The proton flux through the bacterial flagellar motor

Bacterial flagella are driven by a rotary motor that utilizes the free energy stored in the electrochemical proton gradient across the cytoplasmic membrane to do mechanical work. The flux of protons coupled to motor rotation was measured in Streptococcus and found to be directly proportional to motor speed. This supports the hypothesis that the movement of protons through the motor is tightly coupled to the rotation of its flagellar filament. Under this assumption the efficiency of energy conversion is close to unity at the low speeds encountered in tethered cells but only a few percent at the high speeds encountered in swimming cells. This difference appears to be due to dissipation by processes internal to the motor. The efficiency at high speeds exhibits a steep temperature dependence and a sizable deuterium solvent isotope effect.     

The stall torque of the bacterial flagellar motor.

The bacterial flagellar motor couples the flow of protons across the cytoplasmic membrane to the rotation of a helical flagellar filament. Using tethered cells, we have measured the stall torque required to block this rotation and compared it with the torque of the running motor over a wide range of values of proton-motive force and pH. The stall torque and the running torque vary identically: both appear to saturate at large values of the proton-motive force and both decrease at low or high pH. This suggests that up to speeds of approximately 5 Hz the operation of the motor is not limited by the mobility of its internal components or the rates of proton transfer reactions coupled to flagellar rotation.     

Torque-speed relationship of the Na+-driven flagellar motor of Vibrio alginolyticus

The torque-speed relationship of the Na(+)-driven flagellar motor of Vibrio alginolyticus was investigated. The rotation rate of the motor was measured by following the position of a bead, attached to a flagellar filament, using optical nanometry. In the presence of 50mM NaCl, the generated torque was relatively constant ( approximately 3800pNnm) at lower speeds (speeds up to approximately 300Hz) and then decreased steeply, similar to the H(+)-driven flagellar motor of Escherichia coli. When the external NaCl concentration was varied, the generated torque of the flagellar motor was changed over a wide range of speeds. This result could be reproduced using a simple kinetic model, which takes into consideration the association and dissociation of Na(+) onto the motor. These results imply that for a complete understanding of the mechanism of flagellar rotation it is essential to consider both the electrochemical gradient and the absolute concentration of the coupling ion.     

Simultaneous measurement of bacterial flagellar rotation rate and swimming speed.

Swimming speeds and flagellar rotation rates of individual free-swimming Vibrio alginolyticus cells were measured simultaneously by laser dark-field microscopy at 25, 30, and 35 degrees C. A roughly linear relation between swimming speed and flagellar rotation rate was observed. The ratio of swimming speed to flagellar rotation rate was 0.113 microns, which indicated that a cell progressed by 7% of pitch of flagellar helix during one flagellar rotation. At each temperature, however, swimming speed had a tendency to saturate at high flagellar rotation rate. That is, the cell with a faster-rotating flagellum did not always swim faster. To analyze the bacterial motion, we proposed a model in which the torque characteristics of the flagellar motor were considered. The model could be analytically solved, and it qualitatively explained the experimental results. The discrepancy between the experimental and the calculated ratios of swimming speed to flagellar rotation rate was about 20%. The apparent saturation in swimming speed was considered to be caused by shorter flagella that rotated faster but produced less propelling force.     

Mechanical limits of bacterial flagellar motors probed by electrorotation.

We used the technique of electrorotation to apply steadily increasing external torque to tethered cells of the bacterium Escherichia coli while continuously recording the speed of cell rotation. We found that the bacterial flagellar motor generates constant torque when rotating forward at low speeds and constant but considerably higher torque when rotating backward. At intermediate torques, the motor stalls. The torque-speed relationship is the same in both directional modes of switching motors. Motors forced backward usually break, either suddenly and irreversibly or progressively. Motors broken progressively rotate predominantly at integral multiples of a unitary speed during the course of both breaking and subsequent recovery, as expected if progressive breaking affects individual torque-generating units. Torque is reduced by the same factor at all speeds in partially broken motors, implying that the torque-speed relationship is a property of the individual torque-generating units.     

Torque generated by the flagellar motor of Escherichia coli.

