Form of developing bends in reactivated sperm flagella

The first modern description of flagellar wave form was given by Gray (1955), on the tails of sea urchin spermatozoa. Actively swimming spermatozoa were photographed using stroboscopic illumination, and the photographs were analysed. The waveform was described as being similar to a travelling sine wave, originating at the base of a flagellum and propagating to the tip. This characterization has served as the starting point for numerous subsequent studies (e.g. Gray & Hancock, 1955; Machin, 1958; Brokaw, 1965; Holwill, 1965; Holwill & Miles, 1971). It has been refined with the observation that the peaks of waves on actual flagella are more rounded than those of a sine wave: flagellar bends can be more accurately approximated by a series of travelling circular arcs and interconnecting straight lines (Brokaw & Wright, 1963; Brokaw, 1965). This waveform can also be approximated by meander-like waves (Brokaw, Goldstein & Miller, 1970; Rikmenspoel, 1971; Silvester & Holwill, 1972).

Within the past few years, theoretical models have transcended the description of flagellar waveform in terms of such approximations (Brokaw, 1972a,b; Brokaw & Rintala, 1975). These models have been developed into computer programs which produce detailed sketches of swimming flagella; these sketches can be directly compared to photographs of actual flagella.

The sliding microtubule model of flagellar and ciliary motility (Satir, 1965, 1974) implies that the bending occurring along a flagellum measured with respect to the base is directly proportional to the underlying sliding of the microtubules (Goldstein, 1968, 1969). Patterns of microtubular sliding during beating can therefore be directly inferred from light micrographs.

In the study presented here, photographs of actively beating tritonated sea urchin spermatozoa were analysed, in an attempt to provide more detailed information on waveforms and sliding patterns than has been available previously. Particular attention was paid to the region near the flagellar base, where new bends form and develop. These reactivated flagella beat well over a large range of frequencies, even after removal of the sperm heads.

Some of the results on angles of bends have been presented at a symposium (Goldstein, 1975).

Spermatozoa of a sea urchin, Lytechinus pictus, were extracted according to the procedure of Gibbons & Gibbons (1972), as modified by Brokaw, Josslin & Bobrow (1974). Ca²⁺ concentration was buffered to approximately 10⁻⁹ M. Beat frequencies ranged from approximately 0·5 Hz to approximately 20 Hz as the ATP concentration was varied from 10⁻⁵ M to 10⁻³ M. Heads were sheared from some spermatozoa by forcing them through a pipette. Slides were washed and silicone-coated with a 2% solution of Siliclad (Clay Adams, Parsippany, N. J. 07054).

Photographs were taken on Kodak 35 mm Tri-X film, developed for 10–15 min in Acufine (Acufine, Inc., Chicago, IL 60611). A Zeiss shutter and model C35M motor-driven camera were used. The Zeiss optics consisted of an ‘ultra’ oil-immersed dark field condenser, a × 40 oil-immersion planapochromat objective lens, a × 20 eyepiece and a reflex camera adapter (× 0·5), giving a total magnification of × 400. Stroboscopic illumination was provided by a Strobex model 360 power supply and model 72 xenon lamp (Chadwick-Helmuth, Monrovia, CA 91016). The photographs are similar to previously published dark-field multiple-exposure photographs (Brokaw, 1970), except that they were taken while the film was moving through the camera, to prevent the images from overlapping near the flagellar base. This was accomplished by pressing and quickly releasing the cable release while the shutter was set to ‘T’ position. When the film stopped moving, the cable release was pressed and released again to close the shutter and move the film into position for the next photograph. This technique preserves much of the efficiency, convenience of display, resolution of detail and aesthetic appeal of 35 mm multiple-exposure photography while providing the separation of images offered by cine photography. This is especially useful in analysing the movements of slowly beating spermatozoa, such as those shown in Fig. 1 (a, b) and Fig. 2(a, b). Analysis can be made within a single beat cycle, rather than from a series of exposures taken within different cycles. This eliminates the errors arising from small variations in beating which can occur over a series of many cycles. This technique worked well for exposure rates of about 10–20 Hz, and could presumably be used in other frequency ranges by changing the speed of the motor drive.

Measurements of short distances on prints were made with dividers; those of longer distances were made by overlaying thin tubing. Tangents were estimated visually. The centre of a bend was taken to be the point of intersection of that bend with a line bisecting tangents to the straight regions bordering it. The radius of a small bend developing at the base was computed as twice the distance from the base to the centre of that bend, divided by the angle subtended by the entire bend. Radii of larger bends were measured by overlaying circles of known size. The length of a bend was computed as the angle subtended times the radius.

