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.     

Study of the torque of the bacterial flagellar motor using a rotating electric field.

Bacterial flagella are driven by a rotary motor that is energized by an electrochemical ion gradient across the cell membrane. In this study the torque generated by the flagellar motor was measured in tethered cells of a smooth-swimming Escherichia coli strain by using rotating electric fields to determine the relationship between the torque and speed over a wide range. By measuring the electric current applied to the sample cell and combining the data obtained at different viscosities, the torque of the flagellar motor was estimated up to 55 Hz, and also at negative rotation rates. By this method we have found that the torque of the flagellar motor linearly decreases with rotation rate from negative through positive rate of rotation. In addition, the dependence of torque upon temperature was also investigated. We showed that torque at the high speeds encountered in swimming cells had a much steeper dependence on temperature that at the low speeds encountered in tethered cells. From these results, the activation energy of the proton transfer reaction in the torque-generating unit was calculated to be about 7.0 x 10(-20) J.     

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.     

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.     

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.     

Function of Proline Residues of MotA in Torque Generation by the Flagellar Motor of Escherichia coli

Bacterial flagellar motors obtain energy for rotation from the membrane gradient of protons or, in some species, sodium ions. The molecular mechanism of flagellar rotation is not understood. MotA and MotB are integral membrane proteins that function in proton conduction and are believed to form the stator of the motor. Previous mutational studies identified two conserved proline residues in MotA (Pro 173 and Pro 222 in the protein from Escherichia coli) and a conserved aspartic acid residue in MotB (Asp 32) that are important for function. Asp 32 of MotB probably forms part of the proton path through the motor. To learn more about the roles of the conserved proline residues of MotA, we examined motor function in Pro 173 and Pro 222 mutants, making measurements of torque at high load, speed at low and intermediate loads, and solvent-isotope effects (D2O versus H2O). Proton conduction by wild-type and mutant MotA-MotB channels was also assayed, by a growth defect that occurs upon overexpression. Several different mutations of Pro 173 reduced the torque of the motor under high load, and a few prevented motor rotation but still allowed proton flow through the MotA-MotB channels. These and other properties of the mutants suggest that Pro 173 has a pivotal role in coupling proton flow to motor rotation and is positioned in the channel near Asp 32 of MotB. Replacements of Pro 222 abolished function in all assays and were strongly dominant. Certain Pro 222 mutant proteins prevented swimming almost completely when expressed at moderate levels in wild-type cells. This dominance might be caused by rotor-stator jamming, because it was weaker when FliG carried a mutation believed to increase rotor-stator clearance. We propose a mechanism for torque generation, in which specific functions are suggested for the proline residues of MotA and Asp32 of MotB.     

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.     

A rotary molecular motor that can work at near 100% efficiency

A single molecule of F1-ATPase is by itself a rotary motor in which a central gamma-subunit rotates against a surrounding cylinder made of alpha3beta3-subunits. Driven by the three betas that sequentially hydrolyse ATP, the motor rotates in discrete 120 degree steps, as demonstrated in video images of the movement of an actin filament bound, as a marker, to the central gamma-subunit. Over a broad range of load (hydrodynamic friction against the rotating actin filament) and speed, the F1 motor produces a constant torque of ca. 40 pN nm. The work done in a 120 degree step, or the work per ATP molecule, is thus ca. 80 pN nm. In cells, the free energy of ATP hydrolysis is ca. 90 pN nm per ATP molecule, suggesting that the F1 motor can work at near 100% efficiency. We confirmed in vitro that F1 indeed does ca. 80 pN nm of work under the condition where the free energy per ATP is 90 pN nm. The high efficiency may be related to the fully reversible nature of the F1 motor: the ATP synthase, of which F1 is a part, is considered to synthesize ATP from ADP and phosphate by reverse rotation of the F1 motor. Possible mechanisms of F1 rotation are discussed.     

A slow-motility phenotype caused by substitutions at residue Asp31 in the PomA channel component of a sodium-driven flagellar motor

PomA is thought to be a component of the ion channel in the sodium-driven polar-flagellar motor of Vibrio alginolyticus. We have found that some cysteine substitutions in the periplasmic region of PomA result in a slow-motility phenotype, in which swarming and swimming speeds are reduced even in the presence of high concentrations of NaCl. Most of the mutants showed a sodium ion dependence similar to that of the wild type but with significantly reduced motility at all sodium ion concentrations. By contrast, motility of the D31C mutant showed a sharp dependence on NaCl concentration, with a threshold at 38 mM. The motor of the D31C mutant rotates stably, as monitored by laser dark-field microscopy, suggesting that the mutant PomA protein is assembled normally into the motor complex. Mutational studies of Asp31 suggest that, although this residue is not essential for motor rotation, a negative charge at this position contributes to optimal speed and/or efficiency of the motor.     

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.     

