The shape and dynamics of the Leptospiraceae

Most swimming bacteria produce thrust by rotating helical filaments called flagella. Typically, the flagella stick out into the external fluid environment; however, in the spirochetes, a unique group that includes some highly pathogenic species of bacteria, the flagella are internalized, being incased in the periplasmic space; i.e., between the outer membrane and the cell wall. This coupling between the periplasmic flagella and the cell wall allows the flagella to serve a skeletal, as well as a motile, function. In this article, we propose a mathematical model for spirochete morphology based on the elastic interaction between the cell body and the periplasmic flagella. This model describes the mechanics of the composite structure of the cell cylinder and periplasmic flagella and accounts for the morphology of Leptospiraceae. This model predicts that the cell cylinder should be roughly seven times stiffer than the flagellum. In addition, we explore how rotation of the periplasmic flagellum deforms the cell cylinder during motility. We show that the transition between hook-shaped and spiral-shaped ends is purely a consequence of the change in direction of the flagellar motor and does not require flagellar polymorphism.     

A chimeric N-terminal Escherichia coli--C-terminal Rhodobacter sphaeroides FliG rotor protein supports bidirectional E. coli flagellar rotation and chemotaxis

Flagellate bacteria such as Escherichia coli and Salmonella enterica serovar Typhimurium typically express 5 to 12 flagellar filaments over their cell surface that rotate in clockwise (CW) and counterclockwise directions. These bacteria modulate their swimming direction towards favorable environments by biasing the direction of flagellar rotation in response to various stimuli. In contrast, Rhodobacter sphaeroides expresses a single subpolar flagellum that rotates only CW and responds tactically by a series of biased stops and starts. Rotor protein FliG transiently links the MotAB stators to the rotor, to power rotation and also has an essential function in flagellar export. In this study, we sought to determine whether the FliG protein confers directionality on flagellar motors by testing the functional properties of R. sphaeroides FliG and a chimeric FliG protein, EcRsFliG (N-terminal and central domains of E. coli FliG fused to an R. sphaeroides FliG C terminus), in an E. coli FliG null background. The EcRsFliG chimera supported flagellar synthesis and bidirectional rotation; bacteria swam and tumbled in a manner qualitatively similar to that of the wild type and showed chemotaxis to amino acids. Thus, the FliG C terminus alone does not confer the unidirectional stop-start character of the R. sphaeroides flagellar motor, and its conformation continues to support tactic, switch-protein interactions in a bidirectional motor, despite its evolutionary history in a bacterium with a unidirectional motor.     

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.     

The flagellar filament of Rhodobacter sphaeroides: pH-induced polymorphic transitions and analysis of the fliC gene

Flagellar motility in Rhodobacter sphaeroides is notably different from that in other bacteria. R. sphaeroides moves in a series of runs and stops produced by the intermittent rotation of the flagellar motor. R. sphaeroides has a single, plain filament whose conformation changes according to flagellar motor activity. Conformations adopted during swimming include coiled, helical, and apparently straight forms. This range of morphological transitions is larger than that in other bacteria, where filaments alternate between left- and right-handed helical forms. The polymorphic ability of isolated R. sphaeroides filaments was tested in vitro by varying pH and ionic strength. The isolated filaments could form open-coiled, straight, normal, or curly conformations. The range of transitions made by the R. sphaeroides filament differs from that reported for Salmonella enterica serovar Typhimurium. The sequence of the R. sphaeroides fliC gene, which encodes the flagellin protein, was determined. The gene appears to be controlled by a sigma(28)-dependent promoter. It encodes a predicted peptide of 493 amino acids. Serovar Typhimurium mutants with altered polymorphic ability usually have amino acid changes at the terminal portions of flagellin or a deletion in the central region. There are no obvious major differences in the central regions to explain the difference in polymorphic ability. In serovar Typhimurium filaments, the termini of flagellin monomers have a coiled-coil conformation. The termini of R. sphaeroides flagellin are predicted to have a lower probability of coiled coils than are those of serovar Typhimurium flagellin. This may be one reason for the differences in polymorphic ability between the two filaments.     

