Oscillation of cilia and flagella  ©C. J. Brokaw   9/8/07

The mechanisms that regulate dynein-driven interdoublet sliding to cause oscillation and bend propagation by eukaryotic flagella and cilia are still a mystery. This article attempts to figure out whether we now have any better understanding than was possible in an earlier review [Brokaw, 1989].

Most analysis of flagellar and ciliary bending has been carried out with examples that produce planar, or nearly planar, bending patterns, which can be imaged easily at high resolution. These will be considered first.

Outline:

Part I. Observations on planar bending patterns

1. The bending patterns of cilia and flagella contain bends and interbends

2. Flagellar oscillation is the regular activation of sliding initiation events , alternately on two sides of an axoneme. A sliding initiation event involves two processes: (1) Transformation of a basal bend into a propagating bend, and (2) Formation of a new basal bend, usually by interbend growth.

3. Observations of arrest/quiescence indicate a failure of a sliding initiation event to occur at a normal switch point.

4. Searching for a trigger: Observations and experiments

Part II. Observations on three-dimensional bending patterns

1. Bending patterns

2. Chirality

Part III. Direct measurements of interdoublet sliding.

1. Protease-digested axonemes

2. Undigested axonemes

3. Microoscillations

Part IV.Conclusions, ideas and proposals

Part V. Epilogue

 

 Part I. Planar bending patterns

1. The bending patterns of cilia and flagella contain bends and interbends.

This statement is an interpretation, generally used even in the absence of evidence of discontinuities that identify boundaries between bends and interbends. Regions with relatively uniform curvature in one direction are considered to be bends. Interbends are regions with more rapid change in relative curvature, and typically contain inflection points where the curvature changes sign. In some cases, this interpretation can be quantified by fitting images of bending patterns with circular arcs and straight lines [Brokaw, 1965], or by fitting shear curves (plots of tangent angle relative to the basal end as a function of position) with straight lines in bends [Brokaw, 1993]. However, there are no distinct boundaries between bends and interbends that can be mapped to spatial discontinuities in dynein function.

1.1    Interbends

In the simplest cases, interbends contain inflection points between two bends, where both the curvature of the flagellum and the velocity of interdoublet sliding change sign. However, there are exceptional cases involving highly asymmetric bending patterns, where alternate bends have high and low values of curvature in the same direction. The presence of large amounts of “synchronous sliding” [eg. Goldstein, 1977; Gibbons, 1981] can also complicate the interpretation of sliding within an interbend. So, more generally, an interbend is a region where the curvature changes from a value characteristic of one bend to a value characteristic of an adjacent bend.  Typically, interbends are regions of change in both curvature and sliding velocity, without sharp boundaries between bends and interbends. Studies on simple sperm flagella indicate that the relative lengths of bends and interbends can vary between different examples, and that interbends can be longer than bends, especially in sperm beating with attached heads [Hiramoto and Baba, 1978; Baba and Mogami, 1985; Baba and Nonaka, 1990; Eshel and Brokaw, 1988].

Around an inflection point in the middle of an interbend, the curvature has low values, and the bending pattern appears to contain “straight regions”, even when our best methods for measuring curvature from high resolution images cannot detect a true straight region [eg Baba and Mogami, 1985; Baba and Nonaka, 1990; Brokaw 1990]. In rare cases, there are long interbends that do consist of two short curvature transitions separated by a straight region (Examples 2.4, 2.6). In other cases, there can be an abrupt change in the rate of change of curvature with length near the position where the curvature changes sign [Baba and Mogami, 1985]. These observations suggest that it might be more correct to think of interbends generally as consisting of two curvature transitions, possibly separated by a straight region of variable length.

1.2     Bends

Almost all bends on flagella and cilia can be classified as either basal bends or propagating bends:

Propagating bends are bends between two interbends. They are regions in which interdoublet sliding is occurring and is believed to cause propagation of the bend [Brokaw, 1971].  In exceptional cases, where there is a large amount of “synchronous sliding”, the apparent sliding in a propagating bend can be eliminated or even reversed during part of the beat cycle. So, more generally, a propagating bend is a region between two interbends, in which the difference between sliding velocities within the bend and in the interbends is that which is needed to cause propagation of the bend.

Basal bends are bends in which the sliding required for propagation is absent. Their development requires sliding in the interbend at the distal boundary of the bend. As their name implies, basal bends are typically found at the basal end of a flagellum, adjacent to the region of restricted sliding at the base. Basal bends can be found at other locations, on the distal side of a region in which bending and sliding are prevented by mechanical constraint or rigor binding in the absence of ATP [see Examples 2.3, 2.5].

Flagellar bends, including the nearly straight “bends” present during the effective stroke of cilia, often appear to be regions of uniform curvature (circular arcs). In some cases this is illusory, and it would be better to say simply that the rate of change of curvature with length in the bends is lower than in the interbends. Is it significant that uniform curvature implies a uniform sliding velocity within a propagating bend? Is it significant that in some situations a uniform curvature minimizes the elastic energy of bending? These questions would become more significant if there were strong data demonstrating uniform curvature. Unfortunately, measuring curvature precisely on flagellar images is still a difficult problem [Baba and Mogami, 1985; Eshel and Brokaw, 1988; Brokaw 1990].

1.3 Interpretation: active sliding

Propagating bends are regions where active sliding, driven by dynein motors, causes propagation of the bend. This sliding has been termed metachronous sliding [  ]. Interbends are regions where active sliding and active shear forces cause generation and maintenance of adjacent bends [Brokaw, 1971, 1994]. Normally, the direction of active sliding in a propagating bend is the same direction as the active shear force required in its trailing interbend.  However, these statements are interpretative presumptions, because there are no direct methods to distinguish between active sliding and passive sliding, by detecting localized dynein activity within a beating flagellum.

1.4. Interpretation: the moment balance assumption

Biophysical analysis of ciliary and flagellar bending has assumed that the shape of a flagellum is the solution to an equation that represents equilibrium between forces that tend to bend and unbend the flagellum. More precisely, this means a state where bending moments are in equilibrium at every point along the length [Machin 1958; Rikmenspoel 1965]. Bending moments at any point are generally the sum of many forces applied all along the length. The primary contributors to the bending moments are active shear forces produced by dynein motors, forces produced by elastic resistances of the axonemal structure, and forces produced by motion against the viscous resistance of the external fluid environment. Internal viscous resistances could also be present, but are not believed to play a major role, as they would be energetically wasteful.

Some observations, such as the interpretation of a bend as a circular arc, and the maintained straight conformation of a cilium during an effective stroke, are difficult to explain by moment balance, unless there is a dynamic control of active shear force that is designed to maintain these shapes. There is no case where knowledge of internal forces is sufficient to prove that the moment balance assumption is accurate, and can be used to deduce internal forces. With this reservation, the moment balance assumption is still used to make general statements about active force generation in a flagellum. A curvature transition in an interbend must be a region where the elastic bending moment changes along the length. To maintain local bending moment equilibrium, this change in elastic bending moment must be balanced by shear forces that are concentrated within the transition region. The most likely source of these shear forces is active shear force generated within the transition region.

2. Flagellar oscillation is the regular activation of sliding initiation events , alternately on two sides of an axoneme. A sliding initiation event involves two processes: (1) Transformation of a basal bend into a propagating bend, and (2) Formation of a new basal bend, usually by interbend growth.

The sliding initiated in a sliding initiation  event causes the propagation and further growth of an existing basal bend, and the growth of a new basal bend in the opposite direction. Examples of both unusual and usual types of movement provide valuable information:

Example 2.1.  Symmetric bend development in simple sperm flagella

Detailed examination of basal bend development began with sea urchin spermatozoa [Goldstein, 1976; Gibbons, 1981, 1982] and was continued with spermatozoa of the tunicate, Ciona , [Brokaw, 1993, 1996]. These examples clearly show that the sliding initiation event simultaneously initiates interbend growth and basal bend propagation. Plots of shear angle against position along the length, such as Fig. 1 or those in Figs. 1 and 2 of Brokaw [1996], illustrate the following description.

Immediately before the sliding initiation event, there is a basal bend, B1, with nearly uniform curvature, which has been formed by interbend growth involving sliding in the preceding interbend, T0, and propagating bend, B0. The first detectable sign of the sliding initiation event is straightening (unbending) at the basal end of B1, which must be associated with sliding throughout B1 in the opposite direction to the sliding that formed B1. This straightening represents the creation of a new curvature transition at the basal end. Before this event, the elastic bending moment of B1 is believed to be balanced by the passive elastic resistance of structures in the flagellar base. The new curvature transition will take over this function and provide the shear force that balances the elastic bending moment of B1. The direction of active shear force required for this function is the same direction that is required to produce the sliding for propagation of B1.

B1 is now a propagating bend. This transformation is followed immediately by creation of another curvature transition at the basal end, to complete the interbend T1 and balance the elastic bending moment of a new bend, B2, which can be detected at the base. The appearance of B2 confirms that interbend growth [Gibbons, 1981] has begun. Interbend growth involves sliding in T1 in the direction that is propagating B1. This sliding causes the bend angles of B1 and B2 to increase, at equal rates, in opposite directions [Goldstein, 1976]. The growth in B1 adds to the bend angle that was created by the previous interbend growth process. As the new bend B2 attains its final curvature, sliding within B2 diminishes or stops, and further growth of B2 occurs mainly by increase in length, as T1 propagates away from the base.

The sliding in the basal bend that is required for its propagation must be accompanied by shear force to oppose viscous resistances to movement of the flagellum. The sliding that is required for interbend growth must be accompanied by shear force to overcome the elastic bending moments that oppose the growth of the pair of bends at the base. In some way, this sliding must be the result of active, dynein-driven, sliding. The natural assumption that active, dynein-driven sliding occurs throughout the original basal bend and the new interbend cannot be confirmed by existing technology, which lacks capability for direct determination of the location of active sliding. The role of active sliding forces generated in more distal region of the flagellum is not clear, but it is known that flagella that are not much longer than normal basal bends can generate regular oscillatory bending, at least under some conditions (Example 2.8).

Example 2.2. Interbend growth and asymmetry

The same combination of interbend growth and propagation initiation processes appears to fit many other situations where bending is planar and asymmetric, such as asymmetric bending patterns of simple sperm flagella at increased Ca++ concentration, normal bending patterns of Chlamydomonas flagella, and many ciliary bending patterns. However, because cilia frequently occur in large arrays, bending patterns of individual cilia are difficult to photograph. An exception is the cilia on echinoderm embryos, where individual cilia have been photographed with high resolution [Baba and Mogami, 1987].

Asymmetry of basal bend growth does not appear to be very important in asymmetric bending patterns of sea urchin spermatozoa [Gibbons 1981] or in sea urchin embryo cilia [Baba and Mogami, 1987]. Apparent asymmetry in basal bend growth in Ciona spermatozoa and in Chlamydomonas can removed by subtracting a “biased baseline” equivalent to the mean orientation of the flagellum, which has a sharp bend near the basal end [Eshel and Brokaw, 1987], but there is no independent verification of this baseline.

Interbend growth that involves equal and opposite growth of bend angles on both sides of a sliding region requires that there be no sliding in the interbend T0 distal to the region of interbend growth [Goldstein, 1976]. In many examples of asymmetric bending, asymmetry results, at least in part, from failure to meet this requirement. For instance, in embryo cilia, initiation of sliding in a reverse bend, at the end of the recovery stroke, is followed by a rapid lengthening of the reverse bend, without increase in bend angle, until the full length of the cilium becomes the region of sliding that is driving the effective stroke. Because this region extends to the end of the cilium, interbend growth produces a new basal bend but does not cause further growth of the previous basal bend. In contrast, at the other end of the cycle, the principal bend propagates with a relatively small increase in length, and its bend angle increases as part of interbend growth [Baba and Mogami, 1987]. Many ciliary bending patterns fit this pattern, with the effective stroke involving formation of a short basal bend, while the remainder of the cilium is nearly straight, and presumably a long region of active sliding. This would appear to be a functionally significant solution to the problem of providing sufficient force to overcome viscous resistance during the effective stroke of a cilium [ ?? Rikmenspoel ??].

