New evidence for a "biased baseline" mechanism for calcium-regulated asymmetry of flagellar bending

Time-averaged data covering six to ten beat cycles for ATP-reactivated spermatozoa of a sea urchin and Ciona, and from a uniflagellate mutant of Chlamydomonas, were analyzed to obtain parameters of oscillation and mean shear angle at each point along the flagellum. The mean shear angles usually show a sharp change near the base of the flagellum. This sharp basal change in angle is correlated with perceived asymmetry in the development times of principal and reverse bends when these bends are measured directly from the asymmetric bending patterns, without subtracting out the mean shear angle. The asymmetry in development times was previously considered to be evidence against a "biased baseline" mechanism for asymmetric bending waves, in which completely symmetric bending waves develop and propagate on a curved flagellum. Our analysis now shows that the asymmetry in development times can be fully explained by the presence of a sharp static bend near the base of the flagellum, which can confuse the determination of the times of initiation of new bends at the base of the flagellum. Our reinterpretation of these data removes previous objections to the "biased baseline" mechanism for the regulation of bending wave asymmetry by calcium, and supports other evidence favoring a biased baseline mechanism, rather than a "biased switching" mechanism.     

Computer simulation of flagellar movement VIII: coordination of dynein by local curvature control can generate helical bending waves

Computer simulations have been carried out with a model flagellum that can bend in three dimensions. A pattern of dynein activation in which regions of dynein activity propagate along each doublet, with a phase shift of approximately 1/9 wavelength between adjacent doublets, will produce a helical bending wave. This pattern can be termed "doublet metachronism." The simulations show that doublet metachronism can arise spontaneously in a model axoneme in which activation of dyneins is controlled locally by the curvature of each outer doublet microtubule. In this model, dyneins operate both as sensors of curvature and as motors. Doublet metachronism and the chirality of the resulting helical bending pattern are regulated by the angular difference between the direction of the moment and sliding produced by dyneins on a doublet and the direction of the controlling curvature for that doublet. A flagellum that is generating a helical bending wave experiences twisting moments when it moves against external viscous resistance. At high viscosities, helical bending will be significantly modified by twist unless the twist resistance is greater than previously estimated. Spontaneous doublet metachronism must be modified or overridden in order for a flagellum to generate the planar bending waves that are required for efficient propulsion of spermatozoa. Planar bending can be achieved with the three-dimensional flagellar model by appropriate specification of the direction of the controlling curvature for each doublet. However, experimental observations indicate that this "hard-wired" solution is not appropriate for real flagella.     

Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation

Scroll wave (vortex) breakup is hypothesized to underlie ventricular fibrillation, the leading cause of sudden cardiac death. We simulated scroll wave behaviors in a three-dimensional cardiac tissue model, using phase I of the Luo-Rudy (LR1) action potential model. The effects of action potential duration (APD) restitution, tissue thickness, filament twist, and fiber rotation were studied. We found that APD restitution is the major determinant of scroll wave behavior and that instabilities arising from APD restitution are the main determinants of scroll wave breakup in this cardiac model. We did not see a "thickness-induced instability" in the LR1 model, but a minimum thickness is required for scroll breakup in the presence of fiber rotation. The major effect of fiber rotation is to maintain twist in a scroll wave, promoting filament bending and thus scroll breakup. In addition, fiber rotation induces curvature in the scroll wave, which weakens conduction and further facilitates wave break.     

Actuating Mechanism and Design of a Cylindrical Traveling Wave Ultrasonic Motor Using Cantilever Type Composite Transducer

Background

Ultrasonic motors (USM) are based on the concept of driving the rotor by a mechanical vibration excited on the stator via piezoelectric effect. USM exhibit merits such as simple structure, quick response, quiet operation, self-locking when power off, nonelectromagnetic radiation and higher position accuracy.

