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Single-proton torque generation of the bacterial flagellar motor
Abstract
Many important physiological processes such as cell migration, biofilm formation, and pathogenicity require an understanding of the mechanism of cell motility. In particular, bacteria such as Escherichia coli propel themselves by means of rotating a set of flagella powered by 40 nm engines that are known as the bacterial flagellar motor. This bacterial flagellar motor, one of the largest and most complex biological rotary motors, is embedded in the cell membrane and exert torque on cells up to about 1000 pN·nm to navigate toward favorable environments in response to chemical gradients. However, despite extensive studies of the structure and the genetics of the bacterial flagellar motor, we lack sufficient understanding of how their torque generating protein components such as a rotor and stators function. Here, we investigate the relationship between the motor speeds and the number of stators involved in torque generation. Our results indicate that a single proton can generate torque required for a discrete angular step in the rotation of the bacterial flagellar motor.
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Three-dimensional particle tracking is a routine experimental procedure for various biophysical applications including magnetic tweezers. A common method for tracking the axial position of particles involves the analysis of diffraction rings whose pattern depends sensitively on the axial position of the bead relative to the focal plane. To infer the axial position, the observed rings are compared with reference images of a bead at known axial positions. Often the precision or accuracy of these algorithms is measured on immobilized beads over a limited axial range, while many experiments are performed using freely mobile beads. This inconsistency raises the possibility of incorrect estimates of experimental uncertainty. By manipulating magnetic beads in a bidirectional magnetic tweezer setup, we evaluated the error associated with tracking mobile magnetic beads and found that the error of tracking a moving magnetic bead increases by almost an order of magnitude compared to the error of tracking a stationary bead. We found that this additional error can be ameliorated by excluding the center-most region of the diffraction ring pattern from tracking analysis. Evaluation of the limitations of a tracking algorithm is essential for understanding the error associated with a measurement. These findings promise to bring increased resolution to three-dimensional bead tracking of magnetic microspheres.
Significance
Many species of bacteria swim using rotating helical propellers called flagella. Flagellar rotary motors obtain energy from the transmembrane gradient of ions (either H ⁺ or Na ⁺ ). Physiological properties of the motor have been studied for more than 40 y and have led to the longstanding view that the motor is tightly coupled, meaning that each revolution is associated with the movement of a fixed number of ions across the membrane. Simulations described here indicate that this may not be the case: A loosely coupled mechanism can explain all of the observations that have been taken to indicate tight coupling, as well as some measurements that are more difficult to account for within the tight-coupling framework.
Significance
Using new experimental methods, we measure the mechanical output of the bacterial flagellar motor, the rotary molecular machine that propels swimming bacteria, while varying both electrical and chemical components of the ion-motive force that drives it. We find that each independent torque-generating stator in the motor passes 37 ± 2 ions per revolution, at odds with previous indications of 26 or 52 ions. Fitting our data to theoretical models reveals the kinetics of the motor mechanism. Our thorough search of the multidimensional parameter space of generalized motor models, guided by experimental data, is an approach that may be widely applicable.
Rotation and switching of the bacterial flagellum depends on a large rotor-mounted protein assembly composed of the proteins FliG, FliM and FliN, with FliG most directly involved in rotation. The crystal structure of a complex between the central domains of FliG and FliM, in conjunction with several biochemical and molecular-genetic experiments, reveals the arrangement of the FliG and FliM proteins in the rotor. A stoichiometric mismatch between FliG (26 subunits) and FliM (34 subunits) is explained in terms of two distinct positions for FliM: one where it binds the FliG central domain and another where it binds the FliG C-terminal domain. This architecture provides a structural framework for addressing the mechanisms of motor rotation and direction switching and for unifying the large body of data on motor performance. Recently proposed alternative models of rotor assembly, based on a subunit contact observed in crystals, are not supported by experiment.
