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

Questioning rotary functionality in the bacterial flagellar system and proposing a murburn model for motility

Bacterial flagellar system (BFS) was the primary example of a purported 'rotary-motor' functionality in a natural assembly. This mandates the translation of a circular motion of components inside into a linear displacement of the cell body outside, which is supposedly orchestrated with the following features of the BFS: (i) A chemical/electrical differential generates proton motive force (pmf, including a trans-membrane potential, TMP), which is electro-mechanically transduced by inward movement of protons via BFS. (ii) Membrane-bound proteins of BFS serve as stators and the slender filament acts as an external propeller, culminating into a hook-rod that pierces the membrane to connect to a 'broader assembly of deterministically movable rotor'. We had disclaimed the purported pmf/TMP-based respiratory/photosynthetic physiology involving Complex V, which was also perceived as a 'rotary machine' earlier. We pointed out that the murburn redox logic was operative therein. We pursue the following similar perspectives in BFS-context: (i) Low probability for the evolutionary attainment of an ordered/synchronized teaming of about two dozen types of proteins (assembled across five-seven distinct phases) towards the singular agendum of rotary motility. (ii) Vital redox activity (not the gambit of pmf/TMP!) powers the molecular and macroscopic activities of cells, including flagella. (iii) Flagellar movement is noted even in ambiances lacking/countering the directionality mandates sought by pmf/TMP. (iv) Structural features of BFS lack component(s) capable of harnessing/achieving pmf/TMP and functional rotation. A viable murburn model for conversion of molecular/biochemical activity into macroscopic/mechanical outcomes is proposed herein for understanding BFS-assisted motility. HIGHLIGHTSThe motor-like functionalism of bacterial flagellar system (BFS) is analyzedProton/Ion-differential based powering of BFS is unviable in bacteriaUncouplers-sponsored effects were misinterpreted, resulting in a detour in BFS researchThese findings mandate new explanation for nano-bio-mechanical movements in BFSA minimalist murburn model for the bacterial flagella-aided movement is proposedCommunicated by Ramaswamy H. Sarma.

Design principles and optimal performance for molecular motors under realistic constraints

The performance of a molecular motor, characterized by its power output and energy efficiency, is investigated in the motor design space spanned by the stepping rate function and the motor-track interaction potential. Analytic results and simulations show that a gating mechanism that restricts forward stepping in a narrow window in configuration space is needed for generating high power at physiologically relevant loads. By deriving general thermodynamics laws for nonequilibrium motors, we find that the maximum torque (force) at stall is less than its theoretical limit for any realistic motor-track interactions due to speed fluctuations. Our study reveals a tradeoff for the motor-track interaction: while a strong interaction generates a high power output for forward steps, it also leads to a higher probability of wasteful spontaneous back steps. Our analysis and simulations show that this tradeoff sets a fundamental limit to the maximum motor efficiency in the presence of spontaneous back steps, i.e., loose-coupling. Balancing this tradeoff leads to an optimal design of the motor-track interaction for achieving a maximum efficiency close to 1 for realistic motors that are not perfectly coupled with the energy source. Comparison with existing data and suggestions for future experiments are discussed.

Measurements of the Rotation of the Flagellar Motor by Bead Assay

The bacterial flagellar motor is a reversible rotary nano-machine powered by the ion flux across the cytoplasmic membrane. Each motor rotates a long helical filament that extends from the cell body at several hundreds revolutions per second. The output of the motor is characterized by its generated torque and rotational speed. The torque can be calculated as the rotational frictional drag coefficient multiplied by the angular velocity. Varieties of methods, including a bead assay, have been developed to measure the flagellar rotation rate under various load conditions on the motor. In this chapter, we describe a method to monitor the motor rotation through a position of a 1 μm bead attached to a truncated flagellar filament.

Molecular dynamics simulation of bacterial flagella

The bacterial flagellum is a biological nanomachine for the locomotion of bacteria, and is seen in organisms like Salmonella and Escherichia coli. The flagellum consists of tens of thousands of protein molecules and more than 30 different kinds of proteins. The basal body of the flagellum contains a protein export apparatus and a rotary motor that is powered by ion motive force across the cytoplasmic membrane. The filament functions as a propeller whose helicity is controlled by the direction of the torque. The hook that connects the motor and filament acts as a universal joint, transmitting torque generated by the motor to different directions. This report describes the use of molecular dynamics to study the bacterial flagellum. Molecular dynamics simulation is a powerful method that permits the investigation, at atomic resolution, of the molecular mechanisms of biomolecular systems containing many proteins and solvent. When applied to the flagellum, these studies successfully unveiled the polymorphic supercoiling and transportation mechanism of the filament, the universal joint mechanism of the hook, the ion transfer mechanism of the motor stator, the flexible nature of the transport apparatus proteins, and activation of proteins involved in chemotaxis.

