Torque and rotation rate of the bacterial flagellar motor

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.

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.

The rotary motor of bacterial flagella

Flagellated bacteria, such as Escherichia coli, swim by rotating thin helical filaments, each driven at its base by a reversible rotary motor, powered by an ion flux. A motor is about 45 nm in diameter and is assembled from about 20 different kinds of parts. It develops maximum torque at stall but can spin several hundred Hz. Its direction of rotation is controlled by a sensory system that enables cells to accumulate in regions deemed more favorable. We know a great deal about motor structure, genetics, assembly, and function, but we do not really understand how it works. We need more crystal structures. All of this is reviewed, but the emphasis is on function.

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.

Bacterial flagellar motor and H(+)/ATP synthase: two proton-driven rotary molecular devices with different functions

Both the bacterial flagellar motor and the H(+)/ATP synthase are membrane-bound macromolecular complexes in which the movement of protons through channels across the membrane is coupled to the rotation of a part of the complex around an axis perpendicular to the membrane. Despite this similarity, the two devices are designed for quite different functions. The flagellar motor is responsible for a practically smooth rotation of the flagellar filament in order to propel the cell. Smooth rotation is not essential for the H(+)/ATP synthase, which accumulates torque by twisting a rod-shaped structure. Possible mechanisms for generating torque in the two devices are presented, based on the models which have been proposed. The performances of the various mechanisms are discussed.

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.

Constraints on models for the flagellar rotary motor

Most bacteria that swim are propelled by flagellar filaments, each driven at its base by a rotary motor embedded in the cell wall and cytoplasmic membrane. A motor is about 45 nm in diameter and made up of about 20 different kinds of parts. It is assembled from the inside out. It is powered by a proton (or in some species, a sodium-ion) flux. It steps at least 400 times per revolution. At low speeds and high torques, about 1000 protons are required per revolution, speed is proportional to protonmotive force, and torque varies little with temperature or hydrogen isotope. At high speeds and low torques, torque increases with temperature and is sensitive to hydrogen isotope. At room temperature, torque varies remarkably little with speed from about -100 Hz (the present limit of measurement) to about 200 Hz, and then it declines rapidly reaching zero at about 300 Hz. These are facts that motor models should explain. None of the existing models for the flagellar rotary motor completely do so.

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.

Simultaneous measurement of bacterial flagellar rotation rate and swimming speed

Swimming speeds and flagellar rotation rates of individual free-swimming Vibrio alginolyticus cells were measured simultaneously by laser dark-field microscopy at 25, 30, and 35 degrees C. A roughly linear relation between swimming speed and flagellar rotation rate was observed. The ratio of swimming speed to flagellar rotation rate was 0.113 microns, which indicated that a cell progressed by 7% of pitch of flagellar helix during one flagellar rotation. At each temperature, however, swimming speed had a tendency to saturate at high flagellar rotation rate. That is, the cell with a faster-rotating flagellum did not always swim faster. To analyze the bacterial motion, we proposed a model in which the torque characteristics of the flagellar motor were considered. The model could be analytically solved, and it qualitatively explained the experimental results. The discrepancy between the experimental and the calculated ratios of swimming speed to flagellar rotation rate was about 20%. The apparent saturation in swimming speed was considered to be caused by shorter flagella that rotated faster but produced less propelling force.

Fluctuations in rotation rate of the flagellar motor of Escherichia coli

The purpose of this work was to study the changes in rotation rate of the bacterial motor and to try to discriminate between various sources of these changes with the aim of understanding the mechanism of force generation better. To this end Escherichia coli cells were tethered and videotaped with brief stroboscopic light flashes. The records were scanned by means of a computerized motion analysis system, yielding cell size, radius of rotation, and accumulated angle of rotation as functions of time for each cell selected. In conformity with previous studies, fluctuations in the rotation rate of the flagellar motor were invariably found. Employing an exclusively counterclockwise rotating mutant ("gutted" RP1091 strain) and using power spectral density, autocorrelation and residual mean square angle analysis, we found that a simple superposition of rotational diffusion on a steady rotary motion is insufficient to describe the observed rotation. We observed two additional rotational components, one fluctuating (0.04-0.6 s) and one oscillating (0.8-7 s). However, the effective rotational diffusion coefficient obtained after taking these two components into account generally exceeded that calculated from external friction by two orders of magnitude. This is consistent with a model incorporating association and dissociation of force-generating units.

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.

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

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

Rapid changes in flagellar rotation induced by external electric pulses

The bacterial flagellar motor is the only molecular rotary machine found in living organisms, converting the protonmotive force, i.e., the membrane voltage and proton gradients across the cell membrane, into the mechanical force of rotation (torque). We have developed a method for holding a bacterial cell at the tip of a glass micropipette and applying electric pulses through the micropipette. This method has enabled us to observe the dynamical responses of flagellar rotation to electric pulses that change the membrane voltage transiently and repeatedly. We have observed that acceleration and deceleration of motor rotation are induced by application of these electric pulses. The change in the rotation rate occurred within 5 ms after pulse application.