On torque and tumbling in swimming Escherichia coli

Bacteria swim by rotating long thin helical filaments, each driven at its base by a reversible rotary motor. When the motors of peritrichous cells turn counterclockwise (CCW), their filaments form bundles that drive the cells forward. We imaged fluorescently labeled cells of Escherichia coli with a high-speed charge-coupled-device camera (500 frames/s) and measured swimming speeds, rotation rates of cell bodies, and rotation rates of flagellar bundles. Using cells stuck to glass, we studied individual filaments, stopping their rotation by exposing the cells to high-intensity light. From these measurements we calculated approximate values for bundle torque and thrust and body torque and drag, and we estimated the filament stiffness. For both immobilized and swimming cells, the motor torque, as estimated using resistive force theory, was significantly lower than the motor torque reported previously. Also, a bundle of several flagella produced little more torque than a single flagellum produced. Motors driving individual filaments frequently changed directions of rotation. Usually, but not always, this led to a change in the handedness of the filament, which went through a sequence of polymorphic transformations, from normal to semicoiled to curly 1 and then, when the motor again spun CCW, back to normal. Motor reversals were necessary, although not always sufficient, to cause changes in filament chirality. Polymorphic transformations among helices having the same handedness occurred without changes in the sign of the applied torque.     

Bacterial cell-body rotation driven by a single flagellar motor and by a bundle

Using self-trapped Escherichia coli bacteria that have intact flagellar bundles on glass surfaces, we study statistical fluctuations of cell-body rotation in a steady (unstimulated) state. These fluctuations underline direction randomization of bacterial swimming trajectories and plays a fundamental role in bacterial chemotaxis. A parallel study is also conducted using a classical rotation assay in which cell-body rotation is driven by a single flagellar motor. These investigations allow us to draw the important conclusion that during periods of counterclockwise motor rotation, which contributes to a run, all flagellar motors are strongly correlated, but during the clockwise period, which contributes to a tumble, individual motors are uncorrelated in long times. Our observation is consistent with the physical picture that formation and maintenance of a coherent flagellar bundle is provided by a single dominant flagellum in the bundle.     

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.     

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.     

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.     

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.     

The bidirectional polar and unidirectional lateral flagellar motors of Vibrio alginolyticus are controlled by a single CheY species

The bacterial flagellar motor is an elaborate molecular machine that converts ion-motive force into mechanical force (rotation). One of its remarkable features is its swift switching of the rotational direction or speed upon binding of the response regulator phospho-CheY, which causes the changes in swimming that achieve chemotaxis. Vibrio alginolyticus has dual flagellar systems: the Na(+)-driven polar flagellum (Pof) and the H(+)-driven lateral flagella (Laf), which are used for swimming in liquid and swarming over surfaces respectively. Here we show that both swimming and surface-swarming of V. alginolyticus involve chemotaxis and are regulated by a single CheY species. Some of the substitutions of CheY residues conserved in various bacteria have different effects on the Pof and Laf motors, implying that CheY interacts with the two motors differently. Furthermore, analyses of tethered cells revealed that their switching modes are different: the Laf motor rotates exclusively counterclockwise and is slowed down by CheY, whereas the Pof motor turns both counterclockwise and clockwise, and CheY controls its rotational direction.     

cheA, cheB, and cheC genes of Escherichia coli and their role in chemotaxis.

Motile but generally nonchemotatic (che) mutants of Escherichia coli were isolated by a simple screening method. A total of 172 independent mutants were examined, and four genes were defined on the basis of mapping and complemenvestigated by determining their null phenotypes with nonsense or bacteriophage Mu-induced mutations. The cheA and cheB products were essential in producing changes of swimming direction and flagellar rotation. The checC product appeared to be an essential component of the flagellum; however, specific mutational alterations of this component allowed flagellar assembly but prevented directional changes in swimming. Since some cheB mutants changed directions incessantly, this gene product may also serve to control the direction of flagellar rotation in response to chemoreceptor signals. Thus most or all of the common elements in the signalling process were involved in the generation and regulation of changes in the direction of flagellar rotation.     

A study of bacterial flagellar bundling

Certain bacteria, such as Escherichia coli (E. coli) and Salmonella typhimurium (S. typhimurium), use multiple flagella often concentrated at one end of their bodies to induce locomotion. Each flagellum is formed in a left-handed helix and has a motor at the base that rotates the flagellum in a corkscrew motion.We present a computational model of the flagellar motion and their hydrodynamic interaction. The model is based on the equations of Stokes flow to describe the fluid motion. The elasticity of the flagella is modeled with a network of elastic springs while the motor is represented by a torque at the base of each flagellum. The fluid velocity due to the forces is described by regularized Stokeslets and the velocity due to the torques by the associated regularized rotlets. Their expressions are derived. The model is used to analyze the swimming motion of a single flagellum and of a group of three flagella in close proximity to one another. When all flagellar motors rotate counterclockwise, the hydrodynamic interaction can lead to bundling. We present an analysis of the flow surrounding the flagella. When at least one of the motors changes its direction of rotation, the same initial conditions lead to a tumbling behavior characterized by the separation of the flagella, changes in their orientation, and no net swimming motion. The analysis of the flow provides some intuition for these processes.     

