A Model for Flagellar Motility

A Model for Flagellar Motility Charles B. Lindemann and Kathleen S.Kanous

Department of Biological Sciences, Oakland University, Rochester, Michigan

48309

Experimental investigation has provided a wealth of structural, biochemical, and physiological information regarding the motile mechanism of eukaryotic flagellalcilia. This chapter surveys the available literature, selectively focusing on three major objectives. First, it attempts to identify those conserved structural components essential to providing motile function in eukaryotic axonemes. Second, it examines the relationship between these structural elements to determine the interactions that are vital to the mechanism of flagellarlciliary beating. Third, the vital principles of these interactions are incorporated into a tractable theoretical model, referred to as the Geometric Clutch, and this hypothetical scheme is examined to assess its compatibility with experimental observations. KEY WORDS: Flagella, Cilia, Motility, Dynein, t-Force, Axoneme, Oscillator, Molecular motors, Motor proteins, Microtubules.

1. Introduction The eukaryotic flagellum, with its ‘‘9 + 2” internal arrangement of microtubules (MTs), is one of the most curious of all biological constructions. The axoneme, the core of all eukaryotic flagella and cilia, serves in innumerable capacities. It provides motility or other motive force for organisms that range from one-celled algae to human beings. However, throughout its vast array of naturally developed applications, the flagellar axoneme has maintained a remarkably consistent design. The basic arrangement of nine peripheral doublet MTs interlinked by connecting protein strands and surrounding a central pair of MTs forms the flagellar template. Certain flagellar adaptations may lack one or more components, whereas other modifications involve the addition of accessory elements, but by and large these variations

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appear to originate from the standard flagellar configuration. Perhaps most noteworthy is the preservation of the spatial relationship between the axonemal MT components. This strict conservation of geometrical form suggests that the spatial organization of the axonemal elements is integral to flagellar functioning. The first goal of this chapter is to examine some of the variations in form and function that may provide clues to flagellar operation. Because the basic axonemal structure is common to both eukaryotic flagella and cilia, the terms flagella and cilia will be used interchangeably, and information garnered from studies conducted on either form will be included when applicable. Where pertinent information is available, the nature of the dynein-tubulin motor mechanism will also be discussed. Additionally, experimental findings that may shed light on the regulation of this motor will be examined. Finally, we will attempt to consolidate what is currently known into a plausible scheme to elucidate how the flagellar axoneme functions.

II. Structural Components of the Eukaryotic Flagellum A. Basic Axoneme Figure 1 illustrates the component parts of the eukaryotic flagellar axoneme. Nine doublet MTs (each consisting of a semicircular B MT attached to a round A MT) encircle a pair of centrally located single MTs. A central sheath, consisting of two C-shaped projections along each central MT (Warner and Satir, 1974), and a central “bridge” of electron-dense material (Olson and Linck, 1977) hold the central pair MTs together into what is sometimes referred to as the “hub” of the axoneme. Spokes are connected to the A MT of the outer doublets and converge toward the central hub. The spokes of most flagella repeat in a triplet pattern along the axoneme, with a major repeat interval of ~ 9 0 - 1 0 0 nm (Warner and Satir, 1974; Summers, 1975; Witman et al., 1978; Goodenough and Heuser, 1985). Isolated spokes appear straight and unbending when viewed in either negatively stained or freeze-fractured preparations (Olson and Linck, 1977; Goodenough and Heuser, 1985). Additionally, when the axoneme is fractured, bent, or distorted, the spokes are not observed to elongate, but the connection of the spoke head to the hub detaches instead (Warner and Satir, 1974; Summers, 1975; Lindemann and Gibbons, 1975; Olson and Linck, 1977; Goodenough and Heuser, 1985; Lindemann et al., 1992). Protein linkages (nexin links) interconnect the nine outer doublets, stabilizing the outer circular arrangement (Stephens, 1970). The nexin links extend from a point on the A MT, near the inner dynein arm in register with the

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FIG. 1 The eukaryotic flagellar axoneme. Structures commonly found in the typical axoneme are labeled on a silhouette diagram traced from an electron micrograph. The outer doublets. arranged in a ring of nine, each possesses an inner and outer row of dynein arms. In many flagella, doublets 5 and 6 are permanently bridged. prohibiting interdoublet sliding between these doublets. Each of the outer doublets is also linked to its neighbors by nexin links. The outer doublets are connected to the central pair by a series of wagon wheel-like spokes that interact with the axonemal “hub.” Some flagella have demonstrated the existence of a stable connection between outer doublets 3 and 8 that includes the central pair and roughly partitions the axonerne into two unequal “halves.” The flagellar beat is in a plane perpendicular to this partition as indicated by the double-headed arrow.

first spoke of each triplet repeat, to the B MT of the adjacent doublet (Dallai et al., 1973: Warner, 1976; Olson and Linck, 1977; Witman et al., 1978). Unlike the spokes, which detach and reattach, nexin links have been observed to stretch many times their resting length (Dallai et a/., 1973; Warner, 1976: Olson and Linck, 1977; Goodenough and Heuser, 1989). Tryptic digestion of these connections allows sliding disintegration of the axoneme (Summers and Gibbons, 1971, 1973; Lindemann and Gibbons, 1975; Sale and Satir, 1977). When a flagellum bends, the bends are mainly planar in a plane perpendicular to the axis of the central pair (Afzelius, 1961; Gibbons, 1961; Tamm and Horridge, 1970; Gibbons et al., 1987), as indicated by the doubleheaded arrow in Fig. 1. A number of structural factors contribute to the planar beat orientation. If there is no central pair complex (as in the 9 + 0 configuration), a helical wave pattern is observed (Gibbons er al., 1985;

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CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

Ishijima et al., 1988). Another important feature is the ability of the spokes located in the plane of the flagellar bend to change position by detaching and reattaching (“jumping”) at the hub connection (Warner and Satir, 1974). Additionally, there is strong evidence that spokes connecting the central pair to doublets 3 and 8 may not be as free, and instead form a stable midline “partition” that bisects the axoneme (Afzelius, 1959; Fawcett and Phillips, 1970; Lindemann et al., 1992; Kanous et al., 1993). Although the presence of this partition is not yet confirmed as a universal characteristic of flagella and cilia, prior evidence derived from sliding disintegrations points t o the possibility that this is a general characteristic of the axoneme (Tamm and Tamm, 1984; Sale, 1986). Some flagella also exhibit a permanent bridge between doublets 5 and 6 (Afzelius, 1959; Gibbons, 1961; Olson and Linck, 1977), precluding interdoublet sliding at that location and thereby inhibiting the formation of bends in the axis parallel to the central pair. Dynein acts as the molecular motor to power the movement of eukaryotic flagella. First isolated and characterized by Gibbons (Gibbons and Rowe, 1965), the dynein motor molecules (dynein “arms”) are composed of either two or three heavy chains, each with a globular “head” attached to a stalklike projection. The head contains the ATPase site, and the stalk is fixed to the A subtubule by way of an intermediate chain that binds t o tubulin. The dynein head is capable of attaching to the B subtubule of the adjacent doublet (“bridging”). In the presence of Mg-ATP, these arms translocate one doublet relative to its neighbor. In an intact flagellum, interdoublet sliding is impeded at the flagellar base by a centriole or basal body. The nine axonemal elements are permanently linked in a circle at the centriole/ basal body, thwarting translocation of one relative to another. This restraining mechanism results in flagellar bending as the force produced by the dynein arms exerts torque against the basal anchor. Each A subtubule bears two types of dynein arms, inner and outer arms (Fig. 2). Both inner and outer arm dynein are capable of driving microtubule sliding (Gibbons and Gibbons, 1973; Hata et al., 1980; Kamiya and Okamoto, 1985; Mitchell and Rosenbaum, 1985; Okagaki and Kamiya, 1986; Paschal et al., 1987; Kagami et al., 1990; Kurimoto and Kamiya, 1991; Smith and Sale, 1991; Kagami and Kamiya, 1992). However, the presence of outer arms generally results in a faster rate of sliding (Gibbons and Gibbons, 1973; Hata et al., 1980; Mitchell and Rosenbaum, 1985; Brokaw and Kamiya, 1987;Kurimoto and Kamiya, 1991;Hard et al., 1992) while imparting greater driving force (Oko and Clermont, 1990; Minoura and Kamiya, 1995). Additionally, the lack of outer arm dynein does not prevent motility. Inner arm dynein, on the other hand, presents a more complex contribution to flagellar activity, probably due to the existence of three discrete subforms of inner arm dynein (Piperno er al., 1990) that alternately repeat along the A subtubule (Goodenough and Heuser, 1985). Unlike the optional presence of outer