The Limiting Speed of the Bacterial Flagellar Motor

Recent experiments on the bacterial flagellar motor have shown that the structure of this nanomachine, which drives locomotion in a wide range of bacterial species, is more dynamic than previously believed. Specifically, the number of active torque-generating complexes (stators) was shown to vary across applied loads. This finding brings under scrutiny the experimental evidence reporting that limiting (zero-torque) speed is independent of the number of active stators. In this study, we propose that, contrary to previous assumptions, the maximum speed of the motor increases as additional stators are recruited. This result arises from our assumption that stators disengage from the motor for a significant portion of their mechanochemical cycles at low loads. We show that this assumption is consistent with current experimental evidence in chimeric motors, as well as with the requirement that a processive motor driving a large load via an elastic linkage must have a high duty ratio.

Structure of the MotA/B Proton Channel

Flagellar motors utilize the motive force of protons and other ions as an energy source. To elucidate the mechanisms of ion permeation and torque generation, it is essential to investigate the structure of the motor stator complex; however, the atomic structure of the transmembrane region of the stator has not been determined experimentally. We recently constructed an atomic model structure of the transmembrane region of the Escherichia coli MotA/B stator complex based on previously published disulfide cross-linking and tryptophan scanning mutations. Dynamic permeation by hydronium ions, sodium ions, and water molecules was then observed using steered molecular dynamics simulations, and free energy profiles for ion/water permeation were calculated using umbrella sampling. We also examined the possible ratchet motion of the cytoplasmic domain induced by the protonation/deprotonation cycle of the MotB proton binding site, Asp32. In this chapter, we describe the methods used to conduct these analyses, including atomic structure modeling of the transmembrane region of the MotA/B complex; molecular dynamics simulations in equilibrium and in ion permeation processes; and ion permeation-free energy profile calculations.

Gate-controlled proton diffusion and protonation-induced ratchet motion in the stator of the bacterial flagellar motor

The proton permeation process of the stator complex MotA/B in the flagellar motor of Escherichia coli was investigated. The atomic model structure of the transmembrane part of MotA/B was constructed based on the previously published disulfide cross-linking and tryptophan scanning mutations. The dynamic permeation of hydronium/sodium ions and water molecule through the channel formed in MotA/B was observed using a steered molecular dynamics simulation. During the simulation, Leu46 of MotB acts as the gate for hydronium ion permeation, which induced the formation of water wire that may mediate the proton transfer to Asp32 on MotB. Free energy profiles for permeation were calculated by umbrella sampling. The free energy barrier for H3O(+) permeation was consistent with the proton transfer rate deduced from the flagellar rotational speed and number of protons per rotation, which suggests that the gating is the rate-limiting step. Structure and dynamics of the MotA/B with nonprotonated and protonated Asp32, Val43Met, and Val43Leu mutants in MotB were investigated using molecular dynamics simulation. A narrowing of the channel was observed in the mutants, which is consistent with the size-dependent ion selectivity. In MotA/B with the nonprotonated Asp32, the A3 segment in MotA maintained a kink whereas the protonation induced a straighter shape. Assuming that the cytoplasmic domain not included in the atomic model moves as a rigid body, the protonation/deprotonation of Asp32 is inferred to induce a ratchet motion of the cytoplasmic domain, which may be correlated to the motion of the flagellar rotor.

Hybrid-fuel bacterial flagellar motors in Escherichia coli

The bacterial flagellar motor rotates driven by an electrochemical ion gradient across the cytoplasmic membrane, either H(+) or Na(+) ions. The motor consists of a rotor ∼50 nm in diameter surrounded by multiple torque-generating ion-conducting stator units. Stator units exchange spontaneously between the motor and a pool in the cytoplasmic membrane on a timescale of minutes, and their stability in the motor is dependent upon the ion gradient. We report a genetically engineered hybrid-fuel flagellar motor in Escherichia coli that contains both H(+)- and Na(+)-driven stator components and runs on both types of ion gradient. We controlled the number of each type of stator unit in the motor by protein expression levels and Na(+) concentration ([Na(+)]), using speed changes of single motors driving 1-μm polystyrene beads to determine stator unit numbers. De-energized motors changed from locked to freely rotating on a timescale similar to that of spontaneous stator unit exchange. Hybrid motor speed is simply the sum of speeds attributable to individual stator units of each type. With Na(+) and H(+) stator components expressed at high and medium levels, respectively, Na(+) stator units dominate at high [Na(+)] and are replaced by H(+) units when Na(+) is removed. Thus, competition between stator units for spaces in a motor and sensitivity of each type to its own ion gradient combine to allow hybrid motors to adapt to the prevailing ion gradient. We speculate that a similar process may occur in species that naturally express both H(+) and Na(+) stator components sharing a common rotor.

