Rotational and translational swimming of human spermatozoa: a dynamic laser light scattering study

The rotational swimming motion of human spermatozoa is evaluated from measurements of depolarized dynamic laser light scattering at zero angle. The analysis is based on a Maxwellian angular velocity distribution and yields a rotational frequency of about 4 Hz that is ascribed to the rotation of the sperm head. From comparison with the translational swimming motion, a propelling efficiency of about 10 micron per turn is deduced. This parameter describes the linkage between the rotational and translational swimming motion and is likely to be discriminatory in the analysis of physiological and pathological sperm motions.     

Negative Geotactic Behavior of Paramecium Caudatum is Completely Described by the Mechanism of Buoyancy-Oriented Upward Swimming

This paper presents evidence that the negative geotactic behavior of Paramecium caudatum takes place by the mechanism of buoyancy-oriented upward swimming. Photographs of swimming pathways of the organisms were completely described by two dynamic equations for the translational motion of the center of gravity of the organism's body and for the rotational motion of the organism's body about its center of gravity, where the rotational torque is induced by a slight difference in position between the center of gravity and the center of buoyancy. It now seems unlikely that complicated mechanisms such as the statocyst mechanism and the gravity-propulsion mechanism, which have been proposed by many investigators, need be considered for other protozoa since preliminary observation and analysis of other ciliates such as Paramecium multimicronucleatum, Paramecium tetraurelia, and Tetrahymena pyriformis also strongly suggested that their negative geotaxis is due to buoyancy-oriented upward swimming.     

A simulation study of the dynamics of a driven filament in an Aristotelian fluid

We describe a method, based on techniques used in molecular dynamics, for simulating the inertialess dynamics of an elastic filament immersed in a fluid. The model is used to study the "one-armed swimmer". That is, a flexible appendage externally perturbed at one extremity. For small-amplitude motion our simulations confirm theoretical predictions that, for a filament of given length and stiffness, there is a driving frequency that is optimal for both speed and efficiency. However, we find that to calculate absolute values of the swimming speed we need to slightly modify existing theoretical approaches. For the more relevant case of large-amplitude motion we find that while the basic picture remains the same, the dependence of the swimming speed on both frequency and amplitude is substantially modified. For large-amplitudes we show that the one-armed swimmer is comparatively neither inefficient nor slow. This begs the question, why are there little or no one-armed swimmers in nature?     

The dynamics of protein hydration water: a quantitative comparison of molecular dynamics simulations and neutron-scattering experiments

We present results from an extensive molecular dynamics simulation study of water hydrating the protein Ribonuclease A, at a series of temperatures in cluster, crystal, and powder environments. The dynamics of protein hydration water appear to be very similar in crystal and powder environments at moderate to high hydration levels. Thus, we contend that experiments performed on powder samples are appropriate for discussing hydration water dynamics in native protein environments. Our analysis reveals that simulations performed on cluster models consisting of proteins surrounded by a finite water shell with free boundaries are not appropriate for the study of the solvent dynamics. Detailed comparison to available x-ray diffraction and inelastic neutron-scattering data shows that current generation force fields are capable of accurately reproducing the structural and dynamical observables. On the time scale of tens of picoseconds, at room temperature and high hydration, significant water translational diffusion and rotational motion occur. At low hydration, the water molecules are translationally confined but display appreciable rotational motion. Below the protein dynamical transition temperature, both translational and rotational motions of the water molecules are essentially arrested. Taken together, these results suggest that water translational motion is necessary for the structural relaxation that permits anharmonic and diffusive motions in proteins. Furthermore, it appears that the exchange of protein-water hydrogen bonds by water rotational/librational motion is not sufficient to permit protein structural relaxation. Rather, the complete exchange of protein-bound water molecules by translational displacement seems to be required.     

The optomotor system on the ground: on the absence of visual control of speed in walking ladybirds

Summary The strengths of the rotational and possible translational optomotor reflexes were measured over a wide range of closed-loop conditions in walking ladybirds (Coccinella septempunctata), and less thoroughly in three other species of insect. While ladybirds exhibit a strong rotational optomotor reflex, any visual control of speed there might be was found to be too feeble to be biologically significant. To see whether walking speed is instead controlled proprioceptively, changes in speed were measured when ladybirds pulled small weights. But there was no evidence of proprioceptive control either. Flying and swimming insects, on the other hand, do use visual feedback to control their translational velocity, and, unlike walking insects,must do so to cope with winds or watercurrents.     

