The most efficient metazoan swimmer creates a ‘virtual wall’ to enhance performance

It has been well documented that animals (and machines) swimming or flying near a solid boundary get a boost in performance. This ground effect is often modelled as an interaction between a mirrored pair of vortices represented by a true vortex and an opposite sign ‘virtual vortex’ on the other side of the wall. However, most animals do not swim near solid surfaces and thus near body vortex–vortex interactions in open-water swimmers have been poorly investigated. In this study, we examine the most energetically efficient metazoan swimmer known to date, the jellyfish Aurelia aurita, to elucidate the role that vortex interactions can play in animals that swim away from solid boundaries. We used high-speed video tracking, laser-based digital particle image velocimetry (dPIV) and an algorithm for extracting pressure fields from flow velocity vectors to quantify swimming performance and the effect of near body vortex–vortex interactions. Here, we show that a vortex ring (stopping vortex), created underneath the animal during the previous swim cycle, is critical for increasing propulsive performance. This well-positioned stopping vortex acts in the same way as a virtual vortex during wall-effect performance enhancement, by helping converge fluid at the underside of the propulsive surface and generating significantly higher pressures which result in greater thrust. These findings advocate that jellyfish can generate a wall-effect boost in open water by creating what amounts to a ‘virtual wall’ between two real, opposite sign vortex rings. This explains the significant propulsive advantage jellyfish possess over other metazoans and represents important implications for bio-engineered propulsion systems.     

Difference in bacterial motion between forward and backward swimming caused by the wall effect

A bacterial cell that has a single polar flagellum alternately repeats forward swimming, in which the flagellum pushes the cell body, and backward swimming, in which the flagellum pulls the cell body. We have reported that the backward swimming speeds of Vibrio alginolyticus are on average greater than the forward swimming speeds. In this study, we quantitatively measured the shape of the trajectory as well as the swimming speed. The trajectory shape in the forward mode was almost straight, whereas that in the backward mode was curved. The same parameters were measured at different distances from a surface. The difference in the motion characteristics between swimming modes was significant when a cell swam near a surface. In contrast, the difference was indistinguishable when a cell swam >60 microm away from any surfaces. In addition, a cell in backward mode tended to stay near the surface longer than a cell in forward mode. This wall effect on the bacterial motion was independent of chemical modification of the glass surface. The macroscopic behavior is numerically simulated on the basis of experimental results and the significance of the phenomenon reported here is discussed.     

Hydrodynamics of Sperm Cells near Surfaces

Sperm are propelled by an actively beating tail, and display a wide variety of swimming patterns. When confined between two parallel walls, sperm swim either in circles or on curvilinear trajectories close to the walls. We employ mesoscale hydrodynamics simulations in combination with a mechanical sperm model to study the swimming behavior near walls. The simulations show that sperm become captured at the wall due to the hydrodynamic flow fields which are generated by the flagellar beat. The circular trajectories are determined by the chiral asymmetry of the sperm shape. For strong (weak) chirality, sperm swim in tight (wide) circles, with the beating plane of the flagellum oriented perpendicular (parallel) to the wall. For comparison, we also perform simulations based on a local anisotropic friction of the flagellum. In this resistive force approximation, surface adhesion and circular swimming patterns are obtained as well. However, the adhesion mechanism is now due to steric repulsion, and the orientation of the beating plane is different. Our model provides a theoretical framework that explains several distinct swimming behaviors of sperm near and far from a wall. Moreover, the model suggests a mechanism by which sperm navigate in a chemical gradient via a change of their shape.     

Helicobacter pylori strains vary cell shape and flagellum number to maintain robust motility in viscous environments

The helical shape of the human stomach pathogen Helicobacter pylori has been suggested to provide mechanical advantage for penetrating the viscous stomach mucus layer. Using single‐cell tracking and quantitative morphology analysis, we document marked variation in cell body helical parameters and flagellum number among H. pylori strains leading to distinct and broad speed distributions in broth and viscous gastric mucin media. These distributions reflect both temporal variation in swimming speed and morphologic variation within the population. Isogenic mutants with straight‐rod morphology showed 7–21% reduction in speed and a lower fraction of motile bacteria. Mutational perturbation of flagellum number revealed a 19% increase in speed with 4 versus 3 median flagellum number. Resistive force theory modeling incorporating variation of both cell shape and flagellum number predicts qualitative speed differences of 10–30% among strains. However, quantitative comparisons suggest resistive force theory underestimates the influence of cell body shape on speed for helical shaped bacteria.     