The more important feature of ciliary bending patterns is not asymmetry of interbend growth, but the activation of sliding throughout much of the length of the cilium, to initiate the effective stroke. In some cases, such as asymmetric bending patterns of sea urchin embryo cilia and Chlamydomonas flagella, it is obvious that this activation begins in a reverse bend, and extends distally as the bend grows in length. In many other cases [eg. Sleigh, 1968], it is occurring in a region that is nearly straight, and identification of a reverse bend is not possible. The need for a  mechanism to synchronize the activation of sliding at the beginning of the effective stroke was recognized soon after it was understood that the effective stroke of a cilium is driven by sliding, and not by bending near the base of the cilium [R 1970 ?; Rikmenspoel and Sleigh, 1970].

Example 2.3. Initiation of bend propagation in a short distal region

A particularly informative example of basal bend behavior has been found in demembranated sea urchin sperm flagella with most of the flagellum attached to a microscope slide surface, leaving only about 10 µm of the distal end free to bend [Brokaw, 1982]. These flagella were reactivated at low ATP concentration, to give a frequency of about 2 s-1, and photographed at 60 flashes s-1, giving unusually high temporal resolution. Spatial resolution was also high, because basal bends formed with curvature only about half that seen in normal basal bends at the basal end, and this high resolution confirms the near-constant curvature of the bend. The bending pattern is asymmetric, with near 0 curvature in one direction. In the other direction, a bend forms initially near the basal end of the free region, with the more distal portion nearly straight.

An example of shear curves obtained for a portion of one bending cycle are shown in Fig. 2. During at least the second half of bend angle growth, the bend clearly grows by lengthening as the distal transition region propagates. There is no sliding in the basal portion of the bend, and the bend curvature remains nearly constant. Fig. 2 shows the sliding initiation event, occurring between the two images, 209 and 210, indicated by heavy lines in this figure. The shear curves for images 208 and 209 are almost superimposed, indicating almost no sliding, except for a small extension of the bend towards the distal end. The displacement of the shear curves between images 209 and 210 represents sliding of approximately 0.3 rad that extends throughout most of the length of this bend. This sliding is accompanied by straightening in the most basal part of the bend, and bending, an increase in curvature, near the distal end. This represents the beginning of bend propagation, but in this particular example the propagation phase is very brief. The leading transition quickly reaches the end of the flagellum, and then images 211 and 212 show an unbending phase, in which non-uniform sliding rapidly reduces the bend angle and returns the flagellum to a nearly straight configuration. In another example, shown in Fig. 4e of Brokaw [1982], the propagation phase can be seen clearly to last for about 6 images.

In this example, it is very clear that sliding is initiated almost synchronously throughout the bend, and straightening is limited to the most basal end of the bend. It also shows that within most of the bend, the sliding in the direction that is forming the bend stops well before the initiation of sliding in the reverse direction, even when there is no distinct pause before bend propagation begins. In fact, my understanding of normal basal bend behavior is strongly influenced by these high-resolution observations. However, the propagation and unbending phases only return the flagellum to a straight position, so there is no real interbend growth associated with this sliding initiation event.

Example 2.4 Isolated interbend growth

Isolated interbend growth can be induced by localized application of ATP to demembranated flagella [Shinyoji et al. 1977, Shingyoji and Takahashi,  1982, 1995; Cheung and Woolley, 1983]. Demembranated sea urchin sperm flagella, suspended in reactivation solution lacking ATP, are in a motionless rigor state [Gibbons and Gibbons, 1974; Okuno, 1980]. Application of a small localized pulse of ATP by iontophoresis from a micropipette relieves the rigor state in a region 10-15 µm in length, and allows active sliding to occur in the middle of this region. This sliding causes bends to form, with equal and opposite angles, on each side of the sliding region. This appears to be the same paired bend development process normally occurring in the basal region of sea urchin sperm flagella [Goldstein 1976] and designated as interbend growth [Gibbons, 1981].  Using very small ATP pulses, sliding would stop and then be restarted several times before reaching a limit. Further application of ATP pulses resulted in a reversal of sliding, decay of the bend angles and eventually bend formation in the opposite direction. Applications of larger ATP pulses can induce a brief period of cyclic movements of this type, which involve bending and unbending, rather than the combination of bend formation and bend propagation seen in normal flagellar beating.

The rigor sliding resistance at the peripheries of the region supplied with ATP appears to be an integral part of this process of bend formation. (In this abnormal situation, the distal member of the pair of bends is an example of a bend that is neither a basal bend nor a propagating bend.)Application of ATP near the distal end of a flagellum, such that there was an inadequate rigor resistance to sliding at the tip of the flagellum, led to a truncated form of interbend growth, with a bend forming only on the basal side of the region of ATP-activated sliding [Shingyoji and Takahashi, 1982], resembling the early phase of bending seen in Example 2.3. This report did not state whether bend propagation occurred under these conditions.

Possibly the most remarkable new information in these experiments is that with small ATP pulses, so that sliding stops before reaching the reversal point, the system appears to remember the previous direction of sliding, so that it continues sliding in the same direction, irrespective of forces from elastic resistances, when the next ATP pulse arrives. It would be valuable to have more complete data on this evidence for memory of a sliding state.

Asymmetry is clearly seen this example . The bend angles of the pair of bends produced by sliding in one direction are not equal to the bend angles of the pair of bends produced by sliding in the other direction. This interpretation of the asymmetry is made possible by the observation that the flagellum is straight before application of ATP, providing a baseline for measurement of the bend angles.

Example 2.5  A cilium with interbend growth in just one direction

Sleigh [1968] described an unusual bending pattern of a compound cilium found on the cephalic tentacles of the annelid, Sabellaria . This cilium does not have a regular oscillation, but rather an irregular alternation between an extended straight position at the end of the recovery stroke and a position near the surface of the tentacle at the end of the effective stroke. Sleigh states that they “move from one position to the other at more or less random intervals.”

At the end of the recovery stroke, the cilium is extended perpendicularly from the tentacle surface, and is nearly straight. The effective stroke begins by interbend growth, forming a pair of short π/2 rad bends at the basal end of the cilium, while the remainder of the cilium remains perpendicular to the surface. The more distal of these two bends propagates along the cilium, without any change in bend angle, so that the distal portion of the cilium continues to extend perpendicularly from the surface as it moves laterally during the entire effective stroke. This indicates that no sliding is occurring in this distal portion of the cilium during the effective stroke. The propagation of the distal bend creates a long straight interbend between the two bends, just above the tentacle surface. The sliding that is propagating the bend is in the same direction as the sliding that formed the bends by interbend growth, but sliding within the interbend has completely stopped. After this distal bend passes the tip of the cilium, sliding in the opposite direction begins in the basal bend, and it propagates as a relatively typical recovery stroke, with some increase in bend angle. The initiation of sliding in this basal bend does not appear to be associated with interbend growth. Interbend growth only operates in one direction, unlike Example 2.4.

In contrast to Example 2.4, the interpretation of this example as asymmetric interbend growth depends on the assumption, without evidence, that the basal apparatus and the basal region of the cilium orient the “rest position” of the cilium perpendicular to the tentacle surface. A quite different interpretation results if the basal region is tilted at π/4 radians in the direction of the effective stroke. In this case, there would be active arrests at the end of the recovery stroke and at the end of the effective stroke, which is more consistent with other observations of arrested states (Section 3).

Example 2.6 Delaying the sliding initiation event produces long interbends.

In sea urchin spermatozoa reactivated at low ATP concentration, 1 to 10 mM Li+ appears to delay the sliding initiation events. This causes reduced frequency and increased bend angle, and there can be a pronounced delay between the completion of basal bend growth and the initiation of sliding in that basal bend. The curvature transition at the basal end of the preceding interbend propagates more slowly, while the transition at its distal end continues to propagate normally, creating a long straight region in the middle of the interbend [Brokaw, 1989]. There is very little sliding in this interbend, so the basal bend does not continue to grow in angle.

A lateral drag force can be applied to a sea urchin sperm flagellum when the sperm head is held in the tip of a micropipette, and the micropipette is moved laterally. With lateral oscillation with a sawtooth wave, at close to the natural beat frequency, the change in direction of imposed drag at the peaks of the wave triggers the sliding initiation event in basal bends. If the lateral movement of the micropipette is continued past the peak, the sliding initiation event can be delayed, so that the basal bend remains at the base, while the preceding bend, in the opposite direction, continues to propagate at its normal velocity. This creates a long straight interbend in which there is little or no sliding [Eshel et al. 1991].

In these cases, as well as the long interbend in Example 2.5, the curvature transitions at each end of the interbend must continue to produce active shear force to balance the elastic bending moment of the bends. In these cases, there is no synchronous sliding causing sliding in the interbend, so the interbend could be in a passive rigor-like state, which might be sufficient to resist the elastic bending moment at the ends of the interbend. However, this is not true in general for interbends between propagating bends, because they can be regions where there is significant synchronous sliding [Goldstein, 1976; Gibbons, 1981; Brokaw, 1993].

Example 2.7. Mammalian sperm flagella

In addition to the 9+2 axoneme, mammalian sperm flagella have outer dense fibers attached to each outer doublet microtubule, and typically have much of the length of the flagellum encased in a thicker sheath. The outer dense fibers allow transmission of larger longitudinal forces, allowing movement with larger bends. They also provide greater resistance to breakage [  ] and maintain a larger-diameter path for diffusion of energy substrates such as ATP[  ]. Shear resistance at the base is primarily provided for the outer dense fibers, and appears to be less stringent than the basal shear resistance provided for the outer doublets in simple flagella and cilia [  ].

Shear angle curves have been obtained for planar bending patterns of mouse spermatozoa, about 120 µm in length, by Vernon and Woolley [2002]. These curves show a pattern of bend initiation supporting the same view of sliding initiation events described for simple sperm flagella. On the other hand, when bull spermatozoa generate planar bending patterns, the bends start at the basal end with very low curvature and bend angle, and grow in amplitude as they propagate [ ]. This has been generally explained as consistent with a gradually decreasing elastic bend resistance provided by the extra-axonemal structures. With these flagella, it is difficult to see evidence for sliding initiation events comparable to those seen in simple flagella and cilia.

Chinchilla spermatozoa generating planar bending [Vernon and Woolley, 2004], show large basal bends in the principal bend direction. Initiation of a bend in the reverse bend direction appears to fit the sliding initiation event paradigm, but with an interesting peculiarity. The sliding initiation event was observed to be preceded by several cycles of rapid, oscillatory straightening and rebending at the basal end, suggesting repeated, unsuccessful, attempts to trigger the sliding initiation event [Vernon and Woolley, 2004].

Example 2.8. Shortened flagella

Bends reaching the end of a flagellum normally propagate off the end with little change in curvature. Simple sperm flagella from echinoderms and tunicate can be broken by shearing a sperm suspension, producing mixtures with differing lengths. Removal of the distal end of these sperm flagella removes the terminal filament and changes the behavior of bends reaching the distal end of the flagellum [Brokaw, 1965]. Shear curves for 4 examples of broken spermatozoa with close to normal length provide detailed information on the bend behavior [Omoto and Brokaw, 1982]. When a bend reaches the end of the flagellum and its leading interbend transition passes over the broken end, the bend unbends, with a rapid decrease in curvature, and becomes approximately straight. There is a slight increase in propagation velocity of the next interbend, causing a slight increase in bend angle of the following bend, with no change in its curvature.

If the length of the flagellum after breakage is less than about 20 µm, there is an increase in beat frequency [Brokaw 1966a, 1996; Gibbons, 1974; Goldstein, 1981]. With ATP-reactivated Ciona sperm flagella, the frequency increases gradually with reduced length, to about 50% greater than normal at lengths of around 10 µm [Brokaw, 1996]. Shear curves for an example of a sea urchin sperm flagellum with a length of 9 µm and a frequency of about 60 s-1 are shown by Gibbons [1982, Fig. 30]. These data show only two bends, with the more distal bend unbending rapidly at about the same time as the sliding initiation event in the basal bend. There is not enough information to determine whether the rapid unbending of the more distal bend has a direct effect on the timing of the sliding initiation event, causing the increased frequency. An alternative explanation, that the reduced viscous loading opposing the movement of these very short flagella allows more rapid sliding during basal bend formation may not explain the lack of effect at lengths greater than 20 µm, which is not consistent with modelling results [Brokaw, 2001]. At lengths less than 10 µm, it becomes difficult to find examples with stable beating, but under some conditions, beating at lengths as short as 3 to 4 µm has been obtained.

