ABSTRACT

Oscillation is a characteristic feature of eukaryotic flagellar movement. The mechanism involves the control of dynein-driven microtubule sliding under self-regulatory mechanical feedback within the axoneme. To define the essential factors determining the induction of oscillation, we developed a novel experiment by applying mechanical deformation of demembranated, immotile sea urchin sperm flagella at very low ATP concentrations, below the threshold of ATP required for spontaneous beating. Upon application of mechanical deformation at above 1.5 µmol l−1 ATP, a pair of bends could be induced and was accompanied by bend growth and propagation, followed by switching the bending direction. For an oscillatory, cyclical bending response to occur, the velocity of bend propagation towards the flagellar tip must be kept above certain levels. Continuous formation of new bends at the flagellar base was coupled with synchronized decay of the preceding paired bends. Induction of cyclical bends was initiated in a constant direction relative to the axis of the flagellar 9+2 structure, and resulted in the so-called principal bend. In addition, stoppage of the bending response occasionally occurred during development of a new principal bend, and in this situation, formation of a new reverse bend did not occur. This observation indicates that the reverse bend is always active, opposing the principal bend. The results show that mechanical strain of bending is a central component regulating the bend oscillation, and switching of the bend direction appears to be controlled, in part, by the velocity of wave propagation.

INTRODUCTION

A prominent feature of the movement of eukaryotic flagella and cilia is cyclical beating or oscillation. In the case of sea urchin sperm flagella, an S-shaped bend is alternately formed on both sides of the longitudinal axis of the flagellum, with each bend propagating towards the distal end of the flagellum. We now know that the periodic nature of flagellar wave formation and propagation is caused by the orchestrated activities of dynein arms within the flagellar axoneme (Lin and Nicastro, 2018). By the force generation of dynein molecules coupled with their ATP hydrolysis, sliding movements can occur between each pair of neighboring doublet microtubules (Summers and Gibbons, 1971). The spatial and temporal control of dynein activity within the axoneme provides the basis underlying flagellar oscillation. Hitherto, studies have demonstrated that such regulation of dynein activity requires not only the function of substructures within the axoneme, such as the central-pair microtubules and N-DRC (nexin-dynein-regulatory complex), but also the role of mechanical signals, or mechanical strain, resulting from flagellar bending (Hayashibe et al., 1997; Ishikawa and Shingyoji, 2007; Morita and Shingyoji, 2004).

The process of bend oscillation includes: (1) bend initiation at the flagellar base and its propagation towards the flagellar tip, (2) bend alternation or switching the direction of bend and (3) cyclical repeat of these responses. Regulation of bend formation, and bend alternation, have been discussed with respect to the microtubule sliding within the axoneme, and models have been proposed (Bayly and Dutcher, 2016; Bayly and Wilson, 2014; Brokaw, 1971, 2014; Lindemann, 1994a,b; Riedel-Kruse, et al., 2007). The alternation or switching of the bending direction is the key feature of bend oscillation. The mechanism of switching the direction of bending is not understood, but is thought to include alternating activity across the axis of the axoneme and localized, limited microtubule sliding and flagellar bending (Lin and Nicastro, 2018; Morita and Shingyoji, 2004).

The mechanical response of flagella was a phenomenon found in pioneering work by Lindemann and Rikmenspoel (1972). There is ample evidence to show that mechanical deformation influences the regulation of oscillation. Previous studies have demonstrated that certain aspects of flagellar movement can be modified by mechanical manipulation of the flagellum (Eshel et al., 1991, 1992; Gibbons et al., 1987; Okuno and Hiramoto, 1976; Shingyoji and Takahashi, 1995; Shingyoji et al., 1991b). Later, it was also shown that inactive dynein arms in the axoneme are activated by bending the doublet microtubules (Hayashibe et al., 1997; Morita and Shingyoji, 2004). It is probable that bending of the doublet microtubules is an important factor in the feedback system underlying flagellar oscillation (Hayashi and Shingyoji, 2008; Morita and Shingyoji, 2004). In addition, perturbation of beating sperm reveals an inhibition of regular beating, while the lateral vibration of a head-held glass micropipette changes the beat frequency and bending amplitude in accordance with the pipette movement (Shingyoji et al., 1991b, 1995).

Our goal was to elucidate the conditions that regulate the mechanism of flagellar oscillation. We identified important mechanical signals governing flagellar oscillation, and developed a method to induce flagellar response at below the threshold levels of ATP (approximately 2.0 µmol l−1). At 1.5–2.0 µmol l−1 ATP, spontaneous reactivation of movement does not occur, while just above 2.0 µmol l−1 ATP a few sperm can spontaneously be re-activated to swim. Our previous success in initiation of flagellar response in demembranated, motionless sperm at 2.0–3.0 µmol l−1 ATP shows that imposed bending or tapping a manipulator are effective ways to induce flagellar bending responses (Ishikawa and Shingyoji, 2007). Here, we defined experimental conditions to induce oscillation. We used a limited range of very low ATP concentrations (1.5–2.0 µmol l−1) and mechanical deformation was applied to the sperm flagellum to induce oscillatory movement. We defined conditions that not only resulted in elastic relaxation (similar to previous observations), but also resulted in definitive oscillation-like responses. These responses accompanied formation of a pair of bends at the initial state of bend formation following mechanical deformation. Furthermore, the oscillation-like response induced at 1.5–2.0 µmol l−1 ATP first showed development of a new principal bend. For repetitive bend oscillations, bend propagation velocity must be maintained above a certain velocity. From the analysis of curvature, it was also found that in order to form and grow new paired bends at the base of the flagellum, it is necessary for the preceding paired bends to decrease in size. Our finding that cyclical beating always started from developing a new principal bend (P-bend) provides new ideas on the role of the reverse bend (R-bend) in regulating oscillation. These are the first experimental demonstrations that define basic features triggering flagellar oscillation.

