Helix rotation model of the flagellar rotary motor

A new model of the flagellar motor is proposed that is based on established dynamics of the KcsA potassium ion channel and on known genetic, biochemical, and biophysical facts, which accounts for the mechanics of torque generation, force transmission, and reversals of motor rotation. It predicts that proton (or in some species sodium ion) flow generates short, reversible helix rotations of the MotA-MotB channel complex (the stator) that are transmitted by Coulomb forces to the FliG segments at the rotor surface. Channels are arranged as symmetric pairs, S and T, that swing back and forth in synchrony. S and T alternate in attaching to the rotor, so that force transmission proceeds in steps. The sense of motor rotation can be readily reversed by conformationally switching the position of charged groups on the rotor so that they interact with the stator during the reverse rather than forward strokes. An elastic device accounts for the observed smoothness of rotation and a prolonged attachment of the torque generators to the rotor, i.e., a high duty ratio of each torque-generating unit.     

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.     

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.     

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.     

Prototype of simulation models for epizootics in domestic animals

Based on the Reed-Frost model (Model I), the authors conducted computer simulation of an epizootic model (Model II) constructed on the assumption that any infected animal in a group, after a given time-period of infectivity, would be removed from the group at the beginning of the next time-period. Models I and II were simulated 100 times for each of the different conditions, viz. the initial size of group, 100 and 1,000, the five steps of contact rate or contact size, and the five more steps of contact rate for the group of 1,000 animals in Model I. From the results obtained, it is believed that as a constant parameter, contact size may be preferably used instead of contact rate in these models. Model II mostly gave higher morbidities than Model I, and earlier termination of epizootics, except the simulation with the smallest contact size. This fact may be due to the effect of herd immunity involved only in Model I. The long duration of epizootic was demonstrated in two of the 100 simulations of Model II with 1,000 individuals and contact size 1. This is characteristic of probabilistic models which are really instructive to studying the flow of epizootic.     

Coupling of proton flow and rotation in the bacterial flagellar motor: stochastic simulation of a microscopic model

Summary The rotatory motor of bacterial flagella is driven by a transmembrane electrochemical gradient of protons. A model of the flagellar motor is analysed, which is based on the notion that protons passing through the motor use a channel-like pathway formed by ligand groups located partly on the rotor, partly on the stator. Proton translocation is linked to the displacement of stator elements which are elastically bound to the cell wall. The model is described by a cyclic sequence of translocation steps and proton binding and release reactions. Stochastic simulations of the model are carried out in which transitions between the states of the reaction cycle are treated as random events. In this way the rotation frequency can be predicted as a function of experimental variables such as driving force and viscous load. Furthermore, the effects of microscopic parameters such as the transition frequencies of stator elements and the force constant of elastic coupling on the dynamic properties of the motor can be studied. The model allows for intrinsic uncoupling (“slippage”) resulting from translocation steps without associated rotational movement. It is shown that mechanistic information can be obtained by studying random fluctuations of rotational speed. Offprint requests to: P. Lauger     

Roles of charged residues of rotor and stator in flagellar rotation: comparative study using H+-driven and Na+-driven motors in Escherichia coli

In Escherichia coli, rotation of the flagellar motor has been shown to depend upon electrostatic interactions between charged residues of the stator protein MotA and the rotor protein FliG. These charged residues are conserved in the Na+-driven polar flagellum of Vibrio alginolyticus, but mutational studies in V. alginolyticus suggested that they are relatively unimportant for motor rotation. The electrostatic interactions detected in E. coli therefore might not be a general feature of flagellar motors, or, alternatively, the V. alginolyticus motor might rely on similar interactions but incorporate additional features that make it more robust against mutation. Here, we have carried out a comparative study of chimeric motors that were resident in E. coli but engineered to use V. alginolyticus stator components, rotor components, or both. Charged residues in the V. alginolyticus rotor and stator proteins were found to be essential for motor rotation when the proteins functioned in the setting of the E. coli motor. Patterns of synergism and suppression in rotor/stator double mutants indicate that the V. alginolyticus proteins interact in essentially the same way as their counterparts in E. coli. The robustness of the rotor-stator interface in V. alginolyticus is in part due to the presence of additional charged residues in PomA but appears mainly due to other factors, because an E. coli motor using both rotor and stator components from V. alginolyticus remained sensitive to mutation. Motor function in V. alginolyticus may be enhanced by the proteins MotX and MotY.     