Swimming behavior of selected species of Archaea

The swimming behavior of Bacteria has been studied extensively, at least for some species like Escherichia coli. In contrast, almost no data have been published for Archaea on this topic. In a systematic study we asked how the archaeal model organisms Halobacterium salinarum, Methanococcus voltae, Methanococcus maripaludis, Methanocaldococcus jannaschii, Methanocaldococcus villosus, Pyrococcus furiosus, and Sulfolobus acidocaldarius swim and which swimming behavior they exhibit. The two Euryarchaeota M. jannaschii and M. villosus were found to be, by far, the fastest organisms reported up to now, if speed is measured in bodies per second (bps). Their swimming speeds, at close to 400 and 500 bps, are much higher than the speed of the bacterium E. coli or of a very fast animal, like the cheetah, each with a speed of ca. 20 bps. In addition, we observed that two different swimming modes are used by some Archaea. They either swim very rapidly, in a more or less straight line, or they exhibit a slower kind of zigzag swimming behavior if cells are in close proximity to the surface of the glass capillary used for observation. We argue that such a "relocate-and-seek" behavior enables the organisms to stay in their natural habitat.     

Propulsion Modeling and Analysis of a Biomimetic Swimmer

<正> We have studied a biomimetic swimmer based on the motion of bacteria such as Escherichia coli (E. coli) theoretically andexperimentally. The swimmer has an ellipsoidal cell body propelled by a helical filament. The performance of this swimmer wasestimated by modeling the dynamics of a swimmer in viscous fluid. We applied the Resistive Force Theory (RFT) on this modelto calculate the linear swimming speed and the efficiency of the model. A parametric study on linear velocity and efficiency tooptimize the design of this swimmer was demonstrated. In order to validate the theoretical results, a biomimetic swimmer wasfabricated and an experiment setup was prepared to measure the swimming speed and thrust force in silicone oil. The experimentalresults agree well with the theoretical values predicted by RFT. In addition, we studied the flow patterns surrounding thefilament with a finite element simulation with different Reynolds number (Re) to understand the mechanism of propulsion. Thesimulation results provide information on the nature of flow patterns generated by swimming filament. Furthermore, the thrustforces from the simulation were compared with the thrust forces from theory. The simulation results are in good agreement withthe theoretical results.     

Effect of intracellular pH on rotational speed of bacterial flagellar motors

Weak acids such as acetate and benzoate, which partially collapse the transmembrane proton gradient, not only mediate pH taxis but also impair the motility of Escherichia coli and Salmonella at an external pH of 5.5. In this study, we examined in more detail the effect of weak acids on motility at various external pH values. A change of external pH over the range 5.0 to 7.8 hardly affected the swimming speed of E. coli cells in the absence of 34 mM potassium acetate. In contrast, the cells decreased their swimming speed significantly as external pH was shifted from pH 7.0 to 5.0 in the presence of 34 mM acetate. The total proton motive force of E. coli cells was not changed greatly by the presence of acetate. We measured the rotational rate of tethered E. coli cells as a function of external pH. Rotational speed decreased rapidly as the external pH was decreased, and at pH 5.0, the motor stopped completely. When the external pH was returned to 7.0, the motor restarted rotating at almost its original level, indicating that high intracellular proton (H+) concentration does not irreversibly abolish flagellar motor function. Both the swimming speeds and rotation rates of tethered cells of Salmonella also decreased considerably when the external pH was shifted from pH 7.0 to 5.5 in the presence of 20 mM benzoate. We propose that the increase in the intracellular proton concentration interferes with the release of protons from the torque-generating units, resulting in slowing or stopping of the motors.     

Quasi-elastic light-scattering spectra of swimming spermatozoa. Rotational and translational effects.

The electric field autocorrelation functions of light scattered from normal swimming bull spermatozoa are shown to be dependent on the mean head rotation frequency and not on the translational speed of the cells, as previously believed. This result was obtained from numerical generation of functions in which spermatozoa were modeled as Rayleigh-Gans-Debye ellipsoids having semiaxes a = 0.5 micrometer, b = 2.3 micrometer, and c = 9.0 micrometer. The magnitude of c required to achieve agreement with the experimental data is larger than the half-length of the head region of the cell. This implies that the midpiece, which also lies along c, contributes to the scattering power. Details regarding swimming trajectory and head orientation are included in the model. Analyses of the calculated functions and comparisons with experimentally determined ones suggest that at a scattering angle of 15 degrees the electric field autocorrelation function can be fit a simple Lorentzian whose half-width is inversely proportional to the scattering vector and the mean head rotational frequency.     

Number fluctuation spectroscopy of motile microorganisms.