List of abbreviations

     
  • BEAT

    beating

  •  
  • BR

    bend formation and relaxation

  •  
  • GP

    bend growth and propagation

  •  
  • SW

    switching

MATERIALS AND METHODS

Demembranated sperm flagella

Sperm obtained from the sea urchin Hemicentrotus pulcherrimus (A. Agassiz 1863) were used for experiments. To observe sperm motility, dry sperm was diluted with 250,000 volumes of Ca2+-free artificial seawater (465 mmol l−1 NaCl, 10 mmol l−1 KCl, 25 mmol l−1 MgSO4, 25 mmol l−1 MgCl2 and 2 mmol l−1 Tris-HCl; pH 8.0). The quality of sperm motility was examined by counting a swimming rate, which was calculated as a percentage of motile sperm observed in randomly chosen microscopic fields of views. We used the sperm suspension exceeding 80% in swimming rate. The spermatozoa were demembranated by 30 times dilution by adding 1.5 ml of demembranating solution (150 mmol l−1 potassium acetate, 2 mmol l−1 MgSO4, 10 mmol l−1 Tris-HCl, 2 mmol l−1 ethylene glycol-bis (2-aminoethylether)-N,N,N′,N′-tetraacetic acid (EGTA), 1 mmol l−1 dithiothreitol (DTT) and 0.04% (w/v) Triton X-100; pH 8.0) by gentle swirling for 45 s at room temperature (20–28°C). The demembranation was stopped by 160 times dilution by adding 4.0 ml of Ca2+-free re-activating solution [150 mmol l−1 potassium acetate, 2 mmol l−1 MgSO4, 10 mmol l−1 Tris-HCl, 2 mmol l−1 EGTA, 1 mmol l−1 DTT and 2% (w/v) polyethyleneglycol (molecular weight 20,000); pH 8.0] without ATP and kept on ice until use. The demembranated sperm was reactivated by various concentrations of ATP just before the observation of flagellar movement.

Mechanical manipulation

Mechanical deformation was applied to a demembranated flagellum with a glass microneedle made of a glass rod of 1 mm diameter (G-1000; Narishige, Tokyo, Japan) using a micropipette puller (PP-830; Narishige). The glass microneedle with the tip coated with 0.1% poly-l-lysine (P-1264; Sigma-Aldrich, USA) was mounted on a water-pressure micromanipulator (MHW-103; Narishige) on the stage of an inverted microscope with phase-contrast optics (Axiovert 35; Zeiss, Oberkochen, Germany) with a ×40 objective lens. The head of a demembranated motionless sperm and the distal end of the flagellum were caught with two glass microneedles and two kinds of deformation were applied. In the axial deformation, the two needles were pointing towards each other. To bend the flagellum, the head of a sperm was moved towards the distal end of the flagellum to impose bending in the presence of 1.0–2.0 µmol l−1 ATP. In the lateral deformation the head-held needle was also placed some distance away from the other needle. To bend the flagellum, the head-held needle was moved parallel until it pointed towards the other needle. In either method of deformation, the distance between the two needles decreased to approximately 70–80% of the original distance of flagellar length before deformation. All experiments were carried out at room temperature (20–28°C).

Observation, recording and analysis

Flagellar movements were observed with an inverted microscope equipped with phase-contrast optics, and were recorded with an image-intensified CCD camera (C2400-77; Hamamatsu Photonics, Shizuoka, Japan) and a DVD recorder (DMR-EH73V; Panasonic, Tokyo, Japan). Recorded images were captured on computer and the movements of flagella were captured by using Image J (version 1.47v; National Institutes of Health, Bethesda, MD, USA). The traces of the waveforms of flagella were manually plotted every 0.7 µm on the captured flagellar waveform image and those plots were connected smoothly using Bohboh software (Baba and Mogami, 1985). The flagellar waveform created by this work is called reconstructed waveform in this study.

To analyse the bending waveforms of flagella, the shear angle curves, showing microtubule sliding as a function of position along the length of a flagellum, were used. The shear angle curves are obtained as a difference in angular orientation between the axis of the sperm head and the locus on the flagellum (Gibbons, 1981; Satir, 1968; Warner and Satir, 1974). The curves of the shear angle correspond to the straight lines of reconstructed waveforms, and the straight lines correspond to the curves, respectively. Changes of shear angle between two neighboring sequential lines at a given position along the flagellum represent the sliding velocity (rad s−1) (Brokaw, 1991). Shear curves were taken at 1 s intervals in this study.

RESULTS

Induction of flagellar oscillation by mechanical deformation of demembranated immotile flagella in the presence of very low ATP

It is well known that demembranated sperm flagella of sea urchins show stable beating at around 35–40 Hz (at 20–28°C) in the presence of 20 µmol l−1 ATP. Movement of these re-activated sperm flagella is characterized by cyclical formation of bends at the flagellar base and propagation of each bend towards the flagellar tip (Gibbons and Gibbons, 1972). When the ATP concentration was decreased, beat frequency of re-activated swimming sperm decreased (Table 1), and spontaneously beating sperm were not observed at 1.5 µmol l−1 ATP. The threshold ATP concentration for spontaneous beating exists between 1.5 and 2.0 µmol l−1 (Ishikawa and Shingyoji, 2007).

Table 1.

Beat frequency and sliding velocity of spontaneously swimming Hemicentrotus pulcherrimus sperm at ATP concentrations above the threshold

Beat frequency and sliding velocity of spontaneously swimming Hemicentrotus pulcherrimus sperm at ATP concentrations above the threshold
Beat frequency and sliding velocity of spontaneously swimming Hemicentrotus pulcherrimus sperm at ATP concentrations above the threshold

In this study, we demonstrated that a certain kind of mechanical deformation by manipulation of both the head and tip of the sperm is capable of inducing demembranated sperm flagella movements in the presence of 1.5–2.0 µmol l−1 ATP. This induction of flagellar response is similar to the results reported by Ishikawa and Shingyoji (2007), but the previous report of the bend formation and propagation was interpreted as a result of passive sliding. Here, the critical advance is that mechanical deformation of the demembranated sperm flagella can induce oscillation-like responses, produced by active microtubule sliding, at very low ATP levels.

Mechanical deformation induced various types of bending or oscillation responses depending on the Mg–ATP2− concentration and the proximity of the sperm flagella to the glass surface. In the presence of 1.0 µmol l−1 ATP, a bend (or a single bend) (Fig. 1A) was induced but it did not develop further. Similarly, at 1.0 and 1.2 µmol l−1 ATP, paired bends were not induced spontaneously or mechanically. However, at 1.5–2.0 µmol l−1 ATP, paired bends were induced and further developed into different types of responses, including an oscillation-like beating (Figs 1 and 2). In addition, to induce responses at 1.5–2.0 µmol l−1 ATP, the sperm flagellum had to be kept at a certain distance above the glass surface. The distance of the flagellum from the bottom surface influenced the beat frequency and sliding velocity of the flagellum. Interestingly, when the sperm flagellum was held at the middle distance from the surfaces, both beat frequency and sliding velocity showed similar values at both 1.5 and 2.0 µmol l−1 ATP (Table 2). These results indicate that in the vicinity of the threshold (1.5–2.0 µmol l−1 ATP), small changes in ATP concentration are not an exclusive factor determining conditions of oscillation. It has been demonstrated in fish sperm that such an effect of liquid–solid interface on sperm swimming near the bottom surface is important for the regulation of flagellar motile performance (Boryshpolets, et al., 2013).

