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.     

Synchronization,Slippage, and Unbundling of Driven Helical Flagella

Peritrichous bacteria exploit bundles of helical flagella for propulsion and chemotaxis. Here, changes in the swimming direction (tumbling) are induced by a change of the rotational frequency of some flagella. Employing coarse-grained modeling and simulations, we investigate the dynamical properties of helical flagella bundles driven by mismatched motor torques. Over a broad range of distances between the flagella anchors and applied torque differences, we find a stable bundled state, which is important for a robust directional motion of a bacterium. With increasing torque difference, a phase lag in the flagellar rotations develops, followed by slippage and ultimately unbundling, which sensitively depends on the anchoring distance of neighboring flagella. In the slippage and drift states, the different rotation frequencies of the flagella generate a tilting torque on the bacterial body, which implies a change of the swimming direction as observed experimentally.     

The Inhibition Effect of Antiserum on the Motility of Leptospira

Leptospires are a group of bacteria with a unique ultrastructure and a fascinating swimming behavior that cause a number of emerging and re-emerging diseases worldwide called leptospirosis. The unusual form of motility is thought to play a critical role in the infection process. However, the inhibition mechanism of antiserum on the motility of Leptospira to attenuate the infection efficiency is unknown. In this study, effect of antiserum on motility was quantitatively investigated by swimming speed. Relatively low concentration of antiserum was found to inhibit leptospiral motility, suggesting that the basic immunization can affect the infection efficiency. Recovery of motility a few hours later after the addition of antiserum was observed. This raises a hypothesis that Leptospira carries surface molecules bound with antibodies toward the cell end to escape and recovers the motility.     

The Flat-Ribbon Configuration of the Periplasmic Flagella of Borrelia burgdorferi and Its Relationship to Motility and Morphology

Electron cryotomography was used to analyze the structure of the Lyme disease spirochete, Borrelia burgdorferi. This methodology offers a new means for studying the native architecture of bacteria by eliminating the chemical fixing, dehydration, and staining steps of conventional electron microscopy. Using electron cryotomography, we noted that membrane blebs formed at the ends of the cells. These blebs may be precursors to vesicles that are released from cells grown in vivo and in vitro. We found that the periplasmic space of B. burgdorferi was quite narrow (16.0 nm) compared to those of Escherichia coli and Pseudomonas aeruginosa. However, in the vicinity of the periplasmic flagella, this space was considerably wider (42.3 nm). In contrast to previous results, the periplasmic flagella did not form a bundle but rather formed a tight-fitting ribbon that wraps around the protoplasmic cell cylinder in a right-handed sense. We show how the ribbon configuration of the assembled periplasmic flagella is more advantageous than a bundle for both swimming and forming the flat-wave morphology. Previous results indicate that B. burgdorferi motility is dependent on the rotation of the periplasmic flagella in generating backward-moving waves along the length of the cell. This swimming requires that the rotation of the flagella exerts force on the cell cylinder. Accordingly, a ribbon is more beneficial than a bundle, as this configuration allows each periplasmic flagellum to have direct contact with the cell cylinder in order to exert that force, and it minimizes interference between the rotating filaments.     

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.     

Purification, Ultrastructure, and Composition of Axial Filaments from Leptospira

The ultrastructure of three strains of water Leptospira was studied by negative staining, thin sectioning, and freeze-etching. The cells possessed a triple-layered sheath which covered two independent axial filaments, one inserted subterminally in each end of the cell. The protoplasmic cylinder was surrounded by a triple-layered cell wall and possessed ribosomes, lamellar structures, and a typical procaryotic nuclear region. The axial filament was comprised of several component structures. An axial fibril, with a diameter of 20 to 25 nm, consisted of a solid inner core (13 to 16 nm in diameter) surrounded by a coat. A terminal knob (40 to 70 nm in length) was connected to a series of disc insertion structures at the terminal end of the axial fibril. The axial fibril was surrounded by a helical outer coat (35 to 60 nm in diameter) which was composed of a continuously coiled fiber, 3 to 4 nm in diameter, embedded in an electron-dense material. A procedure for the purification of the axial fibrils was presented and their ultrastructural, physical, and chemical properties were determined. Similarities in ultrastructural, physical, and chemical properties were noted between the axial fibrils and bacterial flagella. A schematic model of the leptospiral axial filament is presented, and a mechanism is proposed for its function as a locomotor organelle.     

