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.     

Methods of measuring swimming speed of spermatozoa.

Three basic approaches for determining the mean swimming speed of a suspension of microorganisms were compared, using bull and ram spermatozoa. Number fluctuation counting was performed automatically on a Quantimet 720 image analysing computer, the mean speed being obtained using 'probability after' statistics. The other two approaches were photomicrographic: number flux counting was performed on single photomicrographs; on the same photomicrographs, the mean speed was estimated from measurement of 'whole' and 'half' track lengths. These results were compared with each other and with the Quantimet results. The 'probability after' method was also compared, on additional samples, with cine-photomicrographic tracking. The mean speeds predicted by the 'probability after' method compared favourably with the other methods (range 68 mum/sec to 162 mum/sec). The results also suggested that, on single photomicrographs, measurement of 'half' track lengths or number flux counting were generally preferable to measurement of whole track lengths.     

Critical swimming speed: its ecological relevance.

Critical swimming speed (U(crit)) is a standard measurement to assess swimming capabilities of fishes. To conduct this measurement a fish is introduced into a water tunnel in which the current velocity can be controlled by the investigator. At the beginning of the measurement water velocity is low, approximately 1 body length (BL) s(-1), and is then incrementally increased at prescribed intervals. Fishes tend to maintain their position in the water tunnel against the current until fatigue sets in. The time and velocity at which the fish fatigue are used to calculate the critical swimming speed. This procedure is widely used to assess the effects of environmental conditions and pollutants on fish performance. Since the procedure is conducted in conditions that are far from representing most natural environment experienced by fishes, doubts have been raised about its ecological and ecophysiological relevance. Few studies examined correlations between critical swimming speed and traits that seem to be more ecologically relevant. Positive correlations were found between U(crit) and routine activity, metabolic rates and body size of open water, planktivorous fishes, metabolic rates and body size. These data indirectly suggest ecological relevancy of U(crit), but direct measurements relating U(crit) to reproductive success or survival are required to assess such relevancy.     

A mathematical explanation of an increase in bacterial swimming speed with viscosity in linear-polymer solutions

Bacterial swimming speed is sometimes known to increase with viscosity. This phenomenon is peculiar to bacterial motion. Berg and Turner (Nature. 278:349-351, 1979) indicated that the phenomenon was caused by a loose, quasi-rigid network formed by polymer molecules that were added to increase viscosity. We mathematically developed their concept by introducing two apparent viscosities and obtained results similar to the experimental data reported before. Addition of polymer improved the propulsion efficiency, which surpasses the decline in flagellar rotation rate, and the swimming speed increased with viscosity.     

Using multivariate adaptive regression splines to predict the distributions of New Zealand's freshwater diadromous fish

1. Relationships between probabilities of occurrence for fifteen diadromous fish species and environmental variables characterising their habitat in fluvial waters were explored using an extensive collection of distributional data from New Zealand rivers and streams. Environmental predictors were chosen for their likely functional relevance, and included variables describing conditions in the stream segment where sampling occurred, downstream factors affecting the ability of fish to move upriver from the sea, and upstream, catchment‐scale factors mostly affecting variation in river flows. 2. Analyses were performed using multivariate adaptive regression splines (MARS), a technique that uses piece‐wise linear segments to describe non‐linear relationships between species and environmental variables. All species were analysed using an option that allows simultaneous analysis of community data to identify the combination of environmental variables best able to predict the occurrence of the component species. Model discrimination was assessed for each species using the area under the receiver operating characteristic curve (ROC) statistic, calculated using a bootstrap procedure that estimates performance when predictions are made to independent data. 3. Environmental predictors having the strongest overall relationships with probabilities of occurrence included distance from the sea, stream size, summer temperature, and catchment‐scale drivers of variation in stream flow. Many species were also sensitive to variation in either the average and/or maximum downstream slope, and riparian shade was an important predictor for some species. 4. Analysis results were imported into a Geographic Information System where they were combined with extensive environmental data, allowing spatially explicit predictions of probabilities of occurrence by species to be made for New Zealand's entire river network. This information will provide a valuable context for future conservation management in New Zealand's rivers and streams.     

Collective swimming and the dynamics of bacterial turbulence

To swim, a bacterium pushes against the fluid within which it is immersed, generating fluid flow that dies off on a length scale comparable to the size of the bacterium. However, in dense colonies of bacteria, the bacteria are close enough that flow generated by swimming is substantial. For these cases, complex flows can arise due to the interaction and feedback between the bacteria and the fluid. Recent experiments on dense populations of swimming Bacillus subtilis have revealed a volume fraction-dependent transition from random swimming to transient jet and vortex patterns in the bacteria/fluid mixture. The fluid motions that are observed are reminiscent of flows that are observed around translating objects at moderate to high Reynolds numbers. In this work, I present a two-phase model for the bacterial/fluid mixture. The model explains turbulent flows in terms of the dipole stress that the bacteria exert on the fluid, entropic elasticity due to the rod shape of each bacterium, and the torque on the bacteria due to fluid gradients. Solving the equations in two dimensions using realistic parameters, the model reproduces empirically observed velocity fields. Dimensional analysis provides scaling relations for the dependence of the characteristic scales on the model parameters.     