Principal Findings

A cylindrical type traveling wave ultrasonic motor using cantilever type composite transducer was proposed in this paper. There are two cantilevers on the outside surface of cylinder, four longitudinal PZT ceramics are set between the cantilevers, and four bending PZT ceramics are set on each outside surface of cantilevers. Two degenerate flexural vibration modes spatially and temporally orthogonal to each other in the cylinder are excited by the composite transducer. In this new design, a single transducer can excite a flexural traveling wave in the cylinder. Thus, elliptical motions are achieved on the teeth. The actuating mechanism of proposed motor was analyzed. The stator was designed with FEM. The two vibration modes of stator were degenerated. Transient analysis was developed to gain the vibration characteristic of stator, and results indicate the motion trajectories of nodes on the teeth are nearly ellipses.

Conclusions

The study results verify the feasibility of the proposed design. The wave excited in the cylinder isn''t an ideal traveling wave, and the vibration amplitudes are inconsistent. The distortion of traveling wave is generated by the deformation of bending vibration mode of cylinder, which is caused by the coupling effect between the cylinder and transducer. Analysis results also prove that the objective motions of nodes on the teeth are three-dimensional vibrations. But, the vibration in axial direction is minute compared with the vibrations in circumferential and radial direction. The results of this paper can guide the development of this new type of motor.     

A continuous dynamic beam model for swimming fish

When a fish swims in water, muscle contraction, controlled by the nervous system, interacts with the body tissues and the surrounding fluid to yield the observed movement pattern of the body. A continuous dynamic beam model describing the bending moment balance on the body for such an interaction during swimming has been established. In the model a linear visco-elastic assumption is made for the passive behaviour of internal tissues, skin and backbone, and the unsteady fluid force acting on the swimming body is calculated by the 3D waving plate theory. The body bending moment distribution due to the various components, in isolation and acting together, is analysed. The analysis is based on the saithe (Pollachius virens), a carangiform swimmer. The fluid reaction needs a bending moment of increasing amplitude towards the tail and near-standing wave behaviour on the rear-half of the body. The inertial movement of the fish results from a wave of bending moment with increasing amplitude along the body and a higher propagation speed than that of body bending. In particular, the fluid reaction, mainly designed for propulsion, can provide a considerable force to balance the local momentum change of the body and thereby reduce the power required from the muscle. The wave of passive visco-elastic bending moment, with an amplitude distribution peaking a little before the mid-point of the fish, travels with a speed close to that of body bending. The calculated muscle bending moment from the whole dynamic system has a wave speed almost the same as that observed for EMG-onset and a starting instant close to that of muscle activation, suggesting a consistent matching between the muscle activation pattern and the dynamic response of the system in steady swimming. A faster wave of muscle activation, with a variable phase relation between the strain and activation cycle, appears to be designed to fit the fluid reaction and, to a lesser extent, the body inertia, and is limited by the passive internal tissues. Higher active stress is required from caudal muscle, as predicted from experimental studies on fish muscle. In general, the active force development by muscle does not coincide with the propulsive force generation on the tail. The stiffer backbone may play a role in transmitting force and deformation to maintain and adjust the movement of the body and tail in water.     

Field measurement of the dynamics of the bull kelp Durvillaeaantarctica (Chamisso) Heriot

Seaweed habitats and morphological development are strongly affected by wave forces. Novel measurements were made of the force dynamics of the large intertidal macroalga Durvillaeaantarctica under the influence of wave action. Synchronized video, a pressure sensor and a resistance wave gauge provided data describing the wave field. The response of seaweeds to waves was gauged using instrumentation mounted directly on the seaweed, including accelerometers and displacement and force transducers. These field measurements were used to estimate forces and bending moments acting at the holdfast, where failure is most likely to occur. For waves of the order of 0.5 m high, we measured maximum forces on the stipe of around 300 N and blade accelerations that exceeded 30 m s⁻². During large wave events, inferred bending moments at the base of the stipe reached average values of around 140 N m. There was a decoupling between the blade response and the force experienced at the stipe base. Furthermore, changes in water depth throughout the tidal cycle had a systematic effect on blade accelerations and moments at the holdfast.     