A random-walk model of motility is used to predict the dynamics of fluctuations in the number of particles in a small observation volume. The results show that number fluctuations provide a measure of the mean swimming speed as well as the persistence length. Experimental light-scattering results are presented for three strains of Escherichia coli whose motion appears random-walk in nature. For the strain with th elongest persistence length, excellent agreement is found that theoretical predictions. For the more erratic strains, however, the shape of the measured scattered light intensity correlation functions indicates the presence of a contribution due to orientational fluctuations.     

Visual position stabilization in the hummingbird hawk moth, Macroglossum stellatarum L. I. Behavioural analysis

Optomotor responses of freely flying hawk moths, Macroglossum stellatarum, were characterized while the animals were hovering in front of and feeding on a dummy flower. Compensatory translational and rotational movements of the hawk moth were elicited by vertical grating patterns moving horizontally, mimicking imposed rotational and translational displacements of the animal in the horizontal plane. Oscillatory translational and rotational pattern motion leads to compensatory responses that peak in the frequency range between 2 Hz and 4 Hz. The control systems mediating the translational and rotational components of the optomotor response do not seem to influence each other. The system mediating translational responses is more sensitive in the fronto-lateral part of the visual field than in the lateral part; the opposite is true for the rotational system. The sensitivity of the translational system does not change along the vertical, whereas the rotational system is much more sensitive to motion in the dorsal than in the ventral part of the visual field. These sensitivity gradients may reflect an adaptation to the specific requirements of position stabilization in front of flowers during feeding. Accepted: 13 August 1997     

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.     

Multifunctional Sensor Based on Translational‐Rotary Triboelectric Nanogenerator

Triboelectric nanogenerators with a large number of desirable advantages, such as flexibility, light weight, and easy integration, are unique for sensor design. In this paper, based on the triboelectric nanogenerator (TENG), a cylindrical self‐powered multifunctional sensor (MS) with a translational‐rotary magnetic mechanism is proposed, which has the capacity to detect acceleration, force, and rotational parameters. The MS can transform a translational motion into a swing motion or a multicircle rotational motion of a low damping magnetic cylinder around a friction layer and hence drives the TENG to generate voltages output. For enhancing the output performance of the TENG, an electrode material with small work function, low resistance, and suitable surface topography is the best choice. According to the structure characteristic of the translational‐rotary magnetic mechanism, the MS can easily respond to a weak striking and can be used to measure the rotational parameters without the need of coaxial installation. Based on the MS, some applications are established, for example measuring the punch acceleration of a boxer, the hitting force and swing angle of golf club, which demonstrate the feasibility and efficiency of the MS and exhibit that the MS could find applications in sports.     

Librational motion of an "immobilized" spin label: hemoglobin spin labeled by a maleimide derivative.

The spin label Tempo-maleimide, when "immobilized" in hemoglobin, is shown to exhibit motional fluctuation whose amplitude and/or frequency depend on temperature and solution conditions. These motional fluctuations are observable by several electron spin resonance techniques. For desalted hemoglobin the fluctuations are detectable at approximately -15 degrees C using saturation transfer techniques and at approximately +25 degrees C using line-width measurements of normal absorption spectra. In ammonium sulfate precipitated hemoglobin, however, motional fluctuations are not detectable by either technique up to at least 40 degrees C. The most probable mechanism for spin-label motion appears to be either fluctuations in protein conformation which affect the label binding site or conformational transitions of the nitroxide ring itself. These motional fluctuations are shown to introduce a librational character to the overall label motion during hemoglobin rotational diffusion, with the librational motion significantly affecting the use of spin-label spectral shapes to calculate hemoglobin rotational correlation times.     

Crystallographic analysis of the thermal motion of the inclusion complex of cyclomaltoheptaose (beta-cyclodextrin) with hexamethylenetetramine

The crystal structure of the inclusion complex of cyclomaltoheptaose (beta-cyclodextrin) with hexamethylenetetramine was determined at temperatures of 123, 173, 223, and 293 K. The rigid-body motion of the host and guest molecules was evaluated by means of the TLS method that represents the molecular motion in terms of translation, libration, and screw motion. In increasing the temperature from 123 to 293 K, the amplitude of the rigid body vibration of the host molecule was increased from 1.0 to 1.3 degrees in the rotational motion and from 0.16 to 0.17 A in the translational motion. The cyclomaltoheptaose molecule has the flexibility in seven alpha-(1-->4)-linkages, and each glucose unit was in the rotational vibration around an axis through two glycosidic oxygen atoms. As a result, the rigid-body parameters of cyclomaltoheptaose were considered to be overestimated because of including the contribution from the local motion of glucose units. In contrast, for the guest molecule having no structural flexibility, the TLS analysis demonstrated that the atomic thermal vibration was mostly derived from the rigid body motion. The rotational amplitude of hexamethylenetetramine was changed from 5.2 to 6.6 degrees in increasing the temperature from 123 to 293 K, while the change of the translational amplitude was from 0.20 to 0.23 A. The translational motion of the guest molecule was hindered by the inside wall of the host cavity. The molecular motion was characterized by the rotational vibration around the axis through two nitrogen atoms that were involved in the hydrogen-bond formation.     

