Torque and rotation rate of the bacterial flagellar motor.

This paper describes an analysis of microscopic models for the coupling between ion flow and rotation of bacterial flagella. In model I it is assumed that intersecting half-channels exist on the rotor and the stator and that the driving ion is constrained to move together with the intersection site. Model II is based on the assumption that ion flow drives a cycle of conformational transitions in a channel-like stator subunit that are coupled to the motion of the rotor. Analysis of both mechanisms yields closed expressions relating the torque M generated by the flagellar motor to the rotation rate v. Model I (and also, under certain assumptions, model II) accounts for the experimentally observed linear relationship between M and v. The theoretical equations lead to predictions on the relationship between rotation rate and driving force which can be tested experimentally.     

The Na(+)-translocating F(1)F(0) ATP synthase of Propionigenium modestum: mechanochemical insights into the F(0) motor that drives ATP synthesis

The ATP synthase of Propionigenium modestum encloses a rotary motor involved in the production of ATP from ADP and inorganic phosphate utilizing the free energy of an electrochemical Na(+) ion gradient. This enzyme clearly belongs to the family of F(1)F(0) ATP synthases and uses exclusively Na(+) ions as the physiological coupling ion. The motor domain, F(0), comprises subunit a and the b subunit dimer which are part of the stator and the subunit c oligomer acting as part of the rotor. During ATP synthesis, Na(+) translocation through F(0) proceeds from the periplasm via the stator channel (subunit a) onto a Na(+) binding site of the rotor (subunit c). Upon rotation of the subunit c oligomer versus subunit a, the occupied rotor site leaves the interface with the stator and the Na(+) ion can freely dissociate into the cytoplasm. Recent experiments demonstrate that the membrane potential is crucial for ATP synthesis under physiological conditions. These findings support the view that voltage generates torque in F(0), which drives the rotation of the gamma subunit thus liberating tightly bound ATP from the catalytic sites in F(1). We suggest a mechanochemical model for the transduction of transmembrane Na(+)-motive force into rotary torque by the F(0) motor that can account quantitatively for the experimental data.     

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.     

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.     

Sodium‐powered stators of the bacterial flagellar motor can generate torque in the presence of phenamil with mutations near the peptidoglycan‐binding region

The bacterial flagellar motor powers the rotation that propels the swimming bacteria. Rotational torque is generated by harnessing the flow of ions through ion channels known as stators which couple the energy from the ion gradient across the inner membrane to rotation of the rotor. Here, we used error‐prone PCR to introduce single point mutations into the sodium‐powered Vibrio alginolyticus/Escherichia coli chimeric stator PotB and selected for motors that exhibited motility in the presence of the sodium‐channel inhibitor phenamil. We found single mutations that enable motility under phenamil occurred at two sites: (i) the transmembrane domain of PotB, corresponding to the TM region of the PomB stator from V. alginolyticus and (ii) near the peptidoglycan binding region that corresponds to the C‐terminal region of the MotB stator from E. coli. Single cell rotation assays confirmed that individual flagellar motors could rotate in up to 100 µM phenamil. Using phylogenetic logistic regression, we found correlation between natural residue variation and ion source at positions corresponding to PotB F22Y, but not at other sites. Our results demonstrate that it is not only the pore region of the stator that moderates motility in the presence of ion‐channel blockers.     

Forced rotation of Na+-driven flagellar motor in a coupling ion-free environment

Rotational characteristics of Na+-driven flagellar motor in the presence and absence of coupling ion were analyzed by electrorotation method. The motor rotated spontaneously in the presence of Na+, and the rotation accelerated or decelerated following the direction of the applied external torque. The spontaneous motor rotation was inhibited by removal of external Na+, however, the motor could be forcibly rotated by relatively small external torque applied by the electrorotation apparatus. The observed characteristic of the motor was completely different from that of ATP-driven motor systems, which form rigor bond when their energy source, ATP, is absent. The internal resistance of the flagellar motor increased significantly when the coupling ion could not access the inside of the motor, suggesting that the interaction between the rotor and the stator is changed by the binding of the coupling ion to the internal sites of the motor.     