A fluid-dynamic interpretation of the asymmetric motion of singly flagellated bacteria swimming close to a boundary

The singly flagellated bacterium, Vibrio alginolyticus, moves forward and backward by alternating the rotational direction of its flagellum. The bacterium has been observed retracing a previous path almost exactly and swimming in a zigzag pattern. In the presence of a boundary, however, the motion changes significantly, to something closer to a circular trajectory. Additionally, when the cell swims close to a wall, the forward and backward speeds differ noticeably. This study details a boundary element model for the motion of a bacterium swimming near a rigid boundary and the results of numerical analyses conducted using this model. The results reveal that bacterium motion is apparently influenced by pitch angle, i.e., the angle between the boundary and the swimming direction, and that forward motion is more stable than backward motion with respect to pitching of the bacterium. From these results, a set of diagrammatic representations have been created that explain the observed asymmetry in trajectory and speed between the forward and backward motions. For forward motion, a cell moving parallel to the boundary will maintain this trajectory. However, for backward motion, the resulting trajectory depends upon whether the bacterium is approaching or departing the boundary. Fluid-dynamic interactions between the flagellum and the boundary vary with cell orientation and cause peculiarities in the resulting trajectories.     

Locomotion of Gymnarchus Niloticus： Experiment and Kinematics

In addition to forward undulatory swimming, Gymnarchus niloticus can swim via undulations of the dorsal fin while the body axis remains straight; furthermore, it swims forward and backward in a similar way, which indicates that the undulation of the dorsal fin can simultaneously provide bidirectional propulsive and maneuvering forces with the help of the tail fin. A high-resolution Charge-Coupled Device （CCD） imaging camera system is used to record kinematics of steady swimming as well as maneuvering in G. niloticus. Based on experimental data, this paper discusses the kinematics （cruising speed, wave speed, cycle frequency, amplitude, lateral displacement） of forward as well as backward swimming and maneuvering. During forward swimming, the propulsive force is generated mainly by undulations of the dorsal fin while the body axis remains straight. The kinematic parameters （wave speed, wavelength, cycle frequency, amplitude） have statistically significant correlations with cruising speed. In addition, the yaw at the head is minimal during steady swimming. From experimental data, the maximal lateral displacement of head is not more than 1% of the body length, while the maximal lateral displacement of the whole body is not more than 5% of the body length. Another important feature is that G. niloticus swims backwards using an undulatory mechanism that resembles the forward undulatory swimming mechanism. In backward swimming, the increase of lateral displacement of the head is comparatively significant; the amplitude profiles of the propulsive wave along the dorsal fin are significantly different from those in forward swimming. When G. niloticus does fast maneuvering, its body is first bent into either a C shape or an S shape, then it is rapidly unwound in a travelling wave fashion. It rarely maneuvers without the help of the tail fin and body bending.     

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 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.     

Effect of body roll amplitude and arm rotation speed on propulsion of arm amputee swimmers

Only a limited amount of research has gone into evaluating the contribution made by the upper arm to the propulsion of elite swimmers with an amputation at elbow level. With assistance of computational fluid dynamics (CFD) modelling, the swimming technique of competitive arm amputee swimmers can be assessed through numerical simulations which test the effect of various parameters on the effectiveness of the swimming propulsion.This numerical study investigates the effect of body roll amplitude and of upper arm rotation speed on the propulsion of an arm amputee swimmer, at different mean swimming speeds. Various test cases are simulated resulting in a thorough analysis of the complex body/fluid interaction with a detailed quantitative assessment of the effect of the variation of each parameter on the arm propulsion. It is found that a body roll movement with an amplitude of 45° enhances greatly the propulsive contribution from the upper arm with an increase of about 70% in the propulsive force compared to the no roll condition. An increase in the angular velocity of the upper arm also leads to a concomitant increase in the propulsive forces produced by the arm.Such results have direct implications for competitive arm amputee front crawl swimmers and for those who coach them. One important message that emerges in this present work is that there exists, for any given swimming speed, a minimum angular velocity at which the upper arm must be rotated to generate effective propulsion. Below this velocity, the upper arm will experience a net resistive drag force which adversely affects swimming performance.     