Fig. 1.

Sequential images of Hemicentrotus pulcherrimus flagellar responses obtained from DVD recordings. Included are traces at the beginning step of bend induction (A–E) and reconstructed superimposed traces of the flagellar response (B–E): single bend formation (A), bend relaxation (B), bend growth and propagation (C) and beating (D,E). Mechanical deformation was applied to immotile demembranated sperm flagella at (A) 1.0 µmol l−1 and (B–E) 1.5–2.0 µmol l−1 ATP. Each sperm was caught with two glass microneedles: microneedles 1 and 2 are holding a sperm head and a flagellar distal region, respectively. Mechanical deformation was applied to the flagellum by moving microneedle 1 towards microneedle 2 by their axial (A,B,E) or a lateral (C,D) movement while maintaining parallel orientation of the two microneedles. Numbers in the lower left corner of panels indicate the time in seconds after the beginning of microneedle movement. Movement of microneedles and changes of flagellar shape during mechanical deformation are also shown in the right-hand traces (1–5 s): a single bend in A and a pair of bends (asterisks) in B, C, D and E were induced. Following stoppage of microneedle 1 (red triangle) and induction of paired bends, four types of responses were observed. They are oscillation-like response (BEAT in D,E), bend relaxation (BR in B) and bend growth and propagation (GP in C). D shows the first to third cycles and the final fourth, incomplete cycle with gradual stoppage. E shows sequential wave changes for four cycles of at least a five-cycle response. Superimposed images in B, C, D and E are reconstructed from recorded images. Scale bars: 10 µm.

Fig. 1.

Sequential images of Hemicentrotus pulcherrimus flagellar responses obtained from DVD recordings. Included are traces at the beginning step of bend induction (A–E) and reconstructed superimposed traces of the flagellar response (B–E): single bend formation (A), bend relaxation (B), bend growth and propagation (C) and beating (D,E). Mechanical deformation was applied to immotile demembranated sperm flagella at (A) 1.0 µmol l−1 and (B–E) 1.5–2.0 µmol l−1 ATP. Each sperm was caught with two glass microneedles: microneedles 1 and 2 are holding a sperm head and a flagellar distal region, respectively. Mechanical deformation was applied to the flagellum by moving microneedle 1 towards microneedle 2 by their axial (A,B,E) or a lateral (C,D) movement while maintaining parallel orientation of the two microneedles. Numbers in the lower left corner of panels indicate the time in seconds after the beginning of microneedle movement. Movement of microneedles and changes of flagellar shape during mechanical deformation are also shown in the right-hand traces (1–5 s): a single bend in A and a pair of bends (asterisks) in B, C, D and E were induced. Following stoppage of microneedle 1 (red triangle) and induction of paired bends, four types of responses were observed. They are oscillation-like response (BEAT in D,E), bend relaxation (BR in B) and bend growth and propagation (GP in C). D shows the first to third cycles and the final fourth, incomplete cycle with gradual stoppage. E shows sequential wave changes for four cycles of at least a five-cycle response. Superimposed images in B, C, D and E are reconstructed from recorded images. Scale bars: 10 µm.

Fig. 2.

Schematic diagram summarizing characteristics of flagellar responses induced by mechanical deformation at very low ATP concentrations. At 1.0 and 1.2 µmol l−1 ATP, a single bend was induced while a pair of bends was not induced (N=16). In contrast, at 1.5–2.0 µmol l−1 ATP, mechanical deformation brought about induction of paired bends, which were followed by further flagellar responses (total number of trials=560 by 127 sperm). All illustrations show typical flagellar waveforms depicted from the recorded images. White arrows in the first row indicate direction of head movement to induce bending by mechanical deformation (grey frames at 1.0–1.2 µmol l−1 ATP; pink frames at 1.5–2.0 µmol l−1 ATP). In the second row (State 1), red asterisks in the colored frames indicate the bent region of induced paired bends. Following induction of paired bends, further changes were observed and are shown in States 2–5. Of the total 560 cases that showed paired bends at first bending, no further responses were observed in 342 cases and named paired bend. The first response accompanying the bend formation was bend relaxation (BR; N=126). State 2 seems to be independent of States 3–5. State 3 involves growth and propagation (GP) of bends, which appeared in 11 cases out of 560. States 4 and 5 belong to an oscillation-like response with switching direction of bending [SW: a few cycles (<3); BEAT, ≥3 cycles]. Switching (SW) and beating (BEAT) were observed in 18 and 63 cases out of 560, respectively. N is the number of induced responses.

Fig. 2.

Schematic diagram summarizing characteristics of flagellar responses induced by mechanical deformation at very low ATP concentrations. At 1.0 and 1.2 µmol l−1 ATP, a single bend was induced while a pair of bends was not induced (N=16). In contrast, at 1.5–2.0 µmol l−1 ATP, mechanical deformation brought about induction of paired bends, which were followed by further flagellar responses (total number of trials=560 by 127 sperm). All illustrations show typical flagellar waveforms depicted from the recorded images. White arrows in the first row indicate direction of head movement to induce bending by mechanical deformation (grey frames at 1.0–1.2 µmol l−1 ATP; pink frames at 1.5–2.0 µmol l−1 ATP). In the second row (State 1), red asterisks in the colored frames indicate the bent region of induced paired bends. Following induction of paired bends, further changes were observed and are shown in States 2–5. Of the total 560 cases that showed paired bends at first bending, no further responses were observed in 342 cases and named paired bend. The first response accompanying the bend formation was bend relaxation (BR; N=126). State 2 seems to be independent of States 3–5. State 3 involves growth and propagation (GP) of bends, which appeared in 11 cases out of 560. States 4 and 5 belong to an oscillation-like response with switching direction of bending [SW: a few cycles (<3); BEAT, ≥3 cycles]. Switching (SW) and beating (BEAT) were observed in 18 and 63 cases out of 560, respectively. N is the number of induced responses.

Table 2.

Effects of distance from the bottom surface on the beat frequency and sliding velocity of sperm flagella showing beating by mechanical deformation at low ATP levels

Effects of distance from the bottom surface on the beat frequency and sliding velocity of sperm flagella showing beating by mechanical deformation at low ATP levels
Effects of distance from the bottom surface on the beat frequency and sliding velocity of sperm flagella showing beating by mechanical deformation at low ATP levels

Figure 1 shows typical examples of microneedle manipulation to induce flagellar deformation and the resulting flagellar responses. These responses include: bend relaxation (BR; Fig. 1B; Movie 1), bend growth and propagation (GP; Fig. 1C), and oscillation-like responses that we call here ‘beating’ (BEAT1 and BEAT2; Fig. 1D,E; Movie 2). Details of these four types of responses will be described below.