Serine 26 in the PomB Subunit of the Flagellar Motor Is Essential for Hypermotility of Vibrio cholerae

Vibrio cholerae is motile by means of its single polar flagellum which is driven by the sodium-motive force. In the motor driving rotation of the flagellar filament, a stator complex consisting of subunits PomA and PomB converts the electrochemical sodium ion gradient into torque. Charged or polar residues within the membrane part of PomB could act as ligands for Na⁺, or stabilize a hydrogen bond network by interacting with water within the putative channel between PomA and PomB. By analyzing a large data set of individual tracks of swimming cells, we show that S26 located within the transmembrane helix of PomB is required to promote very fast swimming of V. cholerae. Loss of hypermotility was observed with the S26T variant of PomB at pH 7.0, but fast swimming was restored by decreasing the H⁺ concentration of the external medium. Our study identifies S26 as a second important residue besides D23 in the PomB channel. It is proposed that S26, together with D23 located in close proximity, is important to perturb the hydration shell of Na⁺ before its passage through a constriction within the stator channel.     

Mutations targeting the C-terminal domain of FliG can disrupt motor assembly in the Na(+)-driven flagella of Vibrio alginolyticus

The torque of the bacterial flagellar motor is generated by the rotor-stator interaction coupled with specific ion translocation through the stator channel. To produce a fully functional motor, multiple stator units must be properly incorporated around the rotor by an as yet unknown mechanism to engage the rotor-stator interactions. Here, we investigated stator assembly using a mutational approach of the Na⁺-driven polar flagellar motor of Vibrio alginolyticus, whose stator is localized at the flagellated cell pole. We mutated a rotor protein, FliG, which is located at the C ring of the basal body and closely participates in torque generation, and found that point mutation L259Q, L270R or L271P completely abolishes both motility and polar localization of the stator without affecting flagellation. Likewise, mutations V274E and L279P severely affected motility and stator assembly. Those residues are localized at the core of the globular C-terminal domain of FliG when mapped onto the crystal structure of FliG from Thermotoga maritima, which suggests that those mutations induce quite large structural alterations at the interface responsible for the rotor-stator interaction. These results show that the C-terminal domain of FliG is critical for the proper assembly of PomA/PomB stator complexes around the rotor and probably functions as the target of the stator at the rotor side.     

Forced rotation of Na-driven flagellar motor in a coupling ion-free environment

Rotational characteristics of Na⁺-driven flagellar motor in the presence and absence of coupling ion were analyzed by electrorotation method. The motor rotated spontaneously in the presence of Na⁺, and the rotation accelerated or decelerated following the direction of the applied external torque. The spontaneous motor rotation was inhibited by removal of external Na⁺, however, the motor could be forcibly rotated by relatively small external torque applied by the electrorotation apparatus. The observed characteristic of the motor was completely different from that of ATP-driven motor systems, which form rigor bond when their energy source, ATP, is absent. The internal resistance of the flagellar motor increased significantly when the coupling ion could not access the inside of the motor, suggesting that the interaction between the rotor and the stator is changed by the binding of the coupling ion to the internal sites of the motor.     

Inter-subunit rotation and elastic power transmission in F0F1-ATPase

ATP synthase (F-ATPase) produces ATP at the expense of ion-motive force or vice versa. It is composed from two motor/generators, the ATPase (F1) and the ion translocator (F0), which both are rotary steppers. They are mechanically coupled by 360 degrees rotary motion of subunits against each other. The rotor, subunits gamma(epsilon)C10-14, moves against the stator, (alphabeta)3delta(ab2). The enzyme copes with symmetry mismatch (C3 versus C10-14) between its two motors, and it operates robustly in chimeric constructs or with drastically modified subunits. We scrutinized whether an elastic power transmission accounts for these properties. We used the curvature of fluorescent actin filaments, attached to the rotating c ring, as a spring balance (flexural rigidity of 8.10(-26) N x m2) to gauge the angular profile of the output torque at F0 during ATP hydrolysis by F1. The large average output torque (56 pN nm) proved the absence of any slip. Angular variations of the torque were small, so that the output free energy of the loaded enzyme decayed almost linearly over the angular reaction coordinate. Considering the three-fold stepping and high activation barrier (>40 kJ/mol) of the driving motor (F1) itself, the rather constant output torque seen by F0 implied a soft elastic power transmission between F1 and F0. It is considered as essential, not only for the robust operation of this ubiquitous enzyme under symmetry mismatch, but also for a high turnover rate under load of the two counteracting and stepping motors/generators.     