Photographs of the various types of flagella are shown in Figs. 1 and 2. The arrows indicate the bends measured for the Figures and Table 1. These flagella are typical of their respective types, and will be used to illustrate the general findings. Tritona-tion usually removed the mid-piece, so that the base was more fully exposed than in live spermatozoa. Photographs were taken of spermatozoa both with and without heads, both free-swimming and attached to the cover glass at their base, over a range of frequencies from about 0·5 to 20 Hz. No appreciable differences were noted among the various types of spermatozoa at low frequencies, which had noticeably longer wavelengths than those beating at high frequencies. Among the spermatozoa beating at high frequencies, those which were attached to the glass had shorter wavelengths than the free-swimming ones, and their bends subtended greater angles; live attached spermatozoa also show these effects (Brokaw, 1965). Headless flagella beating at high frequencies proved very difficult to photograph, and little analysis was done on them. In spite of these differences, the essential pattern of bend development was similar in all these flagella.

In all the Figures, the exposure immediately preceding the first image in which a new bend can be discerned is taken as the start of a bend cycle. The time at which the following bend begins is taken to be halfway through that cycle ; this is generally a good approximation in these flagella.

The radii of bends with lengths as short as 2–3 μm can be measured in these photographs. This length was usually attained by the time a cycle was 20–30 % completed. At this stage the radius of a bend was typically about 50–70 % of its size at the time the following bend began. Radii of newly forming bends on the flagella of Figs, 1 and 2 are shown in Fig. 3. The values are normalized to the radius at the time the following bend began. Absolute values of these radii are given in Table 1. The radius sometimes remained at or near its initial value for two or three exposures before increasing, and sometimes remained fairly constant for 2 or 3 exposures about the time the following bend began. The radius usually continued to increase after the start of the following bend, and tended to approach a plateau at about one full cycle; however, it sometimes continued to increase, and, as shown in Fig. 2(b), occasionally decreased.

The positions of developing bends along the flagella of Figs. 1 and 2 are shown in Fig. 4. The values shown are the distances between the base and the centre of a bend, normalized to that distance at the time the following bend began. Absolute values of these distances are given in Table 1. These data resemble those for the movement of the proximal and distal ends of a bend (Brokaw, 1970).

The lengths of developing bends in the flagella of Figs. 1 and 2 are shown in Fig. 5. The values are normalized to the length at the time the following bend began. Absolute values of these lengths are given in Table 1.

By 30–40% of the bend cycle a straight region 1–2 μm long had developed at the base. The lengths of developing straight regions in the flagella of Figs. 1 and 2 are shown in Fig. 6. The straight regions are those immediately distal to the bends of

Figs. 3 to 5. The values are normalized to the length at the time the following bend began. Absolute values of this length are given in Table 1. Lengths were somewhat variable near the tip, and commonly decreased.

The angles subtended by newly forming bends in the flagella of Figs. 1 and 2 are shown in Fig. 7. Values are normalized to the angle at the time the following bend began. Absolute values of these angles are given in Table 1. The angle of a bend increased continually from the first exposure in which it could be measured, for about one bend cycle. It then usually remained roughly constant until the bend began travelling off the tip.

The algebraic sum of the two developing bends nearest the base-i.e. the angle between the base and the straight region immediately distal to the second bend-are summarized in Fig. 8. The acute angles are shown for two pairs of bends on each of the flagella of Figs. 1 and 2. Although the angles of individual bends increased steadily, the sum of the angles of the two developing bends remained nearly constant-often within ± 0·1 radian. The most common deviation, a sharp decrease before a new bend began to form, may be, at least in part, an artefact due to the inability to recognize a new bend while it is still very short. The constant growth of these angles while their sum remains nearly constant implies that they are growing at nearly the same rate, although in opposite directions.

The changes in the angles with respect to the base occurring between successive exposures are shown in Fig. 9, for points at 2 μm intervals along developing bends in the flagellum of Fig. 2 (a). Fig. 1 (b) and Fig. 2 (c) have also been analysed, and show similar patterns. The relative sliding of the microtubules within a beginning bend, which is directly proportional to the change in angle, was initially in the same direction as that within the preceding bend, as can be seen between exposures 1 and 2, and between exposures 7 and 11, in Fig. 9. The direction of sliding soon reversed, however, as can be seen between exposures 2 and 3, and between exposures 11 and 12, in Fig. 9. This occurred before a new straight region developed at the base. This new direction was maintained within the bend for the remainder of its travel along the flagellum. The angle at which this reversal occurred was quite variable, ranging between about 0·7 and 1·5 radians.

