Mechanism and kinetics of a sodium-driven bacterial flagellar motor

Abstract

The bacterial flagellar motor is a large rotary molecular machine that propels swimming bacteria, powered by a transmembrane electrochemical potential difference. It consists of an ∼50-nm rotor and up to ∼10 independent stators anchored to the cell wall. We measured torque-speed relationships of single-stator motors under 25 different combinations of electrical and chemical potential. All 25 torque-speed curves had the same concave-down shape as fully energized wild-type motors, and each stator passes at least 37 ± 2 ions per revolution. We used the results to explore the 25-dimensional parameter space of generalized kinetic models for the motor mechanism, finding 830 parameter sets consistent with the data. Analysis of these sets showed that the motor mechanism has a "powerstroke" in either ion binding or transit; ion transit is channel-like rather than carrier-like; and the rate-limiting step in the motor cycle is ion binding at low concentration, ion transit, or release at high concentration. where V m is the membrane voltage and Δμ = k B T ln(C in /C out ) and q are the transmembrane chemical potential difference and charge of the ions, respectively, with C in and C out the internal and external ion concentrations. In most species the primary form of biological free energy is the proton-motive force (PMF), the IMF for H + ions (1). Physiological PMF is typically in the range −150 mV to −200 mV, with the inside electrically negative and slightly alkaline relative to the outside. Some organisms use sodium-motive force (SMF) to drive numerous cellular processes, such as bacterial motility (2), ATP synthesis (3), and active membrane transport (4). Arguably the most important process driven by IMF is ATP synthesis, which generates cellular ATP by forced rotation of the F 1 part of F 1 F O ATP-synthase. F 1 is mechanically coupled to and rotated by F O , which like the bacterial flagellar motor (BFM) is an ion-driven rotary motor. Understanding the mechanism of these and other ion-driven molecular machines is a fundamental challenge in cellular energetics and biophysics. The BFM (Fig. 1A) is a rotary molecular machine that propels many species of swimming bacteria. It couples ion flow, for example protons (H + ) in Escherichia coli or sodium ions (Na + ) in Vibrio alginolyticus, to the rotation of extracellular helical flagellar filaments at hundreds of revolutions per second (Hz) (2, 5, 6). Torque is generated by interactions between stator complexes (containing the proteins MotA and MotB in E. coli and PomA and PomB in V. alginolyticus) and the rotor protein FliG (7). In E. coli, each motor can be powered by any number between 1 and at least 11 functionally independent stators (8), which exchange with a membrane-bound pool of "spare" stators on a timescale of minutes (9).The most important biophysical method for studying the torque-generating mechanism of the BFM has been to measure its torque-speed curves. This has been done using varying viscous load (10-14) or external torque (15, 16) to control the speed. Fu...

Loose coupling in the bacterial flagellar motor

“…As follows from an assumption of tight coupling, the stall torque of the two-proton motor is exactly twice that of the one-proton motor. The flexible motor produces an intermediate torque that, under the assumption of 26 steps per revolution (33,34), is close to the recent measurements of Lo et al (31) (range indicated by gray bars in Fig. 2 A−C).…”

“…On the basis of extensive measurements with a Na + -fueled motor, Berry and coworkers recently estimated this coupling ratio at 37 ions per revolution (31). Measurements of motor stepping indicate 26 rotor steps per revolution (33,34), and electron microscopic reconstructions (35) and other observations concerning rotor architecture (36)(37)(38) also appear consistent with a FliG copy number of 26 [varying somewhat between specimens (35,39)].…”

“…31). Observation iii indicates that as the external load is decreased, the finite rates of internal processes become important, with proton movement(s) being rate limiting to at least some extent.…”

Diverse high-torque bacterial flagellar motors assemble wider stator rings using a conserved protein scaffold

“…It is noteworthy, however, that an estimated sodium motive force in Vibrio spp. that is lower than the standard E. coli proton motive force nevertheless drives the Vibrio motor with higher torque than the E. coli motor (24,25), further suggesting that torque differences likely exist at the level of the motor. However, the molecular mechanism by which different motors might produce different torques has not been investigated.…”

“…There is good evidence for the assumption that stator complexes exert a constant force in all bacteria, because proton motive forces across bacteria are consistently reported to be between −100 and −200 mV (50); however it should be noted that the sodium motive force in sodium-driven motors may be higher than the proton motive force. Although sodium motive force increases with increasing external sodium ion concentration, it plateaus at an external sodium concentration of ∼250 mM, and the a maximum sodium motive force does not exceed −200 mV (25,51). Thus, given the radius of stator complexes around the axis of rotation and the number of stator complexes, we can predict the torque of a motor by making the approximation that the torque from multiple stator complexes is roughly additive (14).…”