Transitioning to confined spaces impacts bacterial swimming and escape response

Symbiotic bacteria often navigate complex environments before colonizing privileged sites in their host organism. Chemical gradients are known to facilitate directional taxis of these bacteria, guiding them toward their eventual destination. However, less is known about the role of physical features in shaping the path the bacteria take and defining how they traverse a given space. The flagellated marine bacterium Vibrio fischeri, which forms a binary symbiosis with the Hawaiian bobtail squid, Euprymna scolopes, must navigate tight physical confinement during colonization, squeezing through a tissue bottleneck constricting to ～2 μm in width on the way to its eventual home. Using microfluidic in vitro experiments, we discovered that V. fischeri cells alter their behavior upon entry into confined space, straightening their swimming paths and promoting escape from confinement. Using a computational model, we attributed this escape response to two factors: reduced directional fluctuation and a refractory period between reversals. Additional experiments in asymmetric capillary tubes confirmed that V. fischeri quickly escape from confined ends, even when drawn into the ends by chemoattraction. This avoidance was apparent down to a limit of confinement approaching the diameter of the cell itself, resulting in a balance between chemoattraction and evasion of physical confinement. Our findings demonstrate that nontrivial distributions of swimming bacteria can emerge from simple physical gradients in the level of confinement. Tight spaces may serve as an additional, crucial cue for bacteria while they navigate complex environments to enter specific habitats.     

Rapid bacterial swimming measured in swarming cells of Thiovulum majus.

Swarming cells of the sulfide-oxidizing bacterium Thiovulum majus form bands and show bioconvective patterns of swimming when placed in vessels containing H2S/O2 interfaces. Measurements of swimming velocities with video microscopic recordings under such conditions showed mean cell speeds as high as 615 microns s-1, unprecedented in bacteria.     

Variation of swimming speed enhances the chemotactic migration of Escherichia coli

Studies on chemotaxis of Escherichia coli have shown that modulation of tumble frequency causes a net drift up the gradient of attractants. Recently, it has been demonstrated that the bacteria is also capable of varying its runs speed in uniform concentration of attractant. In this study, we investigate the role of swimming speed on the chemotactic migration of bacteria. To this end, cells are exposed to gradients of a non-metabolizable analogue of glucose which are sensed via the Trg sensor. When exposed to a gradient, the cells modulate their tumble duration, which is accompanied with variation in swimming speed leading to drift velocities that are much higher than those achieved through the modulation of the tumble duration alone. We use an existing intra-cellular model developed for the Tar receptor and incorporate the variation of the swimming speed along with modulation of tumble frequency to predict drift velocities close to the measured values. The main implication of our study is that E. coli not only modulates the tumble frequency, but may also vary the swimming speed to affect chemotaxis and thereby efficiently sample its nutritionally rich environment.

Electronic supplementary material

The online version of this article (doi:10.1007/s11693-015-9174-x) contains supplementary material, which is available to authorized users.     

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.     

A gravity-induced regulation of swimming speed in Euglena gracilis

We investigated the autotrophic flagellate Euglena gracilis for gravity-induced modulation of the speed of swimming as previously documented for larger protozoan cells. Methods of video-tracking of swimming and sedimenting cells under 1 g and hypergravity up to 2 g, and computer-assisted data processing were applied. The vertical and horizontal swimming speed, and sedimentation rates of immobilized cells, were found to be linear functions of acceleration. Accounting for sedimentation in the observed upward and downward movements of Euglena, the active component of speed (propulsion) rose in proportion to acceleration. No saturation of gravikinesis was seen within the g-range tested. Gravity-dependent augmentation of speed was maximal in upward swimmers and decreased continuously over horizontal to downward swimmers. Linear extrapolations of the data to zero-g conditions suggest the absence of a threshold of gravikinesis in Euglena. Energetic considerations indicate a high sensitivity of gravitransduction near the level of Brownian molecular motion. Accepted: 22 August 1999     

Turn angle and run time distributions characterize swimming behavior for Pseudomonas putida.

The swimming behavior of Pseudomonas putida was analyzed with a tracking microscope to quantify its run time and turn angle distributions. Monte Carlo computer simulations illustrated that the bimodal turn angle distribution of P. putida reduced collisions with obstacles in porous media in comparison to the unimodal distribution of Escherichia coli.     