A model of flagellar movement based on cooperative dynamics of dynein-tubulin cross-bridges

A theoretical model based on molecular mechanisms of both dynein cross-bridges and radial spokes is used to study bend propagation by eukaryotic flagella. Though nine outer doublets are arranged within an axoneme, a simplified model with four doublets is constructed on the assumption that cross-bridges between two of the four doublets are opposed to those between the other two, corresponding to the geometric array of cross-bridges on the 6-9 and the 1-4 doublets in the axoneme. We also assume that external viscosity is zero, whereas internal viscosity is non-zero in order to reduce numerical complexity. For demonstrating flagellar movement, computer simulations are available by dividing a long flagellum into many straight segments. Considering the fact that dynein cross-bridge spacing is almost equal to attachment site spacing, we may use a localized cross-bridge distribution along attachment sites in each straight segment. Dynamics of cross-bridges are determined by a three-state model, and effects of radial spokes are represented by a periodic mechanical potential whose periodicity is considered to be a stroke distance of the radial spoke. First of all, we examine the model of a short segment to know basic properties of the system. Changing parameters relating to "activation" of cross-bridges, our model demonstrates various phenomena; for example "excitable properties with threshold phenomena" and "limit cycle oscillation". Here, "activation" and "inactivation" (i.e. switching mechanisms) between a pair of oppositely-directed cross-bridges are essential for generation of excitable or oscillatory properties. Next, the model for a flagellar segment is incorporated into a flagellum with a whole length to show bending movement. When excitable properties of cross-bridges, not oscillatory properties, are provided along the length of the flagellum and elastic links between filaments are presented at the base, then our model can demonstrate self-organization of bending waves as well as wave propagation without special feedback control by the curvature of the flagellum. Here, "cooperative interaction" between adjacent short segments, based on "cooperative dynamics" of cross-bridges, is important for wave propagation.     

A MOVING IMAGE OF FLAGELLA: NEWS AND VIEWS ON THE MECHANISMS INVOLVED IN AXONEMAL BEATING

Beating of cilia and flagellae allows movement of the fluid surrounding isolated cells (for example: protists) or epithelia (bronchial tissue) but is also responsible for the movement of unicellular organisms in this medium (such as spermatozoa or protists). This paper aims to describe: (1) the biochemical and structural elements of the ‘9 +2’ structure called the axoneme; (2) the mechanisms of wave generation and propagation along the axoneme of cilia and flagellae are then described, stating that in most models of wave propagation, a clear distinction is made between the dynein-dependent microtubule sliding which represents the oscillatory motor and the bending mechanism which regulates wave propagation. In current models, the bending propagation is supported by a bind /relax cyclic mechanism which propagates in register, but frame-shifted, with the powering action of the dynein motor along the axoneme. While a large amount of knowledge was accumulated about the motor, little is known about the resisting elements regulating the bending. (3) The present study also puts forward ideas as to how these organelles have been highly conserved throughout eucaryotic evolution, and concludes with suggestions for further fields of investigation into this unique mechanical device used for cell movement.     

Gravitropic response inEichhornia cressipes (water hyacinth) I. process of gravitropic bending in the peduncle

In the last half of the anthokinetic cycle inEichhornia cressipes the peduncle showed a two-step bending response which started after the completion of the flowering: the primary bending in the upper region and the second one in the base of the peduncle. In the present study, only the primary bending response was examined and the following results were obtained.

1. Under the condition in the Western Japan, the anthokinetic cycle completed in 36–40 hr. The inflorescence started to grow during night, reaching the full flowering stage next morning, and the bending was initiated in the evening and completed next morning.
2. The bending was a positive gravitropism since the peduncle did not show bending when it was placed on a horizontal clinostat rotating at 2–3 rpm, or when the plant was placed up-side-down.
3. Before the end of flowering phase, the peduncle showed a normal negative gravitropic response but afterward it acquired the property to show a positive gravitropic response.
4. The bending was due to the extension of convex side of the peduncle, accompanied by a shrinkage of the concave side. The extension of the upper side was caused by cell extension. At the turning point from negative to positive gravitropic response, the extension of the peduncle ceased for several hours.