FLAGELLAR MOTILITY

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DRC

LC Base

FIG. 2 Structure of the outer doublets. This diagram attempts to incorporate information garnered from a number of sources into an overview of the structures associated with the axonemal outer doublets. It must be understood that not all details are (or can be) represented within one single diagram. Most of the available structural evidence has been obtained from studies on Clilnmvdornonos, and therefore the SI and S2 spoke pairs have been included. whereas the S3 spokes (found in many cilia and Hagclla) have been omitted. The nexin links attach adjacent doublets from a point just distal to the spoke pairs (Goodenough and Heuser. 1989). with the same 96-nm repeat distance. The outer arms (bottom row) are composed of three dynein heavy chains (DHC) that repeat at 24-nm intervals. are anchored to the doublets with two dynein intermediate chains (IC). and are associated with numerous dynein light chains (LC) (only three of which are shown) (Witnian. 1992). On the other hand, the inner arms (upper row) repeat in a dyad, dyad, triad pattern, with the dyads connected at roughly the same area as the spoke attachments. The dyad associated with spoke S2 is also in close proximity to the protein complex referred to as the dynein regulatory complex (DRC). found on the face of the doublet between the dynein rows (Piperno ef NI., 1992; Mastronarde et nl., 1992; LeDizet and Piperno, 199Sa). The dynein light chains associated with the inner arms are not shown. Both the inner and outer dynein at-ms generally angle baseward from their doublet attachment (Avolio er d.,1984) and evidence suggests their power stroke pulls the N + 1 neighbor tipward. Points of possible regulation have been identified in the DRC. the dynein light chains. the dynein heavy chains. and the nexin links (see text).

arm dynein, those axonemes missing two or more types of inner arm dynein appear immotile (Okagaki and Kamiya, 1986; Kamiya et al., 1991; Kato et 01.. 1993). These observations suggest that the inner and outer arms play differcnt roles in producing the flagellar beat. The axonemal dimensions are highly conserved along with the structure of the outer doublets and central pair. This maintenance of size and composition dictates that interdoublet spacing and microtubule sliding displacement must also be highly conserved. Under the premise that this strict preservation of certain features may be necessary for the operation of the

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CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

flagellar beating mechanism, examination of the variations that nature has permitted on this basic theme are considered next because they provide some interesting insights.

6.Variations on a Theme

+

Naturally occurring variants of the 9 2 axonemal pattern are occasionally seen that have not experienced a complete loss of function. The 9 + 0 pattern found in the sperm flagella of the Asian horseshoe crab (Ishijima et al., 1988) is perhaps the most striking variation. The waveform is more helical (less restricted to one bending plane), but the flagella retain motility. Although it could be argued that such evolutionary departures may have developed a compensatory mechanism to replace the central pair function, ample evidence has been procured demonstrating motility in both normal flagella that have extruded the central pair microtubules (Hosokawa and Miki-Noumara, 1987) and central pair-deficient mutations (Phillips, 1974; SchrCvel and Besse, 1975; Prensier et al., 1980; Gibbons et al., 1985; Brokaw and Luck, 1983; Ishijima et al., 1988). Although it does not inhibit motility, the absence of the central pair does apparently impair the ability to maintain a planar flagellarkiliary beat. This waveform variance could be a result of the incomplete partition because the central pair hub complex is missing from the normally stabilizing 3-central pair-8 structure. This presents an additional argument for the role of the bisecting partition in the maintenance of a normal planar beat. Experiments utilizing both rat and bull sperm confirm that some mammalian sperm axonemes are divided into two halves by this partition, as illustrated in Fig. 3 (Lindemann et al., 1992; Kanous et al., 1993). This feature, initially recognized in simpler flagellakilia (Afzelius, 1961; Tamm and Tamm, 1984; Sale, 1986), has been conserved, even as flagella increased in size and stiffness. In fact, rat sperm yield the greatest percentage of intact partitions (of the flagella studied), suggesting that the partition was reinforced as the flagellum was evolutionarily modified to increase its size. The 9 + 0 axonemal configuration also implies that the spoke apparatus may not be essential to the fundamental mechanism generating the flagellar beat. This is also supported by the induction of motility in spoke-free flagellar mutants (SchrCvel and Besse, 1975; Luck et al., 1977; Huang ef al., 1982; Brokaw et al., 1982; Gibbons et al., 1985). However, these cells usually demonstrate both altered motility (Huang etal., 1982) and reportedly fragile axonemes (Goldstein and SchrCvel, 1982; Gibbons et al., 1985). Therefore, as in the case of the central pair, the spokes are implicated as contributing stability to the axonemal structure yet appear less than crucial to basic motile functioning.

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9.1.2 FIG. 3 The central partition of a rat sperm. The structure of the central partition was reconstructed from electron micrographs of disintegrating rat sperm axonemes. Using two different methods to disrupt the rat sperm flagellum, the microtubule axoneme can be made to come apart by interdoublet sliding. When pH 9.0 extraction was utilized, elements 4-7 were expelled, as shown in the upper inset. Prolonged ATP reactivation of Triton X-100-extracted models at 37°C caused the pattern of sliding disintegration depicted in the lower inset. In those cells, elements 1. 2, and 9 were expelled, emerging as a loop from the head-tail junction. In either case. the complex formed by elements 3, 8, and the central pair remained behind as a stable feature of the axoneme. Reprinted from Journal of Cell Science (Lindemann el al., 1992) with permission.

Attention has focused on the possible role of the spokes in activating inner arm dynein through the cluster of proteins called the dynein regulatory complex (DRC) (Piperno et al., 1992, 1994). The DRC is located on the A subtubule near or at the inner arm dynein attachment (Mastronarde et al., 1992; Piperno et al., 1992, 1994; Gardner et al., 1994; LeDizet and Piperno, 1995a) as illustrated in Fig. 2, and appears to be a factor in repressing dynein activity. The presence of radial spokes can counteract the inhibitory effect of the DRC on inner arm dynein (Smith and Sale,

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CHARLES 6.LINDEMANN AND KATHLEEN

S. KANOUS

1992). Inner dynein arms exposed to spokes undergo a modification that persists even following the removal of the spokes (Smith and Sale, 1992). This points to the ability of the spokes to convey an “activating” signal to the inner dynein arms that coordinates the beat cycle. Observations that the central pair MTs appear to rotate during the beat cycle in certain axonemes (Omoto and Kung, 1979,1980: Omoto and Witman, 1981;Kamiya et al., 1982) have led to hypotheses describing a “distributor” scheme that uses the central pair to selectively activate particular doublets as a form of motility control (Omoto and Kung, 1979,1980; Huang et al., 1982; Huang, 1986).This selective activation of dynein-driven MT sliding may be involved in the flagellar motility of some species. However, those spokeless mutants that also lack an intact DRC are “derepressed” and capable of exhibiting coordinated beating (Porter et al., 1992; Piperno et al., 1994). From experimental evidence that protein kinase inhibitor improves motility in spokeless mutants, others surmise that the spokes regulate dynein activity by suppressing a CAMP-dependent protein kinase mechanism (Howard et al., 1994). In either case, a fairly complex interaction between the spokes and inner dynein arms seems adequately established. Evidence for derepression and kinase A regulation supports the premise that the primary system generating the flagellar beat can function without a spoke-based activation scheme. However, it also appears very likely that the spoke-dynein interaction plays a pivotal role in regulating or modulating the basic beat. This ability to modify the flagellar beat is essential for adaptations such as chemotaxis, phototaxis, and the capacitation/hyperactivation of mammalian sperm. Nature’s evolutionary diversions, resulting in larger flagellar structures that still maintain the basic axonemal apparatus, contribute additional information from a structural/functionaI perspective. One solution for creating a larger cilium that can basically perform the same task as a small cilium (only on a larger scale), without sacrificing velocity, was to unite a number of basic axonemes side by side (Sleigh, 1962). Such “compound” or “macro” cilia are widely observed in nature (Sleigh, 1968, 1974). To harness the power of multiple axonemes most beneficially in a compound cilium, each individual axoneme is oriented such that they all beat in the same plane, as shown in Fig. 4. In the compound cilia of the Ctenophore Beroe, each axoneme comprising the macrocilium is linked t o its neighbor by way of protein connections between doublet 8 of one axoneme and doublet 3 of the adjacent one, cementing them together in lateral rows (Afzelius, 1961; Tamm and Tamm, 1981, 1984). This arrangement, which is depicted in Fig. 4, substantiates that the permanent bonding of these elements between neighboring axonemes does not impair the basic beating mechanism. It also introduces the possibility that the 3-central pair-8 elements may be permanently interconnected because they do not need to slide relative to one another during the course of a normal beat. If this feature is actually

