Torque-speed relationship of the flagellar rotary motor of Escherichia coli

The output of a rotary motor is characterized by its torque and speed. We measured the torque-speed relationship of the flagellar rotary motor of Escherichia coli by a new method, Small latex spheres were attached to flagellar stubs on cells fixed to the surface of a glass slide. The angular speeds of the spheres were monitored in a weak optical trap by back-focal-plane interferometry in solutions containing different concentrations of the viscous agent Ficoll. Plots of relative torque (viscosity x speed) versus speed were obtained over a wide dynamic range (up to speeds of similar to 300 Hz) at three different temperatures, 22.7, 17.7, and 15.8 degrees C, Results obtained earlier by electrorotation (Berg and Turner, 1993, Biophys. J. 65:2201-2216) were confirmed. The motor operates in two dynamic regimes. At 23 degrees C, the torque is approximately constant up to a knee speed of nearly 200 Hz, and then it falls rapidly with speed to a zero-torque speed of similar to 350 Hz. In the low-speed regime, torque is insensitive to changes in temperature. In the high-speed regime, it decreases markedly at lower temperature. These results are consistent with models in which torque is generated by a powerstroke mechanism (Berry and Berg, 1999, Biophys. J, 76:580-587).