An example of a demembranated sea urchin sperm flagellum, broken to a length of about  3-4 µm, and reactivated at low ATP concentration, was photographed with high temporal resolution [Brokaw, 1982]. This example shows basal bends, with some asymmetry. The flagellum bends in one direction,and then unbends, passing through a straight configuration before bending in the opposite direction. Pauses are seen after bending in one bend direction, which is the direction that gives the larger bend angle. No inflection points are visible, so there is no firm evidence for interbends. There is little or no indication of bend propagation. A similar case, at higher ATP concentration, is described by Goldstein [1981].

Example 2.9 Starting transients

2.9.1 Starting transients have been observed when ATP is resupplied to non-motile sea urchin sperm  flagella in a variety of experimental situations [Rikmenspoel 1978; Goldstein 1979, Gibbons 1981]. The most recent experiments using photolytic release of caged ATP to rapidly provide a uniform ATP concentration [Tani and Kamimura 1998] are particularly useful. Four situations can be distinguished:

    A. Flagella with rigor bending waves, obtained by rapid removal of ATP from swimming demembranated flagella reactivated at low ATP concentration [Gibbons and Gibbons 1974]. Addition of ATP causes resumption of bend propagation.[Gibbons and Gibbons 1974; Tani and Kamimura 1998, Figs 3,4]. There appears to be a complete memory of the state of movement before ATP removal, and continuation of this movement when ATP is resupplied.

The other three situations can be found after ATP is removed more slowly:

    B. Flagella with a normal basal bend, and the rest of the flagellum nearly straight. Movement is initiated with a normal sliding initiation event. [Goldstein 1979, Fig. 5,6]

    C. Flagella with a partially formed basal bend, and the rest of the flagellum nearly straight. Movement is initiated by resumption of basal bend growth by interbend growth. [Goldstein 1979, Fig.1; Rikmenspoel 1978, Fig. 12] This involves activation of sliding in the opposite direction to that in case B, and like Example 2.4, suggests a memory of the previous direction of sliding.

    D. Flagella that are nearly straight. Movement is frequently initiated with two regions of interbend growth, involving opposite directions of sliding. [Goldstein 1979, Fig. 4; Tani and Kamimura 1998, Fig. 5A; Rikmenspoel 1978 Fig. 11]

Cases C and D also provide examples of bends that are neither basal bends nor propagating bends.

2.9.2 Spontaneous restarting after arrest with an extreme basal bend in sea urchin spermatozoa also begins with a sliding initiation event [Section 3.6].

2.10  Summary

The common theme in these examples is the sliding initiation event , which appears to initiate sliding simultaneously throughout a basal bend, and sometimes in a more extended region of the axoneme. Typically, this sliding initiates the propagation of the basal bend, and simultaneously  creates a new interbend that becomes a locus of interbend growth. In a few cases (Examples 2.4, and possibly 2.5 and 2.9D), the sliding initiation event can occur, and create a new interbend, in the absence of a pre-existing basal bend. In other cases, a sliding initiation event can initiate propagation in a basal bend, producing straightening at its basal end, with no visible interbend growth (Examples 2.3, 2.5, and possibly other examples of asymmetric ciliary patterns). Although there may be no recognizable basal bend in the “straight region” of a cilium before the beginning of an effective stroke, the properties of the sliding initiation event are equally applicable.

As a basal bend develops, the rate of sliding at its basal end decreases, forming a region in which there is little or no sliding, while the bend continues to grow in angle by growth in length, with nearly constant curvature. The approximately circular shape of the bend, as well as the absence of sliding, suggest that the active shear force that formed the bend is turned off locally within the bend when a final curvature is reached. This implies a time delay, depending upon position within the basal bend, between the cessation of the sliding that formed the bend and the next sliding initiation event, which will produce sliding in the opposite direction.

2.11 Interpretation.

If f lagellar oscillation can be described as the regular alternation of sliding initiation events in opposite directions, we need to know what, exactly, happens during the sliding initiation event? At least three possibilities can be considered:

2.11.1 Switching of the direction of generation of active shear force occurs locally when an appropriate curvature is reached at points within a new basal bend. This local switching propagates as the bend attains its curvature, and is essentially the same switching process that has been proposed to accompany bend propagation and produce metachronous sliding [Brokaw, 1971]. However, dynein kinetics introduce a delay in the actual reversal of force generation, so that the sliding initiation event does not occur immediately. Computer simulations demonstrate that this explanation can generate patterns of bend initiation very similar to those typical of Example 2.1, without any special mechanism for synchronous activation throughout a basal bend [Brokaw, unpublished, see Appendix 1]

2.11.2 Switching of the direction of active shear force generation occurs locally when an appropriate curvature is reached at points within a new basal bend, as in 2.11.1. This causes an immediate reversal in the direction of active shear force, in a region that lengthens progressively as the new basal bend develops. However, no sliding can occur until a block to unbending at the basal end is overcome. It is difficult to understand why the newly activated shear force would not alter the shape of the basal bend, while waiting for release of the block to unbending at the basal end.

2.11.3 Shear force and sliding that are developing a new basal bend are effectively switched off when an appropriate curvature is reached at points within a new basal bend. The basal portion of the new basal bend becomes a region with no active shear force, consistent with maintenance of a uniform curvature. At the time of the sliding initiation event, active shear force is effectively switched on throughout the basal bend. This pattern of switching is not like that occurring during bend propagation, and requires a mechanism for synchronous activation over the length of the basal bend. It has been commonly assumed that this type of synchronous activation is required to explain the onset of the effective stroke in the ciliary beat cycle.

3. Observations of arrest/quiescence indicate a failure of a sliding initiation event to occur at a normal switch point.

Under at least some conditions, most cilia beat continuously, with a regular frequency. Other cilia  commonly pause briefly before initiating an effective stroke, or, less commonly, at the end of an effective stroke [Sleigh, 1968]. These pauses may be significant in allowing the beating of arrays of cilia to be coordinated into metachronal waves. This section deals primarily with other situations, where pauses represent “abnormal” behavior.

Example 3.1. When it was found that sliding during axonemal disintegration is unidirectional [Sale and Satir, 1977], it was suggested that in order to generate cyclic bending, there must be “switch points” in the beat cycle. At these points in time, the direction of sliding throughout a cilium is reversed by changing activation from doublets on one side of the axoneme to the doublets on the other side of the axoneme [Satir and Sale, 1977; Satir 1985]. In the fresh-water mussel, Modiolus , the lateral gill cilia become arrested in a “hands down” position at the end of the effective stroke when exposed to high extracellular concentrations of vanadate ion. (The action of extracellular vanadate is probably less simple than the direct inhibition of dynein that is obtained with demembranated flagella.) They become arrested in a “hands up” position when exposed to conditions that increase intracellular Ca++ concentration; this probably represents arrest near the end of the recovery stroke [Wais-Steider and Satir, 1979]. It appears that arrest in the “hands down” position is the result of blockage of the sliding initiation event that would normally initiate the propagation of a principal bend during the recovery stroke and cause the development of the very shallow reverse bend that characterizes the effective stroke. Arrest in the “hands up” position appears to be the result of blockage of the sliding initiation event for sliding during the effective stroke and creation of a new principal bend at the basal end. In lateral gill cilia of Mytilus , a distinction has been made between spontaneous arrest at the end of the normal recovery stroke, and a more extreme arrest beyond the recovery stroke that appears to be induced by increased Ca++ concentration [Motokawa and Takahashi, 1974; Stommel, 1986]. Because the large ensembles of lateral gill cilia do not provide ideal material for precise characterization of the shapes of the cilia, this reasonable interpretation has not been supported by detailed comparison of the shapes of basal bends in the quiescent or arrested states with the basal bends attained in the normal beat cycle at the time that sliding initiation events occur. The particular interest of these studies is the demonstration that the sliding initiation events in different directions can be inhibited differentially.

Example 3.2. Many paralyzed flagellar mutants ( pf mutants) of Chlamydomonas have been found. These mutants appear to have oscillatory switching defects, because they typically show no deficit when tested for sliding disintegration, and paralysis can be overcome, partially or completely, by conditions such as altered pH [Goldstein, 1982], low ATP concentration and/or competitive inhibition by ADP [Frey et al., 1997; Omoto et al., 1996], mechanical forces [Hayashibe et al., 1997], or extragenic suppressor mutants [Brokaw et al., 1982] that do not restore structural proteins missing in the mutants. The “hands down” or “hands up” characterization is also applicable here, with some mutants favoring one arrest position and other mutants favoring the other arrest position.

Hydin has been identified as a protein component of the central pair apparatus of Chlamydomonas flagella. RNAi methods have been used to suppress production of the protein, leading to an unusual paralyzed phenotype that is characterized by a 50-50 mixture of arrests in either the “hands up” or “hands down”, with no correspondence between the two flagella on each cell. Hydin suppression is not complete, and the flagella often show weak, intermittent, beating.[Lechtreck and Witman, 2007]

Example 3.3. In sperm flagella, arrests similar to the above examples have typically been referred to as “quiescence”. These states are not the same as the quiescence that is obtained, for example, by inhibiting dynein activity with vanadate. Instead, these are arrested states in which a bent conformation appears to be maintained by active shear forces generated on one side of the axoneme. Figure 2 of Omoto and Brokaw [1983] shows multiple exposure photographs of an intact spermatozoon of Ciona , with its head attached to a microscope slide surface. Panel B illustrates the normal beat pattern, with bends developing to an angle of 2 to 2.5 rad, and about 1.5 rad in the basal bend at the time of the sliding initiation event. Panels A and C show the sperm flagellum during periods of intermittent quiescence, with a basal bend in either the principal or reverse direction. These basal bends have a length of about 8 µm and a bend angle of almost 3 rad. The curvature of the flagellum decreases gradually starting 2-4 µm from the base and continuing to about 12 µm from the base to form a counterbend in the direction opposite to the basal bend. This counterbend then continues with relatively constant curvature into the distal regions of the flagellum. The configuration of the basal bend in the quiescent states is different from that at the time of normal sliding initiation events. This configuration suggests that there is an unusually long interbend, with a region of active shear force extending from about 3 µm to 12 µm from the basal end, which is unlike the presumed  distribution of active shear force in a normally beating flagellum. The total angle of the basal bend is much greater than the normal basal bend angle, indicating that interbend growth has continued past the normal “switch point”.

Example 3.4. Ciona spermatozoa that are demembranated and exposed to ATP, without adequate activation by cAMP, show a somewhat similar arrest, with a short basal bend and a long counterbend. In this arrest configuration, the basal bend is always in the reverse bend direction, has an angle of about 1 radian, and a relatively constant curvature [Omoto and Brokaw, 1983]. Basal bend angles in swimming Ciona sperm flagella typically reach 1 to 1.5 rad [Brokaw, 1996]. These features suggest that these flagella may be arrested at or just before a normal switch point, where a sliding initiation event would occur to initiate a new principal bend. These arrests do not occur after the demembranated spermatozoa are exposed to cAMP under conditions appropriate for phosphorylation [Brokaw, 1987].

Example 3.5. Demembranated spermatozoa from the sea urchin, Lytechinus pictus , can also be obtained in a state where incubation with cAMP is required for activation of spontaneous oscillation [Brokaw, 1984]. In this case, the arrested state contains a basal bend in the principal bend direction, with a bend angle of about 2 rad, followed by a nearly straight region, and then a variable distal bend, also in the principal bend direction. Under other conditions, the basal bend angle can be in excess of 5 rad [Sale, 1985]. The basal bend can be relaxed by vanadate, indicating that it is maintained by active forces [Sale, 1985].