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

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

Tail loss, body condition and swimming performances in tiger snakes, Notechis ater occidentalis

In limbless tetrapods such as snakes, propulsive forces are generated by lateral undulations of the body and of the tail. In a large population of tiger snakes from Western Australia, tail loss was extremely common (58% of the individuals) and often very severe (more than two-thirds of the tail was missing in 14% of the cases, and in some instances, the tail was totally lost). Tail loss was not however correlated with body size, mass or body condition of wild individuals, and hence did not influence their abilities to acquire resources. These large venomous snakes exhibit marked aquatic habits. Locomotor tests in controlled conditions revealed that tail loss had a significant negative influence on burst swimming performances. However, no effect was found on routine swimming speed and total distance travelled over 5 min. These results suggest that a long and slender tail, although important for maximal speed, is not necessarily relevant for the locomotor abilities required for successful hunting. Tail-damaged individuals outnumbered intact snakes, suggesting that tail loss did not severely compromise survival. Overall, in this species, a slight deterioration of maximal speed due to severe tail loss probably has a low (undetectable) ecological impact, at least for adults.     

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.     

Characterization of lateral flagella of Selenomonas ruminantium

Selenomonas ruminantium produces a tuft of flagella near the midpoint of the cell body and swims by rotating the cell body along the cell's long axis. The flagellum is composed of a single kind of flagellin, which is heavily glycosylated. The hook length of S. ruminantium is almost double that of Salmonella.     

Propulsive forces on the flagellum during locomotion of Chlamydomonas reinhardtii

The distributed propulsive forces exerted on the flagellum of the swimming alga Chlamydomonas reinhardtii by surrounding fluid were estimated from experimental image data. Images of uniflagellate mutant Chlamydomonas cells were obtained at 350 frames/s with 125-nm spatial resolution, and the motion of the cell body and the flagellum were analyzed in the context of low-Reynolds-number fluid mechanics. Wild-type uniflagellate cells, as well as uniflagellate cells lacking inner dynein arms (ida3) or outer dynein arms (oda2) were studied. Ida3 cells exhibit stunted flagellar waveforms, whereas oda2 cells beat with lower frequency. Image registration and sorting algorithms provided high-resolution estimates of the motion of the cell body, as well as detailed kinematics of the flagellum. The swimming cell was modeled as an ellipsoid in Stokes flow, propelled by viscous forces on the flagellum. The normal and tangential components of force on the flagellum (f_N and f_T) were related by resistive coefficients (C_N and C_T) to the corresponding components of velocity (V_N and V_T).The values of these coefficients were estimated by satisfying equilibrium requirements for force and torque on the cell. The estimated values of the resistive coefficients are consistent among all three genotypes and similar to theoretical predictions.     

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.     

Foreflipper propulsion in the California sea lion, Zalophus californianus

The family Otariidae comprises the only group of marine mammals that habitually use their pectoral appendages to generate propulsive forces during swimming. This method of propulsion was examined in the California sea lion ( Zalophus californianus ), a representative member of the family. High-speed films were taken as a sea lion swam against a water current generated inside a large flow channel. Thrust production was determined by examining the body's movement at various stages of the propulsive cycle. Sea lions generate thrust continuously throughout the stroke. Over its initial three-quarters, foreflippers act as hydrofoils creating forward thrust and lift as they move vertically through the water. Thrust production is greatest, however, near the end of the stroke, when flippers are used as paddles and are oriented broad side to the oncoming flow. The force generated by this three-phased system of propulsion is likely to be greater than that attainable by either an exclusively lift-based hydrofoil or drag-based paddling style of swimming.
The kinematic changes that enable sea lions to change speed were also investigated. Film records revealed that stroke amplitude became greater with speed, although total stroke duration remained essentially constant. Sea lions increase stroke frequency with velocity but large variations in the measured values suggest that changes in amplitude and flipper angle of attack are also important parameters for modulating swimming speed.     