FLAGELLAR MOTILITY

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FIG. 4 The construction of compound cilia. Thc stability of the partition formed by doublets 3 and 8. with the central pair, appears to form the basis for compound cilia assembly. A s illustrated in the diagram, many adjacent axonemes can be functionally linked by 340-8 connections while still permitting individual axonemes to retain their basic function. This arrangement was first described by Afzelius (lY61). Work by Tamm and Tamm (1984) established the stability of the 3-central p a i r 4 linkages in these structures by examining the pattern of microtubule sliding disintegration in the compound cilia of Beroe.

incorporated into the flagellar beat mechanism, maximal sliding must consequently occur between the doublets that interact with this 3-central pair-8 partition. In other words, doublets 2-3-4 and 7-8-9 must account for 60% of the dynein bridge turnover. The results of Warner’s (1979) experiments looking at ATP turnover as a function of axonemal position also point to these as the most active bridge sites.

C. Special Adaptations in Mammalian Sperm The development of compound cilia was only one of nature’s methods to scale up to a bigger flagellum. The sperm of mammals, insects, and birds incorporate a single axoneme to propel substantially larger flagella. The fundamental axoneme is similar lo that of smaller, simpler flagella in both size and interelement spacing (Fawcett and Phillips, 1970; Pedersen, 1970; Linck, 1979). Although the central axoneme displays spatial similarities to simple flagellakilia, there have been discreet evolutionary alterations that may have functional significance. The A subtubule of each outer doublet stains darkly in mammalian sperm (Pedersen, 1970), a phenomenon not observed in simpler axonemes. Additionally, the outer arm dynein of mammalian sperm is not easily removable using simple high-salt extraction (Marchese-

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CHARLES 6.LINDEMANN AND KATHLEEN S. KANOUS

Ragona et al., 1987), an effective method in more rudimentary axonemes (Gibbons and Fronk, 1972; Gibbons and Gibbons, 1973; Piperno and Luck, 1979). These incongruities caution that it would be an oversimplification to assume that the central axoneme itself has not been modified to accommodate an increase in flagellar size. Nevertheless, the basic proportions and structural composition of the basic axoneme appear to have been conserved. In addition to the aforementioned potential differences within the axoneme, an interesting pattern of indisputable modifications evolves allowing the increase in size. The predominant and most conspicuous flagellar modification is the presence of accessory MTs andlor non-MT auxiliary fibers contiguous with the basic nine outer doublets (Fawcett and Phillips, 1970; Fawcett, 1975; Baccetti, 1982; Dallai and Afzelius, 1993). The auxiliary fibers in some of the largest mammalian sperm (referred to as outer dense fibers; ODFs) can be as large as 260 nm in diameter, literally dwarfing the central axoneme (Phillips, 1972) . A cross section of a bull sperm axoneme illustrating the accessory structures is shown in Fig. 5. What was nature’s intended purpose for including these ODFs in the scaled-up version of the motile organelle? Although initially presumed to be contractile motor elements, originating as outgrowths of the outer doublets (Fawcett and Phillips, 1970), later biochemical studies have not successfully identified contractile proteins from isolated ODFs (Price, 1973; Baccetti et af., 1976; Olson and Sammons, 1980). Several investigators propose that the ODFs in mammalian sperm act to reinforce the structure, making the longer flagellum both stronger and stiffer (Phillips, 1972; Fawcett, 1975; Baccetti et af., 1976; Baltz et al., 1990). This view gains support from micromanipulatory techniques that yield a direct flagellar stiffness measurement at the bull sperm flagellar base 20 times greater than that of sea urchin sperm (Lindemann et af., 1973). The measured stiffness was also found to diminish along the flagellar length (Lindemann et af.,1973), corresponding to the fact that the ODFs taper toward the flagellar tip and fail to reach the endpiece (Telkka et af.,1961; Pedersen, 1970; Serres et af.,1983a). Motile human and bull sperm flagella demonstrate an increase in bend curvature as the bend propagates down the tail (Gray, 1958; Rikmenspoel, 1965; Serres et af., 1983b), where the ODFs progressively disappear. However, in sea urchin sperm, which are devoid of ODFs, the maximal curvature is achieved not far from the flagellar base (Gray, 1955; Gibbons, 1982). These motility characteristics implicate O D F stiffness as impacting the waveform of larger flagella. O D F size has been correlated to the length of mammalian sperm flagella, with the longest sperm generally containing the largest ODFs (Phillips, 1972; Baltz et af., 1990). Comparison of spermatozoa1 motility from a variety of mammalian species demonstrates that the achievable bend amplitude is basically inversely proportional to the magnitude of the dense fibers (Phillips, 1972;

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FIG. 5 Special features of the mammalian sperm axoneme. A TEM cross section of a bull sperm axoneme is displayed, with the outer doublets numbered in the same convention applied to other cilia and flagella. The presence of a fibrous (dense staining) outer sheath around the axoneme identifies the section as one from the flagellar principal piece. The outer dense fibers (ODFs) are attached to their respective doublet over much of their length, particularly in the principal piece region. These ODFs are largest at the flagellar base and taper away to a termination point part way down the principal piece. Reproduced from Kanous ei al. (1993) with permission.

Phillips and Olson, 1973). Regarding the strengthening ability of the ODFs, tensile strength measurements of large sperm flagella (which are generally more vulnerable to the killing effect of shear forces than shorter flagella) demonstrate that the ODFs account for an increasing proportion of overall tensile strength relative to the length of the sperm (Baltz et al., 1990). ODFs appear to have other functions in addition to their contribution as structural strengtheners and stiffeners. Studies show that the ODFs in

CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

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mammalian sperm are physically attached to the connecting piece at the flagellar base (Pedersen, 1970; Fawcett, 1975) as diagramed in Fig. 6. They are also attached to the outer doublets along much of their length (Lindemann and Gibbons, 1975; Olson and Linck, 1977), particularly in the distal end (Fawcett and Phillips, 1970). When the mammalian sperm axoneme is disrupted by proteolytic digestion, the doublets can be induced to slide apart with Mg-ATP. Upon inspection, it is generally found that the ODFs remain attached to the connecting piece and the extruded doublets (Olson and Linck, 1977; Lindemann and Gibbons, 1975; Lindemann ef al., 1992; Kanous et al., 1993). In simple flagella, the outer doublets must be anchored in a basal body or centriole to produce motility. In mammalian sperm, the distal centriole (which nucleates the development of axonemal MTs) disintegrates during spermatogenesis (Fawcett and Phillips, 1970; Woolley and Fawcett, 1973). This leaves the ODF-connecting piece complex as the sole basal anchor for the entire axonemal-periaxonemal structure. Figure 6 illustrates this concept. Therefore, in the mammalian sperm, force produced by interdoublet sliding is transferred to the ODFs and thereby transmitted to the basal anchor-connecting piece. The peripheral location of the ODFs amplifies the amount of torque that can be developed between

