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 approximately 300 Hz) at three different temperatures, 22.7, 17.7, and 15.8 degrees C. Results obtained earlier by electrorotation (, 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 approximately 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 (, Biophys. J. 76:580-587).