Cells of the bacterium Escherichia coli were tethered and spun in a high-frequency rotating electric field at a series of discrete field strengths. This was done first at low field strengths, then at field strengths generating speeds high enough to disrupt motor function, and finally at low field strengths. Comparison of the initial and final speed versus applied-torque plots yielded relative motor torque. For backward rotation, motor torque rose steeply at speeds close to zero, peaking, on average, at about 2.2 times the stall torque. For forward rotation, motor torque remained approximately constant up to speeds of about 60% of the zero-torque speed. Then the torque dropped linearly with speed, crossed zero, and reached a minimum, on average, at about -1.7 times the stall torque. The zero-torque speed increased with temperature (about 90 Hz at 11 degrees C, 140 Hz at 16 degrees C, and 290 Hz at 23 degrees C), while other parameters remained approximately constant. Sometimes the motor slipped at either extreme (delivered constant torque over a range of speeds), but eventually it broke. Similar results were obtained whether motors broke catastrophically (suddenly and completely) or progressively or were de-energized by brief treatment with an uncoupler. These results are consistent with a tightly coupled ratchet mechanism, provided that elastic deformation of force-generating elements is limited by a stop and that mechanical components yield at high applied torques.     

Torque generated by the bacterial flagellar motor close to stall.

In earlier work in which electrorotation was used to apply external torque to tethered cells of the bacterium Escherichia coli, it was found that the torque required to force flagellar motors backward was considerably larger than the torque required to stop them. That is, there appeared to be substantial barrier to backward rotation. Here, we show that in most, possibly all, cases this barrier is an artifact due to angular variation of the torque applied by electrorotation, of the motor torque, or both; the motor torque appears to be independent to speed or to vary linearly with speed up to speeds of tens of Hertz, in either direction. However, motors often break catastrophically when driven backward, so backward rotation is not equivalent to forward rotation. Also, cells can rotate backward while stalled, either in randomly timed jumps of 180 degrees or very slowly and smoothly. When cells rotate slowly and smoothly backward, the motor takes several seconds to recover after electrorotation is stopped, suggesting that some form of reversible damage has occurred. These findings do not affect the interpretation of electrorotation experiments in which motors are driven rapidly forward.     

Isotope and thermal effects in chemiosmotic coupling to the flagellar motor of Streptococcus

The torque generated by the flagellar motor of Streptococcus strain V4051 has been determined from rates of rotation of cells tethered by a single flagellum in media of different isotopic composition and temperature. Starved cells were energized artificially with either a potassium diffusion potential or a pH gradient. The torque increased linearly with protonmotive force. Identical results were obtained in media made with D2O or H2O; there was no solvent isotope effect. At a fixed protonmotive force, the torque was approximately constant over a temperature range of 4 degrees -38 degrees C. In cells chemotactically inert to changes in cytoplasmic pH, the motor turned counterclockwise when protons moved inward and clockwise when they moved outward. We conclude that the motor is a reversible engine driven by simple acid-base dissociation. A detailed model is discussed.     

Rhizobium meliloti swims by unidirectional, intermittent rotation of right-handed flagellar helices.

The 5 to 10 peritrichously inserted complex flagella of Rhizobium meliloti MVII-1 were found to form right-handed flagellar bundles. Bacteria swam at speeds up to 60 microns/s, their random three-dimensional walk consisting of straight runs and quick directional changes (turns) without the vigorous angular motion (tumbling) seen in swimming Escherichia coli cells. Observations of R. meliloti cells tethered by a single flagellar filament revealed that flagellar rotation was exclusively clockwise, interrupted by very brief stops (shorter than 0.1 s), typically every 1 to 2 s. Swimming bacteria responded to chemotactic stimuli by extending their runs, and tethered bacteria responded by prolonged intervals of clockwise rotation. Moreover, the motility tracks of a generally nonchemotactic ("smooth") mutant consisted of long runs without sharp turns, and tethered mutant cells showed continuous clockwise rotation without detectable stops. These observations suggested that the runs of swimming cells correspond to clockwise flagellar rotation, and the turns correspond to the brief rotation stops. We propose that single rotating flagella (depending on their insertion point on the rod-shaped bacterial surface) can reorient a swimming cell whenever the majority of flagellar motors stop.     

Microscopic analysis of bacterial motility at high pressure

The bacterial flagellar motor is a molecular machine that converts an ion flux to the rotation of a helical flagellar filament. Counterclockwise rotation of the filaments allows them to join in a bundle and propel the cell forward. Loss of motility can be caused by environmental factors such as temperature, pH, and solvation. Hydrostatic pressure is also a physical inhibitor of bacterial motility, but the detailed mechanism of this inhibition is still unknown. Here, we developed a high-pressure microscope that enables us to acquire high-resolution microscopic images, regardless of applied pressures. We also characterized the pressure dependence of the motility of swimming Escherichia coli cells and the rotation of single flagellar motors. The fraction and speed of swimming cells decreased with increased pressure. At 80 MPa, all cells stopped swimming and simply diffused in solution. After the release of pressure, most cells immediately recovered their initial motility. Direct observation of the motility of single flagellar motors revealed that at 80 MPa, the motors generate torque that should be sufficient to join rotating filaments in a bundle. The discrepancy in the behavior of free swimming cells and individual motors could be due to the applied pressure inhibiting the formation of rotating filament bundles that can propel the cell body in an aqueous environment.     