Basal anchor Outer doublet

I

T 1 Striated columns

I

Central pair

FIG. 6 Force transfer in the mammalian sperm axoneme. A schematic, longitudinal view of a mammalian sperm is depicted. Unlike simple cilia and flagella. the basal body (distal centriole) of mammalian sperm flagella disassembles during development (Fawcett. 1975). leaving the doublets without a direct anchor to the flagellar base. The proximal centriole (PC) remains but is perpendicular to the flagellar shaft. However, the ODFs are securely anchored into the striated columns of the connecting piece, which forms a cap-like structnre at the flagellar base. In mammalian sperm the doublet attachment to the ODFs acts to supply the necessary basal anchoring that allows bend production. The doubletlODF connections also allow the dynein-tubulin interdoublet sliding force to be transferred to the ODFs. Because the distance between the ODFs can be considerably larger than the interdoublet distances, the flagellar force development acting over a larger working diameter produces substantially greater bending torque than would be possible with a simple axoneme. The ODFs and fibrous sheath also serve to stiffen and stabilize the axoneme. a necessary function in accommodating the greater torque development. Adapted from Lindemann (1996). Reproduced with permission.

13 ODFs (over that possible between outer doublets) due to the increased separation distance (which determines the lever arm length for torque production). In some mammalian sperm with extremely large ODFs, such as the ground squirrel, the separation distance between the ODFs becomes many times that of the isolated axoneme (Fawcett and Phillips, 1970). The curvature of the bending waves in large mammalian sperm is less than in smaller flagella. This requires each single bend to include a much longer section of the axoneme, thereby involving more dynein arms. The force contributing to bend formation is proportional to the number of dynein bridges pulling together. Consequently, the force developed to bend the flagellum in mammalian sperm must be greater. If this force is exerted across the longer lever arm provided by the ODFs, the torque (force X lever arm) is substantially magnified. Ultimately, the secret of the megaflagellum probably resides in this relationship (Lindemann, 1996). The ODFs allow a greater accumulation of dynein force plus an increased lever arm, which results in greater bending torque production. Simultaneously, ODFs provide additional stiffening to balance this enhanced force generation. This modified mammalian axoneme is additionally surrounded by a substantial sheath of mitochondria at the midpiece and a fibrous protein sheath at the principal piece (Fawcett and Phillips, 1970; Fawcett, 1975). Although simple invertebrate sperm possess a minimal mitochondria1 sheath, the fibrous sheath of the principal piece is unique to mammalian sperm (Fawcett, 1975). The presence of these supplemental exterior coverings may counteract the increased internal forces in large mammalian sperm, maintaining the integrity of an axoneme that might otherwise rupture. The feasibility of using one power source, provided by the central axoneme, to drive substantially larger mammalian sperm has been tested using a computer model (which will be discussed in more detail later in this chapter). When scaled to incorporate both the measured stiffness of bull sperm and the greater bending torque produced by ODF involvement, the model does in fact beat much like a bull sperm flagellum (Lindemann, 1996). FLAGELLAR MOTILITY

111. The Motor A. The Dynein ATPase The molecular motor dynein was first identified as an adenosine triphosphalase protein from KCl (0.1-0.6 M ) extracts of Tetruhymenupyriformis and isolated as 30 and 14s fractions using sucrose density gradient fractionation (Gibbons and Rowe, 1965). The ATPase activity of these fractions could be activated by either Ca2+or Mg”, with the 14s fraction more specific

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for Mg ion activation. Both dyneins were quite specific for ATP, hydrolyzing other nucleoside triphosphates at less than 10% of the ATP rate, and even ADP was only hydrolyzed 30% as rapidly (Gibbons and Rowe, 1965). Gibbons and Rowe (1965) speculated that dynein formed the “arms” of the axoneme, and experiments demonstrated that KCl extraction of 30s dynein coincided with the disappearance of the outer arm projections on the axonemal doublets (Gibbons, 1965; Gibbons and Fronk, 1972; Gibbons and Gibbons, 1973). KC1-extracted outer arm dynein, from Tetrahymena (Gibbons, 1965; Shimizu, 1975) or Triton X-100 stripped sea urchin sperm (Gibbons and Gibbons, 1973), was found to be capable of microtubular reattachment when the salt concentration was reduced. Using this method, it was demonstrated that removal of outer arm dynein reduced the beat frequency of Mg-ATP-reactivated sperm flagella (Gibbons and Gibbons, 1973), whereas reattachment could reinstate an increased beat frequency (Gibbons and Gibbons, 1976). Experiments such as these definitively established the axonemal arms as the location of the dynein ATPase, also confirming a role for dynein in the mechanism of flagellar motility. Furthermore, there exist outer arm-deficient Chlamydomonas mutants (oda) that beat at half the frequency of wild type (Brokaw and Kamiya, 1987). However, adding outer arm dynein (extracted from wild-type Chlamydomonas) to demembranated flagella of oda mutants increases their beat frequency to nearly that of the wild type (Sakakibara and Kamiya, 1989;Takada et al., 1992). Correspondingly, comparisons of ATPase activity between wild-type and oda mutants demonstrate that the activity of axonemes with outer arms was 5-12 times that of the arm-depleted mutant (Kagami and Kamiya, 1990). The ATPase activity of dynein can be facilitated (up to 30 times) by the presence of microtubules or outer doublets (Warner et af., 1985; Omoto and Johnson, 1986; Warner and McIlvain, 1986; Shimizu et al., 1989, 1992), much as the ATPase activity of myosin is facilitated by actin. Holzbaur and Johnson (1989) postulate that this ATPase activation is due to the microtubule effect of accelerating the rate of ADP release. Brokaw and Benedict (1968) established early on that there exists both a motility-dependent and a motility-independent rate of ATPase activity in intact axonemes. A number of studies have since confirmed a sliding-dependent enhancement of dynein ATPase activity (Gibbons and Gibbons, 1972; Penningroth and Peterson, 1986). A straightforward interpretation of motility-dependent ATPase activity could be based on the possibility that coordinated beating increases MT enhancement of dynein ATPase compared to nonmotile axonemes. Utilizing this simple viewpoint, the coordination mechanism of the beat cycle augments the opportunity for dynein-tubulin cross-bridge formation.

FLAGELLAR MOTILITY

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Dynein ATPase has been extensively investigated, and it is now known that axonemal dyneins constitute a variety of unique proteins. These proteins are all members of a larger group of related molecular motors found in association with the MT cytoskeleton and involved in myriad applications. In their functional, nondenatured state, dyneins are huge protein complexes composed of a number of individual polypeptides (Piperno and Luck, 1979), designated as heavy chains (DHC, 400-500 kDa), intermediate chains (IC, 55-125 kDa), and light chains (LC, =20 kDa) (see Fig. 2). Each dynein is composed of from one to three DHCs and a variable number of ICs and LCs (Porter and Johnson, 1989). The basic form of each dynein arm consists of two or three globular “heads” connected by a “stalk” or “stem” to a common base attachment on the A tubule of the outer doublet. The DHCs make up the heads and a portion of the stems and contain the ATP binding sites (Johnson and Wall, 1983; Shimizu and Johnson, 1983; Pfister et al., 1984; Pfister and Witman, 1984). Each globular head is attached to a stalk composed of an a-helical portion of the DHC (Mitchell and Brown, 1994; Wilkerson et al., 1994).The DHC portion of the stalk does not bind directly to the A tubule but is anchored by an attached IC protein of the dynein complex (King and Witman, 1990; King et al., 1991, 1995; Witman, 1992; Mitchell and Kang, 1993; Wilkerson et al., 1995). The reader may refer to Fig. 2 for an illustration of the structure. The function of ICs in the ATP-insensitive, structural coupling of dynein to the A tubule is still not clear, although there is evidence for a role in attachment and localization (King and Witman, 1990; King et al., 1991; Gagnon et al., 1994). Immunoelectron microscopy was used to localize 78and 69 (70?)-kDa ICs to the base of Chlamydomonas outer arm dynein (King and Witman, 1990). A direct association of IC78 and IC69 has also been established (King et al., 1991,1995).The tendency for IC78 to interact with a-tubulin in an ATP-insensitive manner (King et al., 1991) and its recent identification as a microtubule-binding protein (King et al., 1995) suggest that IC78 plays a role in outer dynein arm attachment to the A tubule of the outer doublets. Certain outer arm-deficient Chlamydomonas mutants ( o d d and o d d ) require the addition of a 70-kDa polypeptide (IC69?) to facilitate attachment of isolated 12s and 18s outer arm dyneins to the outer doublets (Takada and Kamiya, 1994). This 70-kDa fraction is present in wild-type and other oda mutants and forms a pointed structure on the A tubule. Experiments (Takada et al., 1992) had shown that the complete three-headed Chlamydomonas outer arm dynein could combine with o h axonemes, although the separate 12s and 18s dyneins could not, Takada et al. speculated that a functional component necessary for reassociation was missing. In an even earlier study (Mitchell and Rosenbaum, 1986),monoclonal antibody examination found that anti-70 kDa did