Example 3.6. In most sea urchin species, sperm flagellar movement after demembranation can be reactivated well at high ATP concentrations without incubation with cAMP [Gibbons and Gibbons, 1972; Brokaw, 1995]. The symmetry of the bending patterns depends upon calcium concentrations in the demembranation and reactivation solutions. After demembranation at low calcium concentrations, an arrest with an extreme basal bend in the principal bend direction can be obtained with high calcium ion concentrations in the reactivation solution [Gibbons and Gibbons, 1980], or by local iontophoretic application of calcium to the basal region of the flagellum [Katada et al., 1986]. Live spermatozoa show spontaneous temporary arrests, probably resulting from transient increases in internal calcium concentration [Gibbons, 1980]. Demembranated, ATP reactivated sea urchin sperm also showed occasional transient arrests, under conditions where asymmetry of beating was increased by high calcium concentration [Gibbons, 1986].  

These transient arrests have been exploited to examine the bending patterns during the stopping and starting transients, providing evidence that the arrest represents interruption of sliding initiation events, without blocking propagation of previously established bends [Gibbons, 1981, 1982]. With reactivated spermatozoa, the transients were faster and simpler than the ones observed with live spermatozoa, which may have been complicated by changing internal calcium concentrations. In the example shown by Gibbons [1986], in the final beat cycle before arrest, the principal bend reached an angle of 2.4 rad at the time of the sliding initiation event that created a new reverse bend. The next sliding initiation event created an almost identical principal bend, but no sliding event occurred at the expected time. Instead, the principal bend continued to grow in length and angle, reaching a final angle of about 4 rad, with a final configuration that had a graded curvature, similar to other observations of the arrested state in Sections 3.3 to 3.5.  The previous reverse bend propagated almost normally. After a brief arrest, there is a sliding initiation event that involves sliding in the normal location of the basal bend, and at a lower rate in distal portions of the flagellum. The example of a starting transient in a live spermatozoon, in Fig 6 of Gibbons [1981], shows initiation of sliding in the basal 8  µm, with little or no sliding distally.

3.7 Summary. This brief and incomplete review of arrested states supports the idea that the oscillation of cilia and flagella that generate planar bending patterns involves the regular alternation of sliding initiation events. In continuously beating flagella and cilia, the assumption is that sliding initiation events occur as soon as a switch point is reached. Arrests appear to represent sliding initiation event failure when a switch point is reached. In principle, failure of a sliding initiation event could result from failure to reach a switch point, but most arrest configurations appear to be beyond a switch point, rather than before a switch point. A final choice between these alternatives will have to wait until we understand what triggers a sliding initiation event.

There is variation in the conformation that results after failure of a sliding initiation event, so arrested states do not provide a more consistent identification of switch points than is obtained by analysis of regular oscillatory bending. The detailed examination of stopping and starting transients reinforces the interpretation in Section 2.11.3, that the sliding initiation event involves synchronous activation of sliding throughout a basal bend. The idea of switch points was developed by observations of arrested states of cilia, where switching appears to occur over the full length of the cilium. Subsequent analysis of bending patterns of continuously beating flagella indicates that sliding initiation events involve apparently synchronous initiation of sliding over a substantial length of the flagellum, but only as far as the distal end of a basal bend.

At this point, we are faced with two major puzzles: What triggers a sliding initiation event, and what mechanism ensures that sliding is initiated synchronously throughout a basal bend?

4. Searching for a trigger: Observations and experiments

4.1 Beat frequency

4.1.1. Flagellar beat frequency, equivalent to the frequency of sliding initiation events in one direction, is highly sensitive to ATP concentration. Our understanding of the effects of ATP concentration on dynein biochemistry and in vitro sliding makes it seem reasonable to interpret this as an effect of ATP concentration on the velocity of the active sliding that is required to proceed from one switch point to the next one. This sliding velocity will also depend on the opposing load, which can be varied by increasing external viscosity.  Beat frequency of shortened Ciona sperm flagella is reduced by increased viscosity [Brokaw, 1996]. A greater effect of viscosity on beat frequency is obtained with full length sperm flagella, suggesting that the sliding resistance opposing basal bend growth may depend on conditions throughout the length of the flagellum. Perhaps the most extreme example of this is the observation that millimolar concentrations of Li+ can completely inhibit movement of full-length Ciona sperm flagella, but do not inhibit bend initiation, at near-normal frequencies, in flagella broken to lengths less than 17 µm [Brokaw, 1987, 1993].

This simple model for determination of flagellar beat frequency by the rate of sliding between switch points is seriously challenged by two types of experiments:  

Sperm flagellar bend amplitude can be reduced by CO2, NaSO3, increased salt concentration, or anti-tubulin antibodies, with little or no change in beat frequency [Asai, 1980; Brokaw and Simonick, 1977c; Brokaw, 1993]. A Chlamydomonas mutant with partial inner arm deficiency had reduced amplitude of flagellar bending, with near-normal frequency [Brokaw and Kamiya, 1987].  With Ciona sperm flagella at increased salt (potassium acetate) concentration, a constant  frequency was maintained while basal bend amplitude, and therefore the rate of sliding causing basal bend growth, was decreased by more than 50% [Brokaw, 1993].

Sudden jumps between stable frequency modes were observed with live Ciona spermatozoa, swimming in sea water containing 0.15 to 0.2 M thiourea [Brokaw, 1966b]. The mean frequencies of three stable modes differed by factors of 2, although individual spermatozoa switching abruptly between modes did not always switch by exactly a factor of 2. Changes in frequency were accompanied by changes in the sizes of bends, so that propagation velocity and sliding velocity did not change as much as the frequency, but no parameter remained exactly constant. Frequency modes have also been observed with demembranated and ATP-reactivated sea urchin sperm flagella exposed to trypsin, during the last few seconds before disintegration [Brokaw and Simonick, 1977a]. In these cases, there is a frequency increase, which is sometimes an abrupt doubling of frequency accompanied by a decrease in bend angle, such that sliding velocity is approximately constant. Other cases involved more gradual change, or abrupt switching between modes with less than a 2-fold frequency increase. None of these observations involved a focused examination of basal bend development, nor is it known whether multiple frequency modes can be observed with shortened flagella.

4.2 Measuring the parameters of basal bend growth has not identified a critical parameter that defines a switch point or signals sliding initiation events.

In addition to frequency, two parameters are needed to describe basal bend growth [Brokaw, 1993]. Basal shear amplitude is a peak-to-peak measure of the shear, or sliding, that forms basal bends; in a symmetric bending wave this equals twice the shear angle accumulated in a basal bend by the time of the sliding initiation event. Basal curvature is the curvature of the basal bend at the time of the sliding initiation event, and is often characteristic of the basal bend at earlier times as well. Other parameters, such as basal bend length, can be derived from this set.

Attempts to measure basal bend parameters of sperm flagella are relatively recent. Ciona sperm flagella appear to be particularly suitable for such measurements, because the base of the flagellum is solidly inserted into the sperm head, so that the orientation of the sperm head is a reliable indicator of the orientation of the basal end of the flagellum [Brokaw, 1991].  

Bend angles of propagating bends on demembranated and ATP-reactivated Ciona sperm flagella can be reduced by several chemical interventions: increased salt (potassium acetate) concentration, vanadate, or lithium. Vanadate is expected to reduce the number of active dyneins, but the mode of  action of the other agents is unknown. There is a consistent decrease in basal shear angle, which could be responsible for at least some of the decreased angle of propagating bends. Beat frequency was either constant (potassium acetate) or reduced (vanadate and lithium). The reduced basal shear angle may be predominantly associated with a decrease in basal bend curvature, rather than basal bend length, but the data on this point are not strong [Brokaw, 1993]. If these interventions are reducing the shear force that is generating a new basal bend, they might make it easier for sliding in the opposite direction to trigger a sliding initiation event.

Changes in viscosity or ATP concentration cause large changes in frequency and the wavelength and velocity of propagating bends on reactivated Ciona sperm flagella, and small changes in basal bend angle. The effects on basal bend angle are likely to be caused, at least in part, by direct effects of load and ATP concentration on the rate of interbend sliding that is causing growth of a basal bend. However, the rate of interbend sliding to form the basal bend appears to have a relatively low sensitivity to viscous loading. This may be the reason why, in some situations, distal wavelength is more sensitive to viscosity than is frequency [Brokaw, 1975a]. In these experiments, the measurements of basal bend curvature and length are not precise enough to identify changes in one of these parameters as the one responsible for the changes in basal bend angle.

4.3. Mechanical manipulation of flagellar oscillation:

4.3.1. Reduction in amplitude of basal bends [Kaneda 1965; Okuno and Hiramoto 1976].

On the other hand, with bull spermatozoa showing normal reactivated motility, oscillation could be blocked by using a microneedle to prevent the development of curvature in the basal portion of the flagellum [Holcomb-Wygle et al. 1999].

4.3.2 Sea urchin spermatozoa, with the sperm head held by a pipette, can be moved from side to side with a sinusoidal or sawtooth waveform, thereby creating fluid drag forces on the flagellum. By this means, the frequency of bend initiation can be altered over a range below and above the natural frequency [Shingyoji et al., 1991], as seen in earlier experiments by Okuno and Hiramoto [1976].

In these types of experiments, the sliding initiation event can be delayed by adding a drag force on the flagellum in the direction that would tend to increase the basal bend angle and oppose the sliding that is needed for a new sliding initiation event [Eshel et al., 1991, 1992]. No increase in basal bend angle is detected. A sliding initiation event occurs normally as soon as the drag force is either eliminated or reversed. Slower displacement of the sperm head causes only a temporary delay of the sliding initiation event. This observation may suggest that the initiation of sliding in a new basal bend requires the gradual buildup of some as yet unidentified factor.

Two different patterns of response of basal bend parameters have been seen when the initiation of sliding is delayed. In Tripneustes sperm driven at a frequency below the natural beat frequency, the basal bend becomes longer than normal, and its curvature decreases [Eshel and Gibbons, 1989]. In Hemicentrotus spermatozoa driven at the natural frequency and then subjected to a continued displacement beyond the peak of oscillatory drive, the basal bend retains its normal length and curvature, but the preceding interbend increases in length as the preceding bends propagate normally [Eshel et al., 1991]. This increase in interbend length resembles the observations of Li+ -delayed bend initiation (Section 2.6). In another set of experiments with live Hemicentrotus spermatozoa, using sinusoidal oscillations at close to the natural frequency, the effect of increasing the amplitude of lateral oscillation, which increases the drag force on the flagellum, was studied. As the amplitude is increased, there appears to be an increase in basal bend angle achieved by the time the initiation event is induced, so this case indicates that the increased drag force causes an increase in interbend sliding velocity [Shingyoji et al 1991].

The initiation of sliding in basal bends of Hemicentrotus spermatozoa is accelerated when the driving frequency is increased, so that the drag force is reversed after a time interval that is less than half the normal beat period. Although this situation has not been studied in detail, it appears that the increased drag force may increase the rate of sliding that is developing the basal bend, so that the sliding initiation events occur at close to the normal bend angle [Eshel et al., 1990].

4.4 Mechanical stimulation of quiescent cilia and flagella

There are many reports describing restarting of oscillation of quiescent cilia and flagella by mechanical simulation, applied by fluid flow or a microneedle. A problem with interpretation of experiments performed with intact cilia or flagella is that many cilia are known to be involved in mechanotransduction, in which externally imposed movement of the cilium results in changes such as increased Ca++ ion concentration -- which is an important regulator of ciliary beating. A few selected experiments may be relevant to understanding sliding initiation events.

4.4.1 Mammalian sperm flagella

Rat spermatozoa, demembranated and reactivated with ATP at Ca++ concentrations greater than 0.1 mM, assume an arrest position with an extreme basal bend of 3 to 4 rad. Force applied with a microneedle to the tail of an arrested rat spermatozoon, about 50 µm from the head, was able to produce a transient straightening (unbending) of the basal bend, with elastic recovery back to the arrest configuration when the microneedle was removed [Moritz et al. 2001]. In principle, force applied in this direction, opposing the internal active shear force, might cause straightening throughout the existing basal bend, and/or creation of a new basal bend in the opposite direction, next to the base, as occurs when a sliding initiation event is triggered. In these experiments with high Ca++ arrest, only straightening was observed.

