Theories of rotary motors

The bacterial flagellar motor and the ATP-hydrolysing F1 portion of the F1Fo-ATPase are known to be rotary motors, and it seems highly probable that the H+-translocating Fo portion rotates too. The energy source in the case of Fo and the flagellar motor is the flow of ions, either H+ (protons) or Na+, down an electrochemical gradient across a membrane. The fact that ions flow in a particular direction through a well-defined structure in these motors invites the possibility of a type of mechanism based on geometric constraints between the rotor position and the paths of ions flowing through the motor. The two best-studied examples of such a mechanism are the ''turnstile'' model of Khan and Berg and the ''proton turbine'' model of Läuger or Berry. Models such as these are typically represented by a small number of kinetic states and certain allowed transitions between them. This allows the calculation of predictions of motor behaviour and establishes a dialogue between models and experimental results. In the near future structural data and observations of single-molecule events should help to determine the nature of the mechanism of rotary motors, while motor models must be developed that can adequately explain the measured relationships between torque and speed in the flagellar motor.     

Rotary protein motors

Three protein motors have been unambiguously identified as rotary engines: the bacterial flagellar motor and the two motors that constitute ATP synthase (F(0)F(1) ATPase). Of these, the bacterial flagellar motor and F(0) motors derive their energy from a transmembrane ion-motive force, whereas the F(1) motor is driven by ATP hydrolysis. Here, we review the current understanding of how these protein motors convert their energy supply into a rotary torque.     

细菌鞭毛马达——一种卓越的分子机器

鞭毛马达(flagellar motor)是一种分子旋转马达,它在细菌鞭毛的结构与功能中起着中心作用.鞭毛马达的结构已基本清楚,主要由Mot A、Mot B、Fli G、Fli M和Fli N 5种蛋白组成定子(stator)和转子(rotor),其驱动力来自于跨膜的H⁺或Na⁺流.目前对鞭毛马达的旋转动力学及旋转力矩产生机制已有初步的了解.鞭毛马达可作为研究分子旋转马达的理想模型,对其深入研究将有助于认识生物能量转化利用及细胞运动的机制并具有广泛的生物学意义.     

Taming the flagellar motor of pseudomonads with a nucleotide messenger

Pseudomonads rely on the flagellar motor to rotate a polar flagellum for swimming and swarming, and to sense surfaces for initiating the motile-to-sessile transition to adopt a surface-dwelling lifestyle. Deciphering the function and regulation of the flagellar motor is of paramount importance for understanding the behaviours of environmental and pathogenic pseudomonads. Recent studies disclosed the preeminent role played by the messenger c-di-GMP in controlling the real-time performance of the flagellar motor in pseudomonads. The studies revealed that c-di-GMP controls the dynamic exchange of flagellar stator units to regulate motor torque/speed and modulates the frequency of flagellar motor switching via the chemosensory signalling pathways. Apart from being a rotary motor, the flagellar motor is emerging as a mechanosensor that transduces surface-induced mechanical signals into an increase of cellular c-di-GMP concentration to initiate the cellular programs required for long-term colonization. Collectively, the studies generate long-awaited mechanistic insights into how c-di-GMP regulates bacterial motility and the motile-to-sessile transition. The new findings also raise the fundamental questions of how cellular c-di-GMP concentrations are dynamically coupled to flagellar output and the proton-motive force, and how c-di-GMP signalling is coordinated spatiotemporally to fine-tune flagellar response and the behaviour of pseudomonads in solutions and on surfaces.     

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.     

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.     

Protein dynamics and mechanisms controlling the rotational behaviour of the bacterial flagellar motor

The proteins that make up the bacterial flagellar rotary motor have recently been shown to be more dynamic than previously thought, with some key proteins exchanging with pools of proteins in the membrane/cytoplasm. It has also become clear that in addition to simply switching in response to chemosensory signals, the rotation of the bacterial flagellar motor can be slowed or stopped, using a clutch or a brake, by signals from metabolism and growth state.     