Effect of intracellular pH on rotational speed of bacterial flagellar motors

Weak acids such as acetate and benzoate, which partially collapse the transmembrane proton gradient, not only mediate pH taxis but also impair the motility of Escherichia coli and Salmonella at an external pH of 5.5. In this study, we examined in more detail the effect of weak acids on motility at various external pH values. A change of external pH over the range 5.0 to 7.8 hardly affected the swimming speed of E. coli cells in the absence of 34 mM potassium acetate. In contrast, the cells decreased their swimming speed significantly as external pH was shifted from pH 7.0 to 5.0 in the presence of 34 mM acetate. The total proton motive force of E. coli cells was not changed greatly by the presence of acetate. We measured the rotational rate of tethered E. coli cells as a function of external pH. Rotational speed decreased rapidly as the external pH was decreased, and at pH 5.0, the motor stopped completely. When the external pH was returned to 7.0, the motor restarted rotating at almost its original level, indicating that high intracellular proton (H+) concentration does not irreversibly abolish flagellar motor function. Both the swimming speeds and rotation rates of tethered cells of Salmonella also decreased considerably when the external pH was shifted from pH 7.0 to 5.5 in the presence of 20 mM benzoate. We propose that the increase in the intracellular proton concentration interferes with the release of protons from the torque-generating units, resulting in slowing or stopping of the motors.     

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.     

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.     

Suppressor analysis of the MotB(D33E) mutation to probe bacterial flagellar motor dynamics coupled with proton translocation

MotA and MotB form the stator of the proton-driven bacterial flagellar motor, which conducts protons and couples proton flow with motor rotation. Asp-33 of Salmonella enterica serovar Typhimurium MotB, which is a putative proton-binding site, is critical for torque generation. However, the mechanism of energy coupling remains unknown. Here, we carried out genetic and motility analysis of a slowly motile motB(D33E) mutant and its pseudorevertants. We first confirmed that the poor motility of the motB(D33E) mutant is due to neither protein instability, mislocalization, nor impaired interaction with MotA. We isolated 17 pseudorevertants and identified the suppressor mutations in the transmembrane helices TM2 and TM3 of MotA and in TM and the periplasmic domain of MotB. The stall torque produced by the motB(D33E) mutant motor was about half of the wild-type level, while those for the pseudorevertants were recovered nearly to the wild-type levels. However, the high-speed rotations of the motors under low-load conditions were still significantly impaired, suggesting that the rate of proton translocation is still severely limited at high speed. These results suggest that the second-site mutations recover a torque generation step involving stator-rotor interactions coupled with protonation/deprotonation of Glu-33 but not maximum proton conductivity.     

The chemo-mechanical coupled model for F(1)F(0)-motor

F(1)F(0)-motor (ATP synthase) is the universal enzyme in biological energy conversion that is present in the membranes of mitochondria, chloroplasts and bacteria. It uses the energy of the proton gradient across the membrane to synthesize ATP. Previous theory and model about rotation of the ATP synthase is reviewed, then a novel chemo-mechanical coupled model for rotation of the F(1)F(0)-motor is proposed. In the model, more events are considered simultaneously that includes the movement of F(1), the movement of F(0), reactions at F(1) and reactions at F(0). Using the model, the possible substep modes of the rotation for F(1)F(0) are predicted, the dependence of the motor efficiency and its rotation rate on the rigidity of the γ shaft is investigated. We conclude that the γ shaft has a large rotation rate for a limited driving potential because two ends of the γ shaft can rotate alternately for its flexibility. The flexibility also makes the efficiency of F(1)F(0) drop because elastic twisting deformation power is needed during alternate rotation of the γ shaft at two ends.     

Purine but not pyrimidine nucleotides support rotation of F(1)-ATPase

The binding change model for the F(1)-ATPase predicts that its rotation is intimately correlated with the changes in the affinities of the three catalytic sites for nucleotides. If so, subtle differences in the nucleotide structure may have pronounced effects on rotation. Here we show by single-molecule imaging that purine nucleotides ATP, GTP, and ITP support rotation but pyrimidine nucleotides UTP and CTP do not, suggesting that the extra ring in purine is indispensable for proper operation of this molecular motor. Although the three purine nucleotides were bound to the enzyme at different rates, all showed similar rotational characteristics: counterclockwise rotation, 120 degrees steps each driven by hydrolysis of one nucleotide molecule, occasional back steps, rotary torque of approximately 40 piconewtons (pN).nm, and mechanical work done in a step of approximately 80 pN.nm. These latter characteristics are likely to be determined by the rotational mechanism built in the protein structure, which purine nucleotides can energize. With ATP and GTP, rotation was observed even when the free energy of hydrolysis was -80 pN.nm/molecule, indicating approximately 100% efficiency. Reconstituted F(o)F(1)-ATPase actively translocated protons by hydrolyzing ATP, GTP, and ITP, but CTP and UTP were not even hydrolyzed. Isolated F(1) very slowly hydrolyzed UTP (but not CTP), suggesting possible uncoupling from rotation.     