In rat and bull spermatozoa the high Ca++ arrest appears to be the result of a high level of sliding force generated by dyneins on doublets 1 to 4. These dyneins also appear to be those that are most sensitive to inhibition by Ni++ [Kanous et al., 1993; Lindemann et al. 1995]. When inhibited by Ni++, the bull sperm flagellum becomes arrested with a gentle bend throughout most of the length, apparently in the direction opposite to that characteristic of Ca++ arrest. If a microneedle is applied to the distal end of the sperm tail and used to push it in the direction that straightens the flagellum, and then starts to create a bend in the opposite direction, oscillatory beating is reactivated, but only for the duration of the mechanical stimulus. The implication is that the role of the forces normally created when a sliding initiation event is activated on doublets 1 to 4 is replaced by the bend induced by the microneedle. Subsequently, oscillation results from switching of doublets 6 to 9, operating against elastic resistances. This oscillation has only half the normal frequency [Lindemann et al., 1995]. This result can be compared with two other results. In these experiments, some spermatozoa were non-motile even without Ni++. When they were pushed with a microneedle, and then released, they showed one cycle of damped, oscillatory bending before stopping. Continuous beating, at close to normal frequency, could be obtained with a sustained push in either direction [Lindemann et al. 1995].  These micromanipulation experiments are very difficult, but they have the potential to obtain a more complete characterization of the role of mechanical feedback in flagellar oscillation.

4.4.2. The Mytilus abfrontal cilium (cirrus)

The abfrontal cirrus is a compound cilium with about 40 individual cilia acting together in a bundle, with a typical length of about 70 µm. These properties have made them favored material for micromanipulation experiments, such as the classic experiments by Kinoshita and Kamada [1939] that established the idea of cilia as mechanochemical oscillators. They beat intermittently, and normally pause at the end of the effective stroke. By modifying the environment, these pauses can be greatly extended. Beats can be initiated by mechanical stimulation, and unlike other cilia on the Mytilus gill, this mechanical activation is not blocked by using Ca++ free sea water [Thurm, 1970]. In the quiescent state, Thurm [1968] used a microneedle to apply a 10 msec stimulus pulse that raised the cilium briefly away from the surface of the gill. The results are shown as drawings based on photomicrographs. The initial effect of a mechanical pulse is a lengthening of the basal bend without a change in total bend angle, thus decreasing its average curvature. This requires some sliding within the bend, in the direction appropriate for the next sliding initiation event, but this relaxes and the cilium partially recovers towards its original position. After a delay of 20-30 msec, a sliding initiation event is indicated by appearance of a new reverse bend at the base, interbend growth, and continuation of a recovery stroke. The recovery stroke is followed immediately by an effective stroke, and the cilium pauses again at the end of the effective stroke. Mechanical stimulus in the opposite direction did not elicit a response.

4.4.3 Mytilus lateral cilia

Stommel [1986] described similar experiments with the much smaller lateral cilia of Mytilus . In the quiescent state obtained at the end of the recovery stroke under low Ca++ conditions, one or more normal beat cycles can be activated by a small mechanical force applied in the direction that would cause sliding in the direction appropriate for an effective stroke. In the more extreme arrest position obtained with high Ca++ conditions, similar micromanipulation can push the cilia all the way into the effective stroke. When the probe is removed, the cilia snap back into the Ca++ arrest position. No normal beat cycle is initiated under these conditions. This situation resembles the results of Moritz et al. [2001] with rat spermatozoa (Section 4.1.1).

4.4.4 Ctenophore comb plate cilia

The ctenophore Beroë has an unusual type of compound cilia, known as “macrocilia” in which many axonemes are enclosed in a single membrane. These cilia typically rest in a quiescent state at the end of the effective stroke, with a basal bend that can be referred to as a principal bend. A recovery stroke can be initiated by lifting a cilium away from the body surface with a microneedle [Tamm, 1983]. This mechanical stimulus appears to trigger a sliding initiation event, by inducing sliding that creates a new reverse bend at the basal end. As the stimulated cilium proceeds through its recovery stroke, it mechanically stimulates adjacent cilia in the same manner, and a “split metachronal wave” of recovery strokes passes over the array of macrocilia. There is also a pause at the end of the recovery stroke, but this is usually terminated spontaneously after about 12 secs, by initiation of an effective stroke. Earlier initiation of effective strokes can be obtained with mechanical stimulation after a refractory period of at least 7 sec, by pushing the tip of the cilium in the direction of the effective stroke [Tamm, 1983]. This cilium shows consistent differences between quiescent states at the end of the effective stroke and at the end of the recovery stroke, in concordance with the earlier experiments identifying “switch points” [Wais-Steider and Satir, 1979].

4.4.5 Summary

Some of these observations show that external mechanical stimuli that impose sliding or bending in the direction appropriate for a sliding initiation event can trigger a sliding initiation event. Since many examples come from cilia that might be specialized to possess mechanosensitivity required for metachronal coordination or other functions, they do not provide strong evidence for the idea that sliding initiation events are normally triggered by appropriate sliding, but this would be an attractive conclusion.

4.5 Termination of interbend growth

In the simplest cases, the initiation of propagation of a basal bend by a sliding initiation event will also terminate the interbend growth that developed that basal bend. The sliding activated in that basal bend will create an inflection point with 0 sliding velocity in the preceding interbend, T0, and cause the propagation velocity of T0 to double [Brokaw, 1983 cc model], This result requires only that both the curvatures and the sliding velocities of the bends on the two sides of T0 have the same magnitudes, in opposite directions. Most real examples do not exactly meet these conditions. There are many examples where the sliding in T0 does not fall exactly to 0, indicating a continuation of interbend growth. Interbend growth also continues after failure of a sliding initiation event, as in the stopping transients analyzed by Gibbons [1981, 1986] (Section 3.6).

Changes in interbend growth sometime occur, either in whole or in part, before the sliding initiation event. A relatively extreme case is seen under conditions where the sliding initiation event is delayed by Li+ (Example 2.6), where interbend growth stops, while the interbend continues to propagate and elongates. Other examples show a definite pause between formation and propagation of a basal bend (Examples 2.3, 2.5). When the sliding initiation event is delayed by Li+, in Example 2.6, plots of bend angle as a function of time [Brokaw, 1989, Fig. 20-3] show a pronounced slowing of basal bend angle growth before the next sliding initiation event causes growth of a new basal bend and restarts growth of the previous basal bend. Other examples are available where plots of bend angle growth show a slowing of basal bend growth just before the next sliding initiation event [Brokaw 1979, Fig. 3; Gibbons 1982, Fig. 8; Eshel and Brokaw, 1988, Fig. 8a; Brokaw, 1993, Fig. 4]  A more complete picture is shown by shear angle plots, which typically show a decrease in basal bend curvature, retaining a uniform curvature (circular shape), as the curvature transition at the leading edge of the basal bend continues to propagate and increase the length of the basal bend, without an increase in bend angle [Brokaw, 1989; Fig. 20-4; Gibbons, 1982, Fig 31]. (Examples shown in Fig)

Observation that interbend growth starts to decrease before the sliding initiation event suggests that interbend growth is terminated intrinsically, rather than being terminated by the new sliding initiation event. Decreasing curvature of a basal bend requires a non-uniform velocity of sliding in the bend. In the situation discussed here, the sliding is in the same direction that will propagate the bend, and its velocity is highest at the distal end of the bend, adjacent to the preceding transition that begins to propagate with increased velocity before the sliding initiation event. Because this sliding reduces the curvature, it can be passive sliding, driven by the elastic bending moment in the basal bend. This passive sliding could be the trigger that initiates active sliding [Brokaw, 1989]. Under normal conditions, the amount of passive sliding required to trigger a sliding initiation event may be too small to be detected. Li+ may impede the transition from passive sliding to active sliding, thus making the passive sliding very visible. This line of thinking suggests that some measure of the completion of interbend growth might be the trigger for the sliding initiation event, but has not led to a detailed model.

4.6 Summary

All we can say for sure is that a switch point is the point where a sliding initiation event is observed to occur. There appears to be only a loose correlation between a switch point and the configuration of the basal region of the flagellum. Under certain conditions, a sliding initiation event can probably be triggered by imposed sliding in the direction that will be activated by the sliding initiation event. An elastic  relaxation of the basal bend, causing passive sliding, might trigger a sliding initiation event. The idea that this is the normal mechanism for triggering a sliding initiation event is still highly hypothetical, and we have no understanding of why and when such relaxation might occur.

Part II . Three-dimensional bending patterns

1. Observations

One simple three-dimensional bending pattern would be a propagated helical wave, and some flagella come close to this. Examples include eel sperm flagella [Gibbons et al. 1985; Woolley 1998], spermatozoa of Asian horseshoe crabs [Ishijima et al. 1988], spermatozoa of non-passerine birds [[Vernon and Woolley, 1999], and the transverse flagellum of some dinoflagellates [Gaines and Taylor, 1985]. In addition, spermatozoa of Ciona and sea urchin have been observed to switch from planar to helical bending at high viscosities [Brokaw, 1966b; Woolley and Vernon, 2001].  

A helix cannot be described in terms of bends and interbends. Every position along the length is in a bend, and the direction of bending rotates continuously along the length. However, along the line of each outer doublet, there will be a wave of bends in alternate directions, separated by interbends, propagating along that doublet. Since active sliding along any doublet is believed to only be able to occur in one direction, the bends along a doublet should be alternating active sliding with passive sliding, just as occurs in planar bending waves. From one doublet to the next, there must be a phase difference of 1/9 cycle. This type of pattern of phase shifted active sliding required for three-dimensional bending patterns was first described for cilia [Sugino and Naitoh, 1982]. In modelling studies of the generation of quasi-helical bending waves [Brokaw, 2002], the pattern of sliding was termed “doublet metachronism”, in order to emphasize its similarity to ciliary metachronism. In both cases, metachronism describes a spatial succession of phase differences between oscillators that is necessary for their operation in a productive manner, rather than interfering with each other. Doublet metachronism can also be described as “continuous unidirectional transfer of active sliding around the axonemal cylinder” [Machemer, 1977]. At present, it is not possible to distinguish between the idea that circumferential activation of sliding is a mechanism required to generate helical bending waves, and the idea that circumferential activation of sliding is a result of self-organization of independent oscillators into a coherent pattern.  Three-dimensional bending is difficult to study, and there is no detailed information available to establish that the distinction between basal and propagating bends is applicable to helical bending waves or other three-dimensional bending patterns.

Theoretically, the idea of a sliding initiation event can be applied to the progressive activation of sliding from doublet to doublet that occurs in three-dimensional bending patterns. In both planar and helical bending waves, sliding can begin to be inactivated at the basal end of a basal bend sometime before the next sliding initiation event. In helical bending waves, this could be seen in the pattern of doublet metachronism, with, for example, a sliding initiation event on doublet n+2 occurring at about the same time as the appearance of sliding inactivation on doublet n. At any given moment at the basal end, active sliding might be occurring on only 2 or 3 adjacent doublets, while all of the other 6 or 7 doublets are inactive. In more distal regions, there would be 4 or 5 active doublets, with the others inactive. In the most extreme case, there might be only one active doublet at any time; this situation, referred to as “linear transfer of sliding” around the circumference, has been discussed by Sugino and Machemer [1988]. Data available for three-dimensional flagellar bending patterns are not adequate to establish the occurrence of sliding initiation events, as defined here, or to help us understand them. It could be the case that the sliding initiation event is a unique feature of planar bending patterns, and is responsible for making the bending pattern planar.