Author Summary
Many species of bacteria swim to find food or to avoid toxins. Swimming motility depends on helical flagella that act as propellers. Each flagellum is driven by a rotary molecular engine–the bacterial flagellar motor–which draws its energy from an ion flux entering the cell. Despite much progress, the detailed mechanisms underlying the motor's extraordinary power output, as well as its near 100% efficiency, have yet to be understood. Surprisingly, recent experiments have shown that, at low speeds, the motor proceeds by small steps (∼26 per rotation), providing new insight into motor operation. Here we show that a simple physical model can quantitatively account for this stepping behavior as well as the motor's near-perfect efficiency and many other known properties of the motor. In our model, torque is generated via protein-springs that pull on the rotor; the steps arise from contact forces between static components of the motor and a 26-fold periodic ring that forms part of the rotor. Our model allows us to explain some curious properties of the motor, including the observation that backward steps are shorter on average than forward steps, and to make novel, experimentally testable predictions on the motor's speed and diffusion properties.
Bacterial flagellar motors rotate, obtaining power from the membrane gradient of protons or, in some species, sodium ions. Torque generation in the flagellar motor must involve interactions between components of the rotor and components of the stator. Sites of interaction between the rotor and stator have not been identified. Mutational studies of the rotor protein FliG and the stator protein MotA showed that both proteins contain charged residues essential for motor rotation. This suggests that functionally important electrostatic interactions might occur between the rotor and stator. To test this proposal, we examined double mutants with charged-residue substitutions in both the rotor protein FliG and the stator protein MotA. Several combinations of FliG mutations with MotA mutations exhibited strong synergism, whereas others showed strong suppression, in a pattern that indicates that the functionally important charged residues of FliG interact with those of MotA. These results identify a functionally important site of interaction between the rotor and stator and suggest a hypothesis for electrostatic interactions at the rotor-stator interface.
The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel many species of swimming bacteria. The rotor is a set of rings up to 45 nm in diameter in the cytoplasmic membrane; the stator contains about ten torque-generating units anchored to the cell wall at the perimeter of the rotor. The free-energy source for the motor is an inward-directed electrochemical gradient of ions across the cytoplasmic membrane, the protonmotive force or sodium-motive force for H+-driven and Na+-driven motors, respectively. Here we demonstrate a stepping motion of a Na+-driven chimaeric flagellar motor in Escherichia coli at low sodium-motive force and with controlled expression of a small number of torque-generating units. We observe 26 steps per revolution, which is consistent with the periodicity of the ring of FliG protein, the proposed site of torque generation on the rotor. Backwards steps despite the absence of the flagellar switching protein CheY indicate a small change in free energy per step, similar to that of a single ion transit.
Many swimming bacteria are propelled by flagellar filaments driven by a rotary motor. Each of these tiny motors can generate an impressive torque. The motor torque vs. speed relationship is considered one of the most important measurable characteristics of the motor and therefore is a major criterion for judging models proposed for the working mechanism. Here we give an explicit explanation for this torque-speed curve. The same physics also can explain certain puzzling properties of other motors.
Torque is generated in the rotary motor at the base of the bacterial flagellum by ion translocating stator units anchored to the peptidoglycan cell wall. Stator units are composed of the proteins MotA and MotB in proton-driven motors, and they are composed of PomA and PomB in sodium-driven motors. Strains of Escherichia coli lacking functional stator proteins produce flagella that do not rotate, and induced expression of the missing proteins leads to restoration of motor rotation in discrete speed increments, a process known as “resurrection.” Early work suggested a maximum of eight units. More recent indications that WT motors may contain more than eight units, based on recovery of disrupted motors, are inconclusive. Here we demonstrate conclusively that the maximum number of units in a motor is at least 11. Using back-focal-plane interferometry of 1-μm polystyrene beads attached to flagella, we observed at least 11 distinct speed increments during resurrection with three different combinations of stator proteins in E. coli. The average torques generated by a single unit and a fully induced motor were lower than previous estimates. Speed increments at high numbers of units are smaller than those at low numbers, indicating that not all units in a fully induced motor are equivalent.
