Low flagellar motor torque and high swimming efficiency of Caulobacter crescentus swarmer cells

We determined the torque of the flagellar motor of Caulobacter crescentus for different motor rotation rates by measuring the rotation rate and swimming speed of the cell body and found it to be remarkably different from that of other bacteria, such as Escherichia coli and Vibrio alginolyticus. The average stall torque of the Caulobacter flagellar motor was approximately 350 pN nm, much smaller than the values of the other bacteria measured. Furthermore, the torque of the motor remained constant in the range of rotation rates up to those of freely swimming cells. In contrast, the torque of a freely swimming cell for V. alginolyticus is typically approximately 20% of the stall torque. We derive from these results that the C. crescentus swarmer cells swim more efficiently than both E. coli and V. alginolyticus. Our findings suggest that C. crescentus is optimally adapted to low nutrient aquatic environments.     

The Bacillus subtilis catabolite control protein CcpA exerts all its regulatory functions by DNA-binding

Swimming speed (v) and flagellar-bundle rotation rate (f) of Salmonella typhimurium, which has peritrichous flagella, were simultaneously measured by laser dark-field microscopy (LDM). Clear periodic changes in the LDM signals from a rotating bundle indicated in-phase rotation of the flagella in the bundle. A roughly linear relation between v and f was observed, though the data points were widely distributed. The ratio of v to f (v-f ratio), which indicates the propulsive distance during one flagellar rotation, was 0.27 microm (11% of the flagellar pitch) on average. The experimental v-f ratio was twice as large as the calculated one on the assumption that a cell had a single flagellum. A flagellar bundle was considered to propel a cell more efficiently than a single flagellum.     

Rotation and switching of the flagellar motor assembly in Halobacterium halobium.

Halobacterium halobium swims with a polarly inserted motor-driven flagellar bundle. The swimming direction of the cell can be reserved by switching the rotational sense of the bundle. The switch is under the control of photoreceptor and chemoreceptor proteins that act through a branched signal chain. The swimming behavior of the cells and the switching process of the flagellar bundle were investigated with a computer-assisted motion analysis system. The cells were shown to swim faster by clockwise than by counterclockwise rotation of the flagellar bundle. From the small magnitude of speed fluctuations, it is concluded that the majority, if not all, of the individual flagellar motors of a cell rotate in the same direction at any given time. After stimulation with light (blue light pulse or orange light step-down), the cells continued swimming with almost constant speed but then slowed before they reversed direction. The cells passed through a pausing state during the change of the rotational sense of the flagellar bundle and then exhibited a transient acceleration. Both the average length of the pausing period and the transient acceleration were independent of the stimulus size and thus represent intrinsic properties of the flagellar motor assembly. The average length of the pausing period of individual cells, however, was not constant. The time course of the probability for spontaneous motor switching was calculated from frequency distribution and shown to be independent of the rotational sense. The time course further characterizes spontaneous switching as a stochastic rather than an oscillator-triggered event.     

Quantitative measurements of proton motive force and motility in Bacillus subtilis.

The protein motive force of metabolizing Bacillus subtilis cells was only slightly affected by changes in the external pH between 5 and 8, although the electrical component and the chemical component of the proton motive force contributed differently at different external pH. The electrical component of the proton motive force was very small at pH 5, and the chemical component was almost negligible at pH 7.5. At external pH values between 6 and 7.7, swimming speed of the cells stayed constant. Thus, either the electrical component or the chemical component of the proton motive force could drive the flagellar motor. When the proton motive force of valinomycin-treated cells was quantitatively decreased by increasing the external K+ concentration, the swimming speed of the cells changed in a unique way: the swimming speed was not affected until about--100 mV, then decreased linearly with further decrease in the proton motive force, and was almost zero at about--30 mV. The rotation rate of a flagellum, measured by a tethered cell, showed essentially the same characteristics. Thus, there are a threshold proton motive force and a saturating proton motive force for the rotation of the B. subtilis flagellar motor.     