16

CHARLES

B. LINDEMANN AND KATHLEEN S. KANOUS

not comigrate with 18s dynein following sucrose gradient extraction. The 70-kDa intermediate chain had dissociated from the 18sdynein and instead was part of a smaller protein aggregate. It could be deduced from these results that the 70-kDa IC is necessary for proper attachment and localization of the outer dynein arms, and this protein can either be part of the extracted outer arm dynein or removed by certain extraction methods. Dynein LCs have been identified as sites of CAMP-dependent phosphorylation (Hamasaki et af., 1989, 1991; Tash, 1989; Stephens and Prior, 1992; Salathe et af., 1993; Barkalow et al., 1994; Satir et al., 1995). Some LCs are associated with the DHCs (Pfister et al., 1984; Mitchell and Rosenbaum, 1986; Witman, 1992; King and Patel-King, 1995) and are believed to play a part in modulating motor function. A recently investigated LC that binds Ca2+ and is associated with the y-DHC of Chfamydomonas outer arm dynein demonstrated significant homology with calmodulin (King and Patel-King, 1995). Based on its in vitro affinity for 3 X lo-’ M Ca’+, it was speculated that this LC may modulate Ca”-mediated dynein activity (such as waveform symmetry and the flagellar reversal of photophobic responses). LCs have also been localized with the ICs at the A tubule connection (Mitchell and Rosenbaum, 1986; Stephens and Prior, 1992; Witman, 1992) and are thought to regulate dynein arm flexibility or interaction (Stephens and Prior, 1992). A 28,000 MW light chain (p28) has been detected that associates with a subset of Chfamydomonasinner arm D H C (LeDizet and Piperno, 1995a,b). ida4 mutants are missing the p28 protein (encoded by the IDA4 gene) (LeDizet and Piperno, 1995b). The specific DHC subset that complexes with p28 is also missing, suggesting that p28 participates in either the binding of these arms to the axoneme or their assembly (LeDizet and Piperno, 1995a,b). Although morphologically similar, comparison of inner and outer dynein arms demonstrates both structural and functional diversity. Dynein outer arms possess two heads (dyads) in many species (Le., pig tracheal cilia and sea urchin, bull, and trout sperm), whereas three-headed (triad) versions are common in protists (i.e., Chfamydomonas,Tetrahymena,and Paramecium) (Johnson and Wall, 1983; Shimizu and Johnson, 1983; Holzbaur and Vallee, 1994). In either case, the outer arms maintain one form throughout the axoneme, repeating at 24-nm intervals (Warner et al., 1985; Warner, 1989). Dynein inner arms also display dyad and triad formations but combine both varieties on each axoneme in a pattern of two dyads to each triad (Warner et af., 1985; Goodenough and Heuser, 1985, 1989). These arms maintain a periodicity of 24, 32, and 40 nm (a total 96-nm repeat), in agreement with the radial spoke repeat pattern (Warner et af., 1985; Goodenough and Heuser, 1985). The pictorial representation of the relationship of the dynein arms on a doublet as presented in Fig. 2 is modeled on accumulated data obtained from studies on Chlamydomonas.

FLAGELLAR MOTILITY

17

B. The Dynamics of Dynein-Tubulin Sliding Dyncin powers the flagellar beat by translocating each outer doublet relative to its neighbor in a process known as “microtubule sliding.” Satir (1965, 1968) was the first to experimentally confirm that outer doublets of intact axonemes slide. He examined TEM fixed, serially sectioned beating cilia of Elliptio cornplanatus (freshwater mussel) to locate doublet termination points and found the MTs to be uniform in length, verifying that they do not stretch or contract. The development of a method to create detergentextracted “models” of cilia/flagella, which could be “reactivated” with MgATP to simulate the motility of their intact counterparts, permitted induced biochemical modifications within the axoneme and examination of the effects on flagellar motility (Gibbons and Gibbons, 1972). Summers and Gibbons (1971, 1973) demonstrated that brief tryptic digestion of detergentextracted (modeled) sea urchin sperm axonemes, followed by application of Mg-ATP, resulted in axonemal disintegration by longitudinal sliding of outer doublets. In the absence of the basal body, the doublets were observed to telescope up to eight times the original length of the flagellar fragment. MT sliding in this manner implied that the dynein arms are in a unipolar arrangement around the axoneme. The extent to which the MTs were observed to telescope demonstrated that each doublet pair could participate in sliding (except the 5-6 pair. which is permanently bridged, as described earlier). Sale and Satir (1977) conclusively identified the direction and order of MT sliding. The outer doublets were recognized to be sliding baseward on their higher numbered neighbor (based on the numbering system of Afzelius, 1959). This axonemal organization has proven t o be a uniform attribute thus far. As a consequence of this arrangement, the dynein arms on doublets 1-4 would generate sliding to bend the flagellum in one direction, whereas those on doublets 6-9 work to bend it in the opposite. Although efforts to “see” how the dynein arms produce sliding have resulted in interesting findings, the evidence has not been conclusive. Micrographs from the work of Goodenough and Heuser (1982,1985, 1989) with freeze-etch replicas (flagella that have been fast frozen during activity) suggest that, rather than bridging by way of the globular heads, dynein arms are linked to adjacent doublets through thin connections called “B links.” However, it is difficult to conceive of a mechanism capable of conveying lateral force through what appears to be such a slender thread of material. The axonemal dynein arms must exert force between adjacent doublets separated by a considerable distance (19-21 nm) (Warner, 1978; Goodenough and Heuser, 1982). It seems likely that some means of mechanical triangulation would be required to achieve this goal. A structural scheme with this conceptual advantage was proposed by Avolio et al. (1984) based on their own electron micrographs, whereby some dynein arms link

