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.     

Morphology, function and isolation of halobacterial flagella

Halobacterium halobium has right-handed helical flagella. During the logarithmic phase of growth, cells are predominantly monopolar, whereas in the stationary phase they are mostly bipolarly flagellated. The flagellar bundle consists of several filaments. Halobacteria swim forward by clockwise and backwards by counterclockwise rotation of their flagella. The flagellar bundle does not fly apart when the sense of rotation changes. In addition to the flagella attached to the cells, large amounts of loose flagella, which aggregate into thick super-flagella, can be observed at all phases of growth. During stationary phase, the production of these super-flagella, which are generally 10 to 20 times longer than the cell body, is significantly higher. Dissociation and association by high temperature and differential centrifugation allow the isolation of pure flagella. Three different protein bands, of 23,500, 26,500 and 31,500 apparent molecular weights, are seen on sodium dodecyl sulphate/polyacrylamide gels. Antibodies against halobacterial flagella were produced in chicken; these antibodies interact with the flagella even in 4 M-NaCl. Rotation of tethered cells demonstrates that Halobacteria move due to the rotation of the flagella.     

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.     

Ultrastructure and development of the amoebo-flagellate cells of the protostelidProtosporangium articulatum

Summary Amoebo-flagellate cells develop upon spore germination in the protostelidProtosporangium articulatum. The germling may emerge flagellate or as an amoeba. In either case the cell undergoes mitosis within an hour of germination. The spindle is open and centric, and typically has several pairs of kinetosomes at the poles. During telophase, the kinetosomes are found at the surface of the cell and flagella and flagellar rootlets begin to develop. Some flagella remain in close association with the nucleus, the nucleus-associated flagella; others are located away from the nucleus, the supernumerary flagella. The flagellar apparatus is identical for both nucleus-associated flagella and supernumerary flagella. However, only the nucleus-associated flagella are able to generate the jerking, helical swim typical of amoebo-flagellates with a swarm cell-like morphology.     

Trailing flagella rotate faster than leading flagella in unipolar cells of Spirillum volutans.

In unipolar cells of Spirillum volutans, the flagellar rotation frequency is halved, approximately, when the flagellar bundle reorientates to rotate about the cell body and reverse the swimming direction. The viscous drag resulting from a concomitant increase in flagellar wave amplitude is probably responsible for the reduced frequency of flagellar rotation.     

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

We introduce a 3D model for a motile rod-shaped bacterial cell with a single polar flagellum which is based on the configuration of a monotrichous type of bacteria such as Pseudomonas aeruginosa. The structure of the model bacterial cell consists of a cylindrical body together with the flagellar forces produced by the rotation of a helical flagellum. The rod-shaped cell body is composed of a set of immersed boundary points and elastic links. The helical flagellum is assumed to be rigid and modeled as a set of discrete points along the helical flagellum and flagellar hook. A set of flagellar forces are applied along this helical curve as the flagellum rotates. An additional set of torque balance forces are applied on the cell body to induce counter-rotation of the body and provide torque balance. The three-dimensional Navier–Stokes equations for incompressible fluid are used to describe the fluid dynamics of the coupled fluid–microorganism system using Peskin’s immersed boundary method. A study of numerical convergence is presented along with simulations of a single swimming cell, the hydrodynamic interaction of two cells, and the interaction of a small cluster of cells.     

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.     

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.     

Upcoming flow promotes the bundle formation of bacterial flagella

Flagellated bacteria swim by rotating a bundle of helical flagella and commonly explore the surrounding environment in a “run-and-tumble” motility mode. Here, we show that the upcoming flow could impact the bacterial run-and-tumble behavior by affecting the formation and dispersal of the flagellar bundle. Using a dual optical tweezers setup to trap individual bacteria, we characterized the effects of the imposed fluid flow and cell body rotation on the run-and-tumble behavior. We found that the two factors affect the behavior differently, with the imposed fluid flow increasing the running time and decreasing the tumbling time and the cell body rotation decreasing the tumbling time only. Using numerical simulations, we computed the flagellar bundling time as a function of flow velocity, which agrees well with our experimental observations. The mechanical effects we characterized here provide novel, to our knowledge, ingredients for further studies of bacterial chemotaxis in complex environments such as dynamic fluid environments.     

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.     

