The speed of the flagellar rotary motor of Escherichia coli varies linearly with protonmotive force

A protonmotive force (pmf) across the cell's inner membrane powers the flagellar rotary motor of Escherichia coli. Speed is known to be proportional to pmf when viscous loads are heavy. Here we show that speed also is proportional to pmf when viscous loads are light. Two motors on the same bacterium were monitored as the cell was slowly deenergized. The first motor rotated the entire cell body (a heavy load), while the second motor rotated a small latex bead (a light load), The first motor rotated slowly and provided a measure of the cell's pmf. The second motor rotated rapidly and was compared with the first, to give the speed-pmf relation for light loads. Experiments were done at 24.0degreesC and 16.2degreesC, with initial speeds indicating operation well into the high-speed, low-torque regime. Speed was found to be proportional to pmf over the entire (accessible) dynamic range (0-270 Hz). If the passage of a fixed number of protons carries the motor through each revolution, i.e., if the motor is tightly coupled, a linear speed-pmf relation is expected close to stall, where the work done against the viscous load matches the energy dissipated in proton flow. A linear relation is expected at high speeds if proton translocation is rate-limiting and involves multiple steps, a model that also applies to simple proton channels. The present work shows that a linear relation is true more generally, providing an additional constraint on possible motor mechanisms.