18

CHARLES B. LINDEMANN AND KATHLEEN

S. KANOUS

MTs by uniting the multiple globular heads into a triangular-shaped structure that angles baseward toward the higher numbered neighboring doublet. Although these two descriptions of dynein arm structure seem to be mutually exclusive, other studies demonstrate that conformational changes occur in the presence or absence of ATP (Witman and Minervini, 1982), and varied interpretations of dynein structural composition can be obtained depending on the angle of viewing (Witman and Minervini, 1982.) A substantial amount of information on dynein-tubulin interaction has been obtained utilizing either partially disrupted axonemes or isolated dynein in combination with MTs. The MT sliding kinetics of disintegrating axonemes reveals maximal free-sliding rates in the 12-18 pmls range (Yano and Miki-Noumura, 1980; Okagaki and Kamiya, 1986; Sale, 1986; Kurimoto and Kamiya, 1991). Estimates of sliding velocities in working flagella (proportional to shear amplitude X frequency) yield rates in the range of 10-19 pmls (Brokaw and Luck, 1983; Brokaw and Kamiya, 1987; Eshel and Gibbons, 1989). The sliding rate is sensitive to load, and a force-velocity relationship has been measured for dynein-tubulin sliding in sea urchin sperm (Kamimura and Takahashi, 1981; Oiwa and Takahashi, 1988). Functional dynein motors can be isolated by low ionic strength buffer dissociation or high salt extraction of flagella or cilia. These isolated dyneins, when adsorbed to a glass slide or coverslip, can translocate MTs or doublets applied to the glass surface in the presence of ATP (Paschal et a/., 1987; Sale and Fox, 1988; Vale and Toyoshima, 1988, 1989a; Vale et a/., 1989; Kagami et al., 1990; Hamasaki et al., 1991; Kagami and Kamiya, 1992; Yokota and Mabuchi, 1994). Reported MT translocation rates induced by dynein are quite high (3.5-5.6 pmls) (Paschal et a/., 1987;Sale and Fox, 1988) considering the inability to control the number of actively participating arms or their orientation (because MT translocation by dynein is unipolar). These velocities are higher than those reported for other motor proteins such as kinesin at 0.3-0.6 pmls (Vale et al., 1985; Vale and Toyoshima, 1989b; Sheetz, 1989; von Massow et al., 1989; Shirakawa et al., 1995). The rapid MT sliding produced by axonemal dynein is necessary to maintain the rapid beating of cilia and flagella, whereas other molecular motors, such as those driving chromosomal motility, can operate at ik the velocity (Vale, 1992). Additionally, the translocation rate does not appear to be directly dependent on the number of participating dynein arms. Using adsorbed dynein concentrations of 44 pg/ml, MTs would not even attach to the glass, whereas 50 pglml of dynein translocated numerous MTs at near maximal velocity (Vale ef al., 1989). Borderline critical concentrations of adsorbed dynein produced slower sliding velocities, most probably due to the tendency for MTs to pause more frequently during translocation (Vale and Toyoshima, 1989a) rather than a decrease in the actual speed of MT movement. When experiments were conducted in which dynein molecules were densely

19 adsorbed to glass and aligned with the same polarity (Mimori and Miki-Noumura, 1994), MT translocation rates were consistently higher (12 pm/s). When utilizing low concentrations ( 4 0 pg/ml) of randomly adsorbed dynein, longer MTs were translocated faster and over longer distances, most likely due to their increased potential for maintaining contact with randomly distributed dyneins (Vale and Toyoshima, 1989a). An earlier study (apparently using higher concentrations of adsorbed dynein) revealed that translocation rates were independent of MT length (Paschal et al., 1987), whereas a later study (Hamasaki et al., 1995a) demonstrated an initial velocity increase with increased MT length, which then reached a plateau. The experimental data imply that velocity is independent of the number of dyneins producing the force, beyond a certain critical limit. This concurs with observations that MT sliding rates in disintegrating axonemes do not change as sliding progresses, even though the number of dyneins involved in force production must change as the area of doublet overlap decreases (Takahashi et al., 1982). These results point to a threshold-type mechanism in which the minimal number of properly aligned dyneins necessary to bind the MT are capable of propelling it at near maximal velocity. A similar finding was observed involving kinesin molecules (Vale et al., 1989), in which MT translocation speed was independent of kinesin density as long as ATP was available at a saturating concentration of 1 mM. FLAGELLAR MOTILITY

C. Axonemal Dynein Diversity-Variations in Function Both outer arm dynein (Paschal et al., 1987; Vale and Toyoshima, 1988; Sale and Fox, 1988) and inner arm dynein (Kagami et al., 1990; Smith and Sale, 1991; Kagami and Kamiya, 1992; Yokota and Mabuchi, 1994) will translocate MTs in vitro. There is a reported difference (Vale and Toyoshima, 1989a) between the maximal translocation rates of 8-12 pm/s for Tetrahymena 22s outer arm dynein and 4 or 5 pmls for 14s inner arm dynein. 22s dynein was positively identified as outer arm by Ludmann et al. (1993); 14s is not conclusively inner arm dynein, although supportive evidence has been presented (Warner et al., 1985; Warner and McIlvain, 1986; Vale and Toyoshima, 1988). This concurs with higher sliding velocities observed in disintegrating axonemes possessing outer arms (Hata et a/., 1980: Okagaki and Kamiya, 1986; Kurimoto and Kamiya, 1991). As described earlier, three different inner arm dynein complexes alternate within each 96-nm section along the flagellar axoneme. This substantiates the existence of three forms; however, seven distinct subspecies of inner arm dynein have been identified in Chlumydomonas (Kagami and Kamiya, 1992). MT rotation during translocation has been attributed t o certain inner arm dyneins (Vale and Toyoshima, 1988; Kagami and Kamiya,

20

CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

1992), a function that may prove integral in ultimately determining the specific role inner arm dynein plays in flagellar/ciliary motility. In addition, differences in the inner dynein arms located in the proximal and distal areas of Chfamydomonas flagella have been reported (Piperno and Ramanis, 1991). Support can be found for the idea that inner arm dynein force production is negligibly affected by viscous resistance (Minoura and Kamiya, 1995), whereas outer arm functions change under increased viscosity (Brokaw, 1996). This inner arm immunity to viscous load exists even though internal and external resistances vary along the axoneme, such that the force produced by proximally located inner arm dyneins varies from the force produced in the distal portion of the axoneme (Asai. 1995). Although distributed over the length of the cilia (Moss and Tamm, 1987), variability in the localized sensitivity to calcium in Beroe has also been identified (Tamm, 1988), with the highest response residing in the basal region. This lengthwise axonemal inner arm dynein differentiation could also be related to the functions of bend initiation (in the proximal region) and bend propagation (distally) (Witman, 1992). There is also evidence that dyneins that bend the flagellum in each of the two planar bend directions may be different from each other or at least have different activation controls. The asymmetric beat stroke of many flagellakilia consists of two distinct bending waves, a more tightly curved principal (P) bend in one direction and a reverse (R) bend of lesser curvature in the opposite direction. This suggests that the axoneme is structurally asymmetric, with opposite halves of the axoneme active at different times during the flagellar/ciliary beat ( Wais-Steider and Satir, 1979; Satir, 1985). A significant difference between the forces producing opposite flagellar bends in sea urchin sperm has been observed (Eshel ef al., 1991). although the source of this disparity has not been established. Morphological asymmetries of Chlamydomonas axonemes have been identified but not explained (Hoops and Witman, 1983). The sliding of MTs on the 2,3,4 side of the rat sperm axoneme can be selectively suppressed using a pH 9.0 extraction, whereas the same procedure does not disable the 7,8,9 dynein bridges (Lindemann et af., 1992). pH sensitivity differences between the mechanisms generating R and P bends in sea urchin sperm have been recognized (Goldstein, 1979). A more recent study has discovered a Chfumydomonas mutation (bop2-1)that demonstrates (i) flagellar motility patterns similar to those of inner arm mutants (ii) a missing 152-kDa phosphoprotein, and (iii) ultrastructural, doublet-specific, radial asymmetry in the dynein inner arm region of the axoneme (King et af., 1994). When exposed to threshold levels of Ca2+,many flagellakilia exhibit either an arrest response (Walter and Satir, 1978; Gibbons and Gibbons, 1980; Sale, 1986; Stommel, 1986; Satir et af.,1991; Shingyoji and Takahashi, 1995) or a change in beating waveformlsymmetry (Miller and Brokaw,

FLAGELLAR MOTILITY

21

1970; Brokaw ef al., 1974; Brokaw, 1979; Brokaw and Goldstein, 1979; Bessen et al., 1980;Brokaw and Nagayama, 1985; Izumi and Miki-Noumura, 1985: Lindemann and Goltz, 1988). The Ca” arrest response usually leaves the flagellum at one extreme of the beat cycle rather than a straight, relaxed (equilibrium) position. Gibbons and Gibbons (1 980) proposed that calcium-induced quiescence (in reactivated sea urchin sperm) is not a totally passive state but rather an asymmetric activation of dynein arms on only one side of the axoneme. Sale (1985) credits calcium with the ability to override or bypass the normal activation mechanism, thus eliciting quiescence in dcmembranated sperm. The arrest position, in the principal bend direction, may result because the flagella are trapped at the end of the principal bend. Nickel ion addition arrests motility in cilia and flagella (Naitoh and Kaneko, 1973; Lindemann et ul., 1980; Larsen and Satir, 1991) and has been shown to block the flagellar Ca2+response (Lindemann and Goltz, 1988; Satir etal., 1991). Ni” also demonstrated the ability to block sliding between MT doublets 2 and 3 during bull sperm flagellar disintegration while allowing sliding between doublets 7 and 8 (Kanous et al., 1993). Mechanically manipulating Ni?+-arrestedbull sperm revealed that force production in one bending direction is selectively inhibited as shown in Fig. 7A (Lindemann et a/., 1995). The normal beat of bull sperm was altered when Ni” was added to ATP-reactivated cells. Flagellar bending became more and more asymmetrical because bending in one direction decreased progressively until the motility arrested with the flagellum curved in a sustained bend in the opposite direction (Lindemann et al., 1995). This not only implies that nickel selectively inhibits only the dynein bridges on one side of the axoneme but also that switching during normal beating depends on reciprocal action between the two halves of the axoneme.