Water flow generated by movements of nodal cilia is responsible for determining the direction of the asymmetric development of embryos of mammals and some other vertebrates [Nonaka et al. 2002, 2005; Okada et al. 2005]. Although these cilia are short, typically 5 µm or less in length, they are sparsely distributed monocilia, so that their movement is relatively easy to observe. They have a very simple three-dimensional bending pattern that produces a circling motion of the tip of the cilium. Bending must occur close to the basal end, and propagate circumferentially around the axoneme. Although the remainder of the cilium is slightly curved, a pattern of bend propagation along the length of the cilium cannot be resolved. A similar circling pattern was observed earlier in reactivated cilia detached from Tetrahymena, when the base of a cilium became attached to a microscope slide surface [Gibbons, 1965]. Cilia free in the solution appeared to swim and rotate, with a propagated helical bending wave. Parducz [1967] described a circling motion of individual cilia on stationary cells of Paramecium multimicronucleatum and other ciliates. Although Paramecium cilia are longer (10 to 12 µm) than nodal cilia, they normally are in dense arrays on the cell surface, making observation difficult. Their motion is now described as a “conical-helical” beat, based on studies by Machemer [1972] and Tamm [1972]. On swimming cells, especially at increased viscosity, their motion appears to approach a propagated helical wave [Kuzniki et al. 1970].

The circling motions of nodal cilia are effective in producing lateral water flow in one direction because the cilia are predominantly inclined towards the posterior end of the embryo [Nonaka et al., 2005; Okada et al. 2005]. This means that through half of the beat cycle, the cilium is extended away from the cell surface and is moving through an arc that is close to vertical. During the other half of the beat cycle, it is moving in the opposite direction through an arc that is close to the cell surface, where proximity to the surface makes it difficult to produce fluid flow [Blake and Sleigh 1974]. This interpretation was originally applied to the three-dimensional beat of Paramecium cilia, in which movement of the tip of the cilium through an arc away from the cell surface has traditionally been called the effective stroke, and is followed by a recovery stroke that brings the cilium close to the cell surface [Blake, 1974]. It is unclear whether there is any asymmetry in the beat pattern of these cilia that is comparable to the asymmetry of cilia that are making nearly planar bending patterns. It is easy to imagine an evolutionary sequence starting with a simple circling movement of an inclined cilium, followed by a gradual adaptation to produce a more asymmetric bending pattern that increases the propulsive contribution of the effective stroke.

The ciliated protozoon, Stylonychia , has three frontal cirri (compound cilia) that are 50-80 µm long, containing approximately 70 individual cilia operating as a single unit. The three-dimensional bending pattern of these cirri has been subjected to extensive analysis [Sugino and Machemer, 1987, 1988; Teunis and Machemer, 1994]. Movement of the basal region of these cirri has some resemblance to the circling movements of short cilia, such as nodal cilia, but the movement is elliptical rather than circular, with a spatial polarity (ratio of major and minor axes) between 2 and 2.5. This movement pattern is controlled by at least three adjustable parameters: the  inclination (direction and amount) of the center of the circling pattern, the rate of circumferential transfer of active sliding, and the rates of active sliding. Variations within the cycle in either of the latter two parameters, or both, can change the movement from circular to elliptical. Neither one of these two parameters appears to remain constant, so the analysis “does not reveal any simple pattern of propagated activity within the axoneme” [Teunis and Machmer, 1994]. The combination of a complex bending pattern and the absence of any methods to identify regions of active interdoublet sliding make it difficult to gain further insights into the mechanism of circumferential transfer of active sliding.

Evidence for elliptical patterns has also been obtained for some sperm flagella that produce three-dimensional bending waves [eg. Rikmenspoel, 1965; Ishijima et al. 1986]. Spatial polarity ranged from 3 to 5 under normal conditions, but was increased under other conditions such as proximity to a surface or increased viscosity, and became effectively planar.  A bending pattern with an extremely eccentric elliptical motion could be indistinguishable from a planar bending pattern.

It is not known what causes planar bending patterns to be planar. As mentioned above, a few examples are known where flagella switch abruptly between planar or helical bending patterns, suggesting that these represent two stable modes of operation, but it is difficult to reconcile this with the existence of elliptical patterns. Some cilia and flagella clearly have structural specializations that produce anisotropic bending resistance favoring planar bending [Afzelius, 1959, 1961], but these structures may only determine the direction of the bending plane, without being the cause of planar bending. Alternatively, the bending mode might be determined by mechanisms that establish phase differences between sliding initiation events on individual outer doublets.

2, Chirality

Examples of flagella generating three-dimensional bending waves have been observed with either left-handed or right-handed chirality, sometimes within the same species [eg. Brokaw, 1966b; Ishijima et al. 1992]. On the other hand, electron microscopy shows that the structural chirality of the axoneme is always in one direction, with the dynein arms extending in a clockwise direction towards the adjacent doublet, when viewed from base to tip [Gibbons, 1961]. A consistent counterclockwise circling (when viewed from base to tip) is essential for developmental symmetry breaking by nodal cilia. It is not known how this is established; some possibilities have been explored by computer simulations [Brokaw, 2005].

Part III. Direct measurements of interdoublet sliding.

1. Protease-digested axonemes

1.1 Observations

Axonemal fragments can disintegrate by ATP-dependent sliding [Summers and Gibbons, 1971]. Digestion of sliding-resistant structures by proteases, such as elastase [Brokaw, 1980], is usually required to allow this to happen. Axonemes digested thoroughly with trypsin are usually activated by addition of ATP, and can disintegrate by sliding between multiple doublets. Other observations have been made with minimally digested axonemes, either after elastase digestion or in experiments in which protease is added in the presence of ATP. These axonemes typically disintegrate by sliding between two bundles of doublets. Unloaded sliding begins at a high velocity that is maintained until there is only a small overlap between the two doublet bundles [Takahashi et al. 1982]. Any “starting transient” was too brief to be detected in these experiments.

Morita and Shingyoji [2004] examined the effects of curvature on sliding disintegration, using photolysis of caged ATP to initiate sliding in elastase-digested axonemes. A brief release of ATP caused partial sliding between two bundles of doublets. A second brief release of ATP normally produced further sliding in the same direction. However, if after the first ATP release, a microneedle was used to bend the overlap region through an angle of π/2 or more, the second ATP release induced sliding in the opposite direction in about half of the experiments. Since the direction of bending relative to the geometry of the axoneme could not be controlled, 50% reversal is the expectation if the direction of sliding is determined by curvature (or by some other result of bending, such as shear). It is not possible to examine both directions of bending on the same axoneme, in these experiments. Bending also caused two other effects: an increase in the number of axonemes that disintegrated by sliding between multiple doublets, and an increase in the velocity of sliding. These experiments provide the best evidence available for regulation of interdoublet sliding by curvature.

Tani and Kamimura [1999] measured the force generated during sliding disintegration, using thoroughly digested axonemal fragments from sand dollar spermatozoa, attached to a slide surface. Sliding was initiated by photolysis of caged ATP. A flexible glass microneedle on the upper surface of the axoneme was used to measure the force, with sliding displacements of the order of 100 nm. When ATP was released, the force rose to a maximum in about 60 ms, with kinetics that were interpreted in terms of the kinetics of formation of a force-producing ADP-dynein complex. A steady force, in the range of 5 to 50 pN/µm, was then maintained. Earlier measurements using elastase to activate sliding in axonemes held between two microneedles yielded average steady forces of 30 pN/µm [Oiwa and Takahashi, 1988] or 40 pN/µm [Kamimura and Takahashi, 1981], but some values as high as 90 pN/µm were measured.

In the earlier experiments, with sea urchin spermatozoa, in which sliding was initiated by elastase in the presence of ATP, occasional rapid reversals of sliding were observed, followed by recovery. These experiments used more compliant measuring needles, and the reversals in some cases involved  up to 5-10 µm of sliding. The point at which recovery began was not consistent, but recovery usually occurred before the force fell all the way to 0. The fast time course of the reversal was stated to be consistent with the free time constant of the measuring needle in the viscous fluid. These observations suggest a sudden and complete shut down of motor force throughout the region that was actively generating sliding force. The reversal presumably involves sliding in the direction of normal active sliding between at least one doublet that was previously undergoing passive, backwards sliding, but the results do not indicate that this passive forward sliding turns on active sliding between these doublets.

1.2 Interpretation: force generation

To interpret the force measurements, it is not necessary to know whether just one, or several, doublets on one side of the axoneme are producing active shear force. These measured forces seem somewhat lower than expected.  

If the elastic bending resistance of an axoneme is 2 x 10 8 pN nm2 [] and the bending moment is balanced by shear force acting with an effective moment arm of about 180 nm, the required shear force in an interbend  between two bends with curvatures of 2 x 10 -4 rad/nm would be about 450 pN. If the length of the interbend is 5 µm [Brokaw, 1993] a shear force of at least 90 pN/µm would be required. These conditions are typical for normal bend propagation on a sea urchin sperm flagellum, but there are other situations (eg. Example I.2.3, and Brokaw [1965; 1966b]) that involve significantly greater curvatures and similar or shorter interbends. Elastic shear resistances could increase further the amount of active shear force needed.

A force of 30 pN/µm corresponds to about 3 pN for each 96 nm repeat unit along a doublet, containing 15 dynein heavy chain motors.  Maximum forces in the range of 1 to 2 pN have been measured with single-headed dynein motors in vitro [Sakakibara et al. 1999]. Other observations suggest that dyneins attached in an axoneme may produce peak forces of about 6 pN [Shingyoji et al. 1998]. Based on understanding of myosin in skeletal muscle, we expect dyneins to be actively cycling under isometric conditions, so that only a fraction will be force-producing at any moment. In muscle, only a fraction will be positioned relative to an actin binding site such that they can produce maximal force. It is not known whether both motor domains of two-headed dyneins can simultaneously produce force. These considerations indicate that the average steady-state force produced by a motor in an ensemble of motors will be significantly less than the maximal force that can be produced by a motor in vitro. If, on average, only 5 dynein motor domains in a repeat unit are attached in force-producing states, and are producing half their maximum force, the expected force might be 4 to 15 pN, which is not greatly different from measured values of 3 to 9 pN per repeat unit.

It might be incorrect to assume that there is no significant opposing shear force on the other side of the axoneme, where passive, “backwards” sliding is required, but the simple time course of force development in the Tani and Kamimura measurements argues against such a complex situation.

1.3 Interpretation: activation and deactivation

In minimally digested axonemes, the minimal sliding disintegration event requires active sliding between two doublets (m and m+1) and passive, backwards sliding offering very little resistance, between doublets n and n+1. (There are structural constraints that may explain why m and n tend to be more or less on opposite sides of the axoneme.)

If we start with the assumption that the default state for active sliding is the ON state, which is consistent with the complete disintegration of thoroughly digested axonemes, then the critical event for initiation of sliding disintegration must be the collapse of forward sliding force between doublets n and n+1. This could be driven by a positive feedback process, where a small backwards movement causes reduced force, leading to more backward movement, more force reduction, and so on. Models for motor enzyme function can easily be constructed to give this “suppressed ON state” behavior, with “cross-bridge” detachment occurring when a motor is pushed backwards. However, such models require continued backward movement to maintain the OFF state. They do not explain the ability to maintain constant isometric force in experiments such as Tani and Kamimura [1999], and they do not explain the maintenance of an OFF state between doublets n and n+1 when the movement reverses during transients observed in some of these experiments.

If we start with the assumption that the default state for active sliding is the OFF state, there is no obvious mechanism that explains how activation is rapidly turned on throughout the length of a doublet.

It should not be forgotten that the observations in this section were made with axonemes that were damaged by elastase digestion. Although elastase appears to be  effective in eliminating elastic shear resistance between axonemal outer doublets, it may have other damaging, but more subtle, effects on mechanisms involved in the control of sliding. However, elastase digestion did not prevent local oscillation in the experiments of Shingyoji and Takahashi [1982] (Section I.2.3).

2. Undigested axonemes

The presence of an elastase-sensitive sliding resistance has been demonstrated in bending axonemes [Brokaw, 1980; Lindemann et al. 2005], where it can allow sliding excursions equivalent to more than ±100 nm between adjacent doublets. Based on observations of the sliding capability during sliding disintegration, and the localized oscillation described in Section I.2.4 and other experiments [Brokaw and Gibbons, 1973], it was expected that sliding and/or shear oscillation, limited to amplitudes of ±100 nm, might occur between doublets in intact axonemes when conditions did not permit bending. (Absence of basal shear resistance or immobilization by adhesion to a surface.) Initial attempts to find such sliding failed, until it was recognized that it was limited to very small amplitude, high frequency, oscillatory sliding [Kamimura and Kamiya, 1989], that has sometimes been referred to as “hyperoscillation”.