When the sperm head-held needle was moved in either a lateral or axial direction relative to the sperm longitudinal axis, mechanical deformation first induced a pair of bends [Fig. 1B–E: four panels of recorded images (left) with their traces (right) in D for lateral and E for axial movement; in B for axial and C for lateral movement, respectively]. When the microneedle movement stopped (red triangles, Fig. 1) some flagella began to show further responses. These responses were depicted by reconstructed, superimposed traces in Fig. 1B–E at the right-hand side of the recorded images. Characteristic changes occurred in the proximal region of the induced paired bends; in BEAT and GP the propagation of bends was also observed but growth of bends occurred first. Growing waves gradually moved towards the left without changing form and stopped in GP (Fig. 1C), while in BEAT (Fig. 1D,E), bends developed and propagated, and then the direction of bending alternated relative to the flagellar axis. In BEAT most sperm repeated more than five cycles: a sperm shown in Fig. 1D,E continued for 3.5 cycles and at least 5 cycles of response, respectively. The response shown in Fig. 1B appears similar to normal beating, but each bend fails to show growth and propagation. Two bends of opposite curvatures showed a slight increase and then decrease in their curvature (Fig. 1B). We call such apparent elastic responses bend relaxation (BR).

Here, we summarize conditions to induce oscillation-like response at 1.5–2.0 µmol l−1 ATP. The following three conditions were essential. (1) When we applied mechanical deformation to the flagellum, it was necessary to induce a pair of bends near the base of the proximal region of a flagellum. (2) For formation of a pair of bends, the microneedle holding the head of the sperm needed to be moved towards the other needle holding the tip of the flagellum. (3) All the manipulation and observation of the flagellar responses needed to be carried out by keeping the flagellar beating plane approximately 10–15 µm above the glass surface, resulting in stable flagellar beating by limiting surface tension.

Characteristics of flagellar responses induced by mechanical deformation

In the presence of 1.5–2.0 µmol l−1 ATP, four types of responses were observed when paired bends were induced by mechanical deformation, with no further movement of microneedles (Fig. 2). These include BR (Fig. 1B), indicating that simple bend formation of paired bends does not always show bend relaxation owing to elastic normalization. The other three kinds of flagellar responses are BEAT, switching (SW) and GP. In beating, bend formation was followed by bend growth and propagation that further developed with alternation on both sides of the flagellar axis and more than three beat cycles. Of the 560 trials, 11.3% showed beating (BEAT). SW is similar to BEAT but the number of alternation cycles was less than three. This SW response was observed in 3.2% of 560 cases; 11 cases (2.0%) showed growth of bends and their propagation, but alternations of bend direction did not occur. We call this response growth and propagation (GP). GP is probably a step leading towards bending with SW and BEAT.

As sea urchin sperm flagellar length is quite constant, most of the sperm used for the study showed a flagellar response in the full length of the flagellum with the distance between two needles close to the whole length of the flagellum (Fig. 1D). In contrast, some flagella responses were localized to a more proximal, short region of the flagellum (Fig. 1E). However, all five kinds of responses were observed regardless of distance between the two needles. Therefore, the data obtained from flagella with various distances between the two needles were analysed as a group.

Propulsive force of swimming sperm is generated by flagellar oscillatory movement consisting of axial and lateral components of a sperm head movement relative to its longitudinal axis. Among components involved in the sperm movement a slight rotation also occurs (Cosson, et al., 2003). At the stage of bend initiation this regulation is also important. Microtubule sliding in beating flagella is influenced by lateral deformation but not by axial deformation (Shingyoji, et al., 1991b). Thus, in this study mechanical deformation was applied using two different directional methods: a sperm head-held needle was moved either (1) axially (axial movement) or (2) laterally (lateral movement). Figure 3 shows a rough survey of the effects of both procedures on the occurrence of four types of responses. In Fig. 3A, all 25 responses were obtained from 25 individual sperm (six red plots for lateral movement and 19 blue plots for axial movement). In Fig. 3B, repetitive measurements were carried out in two sperm using lateral deformation (red symbols) and axial deformation (blue symbols). Notably, there was little difference between the two types of bend induction for BEAT, SW and GP (Fig. 3A,B). However, the effective speed of axial needle movement seems to be more critical than lateral needle movement for stable responses. Also, there appears to be a minimal speed of needle movement required for SW and BEAT, while speed of needle movement has little effect on BR induction (Fig. 3C).

Fig. 3.

Effects of the movement of the sperm head-held needle on the induction of flagellar responses. Microneedles holding sperm heads were moved axially or laterally to induce a pair of bends in demembranated flagella at 1.5–2.0 µmol l−1 ATP. Distance and duration of the microneedle movement are slightly related to appearance of BEAT, SW and GP (A,B) but not to BR (C) in both axial (blue or green) and lateral (red) needle movements. Twenty-five individual sperm (A), two sperm (B) and 14 sperm (C) were used.

Fig. 3.

Effects of the movement of the sperm head-held needle on the induction of flagellar responses. Microneedles holding sperm heads were moved axially or laterally to induce a pair of bends in demembranated flagella at 1.5–2.0 µmol l−1 ATP. Distance and duration of the microneedle movement are slightly related to appearance of BEAT, SW and GP (A,B) but not to BR (C) in both axial (blue or green) and lateral (red) needle movements. Twenty-five individual sperm (A), two sperm (B) and 14 sperm (C) were used.

Roles of microtubule sliding for the regulation of flagellar responses

Among the various responses, BEAT and SW have in common the induction of oscillatory movement through alternating microtubule sliding. In BEAT and SW, the direction of bending regularly switched to both sides of the axis of the axoneme. However, the number of switching events appeared to have a boundary at three cycles. Therefore, we named responses with less than three beat cycles as SW and responses with more than three cycles as BEAT. To gain a deeper understanding of the role of microtubule sliding in the flagellar response, shear curves in BEAT, SW, GP and BR were obtained and compared (Fig. 4A,C–F). (Gibbons, 1981; Satir, 1968; Warner and Satir, 1974).

Fig. 4.

Typical examples of shear curves showing time-dependent changes of shear angles along the length of the flagellum in five types of responses. Sequential wave changes of each cycle are divided into two panels, and in each panel, an early phase and a later phase of the response are depicted. (A) Three sequential cycles for BEAT; (C) two sequential cycles for SW; (D) GP; (E) BR. (B) BEAT-like SW: this rare response began with a GP-like response, but after a short pause, a new bend appeared at the flagellar base in opposite bending direction. Such switching of bending direction occurred for two cycles. (F) Procedure to obtain shear curves from measurement of shear angle (top) and reconstructed waveforms based on the shear curves. Changes of shear angle between two neighboring sequential lines at a given position along the flagellum represent the sliding velocity (rad s−1). Shear angles are taken at 1 s intervals. P, principal bend; R, reverse bend; δ, sliding velocity.