From the above results it is concluded that the primary bending response of the peduncle in water hyacinth was a positive gravitropism.     

Similar behavior,different mechanisms: the research of the style bending of <Emphasis Type="Italic">Alpinia</Emphasis> species

The styles of the plants of genus Alpinia show a similar bending behavior. Each species has two types—hyper-type and cata-type. The styles of hyper-type bend downward first, and then bend upward second. The styles of cata-type also bend twice, but the bending direction is opposite to hyper-type. We tested the effects of light, IAA, and NPA on the style movement of Alpinia oxyphylla and Alpinia galanga, and analyzed the IAA distribution in their styles. We found that the effects of light were similar for the two species, but the two types of each species responded differently. The first style bending of hyper-type was downward when it was in dark, and was upward when in light; the second bending was upward if in light, and did not move if in dark. The two bendings of cata-type showed no obvious difference between in dark and in light. Effects of IAA and NPA were different for two species. For A. galanga, neither IAA nor NPA had obvious effects on the style bending. For A. oxyphylla, IAA enhanced the second bending of hyper-type and the two bendings of cata-type. NPA enhanced the second bending of hyper-type and the first bendings of cata-type, and significantly inhibited the second bending of cata-type. The results of IAA immunolocalization indicated that IAA was symmetrical in the styles of A. galanga both before the first bending and before the second bending in two types. However, in A. oxyphylla, IAA asymmetry was found in two types. Therefore, we hypothesize that the mechanisms of the style bending of Alpinia plants are different, not only between two types of each species, but also among species.     

Cross-sectional geometry and morphology of the mandibular symphysis in Middle and Late Pleistocene Homo

Studies of the evolutionary emergence of the human "chin" have been investigated from a phylogenetic perspective during the later Pleistocene or from a biomechanical perspective across extant primates. Since it was during the Middle and Late Pleistocene that the distinctive human mentum osseum emerged, the relationship between mentum osseum form and resistance to mechanical stress at the mandibular symphysis was examined for forty-two Middle and Late Pleistocene human mandibles. Mentum osseum variation was scored on a five-point ordinal scale (mentum osseum rank). Resistance to bending was represented by second moments of area calculated from symphyseal cross-sections. Relative strength in bending was represented by second moments of area divided by estimated moment arm or beam length. Vertical bending resistance in the coronal plane was maintained across the range of mentum osseum variation within and between later Pleistocene human groups. In contrast, resistance to lateral transverse bending (wishboning) was significantly negatively correlated with the emergence of a protruding mentum osseum. However, Neandertals and early modern humans were equivalent in their abilities to resist this bending regime, while both groups were less resistant in wishboning than earlier archaic humans. In addition, symphyseal inclination, which decreased throughout the later Pleistocene, was highly correlated with mentum osseum rank. Although the overall pattern of differential stasis and change in vertical bending and wishboning resistance at the symphysis is consistent with aspects of the current biomechanical model of the "chin," the decoupling of bending resistance and mentum osseum form in the Late Pleistocene suggests that the evolutionary emergence of the modern human "chin" was at least partly independent of the biomechanical demands placed on the symphysis.     