Direct Measurement of Helical Cell Motion of the Spirochete Leptospira

Leptospira are spirochete bacteria distinguished by a short-pitch coiled body and intracellular flagella. Leptospira cells swim in liquid with an asymmetric morphology of the cell body; the anterior end has a long-pitch spiral shape (S-end) and the posterior end is hook-shaped (H-end). Although the S-end and the coiled cell body called the protoplasmic cylinder are thought to be responsible for propulsion together, most observations on the motion mechanism have remained qualitative. In this study, we analyzed the swimming speed and rotation rate of the S-end, protoplasmic cylinder, and H-end of individual Leptospira cells by one-sided dark-field microscopy. At various viscosities of media containing different concentrations of Ficoll, the rotation rate of the S-end and protoplasmic cylinder showed a clear correlation with the swimming speed, suggesting that these two helical parts play a central role in the motion of Leptospira. In contrast, the H-end rotation rate was unstable and showed much less correlation with the swimming speed. Forces produced by the rotation of the S-end and protoplasmic cylinder showed that these two helical parts contribute to propulsion at nearly equal magnitude. Torque generated by each part, also obtained from experimental motion parameters, indicated that the flagellar motor can generate torque >4000 pN nm, twice as large as that of Escherichia coli. Furthermore, the S-end torque was found to show a markedly larger fluctuation than the protoplasmic cylinder torque, suggesting that the unstable H-end rotation might be mechanically related to changes in the S-end rotation rate for torque balance of the entire cell. Variations in torque at the anterior and posterior ends of the Leptospira cell body could be transmitted from one end to the other through the cell body to coordinate the morphological transformations of the two ends for a rapid change in the swimming direction.     

Direct Measurement of Helical Cell Motion of the Spirochete Leptospira

Leptospira are spirochete bacteria distinguished by a short-pitch coiled body and intracellular flagella. Leptospira cells swim in liquid with an asymmetric morphology of the cell body; the anterior end has a long-pitch spiral shape (S-end) and the posterior end is hook-shaped (H-end). Although the S-end and the coiled cell body called the protoplasmic cylinder are thought to be responsible for propulsion together, most observations on the motion mechanism have remained qualitative. In this study, we analyzed the swimming speed and rotation rate of the S-end, protoplasmic cylinder, and H-end of individual Leptospira cells by one-sided dark-field microscopy. At various viscosities of media containing different concentrations of Ficoll, the rotation rate of the S-end and protoplasmic cylinder showed a clear correlation with the swimming speed, suggesting that these two helical parts play a central role in the motion of Leptospira. In contrast, the H-end rotation rate was unstable and showed much less correlation with the swimming speed. Forces produced by the rotation of the S-end and protoplasmic cylinder showed that these two helical parts contribute to propulsion at nearly equal magnitude. Torque generated by each part, also obtained from experimental motion parameters, indicated that the flagellar motor can generate torque >4000 pN nm, twice as large as that of Escherichia coli. Furthermore, the S-end torque was found to show a markedly larger fluctuation than the protoplasmic cylinder torque, suggesting that the unstable H-end rotation might be mechanically related to changes in the S-end rotation rate for torque balance of the entire cell. Variations in torque at the anterior and posterior ends of the Leptospira cell body could be transmitted from one end to the other through the cell body to coordinate the morphological transformations of the two ends for a rapid change in the swimming direction.     

A mathematical explanation of an increase in bacterial swimming speed with viscosity in linear-polymer solutions

Bacterial swimming speed is sometimes known to increase with viscosity. This phenomenon is peculiar to bacterial motion. Berg and Turner (Nature. 278:349-351, 1979) indicated that the phenomenon was caused by a loose, quasi-rigid network formed by polymer molecules that were added to increase viscosity. We mathematically developed their concept by introducing two apparent viscosities and obtained results similar to the experimental data reported before. Addition of polymer improved the propulsion efficiency, which surpasses the decline in flagellar rotation rate, and the swimming speed increased with viscosity.     

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.     

Three genes of a motility operon and their role in flagellar rotary speed variation in Rhizobium meliloti.

The peritrichous flagella of Rhizobium meliloti rotate only clockwise and control directional changes of swimming cells by modulating flagellar rotary speed. Using Tn5 insertions, we have identified and sequenced a motility (mot) operon containing three genes, motB, motC, and motD, that are translationally coupled. The motB gene (and an unlinked motA) has been assigned by similarity to the Escherichia coli and Bacillus subtilis homologs, whereas motC and motD are new and without known precedents in other bacteria. In-frame deletions introduced in motB, motC, or motD each result in paralysis. MotD function was fully restored by complementation with the wild-type motD gene. By contrast, deletions in motB or motC required the native combination of motB and motC in trans for restoring normal flagellar rotation, whereas complementation with motB or motC alone led to uncoordinated (jiggly) swimming. Similarly, a motB-motC gene fusion and a Tn5 insertion intervening between motB and motC resulted in jiggly swimming as a consequence of large fluctuations in flagellar rotary speed. We conclude that MotC biosynthesis requires coordinate expression of motB and motC and balanced amounts of the two gene products. The MotC polypeptide contains an N-terminal signal sequence for export, and Western blots have confirmed its location in the periplasm of the R. meliloti cell. A working model suggests that interactions between MotB and MotC at the periplasmic surface of the motor control the energy flux or the energy coupling that drives flagellar rotation.     

