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.     

Difference between forward and backward swimming speeds of the single polar-flagellated bacterium, Vibrio alginolyticus

The forward and backward swimming speeds and periods of a Vibrio alginolyticus strain that has a single polar flagellum were measured. The backward swimming speeds were 1.5 times greater than the forward ones on average and the average period of backward swimming was shorter than forward swimming. However, the swimming speed and period were not correlated. Similar results were obtained for a mutant that has a 1.6 times longer flagellum on average.     

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.     

Swimming behaviour of the unicellular biflagellate Oxyrrhis marina: in vivo and in vitro movement of the two flagella

The movement of the 2 flagella of Oxyrrhis marina was examined with respect to their individual waveforms and the swimming behavior of the organism. The longitudinal flagella propagated helicoidal waves whose amplitude decreased toward the tip of th flagellum. Their beat frequencies were 50-60 Hz. The transverse flagella beat helicoidally within a furrow. Sudden changes in the direction of the cell trajectories were generated by transient arrests of the longitudinal flagellum beat, which were accompanied by a switch from the backward orientation to a forward one. This sweeping motion generated the rotation of the cell body. Ca2+ ions highly stimulated the frequencies of this arrest response, which compared to the "walking-stick" behavior of sea urchin spermatozoa. Isolated flagella were ATA-reactivated after detergent treatment. They exhibited 2 types of motion within the same experimental conditions. A progressive helicoidal motion was generated upon longitudinal flagellum reactivation, whereas a rolling motion with little progression characterized transverse flagellum reactivation. The differences in motile behavior reflect regulations of flagellar movement which were not destroyed by the isolation procedure and may be indicative of regulation by accessory structures.     

How puffers (Teleostei: Tetraodontidae) swim

Two species of marine Indo-Pacific puffers, Arothron meleagris and A. nigropunctatus , were filmed with a high-speed motion picture camera while swimming in a Brett-type water tunnel at speeds of 1-3.5 body lengths (BL) s⁻¹. The puffers generated thrust by use of their pectoral fins in addition to their dorsal and anal fins; the long axis of the body tilted, mouth upwards, by 3–10) while the fishes swam; antero-ventral body profiles of the fishes changed as swimming speeds increased; pectoral fins undulated and moved 180) out of phase from each other, while dorsal and anal fins oscillated in phase with each other; frequencies of fin movements ( F ) increased linearly in relation to swimming speeds ( Uc(rel) ) and were described by the equation F =1.48 Uc(rel) +1.66; stride lengths also increased at higher Uc(rel) ; and, at swimming speeds above 3.0 BL s⁻¹ puffers began to move their tails in sub carangiform-like modes of burst swimming. These results modify significantly the accepted view of the tetraodonti form mode of median and paired fin swimming.     

The response of rhesus monkey sperm motility to cervical mucus and solid surfaces

Movement characteristics of rhesus monkey spermatozoa were analyzed using high-speed cinemicrography. In the first experiment, spermatozoa were studied at 100 frames/sec in diluted semen near a surface, and after entering ovulatory cervical mucus from a bonnet monkey. In mucus, the spermatozoa swam more slowly, with reduced flagellar beat frequencies. The beat shape was altered, and there was less lateral yawing of the sperm head. In the second experiment, spermatozoa in diluted semen were studied at 500 frames/sec in deep preparations, while swimming near a surface or when in the midplane of these preparations. Those sperm in the midplane swam faster, but with lower beat frequencies than those near the surface, and exhibited much more pronounced yawing motions. Such distinctions in sperm motion are probably hydromechanical in origin and may be significant during transport in the female.     

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.     

Impact of microscopic motility on the swimming behavior of parasites: straighter trypanosomes are more directional

Microorganisms, particularly parasites, have developed sophisticated swimming mechanisms to cope with a varied range of environments. African Trypanosomes, causative agents of fatal illness in humans and animals, use an insect vector (the Tsetse fly) to infect mammals, involving many developmental changes in which cell motility is of prime importance. Our studies reveal that differences in cell body shape are correlated with a diverse range of cell behaviors contributing to the directional motion of the cell. Straighter cells swim more directionally while cells that exhibit little net displacement appear to be more bent. Initiation of cell division, beginning with the emergence of a second flagellum at the base, correlates to directional persistence. Cell trajectory and rapid body fluctuation correlation analysis uncovers two characteristic relaxation times: a short relaxation time due to strong body distortions in the range of 20 to 80 ms and a longer time associated with the persistence in average swimming direction in the order of 15 seconds. Different motility modes, possibly resulting from varying body stiffness, could be of consequence for host invasion during distinct infective stages.     