Mechanism and kinetics of a sodium-driven bacterial flagellar motor

The bacterial flagellar motor is a large rotary molecular machine that propels swimming bacteria, powered by a transmembrane electrochemical potential difference. It consists of an ∼50-nm rotor and up to ∼10 independent stators anchored to the cell wall. We measured torque-speed relationships of single-stator motors under 25 different combinations of electrical and chemical potential. All 25 torque-speed curves had the same concave-down shape as fully energized wild-type motors, and each stator passes at least 37 ± 2 ions per revolution. We used the results to explore the 25-dimensional parameter space of generalized kinetic models for the motor mechanism, finding 830 parameter sets consistent with the data. Analysis of these sets showed that the motor mechanism has a "powerstroke" in either ion binding or transit; ion transit is channel-like rather than carrier-like; and the rate-limiting step in the motor cycle is ion binding at low concentration, ion transit, or release at high concentration.

Dynamics of the bacterial flagellar motor: the effects of stator compliance, back steps, temperature, and rotational asymmetry

The rotation of a bacterial flagellar motor (BFM) is driven by multiple stators tethered to the cell wall. Here, we extend a recently proposed power-stroke model to study the BFM dynamics under different biophysical conditions. Our model explains several key experimental observations and reveals their underlying mechanisms. 1), The observed independence of the speed at low load on the number of stators is explained by a force-dependent stepping mechanism that is independent of the strength of the stator tethering spring. Conversely, without force-dependent stepping, an unrealistically weak stator spring is required. 2), Our model with back-stepping naturally explains the observed absence of a barrier to backward rotation. Using the same set of parameters, it also explains BFM behaviors in the high-speed negative-torque regime. 3), From the measured temperature dependence of the maximum speed, our model shows that stator-stepping is a thermally activated process with an energy barrier. 4), The recently observed asymmetry in the torque-speed curve between counterclockwise- and clockwise-rotating BFMs can be quantitatively explained by the asymmetry in the stator-rotor interaction potentials, i.e., a quasilinear form for the counterclockwise motor and a quadratic form for the clockwise motor.

Dynamics of the bacterial flagellar motor with multiple stators

The bacterial flagellar motor drives the rotation of flagellar filaments and enables many species of bacteria to swim. Torque is generated by interaction of stator units, anchored to the peptidoglycan cell wall, with the rotor. Recent experiments [Yuan J, Berg HC (2008) Proc Natl Acad Sci USA 105:1182-1185] show that at near-zero load the speed of the motor is independent of the number of stators. Here, we introduce a mathematical model of the motor dynamics that explains this behavior based on a general assumption that the stepping rate of a stator depends on the torque exerted by the stator on the rotor. We find that the motor dynamics can be characterized by two timescales: the moving-time interval for the mechanical rotation of the rotor and the waiting-time interval determined by the chemical transitions of the stators. We show that these two timescales depend differently on the load, and that their cross-over provides the microscopic explanation for the existence of two regimes in the torque-speed curves observed experimentally. We also analyze the speed fluctuation for a single motor by using our model. We show that the motion is smoothed by having more stator units. However, the mechanism for such fluctuation reduction is different depending on the load. We predict that the speed fluctuation is determined by the number of steps per revolution only at low load and is controlled by external noise for high load. Our model can be generalized to study other molecular motor systems with multiple power-generating units.

Bacterial flagellar motor

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.

The bacterial flagellar motor: structure and function of a complex molecular machine

The bacterial flagellar motor harnesses ion flow to drive rotary motion, at speeds reaching 100000 rpm and with apparently tight coupling. The functional properties of the motor are quite well understood, but its molecular mechanism remains unknown. Studies of motor physiology, together with mutational and biochemical studies of the components, place significant constraints on the mechanism. Rotation is probably driven by conformational changes in membrane-protein complexes that form the stator. These conformational changes occur as protons move on and off a critical aspartate residue in the stator protein MotB, and the resulting forces are applied to the rotor protein FliG. The bacterial flagellum is a complex structure built from about two dozen proteins. Its construction requires an apparatus at the base that exports many flagellar components to their sites of installation by way of an axial channel through the structure. The sequence of events in assembly is understood in general terms, but not yet at the molecular level. A fuller understanding of motor rotation and flagellar assembly will require more data on the structures and organization of the constituent proteins.