Microscopic analysis of bacterial motility at high pressure

The bacterial flagellar motor is a molecular machine that converts an ion flux to the rotation of a helical flagellar filament. Counterclockwise rotation of the filaments allows them to join in a bundle and propel the cell forward. Loss of motility can be caused by environmental factors such as temperature, pH, and solvation. Hydrostatic pressure is also a physical inhibitor of bacterial motility, but the detailed mechanism of this inhibition is still unknown. Here, we developed a high-pressure microscope that enables us to acquire high-resolution microscopic images, regardless of applied pressures. We also characterized the pressure dependence of the motility of swimming Escherichia coli cells and the rotation of single flagellar motors. The fraction and speed of swimming cells decreased with increased pressure. At 80 MPa, all cells stopped swimming and simply diffused in solution. After the release of pressure, most cells immediately recovered their initial motility. Direct observation of the motility of single flagellar motors revealed that at 80 MPa, the motors generate torque that should be sufficient to join rotating filaments in a bundle. The discrepancy in the behavior of free swimming cells and individual motors could be due to the applied pressure inhibiting the formation of rotating filament bundles that can propel the cell body in an aqueous environment.     

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.     

Steady-state running rate sets the speed and accuracy of accumulation of swimming bacteria

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.     

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.     

Unidirectional, intermittent rotation of the flagellum of Rhodobacter sphaeroides.

The single flagellum of the photosynthetic bacterium Rhodobacter sphaeroides was found to be medially located on the cell body. Observation of free-swimming bacteria, and bacteria tethered by their flagellar filaments, revealed that the flagellum could only rotate in the clockwise direction; switching of the direction of rotation was never observed. Flagellar rotation stopped periodically, typically several times a minute for up to several seconds each. Reorientation of swimming cells appeared to be the result of Brownian rotation during the stop periods. The flagellar filament displayed polymorphism; detached and nonrotating filaments were usually seen as large-amplitude helices of such short wavelength that they appeared as flat coils or circles, whereas the filaments on swimming cells showed a normal (small-amplitude, long-wavelength) helical form. With attached filaments, the transition from the normal to the coiled form occurred when the flagellar motor stopped rotating, proceeding from the distal end towards the cell body. It is possible that both the relaxation process and the smaller frictional resistance after relaxation may act to enhance the rate of reorientation of the cell. The transition from the coiled to the normal form occurred when the motor restarted, proceeding from the proximal end outwards, which might further contribute to the reorientation of the cell before it reaches a stable swimming geometry.     

Correlation between bacteriophage chi adsorption and mode of flagellar rotation of Escherichia coli chemotaxis mutants

We studied the adsorption of phage chi to various behavioral mutants (che mutants) of Escherichia coli having different swimming modes. Bacteriophage chi infects only bacteria with active flagella, and it was therefore of interest to examine whether the mode of swimming has an effect on the susceptibility of the bacteria to the phage. Neither the mode of swimming (smooth swimming or tumbling) nor the direction of flagellar rotation affected the degree of chi adsorption to the bacterial cells. Furthermore, the tumbling frequency, the rotation speed (tethered cells of all of the strains examined had the same average speed of rotation), the time proportion of rotation, and the reversal frequency were not important in determining susceptibility to chi. The only variable that influenced chi adsorption was the fraction of the population whose flagella rotated incessantly. A direct, linear correlation was found between chi adsorption and the fraction of unceasing rotation in each population. It seems, therefore, that an individual bacterium whose flagella pause periodically and briefly during rotation is not susceptible to irreversible adsorption of the phage. Pausing of rotation thus seems to be a new feature of motility that is prevalent especially in che mutants. It is concluded that irreversible chi adsorption can serve as a quantitative assay only for incessant flagellar rotation of E. coli.     

Rhizobium meliloti swims by unidirectional, intermittent rotation of right-handed flagellar helices.

The 5 to 10 peritrichously inserted complex flagella of Rhizobium meliloti MVII-1 were found to form right-handed flagellar bundles. Bacteria swam at speeds up to 60 microns/s, their random three-dimensional walk consisting of straight runs and quick directional changes (turns) without the vigorous angular motion (tumbling) seen in swimming Escherichia coli cells. Observations of R. meliloti cells tethered by a single flagellar filament revealed that flagellar rotation was exclusively clockwise, interrupted by very brief stops (shorter than 0.1 s), typically every 1 to 2 s. Swimming bacteria responded to chemotactic stimuli by extending their runs, and tethered bacteria responded by prolonged intervals of clockwise rotation. Moreover, the motility tracks of a generally nonchemotactic ("smooth") mutant consisted of long runs without sharp turns, and tethered mutant cells showed continuous clockwise rotation without detectable stops. These observations suggested that the runs of swimming cells correspond to clockwise flagellar rotation, and the turns correspond to the brief rotation stops. We propose that single rotating flagella (depending on their insertion point on the rod-shaped bacterial surface) can reorient a swimming cell whenever the majority of flagellar motors stop.     