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.     

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.     

Transformations in flagellar structure of Rhodobacter sphaeroides and possible relationship to changes in swimming speed

Rhodobacter sphaeroides is a photosynthetic bacterium which swims by rotating a single flagellum in one direction, periodically stopping, and reorienting during these stops. Free-swimming R. sphaeroides was examined by both differential interference contrast (DIC) microscopy, which allows the flagella of swimming cells to be seen in vivo, and tracking microscopy, which tracks swimming patterns in three dimensions. DIC microscopy showed that when rotation stopped, the helical flagellum relaxed into a high-amplitude, short-wavelength coiled form, confirming previous observations. However, DIC microscopy also revealed that the coiled filament could rotate slowly, reorienting the cell before a transition back to the functional helix. The time taken to reform a functional helix depended on the rate of rotation of the helix and the length of the filament. In addition to these coiled and helical forms, a third conformation was observed: a rapidly rotating, apparently straight form. This form took shape from the cell body out and was seen to form directly from flagella that were initially in either the coiled or the helical conformation. This form was always significantly longer than the coiled or helical form from which it was derived. The resolution of DIC microscopy made it impossible to identify whether this form was genuinely in a straight conformation or was a low-amplitude, long-wavelength helix. Examination of the three-dimensional swimming pattern showed that R. sphaeroides changed speed while swimming, sometimes doubling the swimming speed between stops. The rate of acceleration out of stops was also variable. The transformations in waveform are assumed to be torsionally driven and may be related to the changes in speed measured in free-swimming cells. The roles of and mechanisms that may be involved in the transformations of filament conformations and changes in swimming speed are discussed.     

Three Mutations in Escherichia coli That Generate Transformable Functional Flagella

Hydrodynamics predicts that swimming bacteria generate a propulsion force when a helical flagellum rotates because rotating helices necessarily translate at a low Reynolds number. It is generally believed that the flagella of motile bacteria are semirigid helices with a fixed pitch determined by hydrodynamic principles. Here, we report the characterization of three mutations in laboratory strains of Escherichia coli that produce different steady-state flagella without losing cell motility. E. coli flagella rotate counterclockwise during forward swimming, and the normal form of the flagella is a left-handed helix. A single amino acid exchange A45G and a double mutation of A48S and S110A change the resting flagella to right-handed helices. The stationary flagella of the triple mutant were often straight or slightly curved at neutral pH. Deprotonation facilitates the helix formation of it. The helical and curved flagella can be transformed to the normal form by torsion upon rotation and thus propel the cell. These mutations arose in the long-term laboratory cultivation. However, flagella are under strong selection pressure as extracellular appendages, and similar transformable flagella would be common in natural environments.     

Neither helix in the coiled coil region of the axle of F1-ATPase plays a significant role in torque production

F₁-ATPase is an ATP-driven rotary molecular motor in which the central γ-subunit rotates inside the cylinder made of α₃β₃ subunits. The amino and carboxy termini of the γ-subunit form the axle, an α-helical coiled coil that deeply penetrates the stator cylinder. We previously truncated the axle step by step, starting with the longer carboxy terminus and then cutting both termini at the same levels, resulting in a slower yet considerably powerful rotation. Here we examine the role of each helix by truncating only the carboxy terminus by 25-40 amino-acid residues. Longer truncation impaired the stability of the motor complex severely: 40 deletions failed to yield rotating the complex. Up to 36 deletions, however, the mutants produced an apparent torque at nearly half of the wild-type torque, independent of truncation length. Time-averaged rotary speeds were low because of load-dependent stumbling at 120° intervals, even with saturating ATP. Comparison with our previous work indicates that half the normal torque is produced at the orifice of the stator. The very tip of the carboxy terminus adds the other half, whereas neither helix in the middle of the axle contributes much to torque generation and the rapid progress of catalysis. None of the residues of the entire axle played a specific decisive role in rotation.     