Low flagellar motor torque and high swimming efficiency of Caulobacter crescentus swarmer cells

We determined the torque of the flagellar motor of Caulobacter crescentus for different motor rotation rates by measuring the rotation rate and swimming speed of the cell body and found it to be remarkably different from that of other bacteria, such as Escherichia coli and Vibrio alginolyticus. The average stall torque of the Caulobacter flagellar motor was approximately 350 pN nm, much smaller than the values of the other bacteria measured. Furthermore, the torque of the motor remained constant in the range of rotation rates up to those of freely swimming cells. In contrast, the torque of a freely swimming cell for V. alginolyticus is typically approximately 20% of the stall torque. We derive from these results that the C. crescentus swarmer cells swim more efficiently than both E. coli and V. alginolyticus. Our findings suggest that C. crescentus is optimally adapted to low nutrient aquatic environments.     

Rapid changes in flagellar rotation induced by external electric pulses.

The bacterial flagellar motor is the only molecular rotary machine found in living organisms, converting the protonmotive force, i.e., the membrane voltage and proton gradients across the cell membrane, into the mechanical force of rotation (torque). We have developed a method for holding a bacterial cell at the tip of a glass micropipette and applying electric pulses through the micropipette. This method has enabled us to observe the dynamical responses of flagellar rotation to electric pulses that change the membrane voltage transiently and repeatedly. We have observed that acceleration and deceleration of motor rotation are induced by application of these electric pulses. The change in the rotation rate occurred within 5 ms after pulse application.     

Visualization of functional rotor proteins of the bacterial flagellar motor in the cell membrane

The bacterial flagellar motor is a rotary motor driven by the electrochemical potentials of specific ions across the cell membrane. Direct interactions between the rotor protein FliG and the stator protein MotA are thought to generate the rotational torque. Here, we used total internal reflection fluorescent microscopy to observe the localization of green fluorescent protein (GFP)-fused FliG in Escherichia coli cells. We identified three types of fluorescent punctate signals: immobile dots, mobile dots that exhibited simple diffusion, and mobile dots that exhibited restricted diffusion. When GFP-FliG was expressed in a DeltafliG background, most of the cells were not mobile. When the cells were tethered to a glass side, however, rotating cells were commonly observed and a single fluorescent dot was always observed at the rotational center of the tethered cell. These fluorescent dots were likely positions at which functional GFP-FliG had been incorporated into a flagellar motor. Our results suggest that flagellar basal bodies diffuse in the cytoplasmic membrane until the axial structure and/or other structures assemble.     

Constraints on models for the flagellar rotary motor

Most bacteria that swim are propelled by flagellar filaments, each driven at its base by a rotary motor embedded in the cell wall and cytoplasmic membrane. A motor is about 45 nm in diameter and made up of about 20 different kinds of parts. It is assembled from the inside out. It is powered by a proton (or in some species, a sodium-ion) flux. It steps at least 400 times per revolution. At low speeds and high torques, about 1000 protons are required per revolution, speed is proportional to protonmotive force, and torque varies little with temperature or hydrogen isotope. At high speeds and low torques, torque increases with temperature and is sensitive to hydrogen isotope. At room temperature, torque varies remarkably little with speed from about -100 Hz (the present limit of measurement) to about 200 Hz, and then it declines rapidly reaching zero at about 300 Hz. These are facts that motor models should explain. None of the existing models for the flagellar rotary motor completely do so.     

The bacterial flagellar motor

The bacterial flagellar motor is a remarkable molecular machine that converts chemical energy into work. Knowledge of the structure, genetics, and dynamics of the motor has expanded steadily. Recent progress is reviewed, with an emphasis on the dynamics of flagellar rotation. Previous results with tethered cells, which rotate slowly, are contrasted with recent work on swimming cells, whose motors turn very rapidly. Genetic evidence delineates a small set of proteins that are likely to participate directly in the process of torque generation. An explicit hypothesis for torque generation is described, in which roles are envisaged for each of these proteins.     

Torque-generating units of the bacterial flagellar motor step independently.

Measurements of the variance in rotation period of tethered cells as a function of mean rotation rate have shown that the flagellar motor of Escherichia coli is a stepping motor. Here, by measurement of the variance in rotation period as a function of the number of active torque-generating units, it is shown that each unit steps independently.     

Dynamics of a tightly coupled mechanism for flagellar rotation. Bacterial motility, chemiosmotic coupling, protonmotive force.