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.

Flagellar movement driven by proton translocation

The bacterial flagellar motor couples ion flow to rotary motion at high speed and with apparently fixed stoichiometry. The functional properties of the motor are quite well understood, but its molecular mechanism remains unknown. Recent studies of motor physiology, coupled with mutational and biochemical studies of the components, put significant constraints on the mechanism. Rotation is probably driven by conformational changes in membrane-protein complexes that form the stator. These conformational changes occur as protons move on and off a critical Asp residue in the stator protein MotB, and the resulting forces are applied to the rotor protein FliG.

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.

Rotary protein motors

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

An ultrasonic motor model for bacterial flagellar motors

A model for the transduction of energy occurring in bacterial flagellar motors is presented. In this model, the influx of ions across the channel causes the cyclic conformational change of the channel itself, which in turn produces travelling waves in one of the subcomponents of the motor, the C ring. This wave stabilizes the cyclical movement of the channel which generates the rotating force. The estimated frequency of cyclic conformational change is between 36 kHz and 6.3 MHz, i.e. in the ultrasonic range. This phenomenon is therefore referred to as the ultrasonic micromotor of microorganisms.

Conformational spread in a ring of proteins: a stochastic approach to allostery

We recently suggested that the sensitivity and range of a cluster of membrane receptors in bacteria would be enhanced by cooperative interactions between neighbouring proteins. Here, we examine the consequences of this "conformational spread" mechanism for an idealised one-dimensional system comprising a closed ring of identical allosteric protomers (protein molecules, or a group of protein domains operating as a unit). We show analytically and by means of Monte Carlo simulations that a ring of allosteric protomers can exhibit a switch-like response to changes in ligand concentration. We derive expressions for the sensitivity and cooperativity of switching and show that the maximum sensitivity is proportional to the number of protomers in the ring. A ring of this kind can reproduce the sensitivity and kinetics of the switch complex of a bacterial flagellar motor, for example, which is based on a ring of 34 FliM proteins. We also compare smaller rings of conformationally coupled protomers to classical allosteric proteins such as haemoglobin and show that the canonical MWC and KNF models arise naturally as limiting cases. Conformational spread appears to be a natural extension of the familiar mechanism of allostery: a physically realistic mechanism that should apply widely to many structures built from protein molecules.

Theories of rotary motors

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

An electrostatic mechanism closely reproducing observed behavior in the bacterial flagellar motor

A mechanism coupling the transmembrane flow of protons to the rotation of the bacterial flagellum is studied. The coupling is accomplished by means of an array of tilted rows of positive and negative charges around the circumference of the rotor, which interacts with a linear array of proton binding sites in channels. We present a rigorous treatment of the electrostatic interactions using minimal assumptions. Interactions with the transition states are included, as well as proton-proton interactions in and between channels. In assigning values to the parameters of the model, experimentally determined structural characteristics of the motor have been used. According to the model, switching and pausing occur as a consequence of modest conformational changes in the rotor. In contrast to similar approaches developed earlier, this model closely reproduces a large number of experimental findings from different laboratories, including the nonlinear behavior of the torque-frequency relation in Escherichia coli, the stoichiometry of the system in Streptococcus, and the pH-dependence of swimming speed in Bacillus subtilis.

The bacterial flagella motor

The bacterial flagellum is probably the most complex organelle found in bacteria. Although the ribosome may be made of slightly more subunits, the bacterial flagellum is a more organized and complex structure. The limited number of flagella must be targeted to the correct place on the cell membrane and a structure with cytoplasmic, cytoplasmic membrane, outer membrane and extracellular components must be assembled. The process of controlled transcription and assembly is still not fully understood. Once assembled, the motor complex in the cytoplasmic membrane rotates, driven by the transmembrane ion gradient, at speeds that can reach many 100 Hz, driving the bacterial cell at several body lengths a second. This coupling of an electrochemical gradient to mechanical rotational work is another fascinating feature of the bacterial motor. A significant percentage of a bacterium's energy may be used in synthesizing the complex structure of the flagellum and driving its rotation. Although patterns of swimming may be random in uniform environments, in the natural environment, where cells are confronted with gradients of metabolites and toxins, motility is used to move bacteria towards their optimum environment for growth and survival. A sensory system therefore controls the switching frequency of the rotating flagellum. This review deals primarily with the structure and operation of the bacterial flagellum. There has been a great deal of research in this area over the past 20 years and only some of this has been included. We apologize in advance if certain areas are covered rather thinly, but hope that interested readers will look at the excellent detailed reviews on those areas cited at those points.