Novel ultrastructures of Treponema primitia and their implications for motility

Members of the bacterial phylum Spirochaetes are generally helical cells propelled by periplasmic flagella. The spirochete Treponema primitia is interesting because of its mutualistic role in the termite gut, where it is believed to cooperate with protozoa that break down cellulose and produce H₂ as a by-product. Here we report the ultrastructure of T. primitia as obtained by electron cryotomography of intact, frozen-hydrated cells. Several previously unrecognized external structures were revealed, including bowl-like objects decorating the outer membrane, arcades of hook-shaped proteins winding along the exterior and tufts of fibrils extending from the cell tips. Inside the periplasm, cone-like structures were found at each pole. Instead of the single peptidoglycan layer typical of other Gram-negative bacteria, two distinct periplasmic layers were observed. These layers formed a central open space that contained two flagella situated adjacent to each other. In some areas, the inner membrane formed flattened invaginations that protruded into the cytoplasm. High-speed light microscopic images of swimming T. primitia cells showed that cell bodies remained rigid and moved in a helical rather than planar motion. Together, these findings support the 'rolling cylinder' model for T. primitia motility that posits rotation of the protoplasmic cylinder within the outer sheath.     

Center of mass motion in swimming fish: effects of speed and locomotor mode during undulatory propulsion

Studies of center of mass (COM) motion are fundamental to understanding the dynamics of animal movement, and have been carried out extensively for terrestrial and aerial locomotion. But despite a large amount of literature describing different body movement patterns in fishes, analyses of how the center of mass moves during undulatory propulsion are not available. These data would be valuable for understanding the dynamics of different body movement patterns and the effect of differing body shapes on locomotor force production. In the present study, we analyzed the magnitude and frequency components of COM motion in three dimensions (x: surge, y: sway, z: heave) in three fish species (eel, bluegill sunfish, and clown knifefish) swimming with four locomotor modes at three speeds using high-speed video, and used an image cross-correlation technique to estimate COM motion, thus enabling untethered and unrestrained locomotion. Anguilliform swimming by eels shows reduced COM surge oscillation magnitude relative to carangiform swimming, but not compared to knifefish using a gymnotiform locomotor style. Labriform swimming (bluegill at 0.5 body lengths/s) displays reduced COM sway oscillation relative to swimming in a carangiform style at higher speeds. Oscillation frequency of the COM in the surge direction occurs at twice the tail beat frequency for carangiform and anguilliform swimming, but at the same frequency as the tail beat for gymnotiform locomotion in clown knifefish. Scaling analysis of COM heave oscillation for terrestrial locomotion suggests that COM heave motion scales with positive allometry, and that fish have relatively low COM oscillations for their body size.     

The Hydrodynamics of a Run-and-Tumble Bacterium Propelled by Polymorphic Helical Flagella

To study the swimming of a peritrichous bacterium such as Escherichia coli, which is able to change its swimming direction actively, we simulate the “run-and-tumble” motion by using a bead-spring model to account for: 1), the hydrodynamic and the mechanical interactions among the cell body and multiple flagella; 2), the reversal of the rotation of a flagellum in a tumble; and 3), the associated polymorphic transformations of the flagellum. Because a flexible hook connects the cell body and each flagellum, the flagella can take independent orientations with respect to the cell body. This simulation reproduces the experimentally observed behaviors of E. coli, namely, a three-dimensional random-walk trajectory in run-and-tumble motion and steady clockwise swimming near a wall. We show that the polymorphic transformation of a flagellum in a tumble facilitates the reorientation of the cell, and that the time-averaged flow-field near a cell in a run has double-layered helical streamlines, with a time-dependent flow magnitude large enough to affect the transport of surrounding chemoattractants.     