Fig. 4.

Typical examples of shear curves showing time-dependent changes of shear angles along the length of the flagellum in five types of responses. Sequential wave changes of each cycle are divided into two panels, and in each panel, an early phase and a later phase of the response are depicted. (A) Three sequential cycles for BEAT; (C) two sequential cycles for SW; (D) GP; (E) BR. (B) BEAT-like SW: this rare response began with a GP-like response, but after a short pause, a new bend appeared at the flagellar base in opposite bending direction. Such switching of bending direction occurred for two cycles. (F) Procedure to obtain shear curves from measurement of shear angle (top) and reconstructed waveforms based on the shear curves. Changes of shear angle between two neighboring sequential lines at a given position along the flagellum represent the sliding velocity (rad s−1). Shear angles are taken at 1 s intervals. P, principal bend; R, reverse bend; δ, sliding velocity.

In BR, once the paired bends were induced, their shear curves showed stable changes during their tip-ward movement of the bend (Fig. 4E), indicating that the wave changes are caused by passive microtubule sliding. In contrast, bend propagation occurring during BEAT, SW and GP is an active process with characteristic changes in the amplitude of shear curves (Fig. 4A,C,D). More precisely, in GP, the shear angle increased in the early phase of propagation (Fig. 4D) and its largest angle was maintained in the later phase of propagation. In SW and BEAT, growth of bends in one direction induced an increase in shear angles in the early phase of each cycle (Fig. 4A,C). This was followed by the change in bend direction during the later phase of bend propagation.

The above results indicate that the mechanisms controlling flagellar responses involved in GP, SW and BEAT are different from the mechanism controlling BR. To obtain further information about the cyclical components from differences between BEAT and simple growth and propagation (GP and SW), we studied the wave changes at the beginning as well as at stoppage of BEAT.

Conditions determining start and stop of BEAT

In Fig. 5 we summarize typical waveform changes of three types of responses (BEAT, SW and GP) and use BR as a reference (Fig. 5A,C–E). Responses induced by axial or lateral movement were very similar in each type of response. In lateral needle movement we were able to induce stable flagellar deformation resulting in a pair of slightly asymmetrical bends and oriented with a proximal P-bend and a distal R-bend. Interestingly, bend induction did not result in an oppositely oriented pair of bends. In contrast, during axial needle movement various forms of flagellar deformation were observed. However, in this case again we found that stoppage of a head-held needle movement also resulted in P–R bending pairs. Thus, when axial deformation was applied as well as lateral deformation, new responses started from growth of a P-bend. This type of response, owing to axial deformation, was induced not only in BEAT but also in SW and GP (Fig. 5A,C,D). Flagellar waves appearing at initiation of fish sperm motility show processes similar to those described here (Prokopchuk et al., 2015).

Fig. 5.

Typical axially and laterally induced waveform changes for the five types of flagellar responses. The effects of two types of needle movement (axial and lateral) on waveform changes in five types of responses (A–E) are shown. Sequential wave changes of each cycle are divided into two panels (except in B: two and three panels), including an early phase and a later phase of the response. (A) BEAT; (B) BEAT-like SW; (C) SW; (D) GP; (E) BR. Responses in each type are very similar, regardless of the different needle movement. In lateral and axial conditions, a pair of proximal principal bends with a distal reverse bend (P/R bends) is induced at the flagella base (A–D). An exceptional observation was BEAT-like SW (B). Stoppage of beating also occurred at the stage of P-bend propagation (A–D). A detailed explanation of BEAT-like SW is given in the Discussion.

Fig. 5.

Typical axially and laterally induced waveform changes for the five types of flagellar responses. The effects of two types of needle movement (axial and lateral) on waveform changes in five types of responses (A–E) are shown. Sequential wave changes of each cycle are divided into two panels (except in B: two and three panels), including an early phase and a later phase of the response. (A) BEAT; (B) BEAT-like SW; (C) SW; (D) GP; (E) BR. Responses in each type are very similar, regardless of the different needle movement. In lateral and axial conditions, a pair of proximal principal bends with a distal reverse bend (P/R bends) is induced at the flagella base (A–D). An exceptional observation was BEAT-like SW (B). Stoppage of beating also occurred at the stage of P-bend propagation (A–D). A detailed explanation of BEAT-like SW is given in the Discussion.

Propagation velocity determines the regulation of oscillation

To address the conditions regulating the oscillatory response, shear curves (Fig. 4) were carefully examined and the propagating velocities of wave components were compared (Fig. 6). More precisely, for oscillation, we focused on: (1) growth of bends near the flagellar base, (2) propagation of the grown bends that maintain their size, (3) propagation of the bends with slight decrease in size, and (4) switching of directions in the growth and propagation of bends. Bending waves induced in the opposite directions look similar but are slightly different. They are related to P- and R-bends.

Fig. 6.

Factors important for oscillation: mean propagation velocities determine the response, and minimal propagation velocity is required for oscillation. (A) A model for conditions triggering the mechanism of oscillation. Propagation velocity of each wave component was obtained and compared. Factors we focused on as important for oscillation were as follows: (1) growing state of induced bends near the flagellar base, (2) propagation of the grown bends while maintaining their size, (3) further propagation of the bends with slight decrease in size, and (4) switching of directions in the growth and propagation of bends. For oscillatory beating (gain of oscillation), these states (states 1–3) appeared regardless of the direction of a newly grown bend. Propagation velocities on one side and those on the opposite side were alternately observed. These responses were categorized into a gain of oscillation group. The loss of oscillation group, not accompanied by oscillation (such as in GP and BR), showed propagation of induced bends on only one side. Pink, hatched and purple bars indicate propagation velocities of states 1, 2 and 3, respectively. (B) Relationship between oscillatory conditions and wave propagation velocities. Green and orange bars show velocities of bend movement, observed just before stoppage of movement and BR, and belonging to a loss of oscillation group. Of all the flagellar responses, SW and BEAT showed oscillation-like cyclical bending, while some cases of SW and BEAT showed stoppage after only a few cycles of bending. Responses during continuous repetition of cyclical bending were categorized as gain of oscillation, and responses during cyclical bending before stoppage were categorized as loss of oscillation. Means±s.d. of propagation velocity are shown. Numbers in parentheses (N/N) indicate the number of cycles analysed (first digit) obtained from the number of sperm (second digit). Asterisks indicate that the differences are statistically significant (Mann–Whitney U-test: **P<0.01).