The fast tumble signal in bacterial chemotaxis

We have analyzed repellent signal processing in Escherichia coli by flash photorelease of leucine from photolabile precursors. We found that 1). response amplitudes of free-swimming cell populations increased with leucine jump concentration, with an apparent Hill coefficient of 1.3 and a half-maximal dose of 14.4 microM; 2). at a 0-0.5 mM leucine concentration jump sufficient to obtain a saturation motile response, the swimming cell response time of approximately 0.05 s was several-fold more rapid than the motor response time of 0.39 +/- 0.18 s measured by following the rotation of cells tethered by a single flagellum to quartz coverslips; and 3). the motor response time of individual cells was correlated with rotation bias but not cell size. These results provide information on amplification, rate-limiting step, and flagellar bundle mechanics during repellent signal processing. The difference between the half-maximal dose for the excitation response and the corresponding value reported for adaptation provides an estimate of the increase in the rate of formation of CheYP, the phosphorylated form of the signal protein CheY. The estimated increase gives a lower limit receptor kinase coupling ratio of 6.0. The magnitude and form of the motor response time distribution argue for it being determined by the poststimulus switching probability rather than CheYP turnover, diffusion, or binding. The temporal difference between the tethered and swimming cell response times to repellents can be quantitatively accounted for and suggests that one flagellum is sufficient to cause a measurable change of direction in which a bacterium swims.     

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.     

Characterization of two sets of subpolar flagella in Bradyrhizobium japonicum

Bradyrhizobium japonicum is one of the soil bacteria that form nodules on soybean roots. The cell has two sets of flagellar systems, one thick flagellum and a few thin flagella, uniquely growing at subpolar positions. The thick flagellum appears to be semicoiled in morphology, and the thin flagella were in a tight-curly form as observed by dark-field microscopy. Flagellin genes were identified from the amino acid sequence of each flagellin. Flagellar genes for the thick flagellum are scattered into several clusters on the genome, while those genes for the thin flagellum are compactly organized in one cluster. Both types of flagella are powered by proton-driven motors. The swimming propulsion is supplied mainly by the thick flagellum. B. japonicum flagellar systems resemble the polar-lateral flagellar systems of Vibrio species but differ in several aspects.     

The switching dynamics of the bacterial flagellar motor

Many bacteria are propelled by flagellar motors that stochastically switch between the clockwise and counterclockwise rotation direction. Although the switching dynamics is one of their most important characteristics, the mechanisms that control it are poorly understood. We present a statistical–mechanical model of the bacterial flagellar motor. At its heart is the assumption that the rotor protein complex, which is connected to the flagellum, can exist in two conformational states and that switching between these states depends on the interactions with the stator proteins, which drive the rotor. This couples switching to rotation, making the switch sensitive to torque and speed. Another key element is that after a switch, it takes time for the load to build up, due to conformational transitions of the flagellum. This slow relaxation dynamics of the filament leads, in combination with the load dependence of the switching frequency, to a characteristic switching time, as recently observed. Hence, our model predicts that the switching dynamics is not only controlled by the chemotaxis‐signaling network, but also by mechanical feedback of the flagellum.     

Domain structure of flagellin

The chemotaxis of bacteria such as Salmonella and Escherichia coli involves smooth swimming punctuated by periods of tumbling. In smooth swimming the flagellar filaments are left-handed, in tumbling they are right-handed with a different wavelength. The filaments are constructed from a globular protein, flagellin, by a process of self-assembly. The existing models assume that the flagellin molecule is bistable and longitudinal rows of subunits take one of the two possible conformations. Such a model explains the observed different morphology of the flagellum. We have studied Salmonella and E. coli flagellins in polymeric and monomeric forms by scanning microcalorimetry and circular dichroism. We have inferred that a flagellin molecule consists of several domains, two of which are structured at physiological temperatures and are in the monomeric form, while the others acquire a regular form only in the process of polymerization. This phenomenon may be the basis of a process during which the flagellin molecule, fitting into the flagellum, acquires a conformation analogous to that of the neighbouring molecule in the longitudinal row.