Comparisons of swimming performance in rainbow trout using constant acceleration and critical swimming speed tests

Maximum swimming performance of seasonally acclimated rainbow trout Oncorhynchus mykiss was compared among short-duration constant acceleration tests ( U _max) and with the well established, but longer duration critical swimming speed ( U _crit) test. The present results show that U _max was insensitive to a range of acceleration rates that differed by more than three-fold. Thus, test duration could be reduced from 58 to 18 min without affecting the estimate of U _max. The value of U _max, however, was up to 57% higher than U _crit. Only the slowest acceleration rate tested (an increase of 1 cm s⁻¹ every min) had a significantly lower U _max, and this was up to 19% higher than U _crit. Even so, the potential saving in the test duration was small (70 v. 90 min) when compared with a ramp- U _crit test (a standard U _crit test but with the water velocity initially ramped to c . 50% of the estimated U _crit). Therefore, swim tests that are appreciably shorter in duration than a ramp- U _crit test result in U _max being appreciably greater than U _crit. An additional discovery was that the ramp- U _crit performance of cold-acclimated rainbow trout was independent of the recovery period between tests. These results may prove useful in making comparisons among different swim test protocols and in designing swim tests that assess fish health and toxicological impacts.     

Implications of three-step swimming patterns in bacterial chemotaxis

We recently found that marine bacteria Vibrio alginolyticus execute a cyclic three-step (run-reverse-flick) motility pattern that is distinctively different from the two-step (run-tumble) pattern of Escherichia coli. How this novel, to our knowledge, swimming pattern is regulated by cells of V. alginolyticus is not currently known, but its significance for bacterial chemotaxis is self-evident and will be delineated herein. Using a statistical approach, we calculated the migration speed of a cell executing the three-step pattern in a linear chemical gradient, and found that a biphasic chemotactic response arises naturally. The implication of such a response for the cells to adapt to ocean environments and its possible connection to E. coli's response are also discussed.     

Hydroacoustic measurement of swimming speed of North Sea saithe in the field

Saithe Pollachius virens , tracked diurnally with a split-beam echosounder, showed no relationship between size and swimming speed. The average and the median swimming speeds were 1·05 m s⁻¹(±0·09 m s⁻¹) and 0·93 m s⁻¹, respectively. However, ping-to-ping speeds up to 3·34 m s⁻¹ were measured for 25–29 cm fish, whose swimming speeds were significantly higher at night (1·08 m s⁻¹) than during the day (0·72 m s⁻¹). The high average swimming speed could be related to the foraging or streaming part of the population and not to potential weakness of the methodology. However, the uncertainty of target location increased with depth and resulted in calculated average swimming speeds of 0·15 m s⁻¹ even for a stationary target. With increasing swimming speed the average error decreased to 0 m s⁻¹ for speeds >0·34 m s⁻¹. Species identity was verified by trawling in a pelagic layer and on the bottom.     

Influence of the uterine environment on rat sperm motility and swimming speed

The present study compared several rat sperm parameters in semen samples recovered from a natural uterine environment (i.e., intact estrous female) to those recovered from an artificially induced uterine environment (i.e., ovariectomized hormonally primed female). The sperm parameters measured were percent motile, percent exhibiting forward progressive motility, actual swimming speed, and linear swimming speed. The comparisons were conducted at four postcopulatory time points (0.25, 1.5, 3, and 6 hours) in order to detect differences as a function of residence time within the uterus. No significant differences (P less than 0.05) in the parameters were seen between the two types of uterine environments. Residence time within the reproductive tract had no significant effect on the parameters with the exception of percent motile, which was significantly increased (P less than 0.01) at the 1.5-hour postcopulatory time point.     

The muscle twitch and the maximum swimming speed of giant bluefin tuna, Thunnus thynnus L.

Sustained swimming of bluefin tuna was analysed from video recordings made of a captive patrolling fish school [lengths (L) 1.7–3.3 m, body mass (M) 54–433 kg]. Speeds ranged from 0.6 to 1.2 L s⁻¹ (86–260 km day⁻¹) while stride length during steady speed swimming varied between 0.54 and 0.93 L. Maximum swimming speed was estimated by measuring twitch contraction of the anaerobic swimming muscle in pithed fish 5 min after death. Muscle contraction time increased from the shortest just behind the head (30–50 ms at 20% L) to the longest at the tail peduncle (80–90 ms at 80% L) (all at 28°C). A fish (L = 2.26 m) with a muscle contraction time of 50 ms at 25% L can have a maximum tail beat frequency of 10 Hz and maximum swimming speed of 15m s⁻¹ (54km h⁻¹) with a stride length of 0.65L. With a stride length of 1 L a speed of 22.6 m s⁻¹ (81.4 km h⁻¹) is possible. Power used at maximum speed was estimated for this fish at between 10 and 40 kW, with corresponding values for the drag coefficient at a Reynolds number of 4.43 × 10⁷ of 0.0007 and 0.0027.