• molecular motors
• single molecules
• MotA
• PomA
• resurrection
Many essential cellular processes are carried out by complex biological machines located in the cell membrane. The bacterial flagellar motor is a large membrane-spanning protein complex that functions as an ion-driven rotary motor to propel cells through liquid media. Within the motor, MotB is a component of the stator that couples ion flow to torque generation and anchors the stator to the cell wall. Here we have investigated the protein stoichiometry, dynamics and turnover of MotB with single-molecule precision in functioning bacterial flagellar motors in Escherichia coli. We monitored motor function by rotation of a tethered cell body, and simultaneously measured the number and dynamics of MotB molecules labelled with green fluorescent protein (GFP-MotB) in the motor by total internal reflection fluorescence microscopy. Counting fluorophores by the stepwise photobleaching of single GFP molecules showed that each motor contains approximately 22 copies of GFP-MotB, consistent with approximately 11 stators each containing two MotB molecules. We also observed a membrane pool of approximately 200 GFP-MotB molecules diffusing at approximately 0.008 microm2 s(-1). Fluorescence recovery after photobleaching and fluorescence loss in photobleaching showed turnover of GFP-MotB between the membrane pool and motor with a rate constant of the order of 0.04 s(-1): the dwell time of a given stator in the motor is only approximately 0.5 min. This is the first direct measurement of the number and rapid turnover of protein subunits within a functioning molecular machine.
We present a three-dimensional tracking routine for nondiffraction-limited particles, which significantly reduces pixel bias. Our technique allows for increased resolution compared to that of previous methods, especially at low magnification or at high signal/noise ratio. This enables tracking with nanometer accuracy in a wide field of view and tracking of many particles. To reduce bias induced by pixelation, the tracking algorithm uses interpolation of the image on a circular grid to determine the x-, y-, and z-positions. We evaluate the proposed algorithm by tracking simulated images and compare it to well-known center-of-mass and cross-correlation methods. The final resolution of the described method improves up to an order of magnitude in three dimensions compared to conventional tracking methods. We show that errors in x,y-tracking can seriously affect z-tracking if interpolation is not used. We validate our results with experimental data obtained for conditions matching those used in the simulations. Finally, we show that the increased performance of the proposed algorithm uniquely enables it to extract accurate data for the persistence length and end-to-end distance of 107 DNA tethers in a single experiment.
The bacterial flagellar motor is a reversible rotary nano-machine, about 45 nm in diameter, embedded in the bacterial cell envelope. It is powered by the flux of H+ or Na+ ions across the cytoplasmic membrane driven by an electrochemical gradient, the proton-motive force or the sodium-motive force. Each motor rotates a helical filament at several hundreds of revolutions per second (hertz). In many species, the motor switches direction stochastically, with the switching rates controlled by a network of sensory and signalling proteins. The bacterial flagellar motor was confirmed as a rotary motor in the early 1970s, the first direct observation of the function of a single molecular motor. However, because of the large size and complexity of the motor, much remains to be discovered, in particular, the structural details of the torque-generating mechanism. This review outlines what has been learned about the structure and function of the motor using a combination of genetics, single-molecule and biophysical techniques, with a focus on recent results and single-molecule techniques.
Paralyzed motors of motA and motB point and deletion mutants of Escherichia coli were repaired by synthesis of wild-type protein.
As found earlier with a point mutant of motB, torque was restored in a series of equally spaced steps. The size of the steps
was the same for both MotA and MotB. Motors with one torque generator spent more time spinning counterclockwise than did motors
with two or more generators. In deletion mutants, stepwise decreases in torque, rare in point mutants, were common. Several
cells stopped accelerating after eight steps, suggesting that the maximum complement of torque generators is eight. Each generator
appears to contain both MotA and MotB.
