Torque-Speed Relationships of Na⁺-driven Chimeric Flagellar Motors in Escherichia coli

The bacterial flagellar motor is a rotary motor in the cell envelope of bacteria that couples ion flow across the cytoplasmic membrane to torque generation by independent stators anchored to the cell wall. The recent observation of stepwise rotation of a Na⁺-driven chimeric motor in Escherichia coli promises to reveal the mechanism of the motor in unprecedented detail. We measured torque-speed relationships of this chimeric motor using back focal plane interferometry of polystyrene beads attached to flagellar filaments in the presence of high sodium-motive force (85 mM Na⁺). With full expression of stator proteins the torque-speed curve had the same shape as those of wild-type E. coli and Vibrio alginolyticus motors: the torque is approximately constant (at ∼ 2200 pN nm) from stall up to a "knee" speed of ∼ 420 Hz, and then falls linearly with speed, extrapolating to zero torque at ∼ 910 Hz. Motors containing one to five stators generated ∼ 200 pN nm per stator at speeds up to ∼ 100 Hz/stator; the knee speed in 4- and 5-stator motors is not significantly slower than in the fully induced motor. This is consistent with the hypothesis that the absolute torque depends on stator number, but the speed dependence does not. In motors with point mutations in either of two critical conserved charged residues in the cytoplasmic domain of PomA, R88A and R232E, the zero-torque speed was reduced to ∼ 400 Hz. The torque at low speed was unchanged by mutation R88A but was reduced to ∼ 1500 pN nm by R232E. These results, interpreted using a simple kinetic model, indicate that the basic mechanism of torque generation is the same regardless of stator type and coupling ion and that the electrostatic interaction between stator and rotor proteins is related to the torque-speed relationship.