Structure of the flagellar motor protein complex PomAB: implications for the torque-generating conformation

The bacterial flagellar motor is driven by an ion flux through a channel called MotAB in Escherichia coli or Salmonella and PomAB in Vibrio alginolyticus. PomAB is composed of two transmembrane (TM) components, PomA and PomB, and converts a sodium ion flux to rotation of the flagellum. Its homolog, MotAB, utilizes protons instead of sodium ions. PomB/MotB has a peptidoglycan (PG)-binding motif in the periplasmic domain, allowing it to function as the stator by being anchored to the PG layer. To generate torque, PomAB/MotAB is thought to undergo a conformational change triggered by the ion flux and to interact directly with FliG, a component of the rotor. Here, we present the first three-dimensional structure of this torque-generating stator unit analyzed by electron microscopy. The structure of PomAB revealed two arm domains, which contain the PG-binding site, connected to a large base made of the TM and cytoplasmic domains. The arms lean downward to the membrane surface, likely representing a "plugged" conformation, which would prevent ions leaking through the channel. We propose a model for how PomAB units are placed around the flagellar basal body to function as torque generators.     

Load‐sensitive coupling of proton translocation and torque generation in the bacterial flagellar motor

The Salmonella flagellar motor consists of a rotor and about a dozen stator elements. Each stator element, consisting of MotA and MotB, acts as a proton channel to couple proton flow with torque generation. A highly conserved Asp33 residue of MotB is directly involved in the energy coupling mechanism, but it remains unknown how it carries out this function. Here, we show that the MotB(D33E) mutation dramatically alters motor performance in response to changes in external load. Rotation speeds of the MotA/B(D33E) and MotA(V35F)/B(D33E) motors were markedly slower than the wild‐type motor and fluctuated considerably at low load but not at high load, whereas the rotation rate of the wild‐type motor was stable at any load. At low load, pausing events were frequently observed in both mutant motors. The proton conductivities of these mutant stator channels in their ‘unplugged’ forms were only half of the conductivity of the wild‐type channel. These results suggest that the D33E mutation induces a load‐dependent inactivation of the MotA/B complex. We propose that the stator element is a load‐sensitive proton channel that efficiently couples proton translocation with torque generation and that Asp33 of MotB is critical for this co‐ordinated proton translocation.     

Torque-speed relationships of Na+-driven chimeric flagellar motors in Escherichia coli

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 ∼ 2200 pN nm) from stall up to a “knee” speed of ∼ 420 Hz, and then falls linearly with speed, extrapolating to zero torque at ∼ 910 Hz. Motors containing one to five stators generated ∼ 200 pN nm per stator at speeds up to ∼ 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 ∼ 400 Hz. The torque at low speed was unchanged by mutation R88A but was reduced to ∼ 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.     