The bacterial flagellar motor is a molecular engine that couples the flow of protons across the cytoplasmic membrane to rotation of the flagellar filament. We analyze the steady-state behavior of an explicit mechanical model in which a fixed number of protons carries the filament through one revolution. Predictions of this model are compared with experimentally determined relationships between protonmotive force, proton flux, torque, and speed. All such tightly coupled mechanisms produce the same torque when the motor is stalled but vary greatly in their behavior at high speed. The speed at zero load predicted by our model is limited by the rates of association and dissociation of protons at binding sites on the rotor and by the mobility of force generators containing transmembrane channels that interact with these sites. Our analysis suggests that more could be learned about the motor if it were driven by an externally applied torque backwards (at negative speed) or forwards at speeds greater than the zero-load speed.     

The MotA protein of E. coli is a proton-conducting component of the flagellar motor

A number of mutants of motA, a gene necessary for flagellar rotation in E. coli, were isolated and characterized. Many mutations were dominant, owing to competition between functional and nonfunctional MotA for a limited number of sites on the flagellar motor. A new class of mutant was discovered in which flagellar torque is normal at low speeds but reduced at high speeds. Hydrogen isotope effects on these mutants indicate that MotA catalyzes proton transfer. We confirmed an earlier observation that overproduction of MotA leads to accumulation of the protein in the cytoplasmic membrane and to significant decreases in growth rate. When nonfunctional mutant variants of MotA were overproduced instead, they accumulated in the cytoplasmic membrane, but growth was not impaired. These results also suggest that MotA conducts protons. This was confirmed by measuring the proton permeabilities of vesicles containing wild-type or mutant MotA proteins.     

A model for bacterial flagellar motor: free energy transduction and self-organization of rotational motion

A bacterial flagellar motor is an energy transducing molecular machine which shows some attractive characteristics. First, this motor is driven by a protonmotive force (PMF) across the membrane, two components of which, electric potential delta psi and chemical potential -(2.3RT/F)delta pH, are equivalently transduced to the mechanical work of the motor rotation. Second, a PMF threshold for rotation is observed. Third, this motor can rotate reversibly either counterclockwise (CCW) or clockwise (CW) at almost the same speed. To clarify the osmomechanical coupling of this motor, these characteristics must be explained consistently at the molecular level. In this paper, in order to allow quantitative analyses of the above characteristics, a theoretical model of a bacterial flagellar motor is constructed assuming that the torque generating sites are electrodes which can be charged by protons and that the electrostatic interaction between the electrodes generates the rotation torque. Electrode reaction reasonably derives the equivalence of delta psi and -(2.3RT/F)delta pH. In this model, rates of charging and discharging of protons are influenced by the motor rotation rate, so that the torque generating sites co-operatively work through the motor rotation. We named this kind of co-operativity among them "dynamic co-operativity" in torque generation. This co-operativity causes autocatalytic generation of motor torque and the existence of the rotation threshold. In this model, the appearance of the stable rotational states can be described by phase transition caused by the dynamic co-operativity among torque generating sites. According to this model, the flagellar motor has two stable rotational states corresponding to CCW and CW, which show the same torques. The motor selects one direction from them to rotate, and that is self-organization of rotational motion. Interpretation of the transition between the two stable rotational states as the chemotactic reversals of the flagellar motor is also discussed.     

On torque and tumbling in swimming Escherichia coli

Bacteria swim by rotating long thin helical filaments, each driven at its base by a reversible rotary motor. When the motors of peritrichous cells turn counterclockwise (CCW), their filaments form bundles that drive the cells forward. We imaged fluorescently labeled cells of Escherichia coli with a high-speed charge-coupled-device camera (500 frames/s) and measured swimming speeds, rotation rates of cell bodies, and rotation rates of flagellar bundles. Using cells stuck to glass, we studied individual filaments, stopping their rotation by exposing the cells to high-intensity light. From these measurements we calculated approximate values for bundle torque and thrust and body torque and drag, and we estimated the filament stiffness. For both immobilized and swimming cells, the motor torque, as estimated using resistive force theory, was significantly lower than the motor torque reported previously. Also, a bundle of several flagella produced little more torque than a single flagellum produced. Motors driving individual filaments frequently changed directions of rotation. Usually, but not always, this led to a change in the handedness of the filament, which went through a sequence of polymorphic transformations, from normal to semicoiled to curly 1 and then, when the motor again spun CCW, back to normal. Motor reversals were necessary, although not always sufficient, to cause changes in filament chirality. Polymorphic transformations among helices having the same handedness occurred without changes in the sign of the applied torque.