Control of speed modulation (chemokinesis) in the unidirectional rotary motor of Sinorhizobium meliloti

Swimming cells of Sinorhizobium meliloti are driven by flagella that rotate only clockwise. They can modulate rotary speed (achieve chemokinesis) and reorient the swimming path by slowing flagellar rotation. The flagellar motor is energized by proton motive force, and torque is generated by electrostatic interactions at the rotor/stator (FliG/MotA-MotB) interface. Like the Escherichia coli flagellar motor that switches between counterclockwise and clockwise rotation, the S. meliloti rotary motor depends on electrostatic interactions between conserved charged residues, namely, Arg294 and Glu302 (FliG) and Arg90, Glu98 and Glu150 (MotA). Unlike in E. coli, however, Glu150 is essential for torque generation, whereas residues Arg90 and Glu98 are crucial for the chemotaxis-controlled variation of rotary speed. Substitutions of either Arg90 or Glu98 by charge-neutralizing residues or even by their smaller, charge-maintaining isologues, lysine and aspartate, resulted in top-speed flagellar rotation and decreased potential to slow down in response to tactic signalling (chemokinesis-defective mutants). The data infer a novel mechanism of flagellar speed control by electrostatic forces acting at the rotor/stator interface. These features have been integrated into a working model of the speed-modulating rotary motor.     

Molecular motors of the bacterial flagella

The bacterial flagellum, which is responsible for motility, is a biological nanomachine consisting of a reversible rotary motor, a universal joint, a helical screw, and a protein export apparatus dedicated for flagellar assembly. The motor is fueled by an inward-directed electrochemical gradient of protons or sodium ions across the cytoplasmic membrane. The motor consists of a rotor, a drive shaft, a bushing, and about a dozen stator units. The flagellar protein export apparatus is located at the cytoplasmic side of the rotor. Interactions between the rotor and the stators and those between soluble and membrane components of the export apparatus are highly dynamic. The structures of flagellar basal body components including those of the export apparatus, being revealed at high resolution by X-ray crystallography and electron cryomicroscopy and cryotomography, are giving insights into their mechanisms.     

Exchange of rotor components in functioning bacterial flagellar motor

The bacterial flagellar motor is a rotary motor driven by the electrochemical potential of a coupling ion. The interaction between a rotor and stator units is thought to generate torque. The overall structure of flagellar motor has been thought to be static, however, it was recently proved that stators are exchanged in a rotating motor. Understanding the dynamics of rotor components in functioning motor is important for the clarifying of working mechanism of bacterial flagellar motor. In this study, we focused on the dynamics and the turnover of rotor components in a functioning flagellar motor. Expression systems for GFP-FliN, FliM-GFP, and GFP-FliG were constructed, and each GFP-fusion was functionally incorporated into the flagellar motor. To investigate whether the rotor components are exchanged in a rotating motor, we performed fluorescence recovery after photobleaching experiments using total internal reflection fluorescence microscopy. After photobleaching, in a tethered cell producing GFP-FliN or FliM-GFP, the recovery of fluorescence at the rotational center was observed. However, in a cell producing GFP-FliG, no recovery of fluorescence was observed. The transition phase of fluorescence intensity after full or partially photobleaching allowed the turnover of FliN subunits to be calculated as 0.0007 s⁻¹, meaning that FliN would be exchanged in tens of minutes. These novel findings indicate that a bacterial flagellar motor is not a static structure even in functioning state. This is the first report for the exchange of rotor components in a functioning bacterial flagellar motor.     