Roles of charged residues in the C-terminal region of PomA, a stator component of the Na+-driven flagellar motor

Bacterial flagellar motors use specific ion gradients to drive their rotation. It has been suggested that the electrostatic interactions between charged residues of the stator and rotor proteins are important for rotation in Escherichia coli. Mutational studies have indicated that the Na(+)-driven motor of Vibrio alginolyticus may incorporate interactions similar to those of the E. coli motor, but the other electrostatic interactions between the rotor and stator proteins may occur in the Na(+)-driven motor. Thus, we investigated the C-terminal charged residues of the stator protein, PomA, in the Na(+)-driven motor. Three of eight charge-reversing mutations, PomA(K203E), PomA(R215E), and PomA(D220K), did not confer motility either with the motor of V. alginolyticus or with the Na(+)-driven chimeric motor of E. coli. Overproduction of the R215E and D220K mutant proteins but not overproduction of the K203E mutant protein impaired the motility of wild-type V. alginolyticus. The R207E mutant conferred motility with the motor of V. alginolyticus but not with the chimeric motor of E. coli. The motility with the E211K and R232E mutants was similar to that with wild-type PomA in V. alginolyticus but was greatly reduced in E. coli. Suppressor analysis suggested that R215 may participate in PomA-PomA interactions or PomA intramolecular interactions to form the stator complex.     

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.     

F-ATPase: forced full rotation of the rotor despite covalent cross-link with the stator

In ATP synthase (F(O)F(1)-ATPase) ion flow through the membrane-intrinsic portion, F(O), drives the central "rotor", subunits c(10)epsilongamma, relative to the "stator" ab(2)delta(alphabeta)(3). This converts ADP and P(i) into ATP. Vice versa, ATP hydrolysis drives the rotation backwards. Covalent cross-links between rotor and stator subunits have been shown to inhibit these activities. Aiming at the rotary compliance of subunit gamma we introduced disulfide bridges between gamma (rotor) and alpha or beta (stator). We engineered cysteine residues into positions located roughly at the "top," "center," and "bottom" parts of the coiled-coil portion of gamma and suitable residues on alpha or beta. This part of gamma is located at the center of the (alphabeta)(3) domain with its C-terminal part at the top of F(1) and the bottom part close to the F(O) complex. Disulfide bridge formation under oxidizing conditions was quantitative as shown by SDS-polyacrylamide gel electrophoresis and immunoblotting. As expected both the ATPase activities and the yield of rotating subunits gamma dropped to zero when the cross-link was formed at the center (gammaL262C <--> alphaA334C) and bottom (gammaCys(87) <--> betaD380C) positions. But much to our surprise disulfide bridging impaired neither ATP hydrolysis activity nor the full rotation of gamma and the enzyme-generated torque of oxidized F(1), which had been engineered at the top position (gammaA285C <--> alphaP280C). Apparently the high torque of this rotary engine uncoiled the alpha-helix and forced amino acids at the C-terminal portion of gamma into full rotation around their dihedral (Ramachandran) angles. This conclusion was supported by molecular dynamics simulations: If gammaCys(285)-Val(286) are attached covalently to (alphabeta)(3) and gammaAla(1)-Ser(281) is forced to rotate, gammaGly(282)-Ala(284) can serve as cardan shaft.     

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.     