A new bend begins to form when the angle subtended by the previous bend has attained approximately half of its final value. Bending is initially localized to within a few μm of the base. The length, radius, angle and speed of propagation all increase as the bend develops.

The general features of the waveforms are preserved even at very low frequencies, where the external viscous forces are very low, suggesting that they are characteristic of an internal oscillatory mechanism.

The angles subtended by the two bends nearest the base generally increase at the same or nearly the same rate. A bend thus appears coordinated with the preceding bend during the first half of its development, while it is nearest the base, and with the following bend during the second half. There is little if any net bending associated with these developing bends, and hence little if any net microtubular sliding associated with their formation. This implies that (i) development of new bends is not caused by sliding distal to them ; (ii) development of new bends causes little if any sliding distal to them, and hence does not cause disruption of fully developed bends. Distally to the two developing bends, fully formed bends typically travel to the tip with fairly little change in their bend angle, implying little if any sliding in straight regions and a fairly constant rate of sliding within circular bends, with abrupt transitions between them, as suggested by Brokaw (1966). In the region of the two developing bends, however, the rate of sliding can be quite large in the straight section between the bends, and decreases to zero at the distal end of this region and at the base. Sliding distal to the developing bends can be approximated by the sum of two components: a synchronous component, which occurs simultaneously at all points and corresponds to the net bending in the region of the developing bends; and a metachronous component, which occurs within fully formed bends and is associated with their propagation. The first component is zero or quite small, and the second is appreciable within bends and zero or very small within straight regions. This difference between bends and straight regions occurs over a wide range of frequencies, and hence over a wide range of external viscous forces. The synchronous development of shear forces along these flagella (Rikmenspoel, 1971) therefore seems unlikely.

The development of new bends in echinoderm sperm tails, which typically contain only three or four bends, occupies a large fraction of the flagellum. However, in flagella such as those of urodele sperm tails, which contain many bends (Baker, 1966), the pattern of bend formation described here would allow new bends to be formed within a small fraction of the flagellum without involving microtubular sliding along the entire organelle.

The sliding occurring within a bend depends upon its speed of propagation and the rates of increase of its length, radius and subtended angle. The direction of sliding within a bend as it begins to form-i.e. as its radius decreases-is opposite to the direction of sliding within it as its radius and length increase or as it travels towards the tip. The sliding movements within two adjacent fully developed bends travelling along a flagellum occur in opposite directions. When a new bend begins at the base, the sliding within it is in the same direction as that in the preceding bend, whose direction of sliding is that associated with its propagation. At some point, then, the direction of sliding within the new bend must reverse. As can be seen in Fig. 9, this happens before the bend leaves the base. This pattern suggests the possibility that the shear forces initiating a new bend originate in the preceding bend.

The conservation of total angle in developing bends described here is also exhibited by the computer models of Brokaw (1972 a, b). In these computer models, however, the length and radius of a newly developing bend maintain large values from the outset, rather than growing the way those of actual flagella do. The reason for this discrepancy is not clear; one obvious possibility is that the mechanical characteristic of flagella may not be uniform along their length.

It has been tacitly assumed in this study that the outer doublets remain parallel to the plane of beating. Flagella fixed under some conditions for electron microscopy apparently exhibit some twisting of the outer doublets (Gibbons & Gibbons, 1974). However, this twisting seems unlikely for the flagella analysed in this study, which were photographed while beating with very planar waveforms adjacent to a cover glass.

The angles of developing bends do not always appear to cancel one another perfectly. Perfect cancellation of the two developing bends implies that, within the region of coordinated bend development, bends in one direction grow to the same angle as those in the other direction. This angular symmetry holds reasonably well for most of the flagella analysed, but in some flagella, such as that shown in Fig. 2(a), the bends in one direction obtain a greater angle than those in the other direction. This implies some change in the total angle, which must be either absorbed by neighbouring bends or transmitted as a synchronous sliding component. Some bending might possibly be taken up by either a stretching of the crossbridges or a compression of the flagellar cross section.

The tritonated flagella in this study were selected for reasonably symmetrical waveforms. Live echinoderm spermatozoa typically have waveforms which are somewhat asymmetrical with respect to angle (Gibbons & Gibbons, 1972). A detailed analysis of their waveforms is now under way.

I am indebted to Dr C. J. Brokaw, in whose laboratory these photographs were taken. This work was supported by grants from the Graduate School of the University of Minnesota and National Science Foundation grant number GB-36583 to me, and by National Institutes of Health grant number GM-18711 to C.B.