising pinning of the cells
to the concentration in the gradient at which cells run out of methylation
sites. To validate the positions of maximal drift, we recorded single-cell
trajectories in carefully designed chemical gradients using microfluidics.