Direct upstream motility in Escherichia coli

We provide an experimental demonstration of positive rheotaxis (rapid and continuous upstream motility) in wild-type Escherichia coli freely swimming over a surface. This hydrodynamic phenomenon is dominant below a critical shear rate and robust against Brownian motion and cell tumbling. We deduce that individual bacteria entering a flow system can rapidly migrate upstream (>20 μm/s) much faster than a gradually advancing biofilm. Given a bacterial population with a distribution of sizes and swim speeds, local shear rate near the surface determines the dominant hydrodynamic mode for motility, i.e., circular or random trajectories for low shear rates, positive rheotaxis for moderate flow, and sideways swimming at higher shear rates. Faster swimmers can move upstream more rapidly and at higher shear rates, as expected. Interestingly, we also find on average that both swim speed and upstream motility are independent of cell aspect ratio.     

Potassium homeostasis influences the locomotion and encystment of zoospores of plant pathogenic oomycetes

Zoospores of plant pathogenic oomycetes exhibit distinct swimming speeds and patterns under natural conditions. Zoospore swimming is influenced by ion homeostasis and changes in the ionic composition of media. Therefore, we used video microscopy to investigate swimming patterns of five oomycete species in response to changes in potassium homeostasis. In general, zoospore speed tended to be negatively correlated with zoospore size. Three Phytophthora species (Phytophthora palmivora, Phytophthora megakarya, and Phytophthora infestans) swam in straight patterns with speeds ranging from 50 to 250 microm/s whereas two Pythium species (Pythium aphanidermatum and Pythium dissotocum) swam at similar speeds ranging from 180 to 225 microm/s with a pronounced helical trajectory and varying amplitudes. High external concentrations of potassium salts reduced the swimming speed of Ph. palmivora and induced encystment. This was not observed for Py. aphanidermatum. Application of the potassium ionophores gramicidin, nigericin and valinomycin resulted in reduced swimming speeds and changes in the swimming patterns of the Phytophthora species. Therefore, potassium ions play a key role in regulating zoospore behavior.     

The role of hydrodynamic interaction in the locomotion of microorganisms.

A general Boundary Element Method is presented and benchmarked with existing Slender Body Theory results and reflection solutions for the motion of spheres and slender bodies near plane boundaries. This method is used to model the swimming of a microorganism with a spherical cell body, propelled by a single rotating flagellum. The swimming of such an organism near a plane boundary, midway between two plane boundaries or in the vicinity of another similar organism, is investigated. It is found that only a small increase (less than 10%) results in the mean swimming speed of an organism swimming near and parallel to another identical organism. Similarly, only a minor propulsive advantage (again, less than 10% increase in mean swimming speed) is predicted when an organism swims very close and parallel to plane boundaries (such as a microscopic plate and (or) a coverslip, for example). This is explained in terms of the flagellar propulsive advantage derived from an increase in the ratio of the normal to tangential resistance coefficients of a slender body being offset by the apparently equally significant increase in the cell body drag. For an organism swimming normal to and toward a plane boundary, however, it is predicted that (assuming it is rotating its flagellum, relative to its cell body, with a constant angular frequency) the resulting swimming speed decreases asymptotically as the organism approaches the boundary.     

Cell orientation of swimming bacteria: From theoretical simulation to experimental evaluation

The motion of small bacteria consists of two phases: relatively long runs alternate with intermittent stops, back-ups, or tumbles, depending on the species. In polar monotrichous bacteria, the flagellum is anchored at the cell pole inherited from the parent generation (old pole) and is surrounded by a chemoreceptor cluster. During forward swimming, the leading pole is always the pole recently formed in cell division (new pole). The flagella of the peritrichous bacterium Escherichia coli often form a bundle behind the old pole. Its cell orientation and receptor positioning during runs generally mimic that of monotrichous bacteria. When encountering a solid surface, peritrichous bacteria exhibit a circular motion with the leading pole dipping downward. Some polar monotrichous bacteria also perform circular motion near solid boundaries, but during back-ups. In this case, the leading pole points upward. Very little is known about behavior near milieu-air interfaces. Biophysical simulations have revealed some of the mechanisms underlying these phenomena, but leave many questions unanswered. Combining biophysics with molecular techniques will certainly advance our understanding of bacterial locomotion.     

A quasi-elastic light scattering and cinematographic investigation of motile Chlamydomonas reinhardtii.

Quasi-elastic light scattering and cinematographical techniques were used to investigate the motility of Chlamydomonas reinhardtii (wild type). It was found that quantitative information on the trajectory of motion was required for a meaningful interpretation of the autocorrelation functions. Two models for describing the oscillatory motion of the cell were developed; one based on the instantaneous forward-and-backward motion of the cell, and the other based on a sinusoidal perturbation to the average forward motion. Both models gave satisfactory agreement with the shape of the experimentally measured autocorrelation function, thus making it possible to use this measurement to determine mean progressive swimming velocities in a population of greater than 200 cells.     

Rhizobium meliloti swims by unidirectional, intermittent rotation of right-handed flagellar helices.