In vivo modulation of connexin 43 gene expression and junctional coupling of pancreatic B-cells

We have explored the expression of gap junctional proteins and corresponding mRNAs by insulin-producing B-cells of native rat pancreas and of a transplantable rat insulinoma. By immunostaining cryostat sections (indirect immunofluorescence) and crude membrane preparations (Western blots) with antibodies against connexins 26, 32, and 43 and by hybridizing total islet and insulinoma RNA (Northern blot) with cRNAs for the latter two proteins, we have found that normal and tumoral B-cells express connexin 43 but do not show detectable levels of either connexin 32 or 26. By evaluating the conductance (dual patch-clamp whole-cell recording) and permeability of junctional channels (microinjection of Lucifer yellow), we have found that control B-cells show low levels of electrical and dye coupling in only a portion of the pairs studied. By studying B-cells of glibenclamide-treated rats, we have found that sustained stimulation of insulin release in vivo is associated with a two-fold increase in the level of connexin 43 gene transcripts and in the incidence of both ionic and dye coupling. These observations indicate that (1) connexin 43 is a major component of communicating channels between insulin-producing cells; (2) some but not all B-cells are electrically coupled by low conductance junctional channels; and (3) connexin 43 gene transcripts and incidence of junctional coupling are modulated in parallel during sustained stimulation of B-cell functioning in vivo.

The bacterial flagellum and flagellar motor: structure, assembly and function

The bacterial flagellum is a complex multicomponent structure which serves as the propulsive organelle for many species of bacteria. Rotation of the helical flagellar filament, driven by a proton-powered motor embedded in the cell wall, enables the flagellum to function as a screw propeller. It seems likely that almost all of the genes required for flagellar formation and function have been identified. Continuing analysis of the portions of the genome containing these genes may reveal the existence of a few more. Transcription of the flagellar genes is under the control of the products of a single operon, and so these genes constitute a regulon. Other controls, both transcriptional and post-transcriptional, have been identified. Many of these genes have been sequenced, and the information obtained will aid in the design of experiments to clarify the various regulatory mechanisms of the flagellar regulon. The flagellum is composed of several substructures. The long helical filament is connected via the flexible hook to the complex basal body which is located in the cell wall. The filament is composed of many copies of a single protein, and can adopt a number of distinct helical forms. Structural analyses of the filament are adding to our understanding of this dynamic polymer. The component proteins of the hook and filament have all been identified. Continuing studies on the structure of the basal body have revealed the presence of several hitherto unknown basal-body proteins, whose identities and functions have yet to be elucidated. The proteins essential for energizing the motor, the Mot and switch proteins, are thought to exist as multisubunit complexes peripheral to the basal body. These complexes have yet to be identified biochemically or morphologically. Not surprisingly, flagellar assembly is a complex process, occurring in several stages. Assembly occurs in a proximal-to-distal fashion; the basal body is assembled before the hook, and the hook before the filament. This pattern is also maintained within the filament, with monomers added at the distal end of the polymer; the same is presumably true of the other axial components. An exception to this general pattern is assembly of the Mot proteins into the motor, which appears to be possible at any time during flagellar assembly. With the identification of the genes encoding many of the flagellar proteins, the roles of these proteins in assembly is understood, but the function of a number of gene products in flagellar formation remains unknown.(ABSTRACT TRUNCATED AT 400 WORDS)

Ion selectivity of the Vibrio alginolyticus flagellar motor

The marine bacterium, Vibrio alginolyticus, normally requires sodium for motility. We found that lithium will substitute for sodium. In neutral pH buffers, the membrane potential and swimming speed of glycolyzing bacteria reached maximal values as sodium or lithium concentration was increased. While the maximal potentials obtained in the two cations were comparable, the maximal swimming speed was substantially lower in lithium. Over a wide range of sodium concentration, the bacteria maintained an invariant sodium electrochemical potential as determined by membrane potential and intracellular sodium measurements. Over this range the increase of swimming speed took Michaelis-Menten form. Artificial energization of swimming motility required imposition of a voltage difference in concert with a sodium pulse. The cation selectivity and concentration dependence exhibited by the motile apparatus depended on the viscosity of the medium. In high-viscosity media, swimming speeds were relatively independent of either ion type or concentration. These facts parallel and extend observations of the swimming behavior of bacteria propelled by proton-powered flagella. In particular, they show that ion transfers limit unloaded motor speed in this bacterium and imply that the coupling between ion transfers and force generation must be fairly tight.