Communication by substratum vibration in the New Zealand tree weta, Hemideina femorata (Stenopelmatidae: Orthoptera)

The propagation of vibrations along the trunk and branches of a manuka tree, generated in response to the impact of a steel ball-bearing on the trunk, was measured with an accelerometer. The impact generated bending waves which travelled along the trunk and into the branches. Close to the point of impact the waveform was dominated by a damped oscillation at 518 Hz; as the bending wave progressed away from the point of impact the frequency of the dominant waveform increased. Beyond 200 cm the waveform became increasingly complex and a smallamplitude, high-frequency component progressively preceded the main wave. Branching points also induced complex waveforms, particularly where branches lay at a large angle to the trunk. Stridulating wetas also generated bending waves in the tree at a frequency close to that generated by the ball-bearing, as well as at a higher frequency of 7.5 kHz. The acoustic frequency of stridulation peaked at 0.8 and 3.4 kHz. Records from nerves serving the vibration-sensitive subgenual organs showed that wetas can detect oscillations at 1 kHz at 0.015ms^-2. A stridulating weta placed on the same log as a preparation in which the nerve from the subgenual organ was monitored generated oscillatins well above the threshold for detection.     

Functional state of the axonemal dyneins during flagellar bend propagation

When mouse spermatozoa swim in media of high viscosity, additional waves of bending are superimposed on the primary traveling wave. The additional (secondary) waves are relatively small in scale and high in frequency. They originate in the proximal part of the interbend regions. The initiation of secondary bending happens only in distal parts of the flagellum. The secondary waves propagate along the interbends and then tend to die out as they encounter the next-most-distal bend of the primary wave, if that bend exceeds a certain angle. The principal bends of the primary wave, being of greater angle than the reverse bends, strongly resist invasion by the secondary waves; when a principal bend of the primary wave propagates off the flagellar tip, the secondary wave behind it suddenly increases in amplitude. We claim that the functional state of the dynein motors in relation to the primary wave can be deduced from their availability for recruitment into secondary wave activity. Therefore, only the dyneins in bends are committed functionally to the maintenance and propagation of the flagellar wave; dyneins in interbend regions are not functionally committed in this way. We equate functional commitment with tension-generating activity, although we argue that the regions of dynein thus engaged nevertheless permit sliding displacements between the doublets.     

The area moment of inertia of the tibia: A risk factor for stress fractures

In a prospective study of stress fractures among Israeli infantry recruits, the area moment of inertia of the tibia was found to have a statistically significant correlation with the incidence of tibial, femoral and total stress fractures. Recruits with "low" area moments of inertia of the tibia were found to have higher stress fracture morbidity than those with "high" area moments of inertia. The best correlation was obtained when the area moment of inertia was calculated about the AP axis of bending at a cross-sectional level corresponding to the narrowest tibial width on lateral X-rays, a point which is at the distal quarter of the tibia. This finding indicates that bending forces about the approximate AP axis are an important causal factor for tibial and many other stress fractures. The bone's bending strength, or ability to resist bending moments, as measured by the area moment of inertia, helps determine risk to stress fracture.     

Dynamic reconstruction of the fish locomotor wave

Theoretical modeling substantiates the bionic solution of an optimal wave propulsor for water transport, which must have the amplitude and phase characteristics of the fish bending locomotor waves. Use is made of a computer model of multilink chain bending waves where arbitrary distributions can be set for amplitudes and phases of separate segments. With the linear increase in the amplitude of segmental oscillations, a numerical experiment determines the optimal phasing whereby each segment provides a maximal longitudinal component of the motive force. Two versions of hydrodynamic interaction of the segments with water are compared, implying (i) linear and (ii) quadratic drag: the optimal phasing of the transverse and longitudinal oscillations proves to be (i) orthogonal and (ii) nearly orthogonal. The computed bending wave shapes corresponding to dynamic optimization are consistent with the experimental data.     

Elastic Properties of the Sea Urchin Sperm Flagellum

The theory of flexural vibrations in thin rods, applied to the movement of flagella, has been extended to include an investigation of the influence of the boundary conditions on the theoretical waveforms. It was found that for flagella which are flexible enough, the flexibility can be estimated solely from the wavelength of the wave traveling in it. This can be expected to hold for those flagella which do not possess a fibrous sheath. The bending moment in flagella in which the ampitude of the wave is maintained as the wave travels distally is almost completely produced by active contractile elements. This means that the active bending moment can be estimated from the radius of curvature of the flagellum and the stiffness. The above findings were applied to the case of the sea urchin sperm flagellum. One finds that the stiffness of the flagellum is caused mainly by the nine longitudinal fibers which must have a Young's modulus of slightly less than 10⁸dyne/cm². The longitudinal fibers need to develop a tension of 1.6 × 10⁸dyne/cm² to account for the bending moment in the flagellum. These two figures are in line with those found for muscle fibers.     