Body Fineness Ratio as a Predictor of Maximum Prolonged-Swimming Speed in Coral Reef Fishes

The ability to sustain high swimming speeds is believed to be an important factor affecting resource acquisition in fishes. While we have gained insights into how fin morphology and motion influences swimming performance in coral reef fishes, the role of other traits, such as body shape, remains poorly understood. We explore the ability of two mechanistic models of the causal relationship between body fineness ratio and endurance swimming-performance to predict maximum prolonged-swimming speed (U_max) among 84 fish species from the Great Barrier Reef, Australia. A drag model, based on semi-empirical data on the drag of rigid, submerged bodies of revolution, was applied to species that employ pectoral-fin propulsion with a rigid body at U _max. An alternative model, based on the results of computer simulations of optimal shape in self-propelled undulating bodies, was applied to the species that swim by body-caudal-fin propulsion at U_max. For pectoral-fin swimmers, U_max increased with fineness, and the rate of increase decreased with fineness, as predicted by the drag model. While the mechanistic and statistical models of the relationship between fineness and U_max were very similar, the mechanistic (and statistical) model explained only a small fraction of the variance in U_max. For body-caudal-fin swimmers, we found a non-linear relationship between fineness and U_max, which was largely negative over most of the range of fineness. This pattern fails to support either predictions from the computational models or standard functional interpretations of body shape variation in fishes. Our results suggest that the widespread hypothesis that a more optimal fineness increases endurance-swimming performance via reduced drag should be limited to fishes that swim with rigid bodies.     

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.     

How Does Cilium Length Affect Beating?

The effects of cilium length on the dynamics of cilia motion were investigated by high-speed video microscopy of uniciliated mutants of the swimming alga, Chlamydomonas reinhardtii. Cells with short cilia were obtained by deciliating cells via pH shock and allowing cilia to reassemble for limited times. The frequency of cilia beating was estimated from the motion of the cell body and of the cilium. Key features of the ciliary waveform were quantified from polynomial curves fitted to the cilium in each image frame. Most notably, periodic beating did not emerge until the cilium reached a critical length between 2 and 4 μm. Surprisingly, in cells that exhibited periodic beating, the frequency of beating was similar for all lengths with only a slight decrease in frequency as length increased from 4 μm to the normal length of 10–12 μm. The waveform average curvature (rad/μm) was also conserved as the cilium grew. The mechanical metrics of ciliary propulsion (force, torque, and power) all increased in proportion to length. The mechanical efficiency of beating appeared to be maximal at the normal wild-type length of 10–12 μm. These quantitative features of ciliary behavior illuminate the biophysics of cilia motion and, in future studies, may help distinguish competing hypotheses of the underlying mechanism of oscillation.     

Negative Geotactic Behavior of Paramecium Caudatum is Completely Described by the Mechanism of Buoyancy-Oriented Upward Swimming

This paper presents evidence that the negative geotactic behavior of Paramecium caudatum takes place by the mechanism of buoyancy-oriented upward swimming. Photographs of swimming pathways of the organisms were completely described by two dynamic equations for the translational motion of the center of gravity of the organism's body and for the rotational motion of the organism's body about its center of gravity, where the rotational torque is induced by a slight difference in position between the center of gravity and the center of buoyancy. It now seems unlikely that complicated mechanisms such as the statocyst mechanism and the gravity-propulsion mechanism, which have been proposed by many investigators, need be considered for other protozoa since preliminary observation and analysis of other ciliates such as Paramecium multimicronucleatum, Paramecium tetraurelia, and Tetrahymena pyriformis also strongly suggested that their negative geotaxis is due to buoyancy-oriented upward swimming.     

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

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

Effect of Flow Turbulence on Swimming Speed of Fish

The effect of flow turbulence on the swimming speed was studied in perch (Perca fluviatilis) with different body length. The critical flow rate was used as an index of fish swimming performance. The longer was the fish, the higher turbulence was required to decrease the critical flow rate. The mechanism of turbulence impact on fish locomotion relied on the vortex structure of the flow. The torque produced by hydrodynamic forces in a vortex favors fish overturn and loss of balance. Such effect of turbulence was observed when the sizes of the vortex and fish body were similar. The fish uses the pectoral fins to restore the balance, which increases their hydraulic resistance and, together with energy expenditure for spatial balance control, decreases the swimming speed.