Energetics of swimming by the ferret: consequences of forelimb paddling.

The domestic ferret (Mustela putorius furo) swims by alternate strokes of the forelimbs. This pectoral paddling is rare among semi-aquatic mammals. The energetic implications of swimming by pectoral paddling were examined by kinematic analysis and measurement of oxygen consumption. Ferrets maintained a constant stroke frequency, but increased swimming speed by increasing stroke amplitude. The ratio of swimming velocity to foot stroke velocity was low, indicating a low propulsive efficiency. Metabolic rate increased linearly with increasing speed. The cost of transport decreased with increasing swimming speed to a minimum of 3.59+/-0.28 J N(-1) m(-1) at U=0.44 m s(-1). The minimum cost of transport for the ferret was greater than values for semi-aquatic mammals using hind limb paddling, but lower than the minimum cost of transport for the closely related quadrupedally paddling mink. Differences in energetic performance may be due to the amount of muscle recruited for propulsion and the interrelationship hydrodynamic drag and interference between flow over the body surface and flow induced by propulsive appendages.     

Energetics of swimming by the ferret: consequences of forelimb paddling

The domestic ferret (Mustela putorius furo) swims by alternate strokes of the forelimbs. This pectoral paddling is rare among semi-aquatic mammals. The energetic implications of swimming by pectoral paddling were examined by kinematic analysis and measurement of oxygen consumption. Ferrets maintained a constant stroke frequency, but increased swimming speed by increasing stroke amplitude. The ratio of swimming velocity to foot stroke velocity was low, indicating a low propulsive efficiency. Metabolic rate increased linearly with increasing speed. The cost of transport decreased with increasing swimming speed to a minimum of 3.59+/-0.28 J N(-1) m(-1) at U=0.44 m s(-1). The minimum cost of transport for the ferret was greater than values for semi-aquatic mammals using hind limb paddling, but lower than the minimum cost of transport for the closely related quadrupedally paddling mink. Differences in energetic performance may be due to the amount of muscle recruited for propulsion and the interrelationship hydrodynamic drag and interference between flow over the body surface and flow induced by propulsive appendages.     

Kinematics of swimming garter snakes (Thamnophis sirtalis).

We investigate the kinematics of swimming garter snakes (Thamnophis sirtalis) using a novel nonlinear regression-based digitization method to establish quantitative statistical support for non-constant wavelengths in the undulatory pattern exhibited by swimming snakes. We find that in swimming snakes, the growth of the amplitude of the propulsive wave head-to-tail is strongly correlated (p < 0.005) with the head-to-tail growth in the wavelength. We investigate correlations between kinematic parameters and steady swimming speed, and find a very strong positive correlation between swimming speed and undulation frequency. We furthermore find a statistically well-supported positive correlation between swimming speed and both the initial amplitude of the propulsive wave at the head and the degree of amplitude growth from head to tail.     

Kinematics of swimming garter snakes (Thamnophis sirtalis)

We investigate the kinematics of swimming garter snakes (Thamnophis sirtalis) using a novel nonlinear regression-based digitization method to establish quantitative statistical support for non-constant wavelengths in the undulatory pattern exhibited by swimming snakes. We find that in swimming snakes, the growth of the amplitude of the propulsive wave head-to-tail is strongly correlated (p < 0.005) with the head-to-tail growth in the wavelength. We investigate correlations between kinematic parameters and steady swimming speed, and find a very strong positive correlation between swimming speed and undulation frequency. We furthermore find a statistically well-supported positive correlation between swimming speed and both the initial amplitude of the propulsive wave at the head and the degree of amplitude growth from head to tail.