2.1 Observations: ATP-driven hyperoscillation in demembranated echinoderm sperm flagella

Results are described in three papers, using somewhat different material and techniques. Sea urchin axonemal fragments, attached to slide surfaces without chemical treatment, were used by Kamimura and Kamiya [1989]. Unfragmented sea urchin sperm were also examined, attached to surfaces with or without polylysine [Kamimura and Kamiya 1989, 1992] . Sand dollar axonemal fragments, attached to slide surfaces with aminopropyl-silane were used by Tani and Kamimura [1999]. The movement of beads attached to the axoneme was measured with high resolution. Although in some cases the amplitude of oscillatory movement was not much larger than random movement resulting from thermal fluctuations, Fourier analysis revealed a strong signal at the dominant oscillation frequency.

The most common result was a longitudinal shear oscillation with a peak-to-peak amplitude of 4-5 nm and frequency near 300 Hz at high ATP concentration. The frequency showed the same dependence upon ATP concentration seen for flagellar beat frequency. This suggests that the motor mechanism responsible for generation of hyperoscillations is similar to, or the same as, that responsible for normal flagellar oscillation. The waveform was symmetric at all ATP concentrations, suggesting that the ATP-dependent motor process was functioning in both directions during the oscillation. These oscillations were observed in axonemal fragments as short as 5 µm, and were observed both in axonemal fragments and intact sperm flagella, where the movement could be detected by oscillation of the sperm head. The product of frequency and amplitude indicates that sliding velocity in these oscillations is 1/3 to 1/2 that observed during normal flagellar bending. Other work has shown that the utilization of ATP by axonemal fragments is only about 30% that of beating demembranated flagella, and only slightly greater than that of disintegrated axonemes [Brokaw and Simonick, 1977b].

In some cases, flagella attached to slides with polylysine exhibited oscillations with larger , irregular amplitudes and lower frequencies. The movement tended to occur with steps of 4+8n nm, where n ranged from 0 to 4, suggesting that the 8 nm tubulin lattice was a dominant controlling feature. The product of amplitude and frequency was about 2X larger, closer to that seen in normal flagellar oscillation. The largest amplitudes were still much less than those seen during normal flagellar oscillation. It was stated, without data, that elastase increased the amplitude of oscillation [Kamimura and Kamiya, 1992].

2.2 Observations: hyperoscillations in Chlamydomonas flagella

Chlamydomonas flagella are shorter (10-12 µm) than echinoderm sperm flagella (40-50µm), and normally beat with higher frequencies. All of the following observations were made with detached, demembranated axonemes retaining their normal basal shear resistance, usually without using polylysine to bind the axonemes firmly to a surface [Yagi et al. 1994; Yagi and Kamiya, 1995].

Wild type axonemes show irregular hyperoscillations, with amplitudes up to about 20 nm, and some excursions as large as 40 nm. There was no clear evidence for stepwise excursions with steps that were multiples of 8 nm. There was a tendency for amplitudes to increase when the frequency was reduced by reducing ATP concentration. Axonemes from ida 1, a mutant with a partial inner dynein arm deficiency, showed hyperoscillation that was not significantly different from wildtype. Axonemes from oda 1, a mutant lacking outer dynein arms, showed hyperoscillation with a reduced beat frequency, consistent with lower beat frequency of flagellar beating and lower velocity of sliding disintegration. Hyperoscillation was completely suppressed in oda 1 when axonemes were firmly attached to surfaces with polylysine; this suppression did not occur with wildtype or ida 1. Hyperoscillations were also observed in three other mutants: ida 4 (motile, with partial inner arm deficiency), pf 14 (paralyzed, spoke head deficiency), and pf 18.

The mutant pf 18 is a paralyzed mutant lacking central pair microtubules. Although its axonemes show paralysis when reactivated at ATP concentrations of 0.1 mM or greater, it shows motility, with lower than wild-type beat frequency, at ATP concentrations below 0.05 mM or with 0.1 mM ATP in the presence of 1-3 mM ADP [Omoto et al., 1996]. Axonemes of pf 18 produced the high frequency hyperoscillations, with regular amplitudes of 4-5 nm, that were originally seen with sea urchin sperm flagella. These were only observed when attachment was stabilized by using polylysine coated slides and the axonemes were reactivated under “paralyzed” conditions, with 1 mM ATP. Oscillation frequencies of 400 to 600 s-1 were observed, consistent with the higher normal beat frequency of Chlamydomonas flagella. When axonemes of this mutant were observed under motility-inducing conditions, with 0.1 mM ATP and 0.5 to 3 mM ADP and without using polylysine, some unusual patterns of hyperoscillation were observed. These oscillations were highly asymmetric, with amplitudes as high as 100 nm. There was an ascending phase at a gradually decreasing rate, followed by a very rapid descending phase at a constant rate. The ascending phase could be producing force against a gradually increasing internal resistance of interdoublet elasticity. The fast descending phase consistently requires about 1.5 ms, regardless of amplitude, and does not consistently end at the same position. There is very abrupt switching between these two phases. The fast phase resembles transients seen with elastase-digested axonemes (III.1.1)

2.3 Interpretation of hyperoscillations

The effect of ATP concentration on the frequency of relatively symmetric hyperoscillations suggests that both directions of movement are driven by the same active sliding system that operates during normal flagellar bending.

A molecular model of motor enzyme function that can produce shear oscillations when two opposing arrays of motors are combined with an elastic shear resistance was proposed in [Brokaw, 1975b, 1976]. A somewhat similar model, developed by Murase and Shimizu [1976], was specifically applied to explaining hyperoscillations [Murase 1992]. However, to restrict the amplitude of oscillation to 4 to 5 nm, both of these models require either an amount of elastic shear resistance so high that normal bending would be impossible, or the assumption that only a small fraction of the available motors are involved in producing hyperoscillations. The latter assumption is difficult to reconcile with the regularity of the oscillation, but may be consistent with the low ATPase activity of non-bending axonemes [Brokaw and Simonick, 1977b]. These explanations also predict, incorrectly, that oscillation should be observed when the elastic shear resistance destroyed by elastase is replaced with an elastic measuring needle, as in the experiments of Tani and Kamimura [1999]. Elastase digestion may be destroying more than a simple elastic shear resistance. Finally, these explanations do not explain the 8 nm step increments that characterize some of the observations of hyperoscillations.  At present, we have no adequate model that can explain hyperoscillations.

2.4 other obs by Tani and Kamimura

3. Microoscillations

Shingyoji et al [1998] observed oscillatory sliding, with amplitudes in excess of 50 nm, of a microtubule interacting with one, or a few, dynein motors on an axonemal doublet exposed by sliding disintegration. The frequency (  ) of this oscillation also was ATP concentration dependent, in both directions, and occurred in the absence of the normal elastic shear resistance of the axoneme. Even if it is assumed that individual dynein motors can operate in both directions, it is difficult to design a simple model to explain this oscillation.[  ] More study of the details of this situation is needed to determine its relevance to flagellar oscillation.

Kamiya oscillations in fragments

4. General Interpretations

Taken together, these observations indicate that the active sliding system that generates flagellar bending can also generate sliding, steady-state force, or oscillatory sliding, under conditions where no bending is seen. These movements share many properties with the sliding that occurs during normal flagellar bending, but when bending is completely absent, sliding velocities, oscillatory amplitudes, and possibly forces are usually less than are seen as part of normal flagellar bending. These constraints are especially strong in intact axonemes that have not been subjected to protease digestion, where hyperoscillations are seen in the absence of bending.

Although we have no model to explain hyperoscillations, these observations may inform us, by revealing mechanisms that may be important in normal flagellar oscillation: Firstly, the mechanism that limits active sliding when no bending is produced might be a mechanism that prevents switching dyneins into distinct ON and OFF states when no bending is produced. Secondly, even in an axoneme with dyneins in a uniform ON state, there is not a static equilibrium, but a state that might be interpreted as producing regular small movements that are attempts to start bending, which will then lead to appropriate switching. The proper operation of this regulatory system appears to be eliminated by protease digestion, and appears to be abnormal in the central pair defective mutant pf 18. However, even after protease digestion, a modulation of sliding by bending has been demonstrated by Morita and Shingyoji [2004].

IV.  Conclusions, ideas and proposals

1. Frequency-determining events in a mechanochemical oscillation  

Flagella and cilia appear to be mechanochemical oscillators in which the movement is an integral part of the oscillatory cycle. The movement is not the readout of an underlying chemical oscillation. This conclusion is based on experiments showing sensitivity of frequency to mechanical conditions, and evidence that the phase of the oscillation is retained when the oscillation is mechanically stopped and started [].

Experiments with demembranated flagella have demonstrated that the frequency of oscillation can be varied over a wide range -- from more than 50 Hz to less than 1 Hz, by varying the ATP concentration. ATP concentration is similarly effective in varying the rate of translocation of microtubules by dynein in vitro. It is reasonable to explain the effect of ATP concentration on oscillation frequency as a consequence of the ATP-dependent step in the dynein motor cycle that drives active sliding. This step is believed to be the release of dynein from substrate attachment at or near the end of a “power stroke”. Any additional steps in the the oscillatory mechanochemical cycle must either depend on ATP concentration in the same manner as ATP-dependent substrate detachment, or must become increasingly less significant as the ATP concentration is reduced. The effect of viscous load appears to behave in the latter manner [Brokaw, 1975a]. In terms of internal controlling mechanisms, any timing processes that need to occupy a fixed fraction of the bending cycle are subject to these constraints.

The apparent temporal precision of flagellar oscillation suggests that a large number of dynein motors must be involved in determining switching events that determine beat frequency. However, there is no good data to quantify the impression that flagellar oscillation is very regular.

2. There must be two states of dynein, which persist in the absence of movement.

Most ideas about the regulation that leads to flagellar oscillation assume that there must be distinct ON and OFF states of dynein motors. This assumption is based on “there is no other way it could work” as a response to the circular arrangement of the axonemal outer doublets on which the dyneins are arrayed. However, in vitro studies on axonemal dyneins have not identified distinct ON and OFF states. Although sliding on particular doublets is described as being ON or OFF, it could equally well be stated in terms of active FORWARD or REVERSE sliding. In the latter case, the absence of active sliding would represent activation of all doublets in the same direction. The preference for ON or OFF is based on independent evidence that dyneins consistently produce sliding in one direction [Sale and  Satir, 1977; Brokaw, 1997]. (But see Section III.3.) In the remainder of this discussion, ON and OFF states will be assumed.

Observations of arrested states, in which a bent state is maintained in the presence of ATP, indicate that the distinction between ON and OFF states of dynein can persist in the absence of sliding. (Section I.3 ) This distinction can also be maintained in the absence of curvature in protease-digested axonemes during measurements of isometric force production by dynein. (Section III.1 ) Flagella can remain in rigor wave configurations following the sudden removal of ATP, and resume movement normally after resupply of ATP. An especially interesting memory effect is seen in experiments that involved iontophoretic application of small amounts of ATP (Section I.2.4), implying that the previous direction of sliding can be remembered even under conditions with very similar bend configurations.

It is easy to develop simple theoretical models for the mechanochemical kinetics of motor enzyme function in which force production is drastically reduced when a motor is driven backwards or stalled [eg. Brokaw, 1975b, 1976]. 1t may be convenient to have a name for this low-force state; I propose to call it the “suppressed ON state”. Two anti-parallel ensembles of such models can generate shear oscillations when combined with elastic shear resistance and displaced from equilibrium. There is no net force when the two ensembles are held at 0 sliding velocity. Models that produce a “suppressed ON state” cannot explain the ability of an axoneme to maintain shear force at 0 sliding velocity in arrested states (Section I.3) or in force measurements on protease digested axonemes (Section III.1). They do not have a lasting memory of a previous state. The suppressed ON state does not appear to be the OFF state. At this juncture, the OFF state is still hypothetical.

3 . A regular alternation between ON and OFF states can be viewed as an oscillation, and the ideas of sy nchronization and metachronal coordination may be important.

