Adaptation kinetics in bacterial chemotaxis.

Cells of Escherichia coli, tethered to glass by a single flagellum, were subjected to constant flow of a medium containing the attractant alpha-methyl-DL-aspartate. The concentration of this chemical was varied with a programmable mixing apparatus over a range spanning the dissociation constant of the chemoreceptor at rates comparable to those experienced by cells swimming in spatial gradients. When an exponentially increasing ramp was turned on (a ramp that increases the chemoreceptor occupancy linearly), the rotational bias of the cells (the fraction of time spent spinning counterclockwise) changed rapidly to a higher stable level, which persisted for the duration of the ramp. The change in bias increased with ramp rate, i.e., with the time rate of change of chemoreceptor occupancy. This behavior can be accounted for by a model for adaptation involving proportional control, in which the flagellar motors respond to an error signal proportional to the difference between the current occupancy and the occupancy averaged over the recent past. Distributions of clockwise and counterclockwise rotation intervals were found to be exponential. This result cannot be explained by a response regular model in which transitions between rotational states are generated by threshold crossings of a regular subject to statistical fluctuation; this mechanism generates distributions with far too many long events. However, the data can be fit by a model in which transitions between rotational states are governed by first-order rate constants. The error signal acts as a bias regulator, controlling the values of these constants.