Torque generated by the flagellar motor of Escherichia coli while driven backward

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.

Electrostatic interactions between rotor and stator in the bacterial flagellar motor

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.

Absence of a barrier to backwards rotation of the bacterial flagellar motor demonstrated with optical tweezers

A cell of the bacterium Escherichia coli was tethered covalently to a glass coverslip by a single flagellum, and its rotation was stopped by using optical tweezers. The tweezers acted directly on the cell body or indirectly, via a trapped polystyrene bead. The torque generated by the flagellar motor was determined by measuring the displacement of the laser beam on a quadrant photodiode. The coverslip was mounted on a computer-controlled piezo-electric stage that moved the tether point in a circle around the center of the trap so that the speed of rotation of the motor could be varied. The motor generated approximately 4500 pN nm of torque at all angles, regardless of whether it was stalled, allowed to rotate very slowly forwards, or driven very slowly backwards. This argues against models of motor function in which rotation is tightly coupled to proton transit and back-transport of protons is severely limited.

Residues of the cytoplasmic domain of MotA essential for torque generation in the bacterial flagellar motor

The MotA protein of Escherichia coli is a component of the flagellum that functions, together with MotB, in transmembrane proton conduction. MotA and MotB are believed to form the stator of the flagellar motor. They are integral membrane proteins; MotA has a large (ca 22 kDa) domain in the cytoplasm, and MotB a much smaller one (ca 3 kDa). Recent work suggests that cytoplasmically located parts of MotA and/or MotB might be present at the active site for torque generation in the motor. To test the proposal that the cytoplasmic domain of MotA functions in torque generation, and to identify the amino acid residues most important for function, we have carried out a mutational analysis of this domain. Using random mutagenesis, many mutations of cytoplasmic residues of MotA were isolated, which either abolish or impair torque generation. In most cases the residues affected are not conserved, and many of the replacements involve loss or gain of a proline residue, which suggests that these mutations disrupt function by altering the protein conformation rather than by directly affecting residues of an active site. Using site-directed mutagenesis, the conserved residues in the cytoplasmic domain of MotA were replaced, either singly or, in the case of charged residues, in various combinations. The results identify four residues of MotA that are important for motor function. These are Arg90 and Glu98, located in the cytoplasmic domain, and Pro173 and Pro222, located at the interface between the cytoplasmic domain and the membrane-spanning domain. Possible roles for these residues in torque generation are discussed.

Protein turbines. I: The bacterial flagellar motor

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

The Rhodobacter sphaeroides flagellar motor is a variable-speed rotor

The rotation rate of the unidirectional stop/start motor of Rhodobacter sphaeroides was investigated using computerised motion analysis of tethered cells. The R. sphaeroides motor was found to have a variable rotation rate compared to the virtually constant-speed motor of wild-type and CheR mutant (smooth swimming) Escherichia coli. In addition, the dynamics of the R. sphaeroides motor during stopping was analysed with no consistent correlation behaviour. The motor could go from full rotation to stop, or stop to full rotation within one video frame, i.e. 0.02 s, but it could also slow down into a stop or restart slowly, taking up to 0.25 s. The R. sphaeroides motor under chemokinetic stimulation was also analysed and was found to show increased torque generation and reduced variation in rotation rate.

Charged residues of the rotor protein FliG essential for torque generation in the flagellar motor of Escherichia coli

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.

Mechanical limits of bacterial flagellar motors probed by electrorotation

We used the technique of electrorotation to apply steadily increasing external torque to tethered cells of the bacterium Escherichia coli while continuously recording the speed of cell rotation. We found that the bacterial flagellar motor generates constant torque when rotating forward at low speeds and constant but considerably higher torque when rotating backward. At intermediate torques, the motor stalls. The torque-speed relationship is the same in both directional modes of switching motors. Motors forced backward usually break, either suddenly and irreversibly or progressively. Motors broken progressively rotate predominantly at integral multiples of a unitary speed during the course of both breaking and subsequent recovery, as expected if progressive breaking affects individual torque-generating units. Torque is reduced by the same factor at all speeds in partially broken motors, implying that the torque-speed relationship is a property of the individual torque-generating units.

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.