Fig. 6.

Factors important for oscillation: mean propagation velocities determine the response, and minimal propagation velocity is required for oscillation. (A) A model for conditions triggering the mechanism of oscillation. Propagation velocity of each wave component was obtained and compared. Factors we focused on as important for oscillation were as follows: (1) growing state of induced bends near the flagellar base, (2) propagation of the grown bends while maintaining their size, (3) further propagation of the bends with slight decrease in size, and (4) switching of directions in the growth and propagation of bends. For oscillatory beating (gain of oscillation), these states (states 1–3) appeared regardless of the direction of a newly grown bend. Propagation velocities on one side and those on the opposite side were alternately observed. These responses were categorized into a gain of oscillation group. The loss of oscillation group, not accompanied by oscillation (such as in GP and BR), showed propagation of induced bends on only one side. Pink, hatched and purple bars indicate propagation velocities of states 1, 2 and 3, respectively. (B) Relationship between oscillatory conditions and wave propagation velocities. Green and orange bars show velocities of bend movement, observed just before stoppage of movement and BR, and belonging to a loss of oscillation group. Of all the flagellar responses, SW and BEAT showed oscillation-like cyclical bending, while some cases of SW and BEAT showed stoppage after only a few cycles of bending. Responses during continuous repetition of cyclical bending were categorized as gain of oscillation, and responses during cyclical bending before stoppage were categorized as loss of oscillation. Means±s.d. of propagation velocity are shown. Numbers in parentheses (N/N) indicate the number of cycles analysed (first digit) obtained from the number of sperm (second digit). Asterisks indicate that the differences are statistically significant (Mann–Whitney U-test: **P<0.01).

When the responses show oscillation (‘gain of oscillation’; Fig. 6), the waveforms induced by mechanical deformation undergo alternating cycles of bending. Among the responses showing cyclical switching, there were several examples that showed stoppage of oscillation. When the response showed stoppage during cyclical alternation (‘loss of oscillation’; Fig. 6), the switching of bending direction did not occur in the last state, and propagation velocity decreased rapidly, although the size of bends was maintained through propagation. In addition to the last state of BEAT (three cases of stoppage at the fourth cycle) as well as SW (three cases of stoppage at the second cycle), the state of loss of oscillation was similar to the last state of GP (growth and propagation), as well as the response of BR (bend formation and relaxation). As we have shown in green bars in Fig. 6B, there were no significant differences in the propagation velocities among these three different conditions.

As a result of comparison of propagation velocities in each wave component, we found two differences between the conditions necessary for induction of gain of oscillation (Fig. 6B) and those for loss of oscillation (Fig. 6B). Stoppage of cyclical oscillation with limited amount of switching was observed in the 1.5th cycle (N=3) in SW and the 3.5th cycle (N=3) in BEAT, respectively. These responses at the final cycles were categorized into loss of oscillation (N/N=6/6). Characteristic responses showing a large decrease in propagation velocity, without maintaining a level of bend growth, were recognized in such final cycles before stoppage (Fig. 6B, green bars). This decrease is similar to GP. However, in the responses belonging to gain of oscillation, in which bending directions cyclically alternated, the propagation velocity after the growth of bending was kept at a high level. Usual states showing cyclical bending are induced in this group (Fig. 6B). Maintaining sufficient bend propagation velocity, without a decrease in propagation velocity after bend growth, seems to be important for induction of oscillation.

Characteristic changes in curvature of the flagellar movement that support oscillation

Curvature is known as one of the important parameters associated with regulation of oscillation. However, the role of curvature control in the regulation of oscillation has been difficult to detect. Figure 7 shows the changes in curvature in the induced bends. When the oscillation continued in Fig. 7A,B (BEAT2 and 3), constant changes with stable ranges in curvature were recognized, suggesting that the induced bends propagate while changing their shape. In contrast, without oscillation in Fig. 7C,D (fourth cycle of BEAT1 and second cycle of SW2) the change in curvature decreased and finally the changes disappeared (red arrows).

Fig. 7.

Changes of curvature along flagellar length in BEAT and SWresponses. BEAT2 (A), BEAT3 (B) and BEAT1 (C) are the same sperm flagella shown in Fig. 4A. SW2 (D) is obtained from the data used in Fig. 4C showing 1.5 cycles of beating. Different from the regular repetition of curvature changes in each cycle (in A and B), in C and D, just before the stoppage of beating, curvature changes disappeared (red arrows in the last panel). Curvatures were calculated every second for the recorded images (at 30 frames s−1).

Fig. 7.

Changes of curvature along flagellar length in BEAT and SWresponses. BEAT2 (A), BEAT3 (B) and BEAT1 (C) are the same sperm flagella shown in Fig. 4A. SW2 (D) is obtained from the data used in Fig. 4C showing 1.5 cycles of beating. Different from the regular repetition of curvature changes in each cycle (in A and B), in C and D, just before the stoppage of beating, curvature changes disappeared (red arrows in the last panel). Curvatures were calculated every second for the recorded images (at 30 frames s−1).

When we analysed the change of curvature during propagation of paired bends, we found interesting characteristics. In Fig. 8, curvatures of induced bends obtained during every second (1/30 frames of recording) were depicted in BEAT3 (Fig. 8A), BEAT1 (Fig. 8B), SW2 (Fig. 8C) and GP3 (Fig. 8D). BEAT3 showed nine cycles of repetition, while BEAT1 showed three cycles of oscillation that were followed by the last phase of stoppage (after t=30). In two other cases (Fig. 8C,D), the oscillation stopped in SW2 or did not occur in GP3. As the curvature of paired bends increased (red arrows in Fig. 8), the two consecutive bends in curvature (green boxes in BEAT3, BEAT1 and SW2) (Fig. 8A–C) propagated to the end of the flagellum, and this pair of bends became smaller while balancing each other. By decreasing the size in paired bends in a balanced manner, new paired bends started to develop at the base of the flagellum (red arrows in Fig. 8). If this reduction of curvature of the paired bends did not occur (indicated by yellow boxes in BEAT1 (from t=30 s) (Fig. 8B) and in SW2 (from t=11 s) (Fig. 8C), new paired bends may not start to grow at the base of the flagellum (blue arrows in Fig. 8A–C and in GP3, Fig. 8D). These curvature fluctuation processes and timing coincided very well with the first, second and third cycles in BEAT3 and BEAT1 (Fig. 8A,B).

Fig. 8.