Mot mutants of Escherichia coli are paralysed: their flagella appear to be intact but do not rotate. The motA and motB gene products are found in the cytoplasmic membrane; they do not co-purify with flagellar basal bodies isolated in neutral detergents. Silverman et al. found that mot mutants could be ' resurrected ' through protein synthesis directed by lambda transducing phages carrying the wild-type genes. Here, we have studied this activation at the level of a single flagellar motor. Cells of a motB strain carrying plasmids in which transcription of the wild-type motB gene was controlled by the lac promoter were tethered to a glass surface by a single flagellum. These cells began to spin within several minutes after the addition of a lac inducer, and their rotational speed changed in a series of equally spaced steps. As many as 7 steps were seen in individual cells and, from the final speeds attained, as many as 16 steps could be inferred. These experiments show that each flagellar motor contains several independent force-generating units comprised, at least in part, of motB protein.
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.
The FliG protein of Escherichia coli is essential for assembly and function of the flagellar motor. Certain mutations in FliG give a non-motile, or Mot-, phenotype, in which flagella are assembled but do not rotate. Mutations with this property are clustered in a C-terminal segment of FliG that is stable when expressed alone, and thus probably constitutes an independently folded domain. Previously, we suggested that this domain forms the rotor portion of the active site for torque generation in the motor. In this work, we have used a mutational approach to identify the amino acid residues in the C-terminal domain of FliG that are most important for motor function. Site-directed mutagenesis was used to replace each of the conserved residues in this domain with alanine, and the effects on motor function were measured. Because charged residues have often been suggested to have important roles in torque generation, conserved charged residues were changed individually and in all pairwise combinations. The results show that three charged residues of FliG, Arg279, Asp286 and Asp287, are directly involved in torque generation. Mutations in these residues cause motility defects that suggest that they function jointly, in an active site whose most important property is a specific arrangement of charges. Two other charged residues, Lys262 and Arg295, may also be involved in torque generation, but are less critical than Arg279, Asp286 or Asp287. Unchanged residues of the FliG motility domain do not appear to have direct roles in torque generation, although some are needed for the stability of the protein or for normal clockwise/ counter-clockwise switching. The Mot- mutations of fliG isolated previously by random mutagenesis do not alter the putative active-site residues, but render the proteins abnormally susceptible to proteolysis, suggesting significantly altered conformations or reduced stabilities.
The technique of electrorotation was used to apply torque to cells of the bacterium Escherichia coli tethered to glass coverslips by single flagella. Cells were made to rotate backward, that is, in the direction opposite to the rotation driven by the flagellar motor itself. The torque generated by the motor under these conditions was estimated using an analysis that explicitly considers the angular dependence of both the viscous drag coefficient of the cell and the torque produced by electrorotation. Motor torque varied approximately linearly with speed up to over 100 Hz in either direction, placing constraints on mechanisms for torque generation in which rates of proton transfer for backward rotation are limiting. These results, interpreted in the context of a simple three-state kinetic model, suggest that the rate-limiting step in the torque-generating cycle is a powerstroke in which motor rotation and dissipation of the energy available from proton transit occur synchronously.
The output of a rotary motor is characterized by its torque and speed. We measured the torque-speed relationship of the flagellar rotary motor of Escherichia coli by a new method. Small latex spheres were attached to flagellar stubs on cells fixed to the surface of a glass slide. The angular speeds of the spheres were monitored in a weak optical trap by back-focal-plane interferometry in solutions containing different concentrations of the viscous agent Ficoll. Plots of relative torque (viscosity x speed) versus speed were obtained over a wide dynamic range (up to speeds of approximately 300 Hz) at three different temperatures, 22.7, 17.7, and 15.8 degrees C. Results obtained earlier by electrorotation (, Biophys. J. 65:2201-2216) were confirmed. The motor operates in two dynamic regimes. At 23 degrees C, the torque is approximately constant up to a knee speed of nearly 200 Hz, and then it falls rapidly with speed to a zero-torque speed of approximately 350 Hz. In the low-speed regime, torque is insensitive to changes in temperature. In the high-speed regime, it decreases markedly at lower temperature. These results are consistent with models in which torque is generated by a powerstroke mechanism (, Biophys. J. 76:580-587).