In physics, synchronization of interacting (coupled) oscillators means attainment of a common frequency, without requiring common phases. In biology, a distinction is made between synchronization, involving both a common frequency and a common phase, and metachronism, involving a common frequency and a regular spatial gradient of phase differences. In cilia and flagella, metachronal coordination can be considered at three or possibly four levels:

3.1 Metachronal coordination within an array of cilia. In this case it is clear that individual cilia are independent oscillators, although in some cases their oscillation pauses during the cycle. In ciliary arrays, there is synchronization along one line on the surface, and metachronal coordination along a line perpendicular to the line of synchronization. Computer simulations have shown that this type of coordination can arise spontaneously in an array of model cilia [  ]. Is there a need for a mechanism that prevents synchronization in both directions, or is metachronism the default result under some conditions? Complete synchronization occurs within the dense arrays of cilia in cirri. What determines the borderline between synchronization and metachronism of cilia?

3.2 Metachronal coordination in the circular array of doublets of an axoneme, referred to as “doublet metachronism”. Computer modelling with switching based on curvature [Brokaw, 2002] or sliding velocity [Brokaw 2005] demonstrates that doublet metachronism can be “self-organized”. Metachronism may be an appropriate interpretation here if the linear array of dyneins on each doublet is independent, and senses bending or sliding applied to that doublet. In this case, the geometry of axonemal structure does not permit total synchronization, but planar bending might be interpreted as partial synchronization. Elliptical waveforms imply a continuum between metachronal coordination and synchronization.

3.3 When a cilium or flagellum is producing normal periodic bending patterns, any point along the length is undergoing oscillatory sliding, or shear oscillation. Spatial phase differences between these oscillations can create a pattern of metachronous sliding that is appropriate for propagated bending waves. If local oscillatory sliding occurs without spatial phase differences, it will produce synchronous sliding, which will accomplish no more than waving the base of the flagellum from side to side. Consequently, if a capability for shear oscillation is the underlying mechanism for flagellar oscillation, this idea requires a mechanism to suppress synchronous sliding and establish the phase differences required to produce a useful bending pattern.  Curiously, oscillatory synchronous sliding, with amplitudes of as much as 90 nm, can be observed to occur in the presence of bending, superimposed on the metachronous sliding that is associated with bend propagation [Gibbons, 1982; Brokaw, 1993]. In this case, it is revealed directly by a side to side tilting of the sperm head as it swims, as well as by more detailed analysis of sliding patterns within the axoneme. It disappears when viscous forces are small.

3.4 The progression of a motor enzyme, such as dynein, though a cycle of states can be viewed as a stochastic oscillation. Metachronal coordination might appear along a row of dyneins, with regular phase differences between the mechanochemical cycles of individual dyneins. The structure and spacing of outer arm dyneins are such that mechanical interactions are likely [ ], just as mechanical interactions are likely in closely spaced arrays of cilia. However, if mechanical interactions are weak, an uncoordinated pattern involving stochastic cycling of individual dyneins would be expected. Myosin in skeletal muscle is presumed to operate in this manner. Metachronous dynein cycling would predict that dyneins in a functioning axoneme would be found in groups of recognizable states, as has been found by Burgess [1995].

4 . If there are ON and OFF states of dynein, there must be a switch.

Operation of the switch is potentially very complicated. There is no evidence that all of the approximately 10 varieties of dynein in every 96 nm length of an outer doublet are switched in the same manner. Adjacent doublets may or may not be switched at the same time. In spite of these complexities, observations suggest two general patterns of switch operation:

A. Metachronous switching, at propagated switch points. Most modelling of planar bending patterns has assumed that there are switch points that propagate along with bends, switching all doublets on one side of the axoneme synchronously from the ON to the OFF state, and on the other side of the axoneme from the OFF to the ON state. F or generating a helical bending wave, metachronous switching of one doublet at a time appears to be appropriate . In this case, there is metachrony both along individual doublets and around the ring of 9 outer doublets. Observations of discrete changes in the slope of curvature vs. length plots [Baba and Nonaka, 1990] suggests that there may be other situations where switching involves just a subset of the doublets on one side of the axoneme.

B. Synchronous switching, at temporal switch points. As discussed extensively in Section I.2, there are “sliding initiation events” in the bending cycle, at which switching appears to occur synchronously throughout an extended region of one or more doublets. The region may be a basal bend, or in some case the entire length of a cilium.

Actually, these two patterns are based on descriptions of the results of switching, in terms of observed sliding and presumed shear forces. Interpreting them in terms of ON and OFF states of dynein motors is uncertain if, for example, a sliding initiation event, driven by previously activated dyneins, occurs when a restriction on unbending is released at the basal end of a cilium. Computer modelling is important for relating switching to observed bending patterns, but there are numerous unknown parameters in this relationship.

5. The curvature of the flagellum may provide information that is important for operating the switch.

5.1 Machin [1958] presented, in mathematical formalism, the idea that if the bending produced by active forces within a flagellum is used to control the production of active forces, a feedback loop is created that can lead to oscillation and bend propagation. The mathematical formalism was developed in terms of active and resistive bending moments. These bending moments must be in equilibrium at every point on the flagellum. This equilibrium is described by the bending moment equation, and the solution to the bending moment equation gives the movement of the flagellum. Machin clearly explained that in a traveling wave, the elastic and viscous bending moments are out of phase by 1/4 cycle, so that the feedback control of active force generation must contain a phase delay that creates active moment components that can balance both resistive moments. This appeared problematic until it became known that the active elements within the flagellum develop active shear force and sliding, in which case control of active shear force by curvature, with a less than 1/4 cycle phase delay, can produce the distribution of  active moment components needed to produce a traveling wave [Brokaw, 1971].

This early work provided analytical solutions to a small-amplitude version of the moment balance equation, which were difficult to compare with large-amplitude movements observed with real flagella. Large-amplitude solutions required numerical solution of the moment balance equation, beginning with Brokaw [1972a]. This work was able to demonstrate that control of active shear force by curvature, with an appropriate phase delay, would not only explain bend propagation, but also lead to spontaneous oscillatory bend initiation by the computer models, if sliding is restricted at the base of the flagellum [Brokaw, 1972a]. Initial work obtained the requisite phase delay either with a fixed time delay or, more realistically, with an exponential time delay process [Hines and Blum, 1978], but these ideas are difficult to reconcile with the ability of flagella to oscillate normally over a wide range of frequencies. Later work avoided this difficulty by obtaining the phase delay by switching when the curvature reached a level appropriate for the next bend [Brokaw, 1982, 1985 etc.]. Numerical methods have now been extended to a detailed nine-doublet model of the axoneme, with individual dyneins distributed along each doublet [Brokaw, 2002]. These methods can show that c urvature -controlled switching can generate both planar and helical bending waves [Brokaw, 2002].

5.2 Direct evidence for switching the direction of active sliding by bending an axoneme was obtained from the experiments of Morita and Shingyoji [2004] with ATP-induced axonemal disintegration, described in Section III.3.1. These experiments are most directly interpreted as evidence for control of switching by curvature, but some caution is required because curvature and shear are both inseparably varied by imposed bending. Measurements of higher ATP dephosphorylation rate by suspensions of actively swimming spermatozoa, compared to non-motile broken axonemes [Brokaw and Benedict, 1968; Gibbons and Gibbons, 1972; Brokaw and Simonick, 1977b] implies that dynein-induced sliding is activated by bending. [but see Cosson and Gibbons] On the other hand, the ability of sea urchin sperm flagella to increase the asymmetry of flagellar bending waves at increased Ca++ concentrations, with no change in frequency or mean bend angle, is difficult to explain if curvature is regulating bending.

Computer simulations with curvature-controlled models, both the original version with pure curvature control [, see also Appendix 1] and an expanded version known as the “geometric clutch” [] have been able to replicate many examples of flagellar and ciliary motion. However, they have difficulty replicating effects of increased viscosity and decreased flagellar length [Brokaw, 2001]. They are particularly unsuccessful at reproducing bending in very short flagella [Brokaw, 2005], explaining arrested states, or reproducing localized shear oscillations. It does not appear that control of dynein activity by curvature is sufficient to explain all of the features of flagellar oscillation and bend propagation.

6. Flagellar oscillation may be based on a local mechanism for oscillatory sliding.

Oscillation resulting from curvature-controlled switching can be thought of as a global oscillatory mechanism, with moment balance during basal bend initiation influenced by the moment balance of the entire flagellum. It is completely inappropriate for explaining observations of localized oscillatory sliding. Observations of localized oscillatory sliding suggest that some feature of sliding, other than curvature, can cause switching between ON and OFF states of dynein.

6.1. Most theoretical modelling involving localized oscillation has been based on regulation by sliding velocity, because it is easy to develop models of motor enzyme function that produce a “suppressed ON state”, and these models can produce oscillatory sliding [Brokaw, 1975b, 1976]. Computer simulations of flagella incorporating switching by sliding velocity can produce planar and circular motion of very short flagella [Brokaw, 2002], but have not been successful in replicating bend propagation in full-length flagella against viscous resistances.

6.2. Evidence supporting sliding-based switching includes: Evidence for oscillatory sliding in the absence of bending: hyperoscillations (Sections III.2) and microoscillations (Section III.3). Evidence for oscillatory sliding in interbends (Section I.2.4) and Brokaw and Gibbons [1973]. Evidence for triggering of sliding initiation events by micromanipulation (Section I.6.4), although in experiments with intact axonemes it is difficult to separate effects of sliding or effects of bending. Evidence that elastic relaxation may precede a sliding initiation event, causing passive sliding that triggers active sliding in the same direction (Section I.5). A few observations where superimposed synchronous sliding modulates oscillation [Brokaw and Gibbons, 1973; Woolley and Vernon, 2002].

6.3. Arguments against sliding-based switching include: The ability of simple sperm flagella to allow large amounts of synchronous sliding with no apparent interference with normal bend propagation. Computer simulations indicate that self-organization of local oscillatory sliding is inadequate to generate bending wave propagation under realistic conditions of external viscosity.

6.4 It appears that neither curvature- based switching nor sliding-based switching is, by itself, a sufficient explanation for the control mechanisms responsible for oscillation and bend propagation by flagella. It  seems reasonable that the problems might be solved by some combination of these two switching operators, but so f ar no successful combination has appeared. One reason may be that curvature and sliding vary similarly in a simple bending wave. Neither parameter is appropriate for a direct control of the shear forces required in interbends, and neither type of control explains active arrrests.

7. Circumferential transfer of activation

Computer simulations [Brokaw, 2002] have confirmed the earlier suggestion [Brokaw, 1972b] that uniform doublet metachronism can arise spontaneously in models of flagella in which active sliding on each doublet is regulated by its curvature, if nothing is done to force planar bending. Generation of helical bending waves by these models do not require any activating signal, other than induced curvature, to propagate from doublet to doublet around the axoneme, but that does not prove that flagella do not use such a signal.

These curvature-controlled models were unable to model successfully the circling movement of short nodal cilia. Much more successful modelling of the movement of nodal cilia was obtained with models in which active shear force was regulated by sliding velocity [Brokaw, 2005]. These studies suggest that sliding initiation events involving near-synchronous activation all along the length of each doublet are appropriate for generating the circling movement of short nodal cilia. Active sliding on a group of doublets appears to induce passive sliding of an adjacent doublet, leading to circumferential transfer of activation. It is easy to explore computer models where this transfer can occur, but difficult to demonstrate its occurrence in real cilia.

An unexpected finding was the role for a time delay in the process of regulating active shear force by sliding velocity. With no time delay, the models produced planar bending, although the direction of the bending plane, in the absence of constraints, moved around randomly. When a time delay process was included, and raised above a critical value, there was an abrupt change to a stable, three-dimensional circling pattern. It was speculated that time delay in the regulation might prevent the near-synchronous activation of 4 or 5 doublets on one side of the axoneme that is appropriate for planar bending.

V. Epilogue

Most of the ideas in this review have been generated by intensive study of a very small number of examples of flagellar and ciliary movement. The universe of flagellar movements is much wider, and includes examples that are very difficult to interpret in terms of bends, interbends, and sliding initiation events. Some sobering examples are described in a recent paper by Vernon and Woolley [1999].

 

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