The 5 to 10 peritrichously inserted complex flagella of Rhizobium meliloti MVII-1 were found to form right-handed flagellar bundles. Bacteria swam at speeds up to 60 microns/s, their random three-dimensional walk consisting of straight runs and quick directional changes (turns) without the vigorous angular motion (tumbling) seen in swimming Escherichia coli cells. Observations of R. meliloti cells tethered by a single flagellar filament revealed that flagellar rotation was exclusively clockwise, interrupted by very brief stops (shorter than 0.1 s), typically every 1 to 2 s. Swimming bacteria responded to chemotactic stimuli by extending their runs, and tethered bacteria responded by prolonged intervals of clockwise rotation. Moreover, the motility tracks of a generally nonchemotactic ("smooth") mutant consisted of long runs without sharp turns, and tethered mutant cells showed continuous clockwise rotation without detectable stops. These observations suggested that the runs of swimming cells correspond to clockwise flagellar rotation, and the turns correspond to the brief rotation stops. We propose that single rotating flagella (depending on their insertion point on the rod-shaped bacterial surface) can reorient a swimming cell whenever the majority of flagellar motors stop.     

The temperature acclimatized swimming speed of selected marine dinoflagellates

Video measurements were used to monitor the temperature acclimatizedswimming speeds (24 hours exposure) of 11 species of marinedinoflagellates, some represented by different clones, on atemperature gradient plate. Although the inherent variabilityamong individuals within a population under the same treatmentwas high, each species or clone could be represented by a responsescatter plot that characterized its temperature-dependent swimmingability. A curve-fitting treatment of the data demonstratedthe similarity of the swimming speed versus temperature responsesfor repetitive trials on a single clone or for different clonesand the diversity of the swimming speed versus temperature responsesamong different species. Comparisons among populations includedviable temperature range, maximum swimming speed and responsecurve shape. All species swam over a broader temperature rangethan that over which growth was detected. Maximum swimming speedwithin the measured group occurred at a cell length of -35 µgThis possible optimum in cell size may result from the hydrodynamiccharacteristics of dinoflagellate swimming. Swimming speed variationamong dinoflagellate species can influence the competitive interactionswithin the group or with other kinds of phytoplankton and canaffect predator-prey interactions with herbivores.     

RELATIONSHIPS BETWEEN SPERM LENGTH AND SPEED DIFFER AMONG THREE INTERNALLY AND THREE EXTERNALLY FERTILIZING SPECIES

It is often assumed that longer sperm, by virtue of their increased swimming speed, have a fertilization advantage over shorter sperm when in competition to fertilize eggs. However, there is surprisingly little evidence for a positive correlation between sperm length and speed. Here we use an approach that accounts for within‐male variation in sperm traits to examine the relationships between sperm length and sperm speed across a broad range of species, including three internally fertilizing species and three externally fertilizing species. Our results reveal that correlations between sperm size and speed are indeed present and possibly more common than currently thought. However, the direction of the correlations between sperm length and speed, which are more prevalent within a male's ejaculate than among males, were influenced by fertilization mode in contrasting and unexpected ways. Broadly, the patterns revealed that in externally fertilizing species sperm with longer flagellum and shorter heads relative to their flagellum swam faster, whereas in internally fertilizing species sperm with shorter flagellum and longer heads relative to their flagellum swam faster. We discuss these results in light of sperm competition theory and contrast the intraspecific patterns observed in this study with macroevolutionary patterns of sperm evolution reported elsewhere.     

Electrokinetic movement of Escherichia coli in capillaries

The movement of Escherichia coli K-12 has been studied in capillaries with an 8 μm inside diameter under a DC electric field. At low applied voltages (< 0.2 V cm⁻¹), bacterial motility is the predominant mode of motion, with bacteria swimming, tumbling and moving unidirectionally towards the anode and the cathode, although a significant difference between the mean moving speeds towards the two electrodes was observed. When the electric field was removed, the mean swimming speeds were the same for both directions. At higher voltages, all the cells were swept by electro-osmotic flow exclusively towards the cathode.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Hydrodynamic interactions between two swimming bacteria

This article evaluates the hydrodynamic interactions between two swimming bacteria precisely. We assume that each bacterium is force free and torque free, with a Stokes flow field around it. The geometry of each bacterium is modeled as a spherical or spheroidal body with a single helical flagellum. The movements of two interacting bacteria in an infinite fluid otherwise at rest are computed using a boundary element method, and the trajectories of the two interacting bacteria and the stresslet are investigated. The results show that as the two bacteria approach each other, they change their orientations considerably in the near field. The bacteria always avoided each other; no stable pairwise swimming motion was observed in this study. The effects of the hydrodynamic interactions between two bacteria on the rheology and diffusivity of a semidilute bacterial suspension are discussed.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.