Mechanisms of type III protein export for bacterial flagellar assembly

Flagellar type III protein export is highly organized and well controlled in a timely manner by dynamic, specific and cooperative interactions among components of the export apparatus, allowing the huge and complex macromolecular assembly to be built efficiently. The bacterial flagellum, which is required for motility, consists of a rotary motor, a universal joint and a helical propeller. Most of the flagellar components are translocated to the distal, growing end of the flagellum for assembly through the central channel of the flagellum itself by the flagellar type III protein export apparatus, which is postulated to be located on the cytoplasmic side of the flagellar basal body. The export specificity switching machinery, which consists of at least two proteins that function as a molecular ruler and an export switch, respectively, monitors the state of hook-basal body assembly in the cell exterior and switches export specificity, thereby coupling sequential flagellar gene expression with the flagellar assembly process. The export ATPase complex composed of an ATPase and its regulator acts as a pilot to deliver its export substrate to the export gate and helps initial entry of the substrate N-terminal chain into a narrow pore of the export gate. The energy of ATP hydrolysis appears to be used to disassemble and release the ATPase complex from the protein about to be exported, and the rest of the successive unfolding/translocation process of the long polypeptide chain is driven solely by proton motive force (PMF), perhaps through biased one-dimensional Brownian diffusion. Interestingly, the subunits of the ATPase complex have significant sequence similarities to subunits of F(0)F(1)-ATP synthase, a rotary motor that drives the chemical reaction of ATP synthesis using PMF, and the entire crystal structure of the export ATPase is extremely similar to the alpha/beta subunits of F(0)F(1)-ATP synthase, suggesting that the flagellar export apparatus and F(0)F(1)-ATP synthase share the mechanism for their two distinct functions.     

A programmable optical angle clamp for rotary molecular motors

Optical tweezers are widely used for experimental investigation of linear molecular motors. The rates and force dependence of steps in the mechanochemical cycle of linear motors have been probed giving detailed insight into motor mechanisms. With similar goals in mind for rotary molecular motors we present here an optical trapping system designed as an angle clamp to study the bacterial flagellar motor and F(1)-ATPase. The trap position was controlled by a digital signal processing board and a host computer via acousto-optic deflectors, the motor position via a three-dimensional piezoelectric stage and the motor angle using a pair of polystyrene beads as a handle for the optical trap. Bead-pair angles were detected using back focal plane interferometry with a resolution of up to 1 degrees , and controlled using a feedback algorithm with a precision of up to 2 degrees and a bandwidth of up to 1.6 kHz. Details of the optical trap, algorithm, and alignment procedures are given. Preliminary data showing angular control of F(1)-ATPase and angular and speed control of the bacterial flagellar motor are presented.     

Steps in the Bacterial Flagellar Motor

The bacterial flagellar motor is a highly efficient rotary machine used by many bacteria to propel themselves. It has recently been shown that at low speeds its rotation proceeds in steps. Here we propose a simple physical model, based on the storage of energy in protein springs, that accounts for this stepping behavior as a random walk in a tilted corrugated potential that combines torque and contact forces. We argue that the absolute angular position of the rotor is crucial for understanding step properties and show this hypothesis to be consistent with the available data, in particular the observation that backward steps are smaller on average than forward steps. We also predict a sublinear speed versus torque relationship for fixed load at low torque, and a peak in rotor diffusion as a function of torque. Our model provides a comprehensive framework for understanding and analyzing stepping behavior in the bacterial flagellar motor and proposes novel, testable predictions. More broadly, the storage of energy in protein springs by the flagellar motor may provide useful general insights into the design of highly efficient molecular machines.     

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.     

Quantification of flagellar motor stator dynamics through in vivo proton‐motive force control

The bacterial flagellar motor, one of the few rotary motors in nature, produces torque to drive the flagellar filament by ion translocation through membrane‐bound stator complexes. We used the light‐driven proton pump proteorhodopsin (pR) to control the proton‐motive force (PMF) in vivo by illumination. pR excitation was shown to be sufficient to replace native PMF generation, and when excited in cells with intact native PMF generation systems increased motor speed beyond the physiological norm. We characterized the effects of rapid in vivo PMF changes on the flagellar motor. Transient PMF disruption events from loss of illumination caused motors to stop, with rapid recovery of their previous rotation rate after return of illumination. However, extended periods of PMF loss led to stepwise increases in rotation rate upon PMF return as stators returned to the motor. The rate constant for stator binding to a putative single binding site on the motor was calculated to be 0.06 s^?1. Using GFP‐tagged MotB stator proteins, we found that transient PMF disruption leads to reversible stator diffusion away from the flagellar motor, showing that PMF presence is necessary for continued motor integrity, and calculated a stator dissociation rate of 0.038 s^?1.     