Time-dependent changes of wave dynamics expressed by the curvature change along flagellar length in BEAT, SW and GP. BEAT3 (A), BEAT1 (B) and SW2 (C) are the same sperm flagella shown in Fig. 7. The BEAT3 and BEAT1 showed repetitive cyclical oscillation and limited cycle of oscillation (3.5 cycles), respectively. SW2 also showed a limited cycle of oscillation (1.5 cycles). Development of bends on both sides of the flagellum corresponds to the cyclical bending: in BEAT3 (A), mechanically induced bending (started at t=0) appeared as paired bends and grew within 3 s (at t=4–7 s). These paired bends propagated distally (t=8–10 s) and they gradually decreased in size as pairs until t=14 s. The green boxes show the process of bend decay. As changes progress, a more proximal bend grew and developed (t=12–15 s). These processes form the basis of repetitive cyclical oscillation. In contrast, as shown in the examples of limited cycles in BEAT1 (B) and SW2 (C), we did not observe any formation and propagation of paired bends in the proximal region, when the decrease in size of the bends did not occur. (t=30–33 s in BEAT1; t=11–14 s in SW2). The yellow boxes show the process. Similar responses showing such propagation towards the distal end without a decrease in size of paired bends are also observed in GP3 (D).

Fig. 8.

Time-dependent changes of wave dynamics expressed by the curvature change along flagellar length in BEAT, SW and GP. BEAT3 (A), BEAT1 (B) and SW2 (C) are the same sperm flagella shown in Fig. 7. The BEAT3 and BEAT1 showed repetitive cyclical oscillation and limited cycle of oscillation (3.5 cycles), respectively. SW2 also showed a limited cycle of oscillation (1.5 cycles). Development of bends on both sides of the flagellum corresponds to the cyclical bending: in BEAT3 (A), mechanically induced bending (started at t=0) appeared as paired bends and grew within 3 s (at t=4–7 s). These paired bends propagated distally (t=8–10 s) and they gradually decreased in size as pairs until t=14 s. The green boxes show the process of bend decay. As changes progress, a more proximal bend grew and developed (t=12–15 s). These processes form the basis of repetitive cyclical oscillation. In contrast, as shown in the examples of limited cycles in BEAT1 (B) and SW2 (C), we did not observe any formation and propagation of paired bends in the proximal region, when the decrease in size of the bends did not occur. (t=30–33 s in BEAT1; t=11–14 s in SW2). The yellow boxes show the process. Similar responses showing such propagation towards the distal end without a decrease in size of paired bends are also observed in GP3 (D).

DISCUSSION

The mechanism of oscillation is a long-lasting enigma in understanding flagellar and ciliary motility. The oscillation is composed of a rhythmical cyclical beating and characterized by bi-directional bending waves typically propagating from the proximal to distal end of a flagellum. In case of sea urchin sperm flagella, not only the formation of cyclical bending but also propagation of bends occurs almost in one plane (Shingyoji et al., 1991a). This planarity is an important feature we focused on in this study. Another important feature is the switching of bending direction, a process directed in part by switching in dynein activity across the axis of the sea urchin sperm axoneme (Lin and Nicastro, 2018).

To understand mechanisms for control of flagellar oscillation, boundary conditions leading to oscillation must be identified. ATP concentration determines the flagellar beat frequency (Brokaw, 1975, 1991; Gibbons and Gibbons, 1972; Shingyoji et al., 1977; Summers and Gibbons, 1971). However, it is also true that the frequency of oscillation can be changed by an external mechanical stimulus of beating flagella (Baba and Hiramoto, 1978; Hayashibe et al., 1997; Lindemann and Rikmenspoel, 1972; Morita and Shingyoji, 2004; Shingyoji, et al., 1991b, 1995). Therefore, in order to induce oscillation, both chemical factors resulting from hydrolysis of ATP and mechanical factors resulting from mechanical deformation of the axoneme should be considered. We found in this study that essential experimental conditions necessary for planar beating at very low ATP conditions are: (1) to generate microtubule sliding so as to form a pair of bends, (2) maintenance of the flagellar beating plane at a certain distance from the surface of the glass slide chamber, and (3) application of mechanical deformation to the flagellum so as to induce strain and directional changes between the proximal and distal regions of the flagellum.

The success of the present study, in defining necessary conditions for control of oscillation, began with the idea to mechanically induce bends at very low ATP concentrations, below the ATP concentration required to support re-activation of flagellar bending. This is similar to the method we developed previously in which we succeeded in inducing bend formation and propagation-like transition (Ishikawa and Shingyoji, 2007). However, the present study has been carried out below the threshold levels without an ATP regenerating system, using highly diluted, demembranated sperm. We conclude that the threshold of ATP concentration necessary for spontaneous beating under suitable mechanical deformation is 1.5–2.0 µmol l−1. This result provides new insight into how flagellar movement is initiated in live sperm cells.

The flagellar responses we observed in this study have been categorized into five types, including formation of a pair of bends, relaxation of the bends (BR), growth of the bends and their propagation (GP), switching of bending direction for a few cycles (SW) and repetitive cyclical bending for more than three cycles (BEAT). Mechanical formation of paired bends was always coupled with these five types of responses. To induce oscillatory beating at below-threshold ATP concentrations, formation of paired bends is essential as the first step of the response. In addition, a stable bend plane was important in the case of sea urchin sperm flagella as they have a relatively long flagellar length (Hayashi and Shingyoji, 2008; Ishikawa and Shingyoji, 2007).

This approach resulted in a number of flagellar responses, which provided us with an opportunity to understand the oscillatory mechanism by comparing differences in complete and incomplete beat cycles. The complete and incomplete cycles reflect the conditions necessary for oscillatory and non-oscillatory responses. Both SW and BEAT include oscillatory features, while the other types of responses (BR and GP) do not. We found that even in the responses of SW and BEAT themselves, a few cases showed a stoppage of the response. For example, the second cycle in SW and the fourth cycle in BEAT could show a stoppage. In such cases the first cycle (in SW) and the first to third cycles (in BEAT) showed complete response before the incomplete second cycle (in SW) and the incomplete fourth cycle (in BEAT) responses. We considered that these responses could be grouped as gain of oscillation or loss of oscillation. Analysis of the oscillation and non-oscillation groups in Fig. 6 indicates that the higher propagation velocities of paired bends, throughout every step of flagellar movement, are important for achievement of the oscillation.

We have examined conditions that may transform a simple growth of bends into bi-directional cyclical beating. Several parameters we examined did not show clear effects on oscillation. These include: movement of a sperm head-held needle (distance and duration in Fig. 3), size of grown bends (wave amplitude in red numbers in Fig. 5), and increase in sliding velocities (calculated from shear curves in Fig. 4). However, the following three conditions appear important for control conditions of oscillation: (1) R-bend, (2) propagation velocity, and (3) curvature of the distal bends.

