The chemotactic behavior of Escherichia coli has been studied by exposing cells tethered by a single flagellum to pulses of chemicals delivered iontophoretically. Normally, wild-type cells spin alternately clockwise and counterclockwise, changing their direction on the average approximately once per second. When cells were exposed to a very brief diffusive wave of attractant, the probability of spinning counterclockwise quickly peaked, then fell below the prestimulus value, returning to baseline within a few seconds; repellent responses were similar but inverted. The width of the response indicates that cells integrate sensory inputs over a period of seconds, while the biphasic character implies that they also take time derivatives of these inputs. The sensory system is maximally tuned to concentration changes that occur over a span of approximately 2 sec, an interval over which changes normally occur when cells swim in spatial gradients; it is optimized to extract information from signals subject to statistical fluctuation. Impulse responses of cells defective in methylation were similar to those of wild-type cells, but did not fall as far below the baseline, indicating a partial defect in adaptation. Impulse responses of cheZ mutants were aberrant, indicating a serious defect in excitation.