The Importance of Body Stiffness in Undulatory Propulsion

During steady swimming in fish, the dynamic form taken by theaxial undulatory wave may depend on the bending stiffness ofthe body. Previous studies have suggested the hypothesis thatfish use their muscles to modulate body stiffness. In orderto expand the theoretical and experimental tools available fortesting this hypothesis, we explored the relationship betweenbody stiffness, muscle activity, and undulatory waveform inthe mechanical context of dynamically bending beams. We proposethat fish minimize the mechanical cost of bending by increasingtheir body stiffness, which would allow them to tune their body'snatural frequency to match the tailbeat frequency at a givenswimming speed. A review of the literature reveals that theform of the undulatory wave, as measured by propulsive wavelength,is highly variable within species, a result which calls intoquestion the use of propulsive wavelength as a species-specificindicator of swimming mode. At the same time, the smallest wavelengthwithin a species is inversely proportional to the number ofvertebrae across taxa (r² = 0.21). In order to determine ifintact fish bodies are capable of increasing bending stiffness,we introduce a method for stimulating muscle in the body ofa dead fish while it is being cyclically bent at physiologicalfrequencies. The bending moment (N m) and angular displacement(radians) are measured during dynamic bending with and withoutmuscle stimulation. Initial results from these whole body workloops demonstrate that largemouth bass possess the capabilityto increase body stiffness by using their muscles to generatenegative mechanical work.     

Properties of flagellar "rigor waves" formed by abrupt removal of adenosine triphosphate from actively swimming sea urchin sperm

Sea urchin sperm were demembranated and reactivated with a solution containing 0.04% Triton X-100 and 0.03 mM ATP. The ATP concentration was then lowered abruptly by diluting the sperm suspension 50-fold into reactivating solution containing no ATP. The flagella of the sperm in the diluted suspension were not motile, but they were bent into a variety of stationary rigor wave forms closely resembling the wave forms occurring at different stages of the flagellar bending cycle during normal movement. The form of these rigor waves was unchanged upon storage for several hours in the presence of dithiothreitol and EDTA. Addition of 1 µM ATP induced slow relaxation of the waves, with most of the sperm becoming partially straightened over a period of about 30 min; somewhat higher concentrations gave a more rapid and complete relaxation. Concentrations of ATP above 10 µM induced resumption of normal beating movements. Addition of ITP, GTP, or GDP (up to 1 mM) produced no relaxation of the rigor waves. Digestion with trypsin to an extent sufficient to disrupt the radial spokes and the nexin links caused no change in the rigor wave forms, suggesting that these wave forms could be maintained by the dynein cross-bridges between the outer doublet tubules of the flagellar axoneme. Study of the effects of viscous shear on the rigor wave axonemes has shown that they are resistant to distortion by bending, although they can be twisted relatively easily.     

Growth and phototropic bending in Boergesenia rhizoid

The rhizoid of Boergesenia forbesii. a coenocytic green alga,exhibited typical tip growth. The growth stopped at temperatureslower than 15?C and was promoted by red light but inhibitedby blue light (430 nm). The rhizoid showed negative phototropicbending caused by blue light, and the mode of bending was the"bulging" type. The dioptric effect was not involved in thisnegative phototropism. The phototropicbending process was modifiedgreatly by temperature. At low temperature (18?C), bending didnot occur but the phototropic effect could be accumulated andstored. The accumulated effect appeared as a bending in thedark when the temperature was raisedto 25?C. This accumulatedphototropic effect, designated "stored bending", attenuatedat a half-life of 1.5 hr at 18?C in the dark. (Received February 24, 1979; )