Escherichia coli swim in a three-dimensional random walk of alternating runs and tumbles, using their flagella for propulsion. When moving in a gradient of an attractant or repellent, they bias the walk in such a way as to migrate into a favorable region; this is a basis for chemotaxis. Bacteria may be tethered to a glass surface by means of a single flagellum. When tethered, cell bodies spin alternately clockwise (CW) and counterclockwise (CCW) under the influence of the rotary motor that drives the flagellum. The CCW state corresponds to the run mode and the CW state to the tumble mode. Tethered bacteria remain fixed in place, thereby providing an opportunity to study chemotactic behavior by direct manipulation of attractant or repellent concentration near the cells. Two experimental approaches have been used to exploit this opportunity. In the first, a mixing device that provides programmable concentration changes was used to stimulate tethered cells with exponential temporal gradients or exponentiated sine waves of the attractant α-methyl-D,L-aspartate. Such changes cause chemoreceptor occupancy to be changed linearly or sinusoidally, respectively. Exponential temporal gradients (both positive and negative) were found to shift the rotational bias (defined as the fraction of time spent spinning CCW) by a fixed amount related to the steepness of the gradient. The bias shifts produced indicate that cells are exquisitely sensitive to small changes in chemoreceptor occupancy. Distributions of CW and CCW intervals remained exponential during such gradients. This result is inconsistent with a response regulator model in which rotational transitions are associated with level-crossings of a fluctuating, hypothetical intermediate. It is consistent with amodel in which transitions occur at random between rotational states, the transition probabilities being governed by chemotactic signals. In the second approach, short bursts of an attractant or repellent were delivered iontophoretically, producing an impulse response in the tethered bacteria. Properties of the impulse response show both adaptive and integrative behavior, and imply that cells respond maximally to changes in concentration which occur over times comparable with the length of a run. The impulse response can be used to predict the behavior of cells towards an arbitrary stimulus in the linear domain. Impulse responses from aseries of chemotaxis mutants showed that some were defective in adaptation but not excitation; others were defective in both. Taken together, the experiments provide information about the spectral response of bacteria to concentration changes with frequencies ranging from 10-3 Hz up to almost 10 Hz. Both sets of data are consistent with the notion of acellular "bias regulator" signal that sets the transition probabilities between two states; one representing CCW and the other representing CW rotation.