IV. Regulation of Flagellar Motility A. Signal Pathways Two types of regulatory control are widespread (if not universal) attributes of eukaryotic flagella and cilia. First, both flagella and cilia can be turned on (activated) or turned off (deactivated) by phosphorylation/dephosphorylation of axonemal proteins. Second, the shape of the flagellar/ciliary wave can be altered to produce a more symmetrical (equal in both bend directions) or asymmetrical (lopsided, more pronounced in one direction than the other) beat. The activation/deactivation control has been linked to the cAMP/kinase A signaling pathway (Garbers et a/., 1971, 1973a,b; Morton

22

CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

A

Equilibrium

B

FIG. 7 Restoring a beat cycle in Ni2+-treated sperm. Spontaneous beating can be inhibited in ATP-reactivated, Triton-extracted bull sperm models by the addition of 0.4-0.6 mM nickel ion. The flagella cease moving, arresting in a curved endpoint of the beating pattern. (A) If these inhibited sperm are manipulated with a microprobe so as to bend the flagellum in the direction opposite to the prevailing curvature, the flagellum exhibits an active response to the probe. This active response is not elicited if the same flagellum is pushed in the same direction as the prevailing curve. (B) If the flagellum is pinioned and held in the position that triggers an active response, a pattern of repetitive beating can be reestablished in flagella following Ni2+treatment. Reproduced from Lindemann et al. (1995) with permission.

FLAGELLAR MOTILITY

23

eta/., 1974; Lindemann, 1978; Morisawa and Okuno, 1982; Morisawa et al., 1983, 1984; Opresko and Brokaw, 1983; Brokaw, 1984; Lindemann et a/., 1987; Brokaw, 1987; Ishida et al., 1987; Tash and Means, 1988; Tamaoki et al., 1989; Chaudhry et al., 1995). The modification of the beat waveform has been traced to a cytosolic Ca2+-mediatedcontrol (Miller and Brokaw, 1970; Brokaw et al., 1974; Brokaw, 1979; Brokaw and Goldstein, 1979; Bessen ef al., 1980; Brokaw and Nagayama, 1985; Lindemann and Goltz, 1988). These two control pathways make a variety of responses possible in the living cells.

6 . Responses in the Living Cell It may be beneficial to take note of the role that flagellarcontrol mechanisms play in nature. Gametes lack RNA to synthesize replacement proteins (parts of the living machinery), consequently the high metabolic rate required t o support flagellar motility ultimately leads to senescence (Norman et al., 1962). Therefore, it seems likely that the ability to turn off the motor mechanism during sperm storage could delay the period of effective motility to coincide with the opportunity to achieve successful fertilization. The flagella of preejaculatory sperm are quiescent in many species, becoming activated to motility only upon release/dilution just prior t o fertilization. This is true of sperm from invertebrates, such as sea urchin and tunicates (Lee ef al., 1983; Brokaw, 1984), as well as vertebrates, including fish (Morisawa et al., 1983; Morisawa and Ishida, 1987; Morisawa and Morisawa, 1988) and mammals (Morton et a/., 1974, 1979; Cascieri et al., 1976; Turner and Howards, 1978; Mohri and Yanagimachi, 1980; Wong et al., 1981; Chulavatnatol, 1982; Carr and Acott, 1984; Usselman et al., 1984; Turner and Reich, 1985). A sperm motility activation mechanism is triggered by various stimuli in different species. Sperm dilution into hypotonic (freshwater) or hypertonic (seawater) environments at spawning (which lowers K + and increases CAMP)activates flagellar motility in some fish and amphibians (Morisawa and Suzuki, 1980; Morisawa el af., 1983; Morisawa and Ishida, 1987: Christen et a/., 1987; M. Morisawa and Morisawa, 1988; S. Morisawa and Morisawa, 1990). Intracellular alkalinization after exposure to seawater stimulates sea urchin sperm motility (Nishioka and Cross, 1978; Christen et al., 1982; Lee et al., 1983; Shapiro e f al., 1985). In most mammals, mixing with seminal fluid (to lower Ca”. dilute an inhibiting factor, or contribute H C 0 3 - ? ) induces sperm flagellar activity (Morisawa and Morisawa, 1990). Once sperm have been activated, the duration of flagellar motility is usually fairly brief, ranging from seconddminutes in some freshwater fish (Ginsburg, 1963; Nelson, 1967; Okuno and Morisawa, 1982; Christen et al., 1987; Billard and Cosson, 1990) to hourddays in most mammals (Soderwall and

24

CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

Blandau, 1941; Green, 1947; Vandeplassche and Paredis, 1948; Tyler and Tanabe, 1952; Perloff and Steinberger, 1964; Doak et al., 1967; Thibault, 1973; Parker, 1984; Critchlow etal., 1989). It should be noted that the actual in vivo motility period is difficult to determine in mammals (and other animals in which internal fertilization takes place) because of the tendency for sperm to be stored in a virtually dormant state for various periods within the female reproductive tract (Thibault, 1973; Katz, 1983; Smith and Y anagimachi, 1990). The ability of a flagellated cell to change its beating waveform in response to external stimuli makes the observed behaviors of chemotaxis and phototaxis possible. A chemotactic waveform response of sperm flagella was first characterized in studies of Nereis, Arbacia (Lillie, 1913), and Tubuluria sperm (Brokaw et al., 1970; Miller and Brokaw, 1970). Exposure to compounds released from egg jelly induced a change in swimming direction by an asymmetry in flagellar beating. The flagellar bends in one beat direction became increasingly curved, biasing the overall beating curvature to one side and causing the sperm path to curve into a circular arc. This pattern of motility was later duplicated in reactivated sea urchin sperm by elevating intracellular Ca2+within the range of lo-’ to lo-‘ M (Brokaw e? al., 1974; Brokaw and Goldstein, 1979; Brokaw, 1987). The phototactic response (beat reversal) in wall-less Chlamydomonas mutants (Schmidt and Eckert, 1976), and the “mechanoshock” avoidance response of the green alga Spermatozopsis similis (Kreimer and Witman, 1994), were found to be dependent on the presence of at least M calcium. The “photostop” response of intact Chlamydomonas was found to require a minimum of 300 nM external calcium, with increased calcium inducing prolonged stop durations (Hegemann and Bruck, 1989). Ciliary beat reversal in Parameciitm was also shown to be triggered by increasing internal calcium levels (Naitoh, 1968, 1969; Naitoh and Kaneko, 1972, 1973), and the mutant Paramecium “pawn” (which does not exhibit beat reversal while intact) will demonstrate backward swimming in response to calcium when the membrane has been extracted with Triton X-100 (Kung and Naitoh, 1973). A calcium-induced change in waveform has been identified in Crithidia (Holwill and McGregor, 1976) and reactivated Chlamydomonas (Hyams and Borisy, 1978; Bessen et al., 1980) and Tetrahymena (Izumi and MikiNoumura, 1985) as well, thus demonstrating this calcium modification of waveform to be a fairly prevalent phenomenon in flagellakilia. The calcium response requires the presence of calmodulin (Rauh etal., 1980; Brokaw and Nagayama, 1985), which has been detected in cilia and flagella ( Jamieson et al., 1979; Gitelman and Witman, 1980; Jones et al., 1980; Feinberg et al., 1981; Ohnishi et al., 1982; Stommel et al., 1982; Gordon et al., 1983). Mammalian sperm also demonstrate modifications in both swimming pattern and flagellar waveform in response to physiological conditions en-