Energy transduction in the bacterial flagellar motor. Effects of load and pH

The effect of load and pH on the relation between proton potential and flagellar rotation has been studied in cells of a smooth-swimming Streptococcus strain. The driving potential, speeds of free-swimming bacteria, and rotation rates of bacteria tethered to glass by a single flagellum were measured. The relation between rotation rate of tethered bacteria and potential was remarkably linear up to nearly -200 mV. The relation between swimming speed and potential exhibited both saturation and threshold, as previously observed in other species. The form of these relations depended on pH. The equivalence of the electrical and chemical potential components of the proton potential in enabling swimming depended on the voltage. Our observations may be most simply accommodated by a kinetic scheme that links transmembrane proton transits to a tightly coupled work cycle. The properties of this scheme were elucidated by computer simulations of the experimental plots. These simulations indicated that the protonable groups that participate in the rate limiting reactions have a fractional electrical distance between three-fourths to all of the way toward the cytoplasm with a corresponding mean proton binding affinity of 10(-7.3)-10(-7.0) M, respectively.

Functions of the flagellar modes of rotation in bacterial motility and chemotaxis

Bacteria swim by rotating their flagella, the rotation being due to a motor located at the base of each flagellum. In this paper the correlation between motor function and mode of swimming is reviewed, with special emphasis on recent data that indicate that the motor is a three-state device. Novel findings with regard to the motor function and bioenergetics are surveyed, and mechanisms are proposed to account for these findings.

Na+-driven bacterial flagellar motors

Bacterial flagellar motors are the reversible rotary engine which propels the cell by rotating a helical flagellar filament as a screw propeller. The motors are embedded in the cytoplasmic membrane, and the energy for rotation is supplied by the electrochemical potential of specific ions across the membrane. Thus, the analysis of motor rotation at the molecular level is linked to an understanding of how the living system converts chemical energy into mechanical work. Based on the coupling ions, the motors are divided into two types; one is the H+-driven type found in neutrophiles such as Bacillus subtilis and Escherichia coli and the other is the Na+-driven type found in alkalophilic Bacillus and marine Vibrio. In this review, we summarize the current status of research on the rotation mechanism of the Na+-driven flagellar motors, which introduces several new aspects in the analysis.

A model for bacterial flagellar motor: free energy transduction and self-organization of rotational motion

A bacterial flagellar motor is an energy transducing molecular machine which shows some attractive characteristics. First, this motor is driven by a protonmotive force (PMF) across the membrane, two components of which, electric potential delta psi and chemical potential -(2.3RT/F)delta pH, are equivalently transduced to the mechanical work of the motor rotation. Second, a PMF threshold for rotation is observed. Third, this motor can rotate reversibly either counterclockwise (CCW) or clockwise (CW) at almost the same speed. To clarify the osmomechanical coupling of this motor, these characteristics must be explained consistently at the molecular level. In this paper, in order to allow quantitative analyses of the above characteristics, a theoretical model of a bacterial flagellar motor is constructed assuming that the torque generating sites are electrodes which can be charged by protons and that the electrostatic interaction between the electrodes generates the rotation torque. Electrode reaction reasonably derives the equivalence of delta psi and -(2.3RT/F)delta pH. In this model, rates of charging and discharging of protons are influenced by the motor rotation rate, so that the torque generating sites co-operatively work through the motor rotation. We named this kind of co-operativity among them "dynamic co-operativity" in torque generation. This co-operativity causes autocatalytic generation of motor torque and the existence of the rotation threshold. In this model, the appearance of the stable rotational states can be described by phase transition caused by the dynamic co-operativity among torque generating sites. According to this model, the flagellar motor has two stable rotational states corresponding to CCW and CW, which show the same torques. The motor selects one direction from them to rotate, and that is self-organization of rotational motion. Interpretation of the transition between the two stable rotational states as the chemotactic reversals of the flagellar motor is also discussed.

Dynamics of a tightly coupled mechanism for flagellar rotation. Bacterial motility, chemiosmotic coupling, protonmotive force

The bacterial flagellar motor is a molecular engine that couples the flow of protons across the cytoplasmic membrane to rotation of the flagellar filament. We analyze the steady-state behavior of an explicit mechanical model in which a fixed number of protons carries the filament through one revolution. Predictions of this model are compared with experimentally determined relationships between protonmotive force, proton flux, torque, and speed. All such tightly coupled mechanisms produce the same torque when the motor is stalled but vary greatly in their behavior at high speed. The speed at zero load predicted by our model is limited by the rates of association and dissociation of protons at binding sites on the rotor and by the mobility of force generators containing transmembrane channels that interact with these sites. Our analysis suggests that more could be learned about the motor if it were driven by an externally applied torque backwards (at negative speed) or forwards at speeds greater than the zero-load speed.