DEVELOPMENT OF THE FLAGELLAR APPARATUS AND FLAGELLAR POSITION IN THE COLONIAL GREEN ALGA PLATYDORINA CAUDATA (CHLOROPHYCEAE)1

The ultrastructure of the flagellar apparatus in pre-inversion and inversion stages of Platydorina resembles that of Chlamydomonas in having 180° rotational symmetry and clockwise absolute orientation. Basal bodies are in a “V” configuration and connected by one distal and two proximal fibers. Alternating two- and four-membered microtubular rootlets are cruciately arranged. During maturation, the basal bodies rotate and separate, and 180° rotational symmetry is lost. Simultaneously, each proximal fiber detaches from one of the functional basal bodies, and the distal fiber detaches from both. The mature apparatus has widely separated and nearly parallel basal bodies. Flagellar orientation in Platydorina is completed just after inversion and a flattening of the colony called intercalation, resulting in the pairs of flagella of neighboring cells extending from the colony in opposite directions in an alternating fashion. Flagellar orientation and separated basal bodies minimize the interference between the flagella of neighboring cells. Basal bodies and rootlets of the two intercalated halves of a colony rotate, resulting in the effective strokes of the flagella of every cell being towards the colonial posterior. The flagella of each cell beat with an effective stroke in the direction of the two inner rootlets. The flagella have an asymmetrical ciliary type beat. The rotated, separated, and parallel basal bodies, together with the nearly parallel rootlets probably are adaptations for movement of this colonial volvocalean alga. The flagellar apparatus in immature stages of Platydorina lends support to the suggestion that the alga has evolved from a Chlamydomonas-like ancestor.     

How dinoflagellates swim

Dinoflagellates possess two flagella; usually these are directed perpendicular to one another constituting a transversal flagellum and a longitudinal, trailing flagellum, respectively. The transversal flagellum causes the cell to rotate around its length axis. The trailing flagellum is responsible for the translation of the cell; due to its asymmetric insertion it also causes a rotation of the cell around an axis perpendicular to the longitudinal axis. Together, these two rotational components result in a helical swimming path. Cells can vary the two rotational components independently as well as the translational velocity. With these three degrees of freedom, cells can vary the parameters of their helical swimming paths for steering. Dinoflagellates use this mechanism for orientation in chemical concentration gradients (“helical klinotaxis”).     

Spirochetes flagellar collar protein FlbB has astounding effects in orientation of periplasmic flagella,bacterial shape,motility, and assembly of motors in Borrelia burgdorferi

Borrelia burgdorferi, the causative agent of Lyme disease, is a highly motile spirochete, and motility, which is provided by its periplasmic flagella, is critical for every part of the spirochete's enzootic life cycle. Unlike externally flagellated bacteria, spirochetes possess a unique periplasmic flagellar structure called the collar. This spirochete‐specific novel component is linked to the flagellar basal body; however, nothing is known about the proteins encoding the collar or their function in any spirochete. To identify a collar protein and determine its function, we employed a comprehensive strategy that included genetic, biochemical, and microscopic analyses. We found that BB0286 (FlbB) is a novel flagellar motor protein, which is located around the flagellar basal body. Deletion of bb0286 has a profound effect on collar formation, assembly of other flagellar structures, morphology, and motility of the spirochete. Orientation of the flagella toward the cell body is critical for determination of wild‐type spirochete's wave‐like morphology and motility. Here, we provide the first evidence that FlbB is a key determinant of normal orientation of the flagella and collar assembly.     

The cell biology of peritrichous flagella in Bacillus subtilis

Bacterial flagella are highly conserved molecular machines that have been extensively studied for assembly, function and gene regulation. Less studied is how and why bacteria differ based on the number and arrangement of the flagella they synthesize. Here we explore the cell biology of peritrichous flagella in the model bacterium Bacillus subtilis by fluorescently labelling flagellar basal bodies, hooks and filaments. We find that the average B. subtilis cell assembles approximately 26 flagellar basal bodies and we show that basal body number is controlled by SwrA. Basal bodies are assembled rapidly (< 5 min) but the assembly of flagella capable of supporting motility is rate limited by filament polymerization (> 40 min). We find that basal bodies are not positioned randomly on the cell surface. Rather, basal bodies occupy a grid‐like pattern organized symmetrically around the midcell and that flagella are discouraged at the poles. Basal body position is genetically determined by FlhF and FlhG homologues to control spatial patterning differently from what is seen in bacteria with polar flagella. Finally, spatial control of flagella in B. subtilis seems more relevant to the inheritance of flagella and motility of individual cells than the motile behaviour of populations.     

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.     

Coarse-grained molecular dynamics simulations of a rotating bacterial flagellum

Many types of bacteria propel themselves using elongated structures known as flagella. The bacterial flagellar filament is a relatively simple and well-studied macromolecular assembly, which assumes different helical shapes when rotated in different directions. This polymorphism enables a bacterium to switch between running and tumbling modes; however, the mechanism governing the filament polymorphism is not completely understood. Here we report a study of the bacterial flagellar filament using numerical simulations that employ a novel coarse-grained molecular dynamics method. The simulations reveal the dynamics of a half-micrometer-long flagellum segment on a timescale of tens of microseconds. Depending on the rotation direction, specific modes of filament coiling and arrangement of monomers are observed, in qualitative agreement with experimental observations of flagellar polymorphism. We find that solvent-protein interactions are likely to contribute to the polymorphic helical shapes of the filament.