Rotation of a complex of the gamma subunit and c ring of Escherichia coli ATP synthase. The rotor and stator are interchangeable

ATP synthase (F0F1) transforms an electrochemical proton gradient into chemical energy (ATP) through the rotation of a subunit assembly. It has been suggested that a complex of the gamma subunit and c ring (c(10-14)) of F0F1 could rotate together during ATP hydrolysis and synthesis (Sambongi, Y., Iko, Y., Tanabe, M., Omote, H., Iwamoto-Kihara, A., Ueda, I., Yanagida, T., Wada, Y., and Futai, M. (1999) Science 286, 1722-1724). We observed that the rotation of the c ring with the cI28T mutation (c subunit cIle-28 replaced by Thr) was less sensitive to venturicidin than that of the wild type, consistent with the antibiotic effect on the cI28T mutant and wild-type ATPase activities (Fillingame, R. H., Oldenburg, M., and Fraga, D. (1991) J. Biol. Chem. 266, 20934-20939). Furthermore, we engineered F0F1 to see the alpha(3)beta(3) hexamer rotation; a biotin tag was introduced into the alpha or beta subunit, and a His tag was introduced into the c subunit. The engineered enzymes could be purified by metal affinity chromatography and density gradient centrifugation. They were immobilized on a glass surface through the c subunit, and an actin filament was connected to the alpha or beta subunit. The filament rotated upon the addition of ATP and generated essentially the same frictional torque as one connected to the c ring. These results indicate that the gammaepsilonc(10-14) complex is a mechanical unit of the enzyme and that it can be used as a rotor or a stator experimentally, depending on the subunit immobilized.     

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).     

Torque and switching in the bacterial flagellar motor. An electrostatic model.

A model is presented for the rotary motor that drives bacterial flagella, using the electrochemical gradient of protons across the cytoplasmic membrane. The model unifies several concepts present in previous models. Torque is generated by proton-conducting particles around the perimeter of the rotor at the base of the flagellum. Protons in channels formed by these particles interact electrostatically with tilted lines of charges on the rotor, providing "loose coupling" between proton flux and rotation of the flagellum. Computer simulations of the model correctly predict the experimentally observed dynamic properties of the motor. Unlike previous models, the motor presented here may rotate either way for a given direction of the protonmotive force. The direction of rotation only depends on the level of occupancy of the proton channels. This suggests a novel and simple mechanism for the switching between clockwise and counterclockwise rotation that is the basis of bacterial chemotaxis.     

A rotary nano ion pump: a molecular dynamics study

The dynamics of a rotary nano ion pump, inspired by the F (0) part of the F(0)F(1)-ATP synthase biomolecular motor, were investigated. This nanopump is composed of a rotor, which is constructed of two carbon nanotubes with benzene rings, and a stator, which is made of six graphene sheets. The molecular dynamics (MD) method was used to simulate the dynamics of the ion nanopump. When the rotor of the nanopump rotates mechanically, an ion gradient will be generated between the two sides of the nanopump. It is shown that the ion gradient generated by the nanopump is dependant on parameters such as the rotary frequency of the rotor, temperature and the amounts and locations of the positive and negative charges of the stator part of the nanopump. Also, an electrical potential difference is generated between the two sides of the pump as a result of its operation.     

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.     

FRET reveals changes in the F1-stator stalk interaction during activity of F1F0-ATP synthase

A stator is proposed as necessary to prevent futile rotation of the F(1) catalytic sector of mitochondrial ATP synthase (mtATPase) during periods of ATP synthesis or ATP hydrolysis. Although the second stalk of mtATPase is generally believed to fulfil the role of a stator capable of withstanding the stress produced by rotation of the central rotor, there is little evidence to directly support this view. We show that interaction between two candidate proteins of the second stalk, OSCP and subunit b, fused at their C-termini to GFP variants and assembled into functional mtATPase can be monitored in mitochondria using fluorescence resonance energy transfer (FRET). Substitution of native OSCP with a variant containing a glycine 166 to asparagine (G166N) substitution yielded a metastable complex. In contrast to the enzyme containing native OSCP, FRET could be irreversibly lowered for the enzyme containing G166N at a rate that correlated closely with the rate of enzyme activity (ATP hydrolysis). The non-hydrolysable ATP analogue, AMP-PCP did not have this effect. We conclude that two candidate proteins of the stator stalk, OSCP and b, are subject to stresses during enzyme catalytic activity commensurate with their role as a part of a stator stalk.     

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.     

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.