Using the present method, we found that all responses belonging to BEAT started from growth of a P-bend. This is also true in SW and GP responses. In addition, as part of the responses of BEAT and SW that showed stoppage, the responses always stopped at the stage of P-bend growth. Although it is only one observation, we found an interesting response, i.e. the delayed appearance of R-bend growth. The response is named as ‘BEAT-like SW’ and is shown in Figs 4B and 5B. In the first cycle of this response P-bend growth occurred, but the bend gradually decreased in propagation speed and finally showed stoppage-like behavior. This stoppage behavior is similar to stoppage of GP at the distal region of the flagella (during 6 and 10 s of the first cycle in Fig. 5B). Slight decay in curvature of the distal bend and new R-bend growth occurred (during 4 s of the first cycle in Fig. 5B). R-bend growth, coupled with the next P-bend initiation at the proximal region, further produced a 1.5 bend cycle. The results indicate that R-bend growth seems to be necessary for both the start and stop of oscillation. This may be related to R-bend-dependent regulation, probably through a balance between the preceding R-bend and the newly grown P-bend in speed of wave propagation.

It should be noted that most of the present data could provide support of the geometric clutch (GC) model (Lindemann, 1994a,b). The mechanism of oscillation has been sought by various cell motility researchers. Ideas proposed for explaining those models, such as the sliding-controlled switching model, curvature-controlled switching model and GC model are historically important (Brokaw, 1971, 1972, 1985, 1994, 2002, 2005; Lindemann, 1994a,b). The mechanism is clearly complex, and oscillation can only occur when various control systems work cooperatively.

In normal sperm flagella, ATP concentration is around the millimolar level and the regulation at the base of the flagellum must differ from that in the present study. However, the initiation process of beating is thought to be similar to live sperm as well as re-activated sperm (Gibbons, 1981; Gibbons and Gibbons, 1980). At the starting transient, proximal region of the flagellum is important for formation and propagation of bends. Holding the distal tip of the flagellum in the present study did not seem to affect the beat initiation process. Therefore, the basic mechanism we found in this study possibly applies in the normal initiation of bending of flagella. We must also consider how the beating plane is kept stable. The mechanism of maintaining the flagellar bending plane is related to the stability of the central-pair microtubules through the function between the central-pair (CP) and radial spokes (RS) (it is known that the beating plane is to be perpendicular to the plane of the central pair). The axonemal architecture controlling CP/RS interaction involved in the stability of switching mechanism (Lin and Nicastro, 2018; Lindemann, 1994a,b; Oda et al., 2014; Shingyoji, 2018) and related formation of a pair of planar bends is essential for initiation of normal oscillation.

When comparing the bend initiation process of the present study with the starting process of freely swimming sperm in previous reports (Gibbons, 1981; Gibbons and Gibbons, 1980), we have found that in both cases the induction of bends shows similar waveforms so as to generate a pair of bends near the base of the flagellum. Paired bend generation is followed by propagation with an increase in velocity. However, there is a large difference. In the present study, although ATP concentration was low, induced waveforms were relatively large at the flagellar base and then propagated to the distal region. In contrast, in the analysis of starting transient of live and re-activated sea urchin sperm (Gibbons, 1981; Gibbons and Gibbons, 1980), paired bends were first small and located at the flagellar base. The initial small bends did not propagate but disappeared immediately. Thereafter, such bend induction was repeated with increasing size of bends that finally propagated towards the distal end and resulted in cyclic flagellar beating. This difference was probably caused by the presence of more effective mechanical strain in sperm in the present study. In this study, strain was applied to both flagellar ends (head and flagellar tip), which makes dynein molecules respond to generate oscillatory movement by a strain-dependent, self-regulatory nature of dynein (Shingyoji, 2018; Shingyoji et al., 2015; Yoke and Shingyoji, 2017).

Here, a special role of the head for contributing more effective generation of flagellar oscillation should be discussed. Experiments similar to the present procedure with head-less sperm are possible but it must be difficult to stably hold the two ends of a flagellum. Instead, our previous challenge to analyse responses to mechanical deformation with holding a flagellum by attaching the head and basal part of the flagellum was useful, and we found that the head–flagellum junction did not play special role in oscillation (Ishikawa and Shingyoji, 2007). Thus, strain-dependent regulation of dynein activity is essential for oscillation. Also, asymmetry in axonemal structures and dyneins may play a role in bend initiation in live sperm (Dutcher, 2019).

In sea urchin sperm, which have relatively long flagella compared with cilia or Chlamydomonas flagella, an induction of a pair of bends seems to be an essential condition for start of oscillation. How the asymmetrical characteristics owing to P- and R-bends are determined is still a mystery, but a kind of robustness of R-bend features has suggested a possible role in the regulation of switching in oscillation (Eshel et al., 1991, 1992). Here, we found a different role of the P- and R-bends in the process of beginning of cyclical bending. For example, following mechanical deformation, P-bend-dependent growth and stoppage are stably induced compared with R-bends. Asymmetry of flagellar bending is influenced by Ca2+. Therefore, study of the effects of different Ca2+ levels may be one way to further understand the roles of R-bends in induction of oscillation.

The present study suggests that ATP-driven microtubule sliding by dynein molecules is regulated, in part, by strain in order to generate a pair of bends near the base of the flagellum. These bends then propagate with increasing velocity, gradually decreasing the amount of sliding in the distal region. This process then leads to generate a new bend at the basal region. Together, these elements provide part of the foundation underlying the mechanism of oscillation. What causes the microtubule sliding length between paired bends? This is one of many remaining questions.

Acknowledgements

We thank Professor Winfield S. Sale for discussion and improving of the manuscript. We also thank the director and staff of the Misaki Marine Biological Station, the University of Tokyo, Education and Research Center for Marine Biology, Tohoku University and Tateyama Marine Laboratory, Ochanomizu University for supplying Hemicentrotus pulcerrimus sea urchins.

Footnotes

Author contributions

Conceptualization: C.S.; Methodology: C.S., Y.I.; Formal analysis: Y.I.; Investigation: C.S., Y.I.; Data curation: C.S., Y.I.; Writing - original draft: Y.I.; Writing - review & editing: C.S.; Supervision: C.S.; Project administration: C.S.; Funding acquisition: C.S.

Funding

This work was supported by the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research on Innovative Areas, 26102510 and 16H00752 to C.S.

Data availability

The data obtained in this study will become available through the University of Tokyo Academic Institutional Repository, 6 months after publication.

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Competing interests

The authors declare no competing or financial interests.

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