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.     

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.     

Uncovering the Mechanism of Trapping and Cell Orientation during Neisseria gonorrhoeae Twitching Motility

Neisseria gonorrheae bacteria are the causative agent of the second most common sexually transmitted infection in the world. The bacteria move on a surface by means of twitching motility. Their movement is mediated by multiple long and flexible filaments, called type IV pili, that extend from the cell body, attach to the surface, and retract, thus generating a pulling force. Moving cells also use pili to aggregate and form microcolonies. However, the mechanism by which the pili surrounding the cell body work together to propel bacteria remains unclear. Understanding this process will help describe the motility of N. gonorrheae bacteria, and thus the dissemination of the disease which they cause. In this article we track individual twitching cells and observe that their trajectories consist of alternating moving and pausing intervals, while the cell body is preferably oriented with its wide side toward the direction of motion. Based on these data, we propose a model for the collective pili operation of N. gonorrheae bacteria that explains the experimentally observed behavior. Individual pili function independently but can lead to coordinated motion or pausing via the force balance. The geometry of the cell defines its orientation during motion. We show that by changing pili substrate interactions, the motility pattern can be altered in a predictable way. Although the model proposed is tangibly simple, it still has sufficient robustness to incorporate further advanced pili features and various cell geometries to describe other bacteria that employ pili to move on surfaces.     

Uncovering the Mechanism of Trapping and Cell Orientation during Neisseria gonorrhoeae Twitching Motility

Neisseria gonorrheae bacteria are the causative agent of the second most common sexually transmitted infection in the world. The bacteria move on a surface by means of twitching motility. Their movement is mediated by multiple long and flexible filaments, called type IV pili, that extend from the cell body, attach to the surface, and retract, thus generating a pulling force. Moving cells also use pili to aggregate and form microcolonies. However, the mechanism by which the pili surrounding the cell body work together to propel bacteria remains unclear. Understanding this process will help describe the motility of N. gonorrheae bacteria, and thus the dissemination of the disease which they cause. In this article we track individual twitching cells and observe that their trajectories consist of alternating moving and pausing intervals, while the cell body is preferably oriented with its wide side toward the direction of motion. Based on these data, we propose a model for the collective pili operation of N. gonorrheae bacteria that explains the experimentally observed behavior. Individual pili function independently but can lead to coordinated motion or pausing via the force balance. The geometry of the cell defines its orientation during motion. We show that by changing pili substrate interactions, the motility pattern can be altered in a predictable way. Although the model proposed is tangibly simple, it still has sufficient robustness to incorporate further advanced pili features and various cell geometries to describe other bacteria that employ pili to move on surfaces.     

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.     

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.     

Cooperative symmetry-breaking by actin polymerization in a model for cell motility

Polymerizing networks of actin filaments are capable of exerting significant mechanical forces, used by eukaryotic cells and their prokaryotic pathogens to change shape or to move. Here we show that small beads coated uniformly with a protein that catalyses actin polymerization are initially surrounded by symmetrical clouds of actin filaments. This symmetry is broken spontaneously, after which the beads undergo directional motion. We have developed a stochastic theory, in which each actin filament is modelled as an elastic brownian ratchet, that quantitatively accounts for the observed emergent symmetry-breaking behaviour. Symmetry-breaking can only occur for polymers that have a significant subunit off-rate, such as the biopolymers actin and tubulin.     

Spatial Cytoskeleton Organization Supports Targeted Intracellular Transport

The efficiency of intracellular cargo transport from specific sources to target locations is strongly dependent upon molecular motor-assisted motion along the cytoskeleton. Radial transport along microtubules and lateral transport along the filaments of the actin cortex underneath the cell membrane are characteristic for cells with a centrosome. The interplay between the specific cytoskeleton organization and the motor performance results in a spatially inhomogeneous intermittent search strategy. To analyze the efficiency of such intracellular search strategies, we formulate a random velocity model with intermittent arrest states. We evaluate efficiency in terms of mean first passage times for three different, frequently encountered intracellular transport tasks: 1) the narrow escape problem, which emerges during cargo transport to a synapse or other specific region of the cell membrane; 2) the reaction problem, which considers the binding time of two particles within the cell; and 3) the reaction-escape problem, which arises when cargo must be released at a synapse only after pairing with another particle. Our results indicate that cells are able to realize efficient search strategies for various intracellular transport tasks economically through a spatial cytoskeleton organization that involves only a narrow actin cortex rather than a cell body filled with randomly oriented actin filaments.     