Real-time imaging of fluorescent flagellar filaments of Rhizobium lupini H13-3: flagellar rotation and pH-induced polymorphic transitions

The soil bacterium Rhizobium lupini H13-3 has complex right-handed flagellar filaments with unusual ridged, grooved surfaces. Clockwise (CW) rotation propels the cells forward, and course changes (tumbling) result from changes in filament speed instead of the more common change in direction of rotation. In view of these novelties, fluorescence labeling was used to analyze the behavior of single flagellar filaments during swimming and tumbling, leading to a model for directional changes in R. lupini. Also, flagellar filaments were investigated for helical conformational changes, which have not been previously shown for complex filaments. During full-speed CW rotation, the flagellar filaments form a propulsive bundle that pushes the cell on a straight path. Tumbling is caused by asynchronous deceleration and stops of individual filaments, resulting in dissociation of the propulsive bundle. R. lupini tumbles were not accompanied by helical conformational changes as are tumbles in other organisms including enteric bacteria. However, when pH was experimentally changed, four different polymorphic forms were observed. At a physiological pH of 7, normal flagellar helices were characterized by a pitch angle of 30 degrees, a pitch of 1.36 micro m, and a helical diameter of 0.50 micro m. As pH increased from 9 to 11, the helices transformed from normal to semicoiled to straight. As pH decreased from 5 to 3, the helices transformed from normal to curly to straight. Transient conformational changes were also noted at high viscosity, suggesting that the R. lupini flagellar filament may adapt to high loads in viscous environments (soil) by assuming hydrodynamically favorable conformations.     

Flagellar hydrodynamics. A comparison between resistive-force theory and slender-body theory.

This paper investigates the accuracy of the resistive-force theory (Gray and Hancock method) which is commonly used for hydrodynamic analysis of swimming flagella. We made a comparison between the forces, bending moments, and shear moments calculated by resistive-force theory and by the more accurate slender-body theory for large-amplitude, planar wave forms computed for a flagellar model. By making an upward empirical adjustment, by about 35%, of the classical drag coefficient values used in the resistive-force theory calculations, we obtained good agreement between the distributions of the forces and moments along the length of the flagellum predicted by the two methods when the flagellum has no cell body attached. After this adjustment, we found the rate of energy expenditure calculated by the two methods for the few typical test cases to be almost identical. The resistive-force theory is thus completely satisfactory for use in analysis of mechanisms for the control of flagellar bending, at the current level of sophistication of this analysis. We also examined the effects of the presence of a cell body attached to one end of the flagellum, which modifies the flow field experienced by the flagellum. This interaction, which is not considered in resistive-force theory, is probably insignificant for small cell bodies, such as the heads of simple spermatozoa, but for larger cell bodies, or cell bodies that have large-amplitude motions transverse to the swimming direction, use of slender-body theory is required for accurate analysis.     

Comparative analysis of movement characteristics of lancelet and fish spermatozoa having different morphologies

The movement characteristics of the sperm and their flagella obtained from a lancelet and 35 species from almost all orders of fishes were examined using high-speed video microscopy. The aim was to clarify the relationship between the motility parameters of the spermatozoa having different morphologies and how these motility parameters affect the swimming speed of the spermatozoa. The motility parameters representing the flagellar waveform, the wavelength, and the amplitude were neither very different between the spermatozoa of the different species nor related to the swimming speed. In contrast, the beat frequency was remarkably changed in the different spermatozoa and was proportional to the swimming speed. The maximum shear angle of the flagellar wave, which is directly related to the maximum sliding displacement between the doublet microtubules, remained nearly constant while the beat frequency varied widely; therefore, the spermatozoa beat in the constant sliding displacement mode. An analysis of the relationship between swimming speed and flagellar length revealed that short flagella were at a disadvantage in developing swimming speed; however, so were extra-long flagella. The ratio of the swimming speed to the wave velocity calculated from the wavelength and the beat frequency depended on the distance from the glass surface. The swimming speeds calculated using the original resistive-force theory were greater than the measured values. To rationalize the measured values, the ratio between the normal and tangential drag coefficient in the resistive-force theory was corrected; namely, 1.99 at 1 μm and 1.63 at 3 μm from the glass surface.