Rotation of the bacterial flagellar motor is driven by an ensemble of torque-generating units containing the proteins MotA and MotB. Here, by inducing expression of MotA in motA- cells under conditions of low viscous load, we show that the limiting speed of the motor is independent of the number of units: at vanishing load, one unit turns the motor as rapidly as many. This result indicates that each unit may remain attached to the rotor for most of its mechanochemical cycle, that is, that it has a high duty ratio. Thus, torque generators behave more like kinesin, the protein that moves vesicles along microtubules, than myosin, the protein that powers muscle. However, their translation rates, stepping frequencies and power outputs are much higher, being greater than 30 microm s(-1), 12 kHz and 1.5 x 10(5) pN nm s(-1), respectively.
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.
The bacterial flagellum is both a motor organelle and a protein export/assembly apparatus. It extends from the cytoplasm to the cell exterior. All the protein subunits of the external elements have to be exported. Export employs a type III pathway, also utilized for secretion of virulence factors. Six of the components of the export apparatus are integral membrane proteins and are believed to be located within the flagellar basal body. Three others are soluble: the ATPase that drives export, a regulator of the ATPase, and a general chaperone. Exported substrates diffuse down a narrow channel in the growing structure and assemble at the distal end, often with the help of a capping structure.
The FliF ring is the base for self-assembly of the bacterial flagellum and the FliF/FliG ring complex is the core of the rotor of the flagellar motor. We report the structures of these two ring complexes obtained by electron cryomicroscopy and single-particle image analysis at 22A and 25A resolution, respectively. Direct comparison of these structures with the flagellar basal body made by superimposing the density maps on the central section reveals many interesting features, such as how the mechanically stable connection between the ring and the rod is formed, how directly FliF domains are involved in the near axial density of the basal body forming the proximal end of the central channel for a potential gating mechanism, some indication of flexibility in the connection of FliF and FliG, and structural and functional similarities to the head-to-tail connectors of bacteriophages.
Many bacterial species swim using flagella. The flagellar motor couples ion flow across the cytoplasmic membrane to rotation. Ion flow is driven by both a membrane potential (V(m)) and a transmembrane concentration gradient. To investigate their relation to bacterial flagellar motor function we developed a fluorescence technique to measure V(m) in single cells, using the dye tetramethyl rhodamine methyl ester. We used a convolution model to determine the relationship between fluorescence intensity in images of cells and intracellular dye concentration, and calculated V(m) using the ratio of intracellular/extracellular dye concentration. We found V(m) = -140 +/- 14 mV in Escherichia coli at external pH 7.0 (pH(ex)), decreasing to -85 +/- 10 mV at pH(ex) 5.0. We also estimated the sodium-motive force (SMF) by combining single-cell measurements of V(m) and intracellular sodium concentration. We were able to vary the SMF between -187 +/- 15 mV and -53 +/- 15 mV by varying pH(ex) in the range 7.0-5.0 and extracellular sodium concentration in the range 1-85 mM. Rotation rates for 0.35-microm- and 1-microm-diameter beads attached to Na(+)-driven chimeric flagellar motors varied linearly with V(m). For the larger beads, the two components of the SMF were equivalent, whereas for smaller beads at a given SMF, the speed increased with sodium gradient and external sodium concentration.
Flagellated bacteria, such as Escherichia coli, swim by rotating thin helical filaments, each driven at its base by a reversible rotary motor, powered by an ion flux. A motor is about 45 nm in diameter and is assembled from about 20 different kinds of parts. It develops maximum torque at stall but can spin several hundred Hz. Its direction of rotation is controlled by a sensory system that enables cells to accumulate in regions deemed more favorable. We know a great deal about motor structure, genetics, assembly, and function, but we do not really understand how it works. We need more crystal structures. All of this is reviewed, but the emphasis is on function.
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 approximately 2200 pN nm) from stall up to a "knee" speed of approximately 420 Hz, and then falls linearly with speed, extrapolating to zero torque at approximately 910 Hz. Motors containing one to five stators generated approximately 200 pN nm per stator at speeds up to approximately 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 approximately 400 Hz. The torque at low speed was unchanged by mutation R88A but was reduced to approximately 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.
The rotary motor of bacterial flagella
- H C Berg
- HC Berg