Characterization of gliding motility in Flexibacter polymorphus

Motility of the marine gliding bacterium Flexibacter polymorphus was studied by using microcinematographic techniques. Following adhesion to a glass surface, multicellular filaments and individual cells usually began to glide within a few seconds at a speed of approximately 12 micron per second (at 23 degrees C). Adhesion to the glass surface was evidently mediated by multitudes of extremely fine extracellular fibrils. Gliding velocity was independent of filament length but directly related to electron-transport activity and substratum temperature in the range 3-35 degrees C. The rate of gliding was inversely related to medium viscosity, suggesting that the locomotor apparatus functions at constant torque. Forward motion was occasionally interrupted by direction reversals, somersaults (observed primarily in single cells of short filaments), or spinning of filaments tethered by one pole. The frequency of direction reversal was found to be an inverse function of filament length. Translational motility was invariably accompanied by sinistral revolution about the longitudinal axis of a filament. The sense and pitch of revolution were constant among filaments of different length. Polystyrene microspheres or India ink particles adsorbed to gliding cells were actively displaced in either direction, their movement tracing either a regular zigzag or helical path along the filament surface. Because microspheres were also observed to move on nonmotile filaments, particle translocation was evidently not obligatorily linked to gliding locomotion. Multiple particles adsorbed to a single filament often moved independently. The data are consistent with a motility mechanism involving limited motion in numerous mechanically independent (yet functionally coordinated) domains on the cell surface.     

Bacillus subtilis MreB paralogues have different filament architectures and lead to shape remodelling of a heterologous cell system

Like many bacteria, Bacillus subtilis cells contain three actin-like MreB proteins. We show that the three paralogues, MreB, Mbl and MreBH, have different filament architectures in a heterologous cell system, and form straight filaments, helices or ring structures, different from the regular helical arrangement in B. subtilis cells. However, when coexpressed, they colocalize into a single filamentous helical structure, showing that the paralogues influence each other's filament architecture. Ring-like MreBH structures can be converted into MreB-like helical filaments by a single point mutation affecting subunit contacts, showing that MreB paralogues feature flexible filament arrangements. Time-lapse and FRAP experiments show that filaments can extend as well as shrink at both ends, and also show internal rearrangement, suggesting that filaments consist of overlapping bundles of shorter filaments that continuously turn over. Upon induction in Escherichia coli cells, B. subtilis MreB (BsMreB) filaments push the cells into strikingly altered cell morphology, showing that MreB filaments can change cell shape. E. coli cells with a weakened cell wall were ruptured upon induction of BsMreB filaments, suggesting that the bacterial actin orthologue may exert force against the cell membrane and envelope, and thus possibly plays an additional mechanical role in bacteria.     

Mechanical Control of Bacterial Cell Shape

In bacteria, cytoskeletal filament bundles such as MreB control the cell morphology and determine whether the cell takes on a spherical or a rod-like shape. Here we use a theoretical model to describe the interplay of cell wall growth, mechanics, and cytoskeletal filaments in shaping the bacterial cell. We predict that growing cells without MreB exhibit an instability that favors rounded cells. MreB can mechanically reinforce the cell wall and prevent the onset of instability. We propose that the overall bacterial shape is determined by a dynamic turnover of cell wall material that is controlled by mechanical stresses in the wall. The model affirms that morphological transformations with and without MreB are reversible, and quantitatively describes the growth of irregular shapes and cells undergoing division. The theory also suggests a unique coupling between mechanics and chemistry that can control organismal shapes in general.     

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.     