Function of Protonatable Residues in the Flagellar Motor of Escherichia coli: a Critical Role for Asp 32 of MotB

Rotation of the bacterial flagellar motor is powered by a transmembrane gradient of protons or, in some species, sodium ions. The molecular mechanism of coupling between ion flow and motor rotation is not understood. The proteins most closely involved in motor rotation are MotA, MotB, and FliG. MotA and MotB are transmembrane proteins that function in transmembrane proton conduction and that are believed to form the stator. FliG is a soluble protein located on the cytoplasmic face of the rotor. Two other proteins, FliM and FliN, are known to bind to FliG and have also been suggested to be involved to some extent in torque generation. Proton (or sodium)-binding sites in the motor are likely to be important to its function and might be formed from the side chains of acidic residues. To investigate the role of acidic residues in the function of the flagellar motor, we mutated each of the conserved acidic residues in the five proteins that have been suggested to be involved in torque generation and measured the effects on motility. None of the conserved acidic residues of MotA, FliG, FliM, or FliN proved essential for torque generation. An acidic residue at position 32 of MotB did prove essential. Of 15 different substitutions studied at this position, only the conservative-replacement D32E mutant retained any function. Previous studies, together with additional data presented here, indicate that the proteins involved in motor rotation do not contain any conserved basic residues that are critical for motor rotation per se. We propose that Asp 32 of MotB functions as a proton-binding site in the bacterial flagellar motor and that no other conserved, protonatable residues function in this capacity.     

Second-chance signal transduction explains cooperative flagellar switching

The reversal of flagellar motion (switching) results from the interaction between a switch complex of the flagellar rotor and a torque-generating stationary unit, or stator (motor unit). To explain the steeply cooperative ligand-induced switching, present models propose allosteric interactions between subunits of the rotor, but do not address the possibility of a reaction that stimulates a bidirectional motor unit to reverse direction of torque. During flagellar motion, the binding of a ligand-bound switch complex at the dwell site could excite a motor unit. The probability that another switch complex of the rotor, moving according to steady-state rotation, will reach the same dwell site before that motor unit returns to ground state will be determined by the independent decay rate of the excited-state motor unit. Here, we derive an analytical expression for the energy coupling between a switch complex and a motor unit of the stator complex of a flagellum, and demonstrate that this model accounts for the cooperative switching response without the need for allosteric interactions. The analytical result can be reproduced by simulation when (1) the motion of the rotor delivers a subsequent ligand-bound switch to the excited motor unit, thereby providing the excited motor unit with a second chance to remain excited, and (2) the outputs from multiple independent motor units are constrained to a single all-or-none event. In this proposed model, a motor unit and switch complex represent the components of a mathematically defined signal transduction mechanism in which energy coupling is driven by steady-state and is regulated by stochastic ligand binding. Mathematical derivation of the model shows the analytical function to be a general form of the Hill equation (Hill AV (1910) The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 40: iv-vii).     

Characterization of PomA mutants defective in the functional assembly of the Na(+)-driven flagellar motor in Vibrio alginolyticus

The polar flagellar motor of Vibrio alginolyticus rotates using Na(+) influx through the stator, which is composed of 2 subunits, PomA and PomB. About a dozen stators dynamically assemble around the rotor, depending on the Na(+) concentration in the surrounding environment. The motor torque is generated by the interaction between the cytoplasmic domain of PomA and the C-terminal region of FliG, a component of the rotor. We had shown previously that mutations of FliG affected the stator assembly around the rotor, which suggested that the PomA-FliG interaction is required for the assembly. In this study, we examined the effects of various mutations mainly in the cytoplasmic domain of PomA on that assembly. All mutant stators examined, which resulted in the loss of motor function, assembled at a lower level than did the wild-type PomA. A His tag pulldown assay showed that some mutations in PomA reduced the PomA-PomB interaction, but other mutations did not. Next, we examined the ion conductivity of the mutants using a mutant stator that lacks the plug domain, PomA/PomB(ΔL)(Δ41-120), which impairs cell growth by overproduction, presumably because a large amount of Na(+) is conducted into the cells. Some PomA mutations suppressed this growth inhibition, suggesting that such mutations reduce Na(+) conductivity, so that the stators could not assemble around the rotor. Only the mutation H136Y did not impair the stator formation and ion conductivity through the stator. We speculate that this particular mutation may affect the PomA-FliG interaction and prevent activation of the stator assembly around the rotor.     