Cooperative Integration and Representation Underlying Bilateral Network of Fly Motion-Sensitive Neurons

How is binocular motion information integrated in the bilateral network of wide-field motion-sensitive neurons, called lobula plate tangential cells (LPTCs), in the visual system of flies? It is possible to construct an accurate model of this network because a complete picture of synaptic interactions has been experimentally identified. We investigated the cooperative behavior of the network of horizontal LPTCs underlying the integration of binocular motion information and the information representation in the bilateral LPTC network through numerical simulations on the network model. First, we qualitatively reproduced rotational motion-sensitive response of the H2 cell previously reported in vivo experiments and ascertained that it could be accounted for by the cooperative behavior of the bilateral network mainly via interhemispheric electrical coupling. We demonstrated that the response properties of single H1 and Hu cells, unlike H2 cells, are not influenced by motion stimuli in the contralateral visual hemi-field, but that the correlations between these cell activities are enhanced by the rotational motion stimulus. We next examined the whole population activity by performing principal component analysis (PCA) on the population activities of simulated LPTCs. We showed that the two orthogonal patterns of correlated population activities given by the first two principal components represent the rotational and translational motions, respectively, and similar to the H2 cell, rotational motion produces a stronger response in the network than does translational motion. Furthermore, we found that these population-coding properties are strongly influenced by the interhemispheric electrical coupling. Finally, to test the generality of our conclusions, we used a more simplified model and verified that the numerical results are not specific to the network model we constructed.     

Improvement in motion efficiency of the spirochete Brachyspira pilosicoli in viscous environments

Spirochetes are unique among swimming bacteria in terms of their lack of external flagella. They actively move in viscous environments, and, surprisingly, the swimming speed of the spirochete Leptospira interrogans has been reported to increase with viscosity in methylcellulose solutions. Many researchers consider that the presence of a loose, quasi-rigid network formed by linear polymer molecules is related to this strange phenomenon. One of the authors has proposed a theory that expresses this idea mathematically and successfully explains the speed properties of an externally flagellated bacterium in viscous environments. This theory predicts that the ratio of swimming speed to wave frequency (v/f ratio, motion efficiency in a sense) increases with viscosity. In this study, we demonstrated a new method of measuring the swimming speed and wave frequency of spirochetes and the motion characteristics of a swine intestinal spirochete, Brachyspira pilosicoli strain NK1f, measured in viscous environments. Several sets of swimming speed and wave frequency data were simultaneously derived from an animation obtained by our method. The v/f ratio of NK1f displayed a tendency to increase with increasing viscosity, suggesting the validity of the above-mentioned theory. Improvement of motion efficiency is at least one of the factors that maintain spirochete motility in viscous environments.     

Spirillum swimming: theory and observations of propulsion by the flagellar bundle.

The hydrodynamics and energetics of helical swimming by the bacterium Spirillum sp. is analysed using observations from medium speed cine photomicrography and theory. The photographic records show that the swimming organism's flagellar bundles beat in a helical fashion just as other bacterial flagella do. The data are analysed according to the rotational resistive theory of Chwang & Wu (1971) in a simple-to-use parametric form with the viscous coefficients Cs and Cn calculated according to the method of Lighthill (1975). Results of the analysis show that Spirillum dissipated biochemical energy in performing work against fluid resistance to motion at an average rate of about 6 X 10(-8) dyne cm s-1 with some 62-72% of the power dissipation due to the non-contractile body. These relationships yield a relatively low hydromechanical efficiency which is reflected in swimming speeds much smaller than a representative eukaryote. In addition the Cn/Cs ratio for the body is shown to lie in the range 0-86-1-51 and that for the flagellar bundle in the range 1-46-1-63. The implications of the power calculations for the Berg & Anderson (1973) rotating shaft model are discussed and it is shown that a rotational resistive theory analysis predicts a 5-cross bridge M ring for each flagellum of Spirillum.