Coupling cell shape and velocity leads to oscillation and circling in keratocyte galvanotaxis

During wound healing, fish keratocyte cells undergo galvanotaxis where they follow a wound-induced electric field. In addition to their stereotypical persistent motion, keratocytes can develop circular motion without a field or oscillate while crawling in the field direction. We developed a coarse-grained phenomenological model that captures these keratocyte behaviors. We fit this model to experimental data on keratocyte response to an electric field being turned on. A critical element of our model is a tendency for cells to turn toward their long axis, arising from a coupling between cell shape and velocity, which gives rise to oscillatory and circular motion. Galvanotaxis is influenced not only by the field-dependent responses, but also cell speed and cell shape relaxation rate. When the cell reacts to an electric field being turned on, our model predicts that stiff, slow cells react slowly but follow the signal reliably. Cells that polarize and align to the field at a faster rate react more quickly and follow the signal more reliably. When cells are exposed to a field that switches direction rapidly, cells follow the average of field directions, while if the field is switched more slowly, cells follow a “staircase” pattern. Our study indicated that a simple phenomenological model coupling cell speed and shape is sufficient to reproduce a broad variety of different keratocyte behaviors, ranging from circling to oscillation to galvanotactic response, by only varying a few parameters.     

Single-vesicle tracking reveals the potential correlation of the movement of cell-bound membrane vesicles (CBMVs) with cell migration

The movement of cell-bound membrane vesicles (CBMVs) on migrating cells is poorly understood. We hypothesized that the movement of CBMVs on migrating cells is different from that on non-migrating cells and can be interfered by external stimuli. To test it, single-vesicle tracking was performed to analyze motion type, speed, displacement, and direction of CBMVs on migrating cells treated with different reagents (Ang-1, TNF-α, LPS, VEGFα, endostatin, Cytochalasin D, and nocodazole) among which the former four promoted cell migration whereas the others inhibited cell migration. We found that cell migration changed CBMVs from non-directed to directed motion and that most CBMVs on untreated migrating cells moved along the migration axis. Interestingly, the migration-promoting reagents played positive roles in CBMV movement (improving directed motion, speed and/or maximal displacement, upregulating the amount of vesicles moving in migration direction) whereas the migration-inhibiting reagents played negative roles (impairing/abolishing directed motion, speed and/or maximal displacement, downregulating the vesicles moving forward or causing an even distribution of motion direction). The cytoskeleton (particularly microtubules) probably played vital roles in CBMV movement on migrating cells and mediated the effects of stimuli on vesicle movement. The data may provide important information for understanding the properties, behaviors, and functions of CBMVs.     

Keratin filament disruption in interphase and mitotic cells--how is it induced?

We have studied the lability of keratin intermediate filaments in epithelial cell lines to try to understand the molecular mechanism that cause the ultrastructural transition from 10 nm filaments to the ball-like aggregates containing 2 to 3 nm filaments. Our results suggest that different growth conditions used in different laboratories may explain some but not all of the discrepancies in the literature on mitotic keratin filament disruption. Such disruption is not only cell type, but also subclone dependent and can be manipulated in one instance by altering the NaHCO3 concentration of the growth medium. An apparently similar filament to aggregate transition can be induced in interphase cells of some epithelial cell lines by incubation in a cold hypotonic buffer, or when cells are pretreated with phorbol ester and then incubated in cold physiological saline. A putative dialyzable and heat-stable factor present in medium conditioned by the growth of particular epithelial cell types may be required for disruption. Keratin polypeptide phosphorylation may play a role in filament labilization.     

Changes in the microstructure of cultured porcine aortic endothelial cells in the early stage after applying a fluid-imposed shear stress.

Time course changes in the cell shape and in the patterns of microfilament distribution were analyzed quantitatively using cultured porcine aortic endothelial cell monolayers before and after a shear flow exposure. Geometrical parameters of the cell and of the microfilament were measured on fluorescent photomicrographs of the cells stained with rhodamine-phalloidin. After the shear flow exposure (20 dyn cm-2, 0-24 h), the endothelial cells on glass were elongated and oriented to the direction of the flow. Under the no-flow condition, F-actin filaments were mainly localized at the periphery of the cell, although some filaments were seen in the more central portion. The angles of the filaments were randomly distributed. After 3 h, the stress fiber-like structure of an F-actin bundle was formed in the central part of the cells, and these filaments were oriented to the direction of the flow. The degree of orientation increased as the time of exposure to shear stress became longer. This change in F-actin preceded cell elongation and orientation; these changes were statistically significant only after 6 h. After 24 h, peripheral filaments were again observed, and the fluorescence intensity of rhodamine-phalloidin-stained cells was enhanced. These findings suggest that the redistribution of F-actin filaments is one of the early cellular responses to the onset of shear stress and that it is one of the most important factors controlling cell elongation and orientation to the direction of the flow.     