In situ structure of the Caulobacter crescentus flagellar motor and visualization of binding of a CheY-homolog

Bacterial flagellar motility is controlled by the binding of CheY proteins to the cytoplasmic switch complex of the flagellar motor, resulting in changes in swimming speed or direction. Despite its importance for motor function, structural information about the interaction between effector proteins and the motor are scarce. To address this gap in knowledge, we used electron cryotomography and subtomogram averaging to visualize such interactions inside Caulobacter crescentus cells. In C. crescentus, several CheY homologs regulate motor function for different aspects of the bacterial lifestyle. We used subtomogram averaging to image binding of the CheY family protein CleD to the cytoplasmic Cring switch complex, the control center of the flagellar motor. This unambiguously confirmed the orientation of the motor switch protein FliM and the binding of a member of the CheY protein family to the outside rim of the C ring. We also uncovered previously unknown structural elaborations of the alphaproteobacterial flagellar motor, including two novel periplasmic ring structures, and the stator ring harboring eleven stator units, adding to our growing catalog of bacterial flagellar diversity.     

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.     

Sodium-dependent dynamic assembly of membrane complexes in sodium-driven flagellar motors

The bacterial flagellar motor is driven by the electrochemical potential of specific ions, H⁺ or Na⁺. The motor consists of a rotor and stator, and their interaction generates rotation. The stator, which is composed of PomA and PomB in the Na⁺ motor of Vibrio alginolyticus , is thought to be a torque generator converting the energy of ion flux into mechanical power. We found that specific mutations in PomB, including D24N, F33C and S248F, which caused motility defects, affected the assembly of stator complexes into the polar flagellar motor using green fluorescent protein-fused stator proteins. D24 of PomB is the predicted Na⁺-binding site. Furthermore, we demonstrated that the coupling ion, Na⁺, is required for stator assembly and that phenamil (an inhibitor of the Na⁺-driven motor) inhibited the assembly. Carbonyl cyanide m -chlorophenylhydrazone, which is a proton ionophore that collapses the sodium motive force in this organism at neutral pH, also inhibited the assembly. Thus we conclude that the process of Na⁺ influx through the channel, including Na⁺ binding, is essential for the assembly of the stator complex to the flagellar motor as well as for torque generation.     

Protein turbines. I: The bacterial flagellar motor.

The bacterial flagellar motor is driven by a flux of ions between the cytoplasm and the periplasmic lumen. Here we show how an electrostatic mechanism can convert this ion flux into a rotary torque. We demonstrate that, with reasonable parameters, the model can reproduce many of the experimental measurements.     

Flagellated ectosymbiotic bacteria propel a eucaryotic cell

A devescovinid flagellate from termites exhibits rapid gliding movements only when in close contact with other cells or with a substrate. Locomotion is powered not by the cell's own flagella nor by its remarkable rotary axostyle, but by the flagella of thousands of rod bacteria which live on its surface. That the ectosymbiotic bacteria actually propel the protozoan was shown by the following: (a) the bacteria, which lie in specialized pockets of the host membrane, bear typical procaryotic flagella on their exposed surface; (b) gliding continues when the devescovinid's own flagella and rotary axostyle are inactivated; (c) agents which inhibit bacterial flagellar motility, but not the protozoan's motile systems, stop gliding movements; (d) isolated vesicles derived from the surface of the devescovinid rotate at speeds dependent on the number of rod bacteria still attached; (e) individual rod bacteria can move independently over the surface of compressed cells; and (f) wave propagation by the flagellar bundles of the ectosymbiotic bacteria is visualized directly by video-enhanced polarization microscopy. Proximity to solid boundaries may be required to align the flagellar bundles of adjacent bacteria in the same direction, and/or to increase their propulsive efficiency (wall effect). This motility-linked symbiosis resembles the association of locomotory spirochetes with the Australian termite flagellate Mixotricha (Cleveland, L. R., and A. V. Grimstone, 1964, Proc. R. Soc. Lond. B Biol. Sci., 159:668-686), except that in our case propulsion is provided by bacterial flagella themselves. Since bacterial flagella rotate, an additional novelty of this system is that the surface bearing the procaryotic rotary motors is turned by the eucaryotic rotary motor within.