None of the Rotor Residues of F1-ATPase Are Essential for Torque Generation

F₁-ATPase is a powerful rotary molecular motor that can rotate an object several hundred times as large as the motor itself against the viscous friction of water. Forced reverse rotation has been shown to lead to ATP synthesis, implying that the mechanical work against the motor’s high torque can be converted into the chemical energy of ATP. The minimal composition of the motor protein is α₃β₃γ subunits, where the central rotor subunit γ turns inside a stator cylinder made of alternately arranged α₃β₃ subunits using the energy derived from ATP hydrolysis. The rotor consists of an axle, a coiled coil of the amino- and carboxyl-terminal α-helices of γ, which deeply penetrates the stator cylinder, and a globular protrusion that juts out from the stator. Previous work has shown that, for a thermophilic F₁, significant portions of the axle can be truncated and the motor still rotates a submicron sized bead duplex, indicating generation of up to half the wild-type (WT) torque. Here, we inquire if any specific interactions between the stator and the rest of the rotor are needed for the generation of a sizable torque. We truncated the protruding portion of the rotor and replaced part of the remaining axle residues such that every residue of the rotor has been deleted or replaced in this or previous truncation mutants. This protrusionless construct showed an unloaded rotary speed about a quarter of the WT, and generated one-third to one-half of the WT torque. No residue-specific interactions are needed for this much performance. F₁ is so designed that the basic rotor-stator interactions for torque generation and control of catalysis rely solely upon the shape and size of the rotor at very low resolution. Additional tailored interactions augment the torque to allow ATP synthesis under physiological conditions.     

Voltage-generated torque drives the motor of the ATP synthase.

The mechanism by which ion-flux through the membrane-bound motor module (F0) induces rotational torque, driving the rotation of the gamma subunit, was probed with a Na+-translocating hybrid ATP synthase. The ATP-dependent occlusion of 1 (22)Na+ per ATP synthase persisted after modification of the c subunit ring with dicyclohexylcarbodiimide (DCCD), when 22Na+ was added first and ATP second, but not if the order of addition was reversed. These results support the model of ATP-driven rotation of the c subunit oligomer (rotor) versus subunit a (stator) that stops when either a 22Na+-loaded or a DCCD-modified rotor subunit reaches the Na+-impermeable stator. The ATP synthase with a Na+-permeable stator catalyzed 22Na+out/Na+in-exchange after reconstitution into proteoliposomes, which was not significantly affected by DCCD modification of the c subunit oligomer, but was abolished by the additional presence of ATP or by a membrane potential (DeltaPsi) of 90 mV. We propose that in the idling mode of the motor, Na+ ions are shuttled across the membrane by limited back and forth movements of the rotor against the stator. This motional flexibility is arrested if either ATP or DeltaPsi induces the switch from idling into a directed rotation. The Propionigenium modestum ATP synthase catalyzed ATP formation with DeltaPsi of 60-125 mV but not with DeltapNa+ of 195 mV. These results demonstrate that electric forces are essential for ATP synthesis and lead to a new concept of rotary-torque generation in the ATP synthase motor.     

Direct observation of speed fluctuations of flagellar motor rotation at extremely low load close to zero

The bacterial flagellar motor accommodates ten stator units around the rotor to produce large torque at high load. But when external load is low, some previous studies showed that a single stator unit can spin the rotor at the maximum speed, suggesting that the maximum speed does not depend on the number of active stator units, whereas others reported that the speed is also dependent on the stator number. To clarify these two controversial observations, much more precise measurements of motor rotation would be required at external load as close to zero as possible. Here, we constructed a Salmonella filament-less mutant that produces a rigid, straight, twice longer hook to efficiently label a 60 nm gold particle and analyzed flagellar motor dynamics at low load close to zero. The maximum motor speed was about 400 Hz. Large speed fluctuations and long pausing events were frequently observed, and they were suppressed by either over-expression of the MotAB stator complex or increase in the external load, suggesting that the number of active stator units in the motor largely fluctuates near zero load. We conclude that the lifetime of the active stator unit becomes much shorter when the motor operates near zero load.