Analysis of the Actin–Myosin II System in Fish Epidermal Keratocytes: Mechanism of Cell Body Translocation

While the protrusive event of cell locomotion is thought to be driven by actin polymerization, the mechanism of forward translocation of the cell body is unclear. To elucidate the mechanism of cell body translocation, we analyzed the supramolecular organization of the actin–myosin II system and the dynamics of myosin II in fish epidermal keratocytes. In lamellipodia, long actin filaments formed dense networks with numerous free ends in a brushlike manner near the leading edge. Shorter actin filaments often formed T junctions with longer filaments in the brushlike area, suggesting that new filaments could be nucleated at sides of preexisting filaments or linked to them immediately after nucleation. The polarity of actin filaments was almost uniform, with barbed ends forward throughout most of the lamellipodia but mixed in arc-shaped filament bundles at the lamellipodial/cell body boundary. Myosin II formed discrete clusters of bipolar minifilaments in lamellipodia that increased in size and density towards the cell body boundary and colocalized with actin in boundary bundles. Time-lapse observation demonstrated that myosin clusters appeared in the lamellipodia and remained stationary with respect to the substratum in locomoting cells, but they exhibited retrograde flow in cells tethered in epithelioid colonies. Consequently, both in locomoting and stationary cells, myosin clusters approached the cell body boundary, where they became compressed and aligned, resulting in the formation of boundary bundles. In locomoting cells, the compression was associated with forward displacement of myosin features. These data are not consistent with either sarcomeric or polarized transport mechanisms of cell body translocation. We propose that the forward translocation of the cell body and retrograde flow in the lamellipodia are both driven by contraction of an actin–myosin network in the lamellipodial/cell body transition zone.     

Orientation by helical motion—II. Changing the direction of the axis of motion

We analyse the helical motion of organisms, concentrating on the means by which organisms change the direction in space of the axis of the helical trajectory, which is the net direction of motion. We demonstrate that the direction of the axis is determined largely by the direction of the organism's rotational velocity. Changes in direction of the rotational velocity, with respect to the organism's body, change the direction in space of the axis of the helical trajectory. Conversely, changes in direction of the translational velocity, with respect to the body of the organism, have little effect on the direction in space of the axis of the trajectory. Because the axis of helical motion is the net direction of motion, it is likely that organisms that move in helices change direction by pointing their rotational velocity, not their translational velocity, in a new direction.     

Coordination of protrusion and translocation of the keratocyte involves rolling of the cell body

We have investigated the relationship between lamellipodium protrusion and forward translocation of the cell body in the rapidly moving keratocyte. It is first shown that the trailing, ellipsoidal cell body rotates during translocation. This was indicated by the rotation of the nucleus and the movement of cytoplasmic organelles, as well as of exogenously added beads used as markers. Activated or Con A-coated fluorescent beads that were overrun by cells were commonly endocytosed and rotated with the internal organelles. Alternatively, beads applied to the rear of the cell body via a micropipette adhered to the dorsal cell surface and also moved forward, indicating that both exterior and underlying cortical elements participated in rotation. Manipulation of keratocytes with microneedles demonstrated that pushing or restraining the cell body in the direction of locomotion, and squeezing it against the substrate, which temporarily increased the intracellular pressure, did not effect the rate of lamellipodium protrusion. Rotation and translocation of the cell body continued momentarily after arrest of lamellipodium protrusion by cytochalasin B, indicating that these processes were not directly dependent on actin polymerization. The cell body was commonly flanked by phase-dense "axles," extending from the cell body into the lamellipodium. Phalloidin staining showed these to be comprised of actin bundles that splayed forward into the flanks of the lamellipodium. Disruption of the bundles on one side of the nucleus by traumatic microinjection resulted in rapid retraction of the cell body in the opposite direction, indicating that the cell body was under lateral contractile stress. Myosin II, which colocalizes with the actin bundles, presumably provides the basis of tension generation across and traction of the cell body. We propose that the basis of coupling between lamellipodium protrusion and translocation of the cell body is a flow of actin filaments from the front, where they are nucleated and engage in protrusion, to the rear, where they collaborate with myosin in contraction. Myosin-dependent force is presumably transmitted from the ends of the cell body into the flanks of the lamellipodium via the actin bundles. This force induces the spindle-shaped cell body to roll between the axles that are created continuously from filaments supplied by the advancing lamellipodium.