Switching of the Bacterial Flagellar Motor Near Zero Load

Flagellated bacteria, such as Escherichia coli, are able to swim up gradients of chemical attractants by modulating the direction of rotation of their flagellar motors, which spin alternately clockwise (CW) and counterclockwise (CCW). Chemotactic behavior has been studied under a variety of conditions, mostly at high loads (at large motor torques). Here, we examine motor switching at low loads. Nano-gold spheres of various sizes were attached to hooks (the flexible coupling at the base of the flagellar filament) of cells lacking flagellar filaments in media containing different concentrations of the viscous agent Ficoll. The speeds and directions of rotation of the spheres were measured. Contrary to the case at high loads, motor switching rates increased appreciably with load. Both the CW → CCW and CCW → CW switching rates increased linearly with motor torque. Evidently, the switch senses stator-rotor interactions as well as the CheY-P concentration.     

Real time computer tracking of free-swimming and tethered rotating cells

A computerized image processing system has been developed that tracks individual free-swimming cells and rotating bacterial cell bodies tethered by their flagella in real time. Free-swimming bacteria of Rhodobacter sphaeroides, Rhodospirullum rubrum, and Salmonella typhimurium have been tracked swimming at speeds from 0 to over 120 microns s-1. A high level of discrimination is exerted against noncellular objects, allowing analysis of stopped as well as moving cells. This enabled detection of both speed and qualitative change in the swimming patterns of R. sphaeroides WS8 upon tactic stimulation. Comparison with darkfield microscopy indicated that the two techniques were in substantial agreement. The unidirectional rotation of cells of R. sphaeroides WS8 could be detected when the cells were either parallel to the microscope slide or end on. Frequencies of rotation of up to 10 Hz were monitored before image blurring became a problem. True rods would be easier to analyze at higher speeds of rotation. Although developed for photosynthetic bacteria, a wide range of bacteria, eucaryotic organisms, and subcellular organelles could be tracked with this system. Minor modifications to the software allow customization to different types of motility analysis.     

The effects of altered membrane sterol composition on oxidative phosphorylation in a haem mutant of Saccharomyces cerevisiae

1. The sterol, unsaturated fatty acid and cytochrome contents of cells of a delta-aminolaevulinate synthase mutant of Saccharomyces cerevisiae are manipulated by growing the organism in media containing defined supplements of delta-aminolaevulinate and other porphyrin intermediates. 2. If unsaturated fatty acids are added to the growth medium as Tween 80, sterol content and respiratory cytochromes alone are manipulated. 3. In the presence of delta-aminolaevulinate (10-50mg/1) cells exhibit moderate to high respiratory activity, but growth yields are low, indicating a loss of oxidative phosphorylation. This is associated with the depletion of membrane lipids, either unsaturated fatty acids and sterols together or sterols alone. 4. Sterol depletion leads to the loss of coupled mitochondrial oxidative phosphorylation in vitro. 5. The lesion in oxidative phosphorylation is associated with an increase in the passive permeability of sterol-depleted mitochondria to protons. 6. Arrhenius plots of mitochondrial permeability to protons indicate that the activation energy for proton entry increases as the sterol content of the membranes decreases. 7. Studies on a cytoplasmic petite mutant isolated from strain ole-3, which lacks a functional membrane-bound protein-translocating adenosine triphosphatase, indicate that proton permeability of the petite mitochondria varies as a function of sterol composition in the same way as that of ole-3 grande mitochondria. This indicates that sterols alone are probably directly responsible for the increased proton entry, owing to a reorganization of the lipid in the membrane. 8. Supplemented ole-3 cells with a normal lipid composition and normal or higher than normal respiratory activities have a growth efficiency only 65% of that of the wild-type, indicating that a further lesion in energy metabolism may be present.     

Myosin motor domain lever arm rotation is coupled to ATP hydrolysis

We have investigated coupling of lever arm rotation to the ATP binding and hydrolysis steps for the myosin motor domain. In several current hypotheses of the mechanism of force production by muscle, the primary mechanical feature is the rotation of a lever arm that is a subdomain of the myosin motor domain. In these models, the lever arm rotates while the myosin motor domain is free, and then reverses the rotation to produce force while it is bound to actin. These mechanical steps are coupled to steps in the ATP hydrolysis cycle. Our hypothesis is that ATP hydrolysis induces lever arm rotation to produce a more compact motor domain that has stored mechanical energy. Our approach is to use transient electric birefringence techniques to measure changes in hydrodynamic size that result from lever arm rotation when various ligands are bound to isolated skeletal muscle myosin motor domain in solution. Results for ATP and CTP, which do support force production by muscle fibers, are compared to those of ATPgammaS and GTP, which do not. Measurements are also made of conformational changes when the motor domain is bound to NDP's and PP(i) in the absence and presence of the phosphate analogue orthovanadate, to determine the roles the nucleoside moieties of the nucleotides have on lever arm rotation. The results indicate that for the substrates investigated, rotation does not occur upon substrate binding, but is coupled to the NTP hydrolysis step. The data are consistent with a model in which only substrates that produce a motor domain-NDP-P(i) complex as the steady-state intermediate make the motor domain more compact, and only those substrates support force production.