25 countered in the female reproductive tract (Katz and Yanagimachi, 1980; Katz, 1983; Suarez et af.,1983; Suarez and Osman, 1987; Shalgi and Phillips, 1988). Sperm undergo a transition from linear swimming to a nonprogressive tumbling form of motility that Yanagimachi (1981) dubbed “hyperactivation.” External calcium is necessary for the transition to hyperactivated motility (Yanagimachi and Usui, 1974; Cooper and Woolley, 1982; Fraser, 1987; White and Aitken, 1989). Suarez et af. (1993) demonstrated that Ca2+ enters the cell during the transition to hyperactivated motility and that the addition of calcium ionophores can trigger the same transition in intact sperm (Suarez et al., 1987). It is also possible to induce hyperactivationlike beating in demembranated sperm models by adjusting the free Ca2+ levels in the reactivation mixture (Lindemann and Goltz, 1988; Mohri et af.,1989; Lindemann et al., 1991b). Like the chemotaxic responses of invertebrate sperm, hyperactivation may serve to localize sperm in the vicinity of the cumulus oophorus by terminating progressive swimming, thereby causing sperm to accumulate near the egg. At its most severe, the flagelladciliary response to high levels of calcium ion is a conformational “arrest” in one extreme curvature of the beat cycle. In sea urchin sperm, flagella take on the form of a “candy cane,” with a sharp bend at the proximal end of the flagellum (Gibbons, 1980; Gibbons and Gibbons, 1980). In Mytifus gill cilia, the arrest is also a curved, hooklike configuration that is similar to the end of the recovery stroke (Tsuchiya, 1976, 1977; Waiter and Satir, 1978; Wais-Steider and Satir, 1979; Satir et al., 1991). In rat and mouse sperm, the arrest condition resembles a fishhook, with the most severe bending occurring in the middle piece (Lindemann et a/., 1987, 1990, 1992; Lindemann and Goltz, 1988). This calcium arrest configuration does not appear to involve permanent “rigor-like’’ crossbridge formation because arrested Mytifus gill cilia are capable of resuming a beat if mechanically stimulated by using a microprobe to bend the cilia in the direction opposite that of the arrest position (Stommel, 1986). FLAGELLAR MOTILITY

C. Underlying Mechanisms of Control The two flagellar regulatory responses, mediated through CAMPand Ca”, have been elusive to define at the structural/functional level. Many false starts have diverted the quest to identify the regulatory sites. The endeavor has been complicated by the axonemal localization of multiple Ca2+-binding proteins (Salisbury et al., 1986; Otter, 1989; Salisbury, 1989; King and PatelKing, 1995) and a plethora of intracelluiar phosphoproteins (Hamasaki et al., 1989; Stephens and Stommel, 1989; King and Witman, 1994; Chaudhry et a!., 1995).

26

CHARLES 6. LINDEMANN AND KATHLEEN S. KANOUS

Some significant progress has been made, in the past several years, toward identifying phosphorylation sites that appear to impact dynein activity (Pipern0 et af.,1981; Tash, 1989; Hamasaki et af., 1989,1991; King and Witman, 1994). Possibly the best candidate site of kinase A control currently identified is located on one of the dynein light chains associated with outer arm dynein (Barkalow et al., 1994). Phosphorylation at this site appears to modulate in vitro outer arm dynein-dependent MT translocation (Hamasaki et af., 1995b; Satir et af.,1995). As mentioned previously, the outer arms are not essential for beat coordination but do add power to the beat and increase its frequency (Hata et af., 1980; Mitchell and Rosenbaum, 1985; Okagaki and Kamiya, 1986; Kurimoto and Kamiya, 1991). In most flagella and cilia, CAMP-dependent phosphorylation results in an increase in beat frequency (Lindemann, 1978; Nakaoka and Ooi, 1985; Bonini and Nelson, 1988, Hamasaki et af., 1991), indicating that at least one of its actions is to augment both the speed and the power output of the beat. In what may be a related phenomenon, Hard’s laboratory demonstrated that newt respiratory cilia can be induced to exhibit two distinct states of motility (Weaver and Hard, 1985; Hard and Cypher, 1992; Hard et af., 1992). In both states the beat pattern is maintained, but the power output and beat frequency are biphasic. These ciliary axonemes function in two distinctly different modes of operation, one low output and one high output. This transitional behavior was initially induced by adjusting Mg-ATP concentrations and experimental temperature, although it was suggested that the transition to the higher beat frequency was also CAMP dependent (Hard and Cypher, 1992). Most significantly, Hard’s group demonstrated that conversion to the energetic mode was eliminated if the outer dynein arms were extracted, clearly establishing the role of outer arms in mediating the transition to the higher frequency condition (Hard et al., 1992). This transition between the two modes of motility has since been established to be under the control of CAMP-dependent kinase (R. Hard, personal communication). This links both the phosphorylation site and the motile response within the same experimental system. Similarly to the previous work (Gibbons and Gibbons, 1973; Brokaw and Kamiya, 1987), these findings suggest that outer arms contribute power to the beat without markedly affecting the beat cycle coordination. This corroborates the findings that the regulation site for flagellar power output resides with the outer arms (Hamasaki et af., 1991, 1995b). On the other hand, where outer arms are unnecessary for beating (serving as power amplifiers or auxiliary power sources), genetic dissection of the axoneme has demonstrated that the ability to beat is lost when all inner arm dyneins are dispensed with. Therefore, inner arms must be capable of carrying out all the phenomena necessary to initiate and perpetuate the

FLAGELLAR MOTILITY

27

beat cycle. If the initiation of MT sliding is a function of the inner arms, this would make them the most logical site for control of axonemal Ca2+bias. In both sea urchin (Gibbons and Gibbons, 1980; Okuno and Brokaw, 1981) and rat sperm (Lindemann and Goltz, 1988), the calcium response can be induced even when active beating has been blocked with vanadate. This finding presents an enigmatic situation. On the one hand, as noted earlier, ciliary/flagellar beat arrest seems to represent a switching failure at one extreme of the beat cycle. This view is supported by the demonstration of progressive lopsidedness in the flagellar beat at increasing Ca2+ concentrations. One would reason that the uneven activation of the bridge set on one side of the axoneme ultimately stalls the beat cycle when the dominant bridge set fails to disengage (or the opposing set fails to engage), causing the beat to arrest at one extreme of the beat cycle. The fact that the same flagellar configuration can slowly develop under vanadate-induced inhibition of beating is problematic to the basic view that flagellar arrest is the result of a switching failure. These events were reconciled by Brokaw’s “biased baseline” hypothesis (Brokaw, 1979; Eshel and Brokaw, 1987) contending that calcium ion controls the equilibrium position (or baseline) of nonbeating flagella. In other words, the beat, but not the baseline curvature, of the flagellum is selectively inhibited by vanadate. Therefore, the biased baseline concept suggests that one process is at work in controlling the beat, whereas an independent one controls the arrest formation of the candy cane or fishhook. In this view, the normal beating action is superimposed on the baseline curvature. In experimental support of Brokaw’s view, examination of Ciona, sea urchin, and ram sperm flagellar motility established that the observed asymmetric beating patterns were developed by the propagation of basically symmetric bending waves on a flagellum with a sharp static basal curvature (Brokaw, 1979; Eshel and Brokaw, 1987; Chevrier and Dacheux, 1991). This baseline curvature is probably maintained by a separate system within the axoneme that modifies the structural equilibrium. Because this function is relatively insensitive to vanadate, it could be presumed that the underlying mechanism is independent of the dynein bridges, which are the target of vanadate’s inhibitory action (Kobayashi et al., 1978; Gibbons et al., 1978). Examination of the literature documenting the action of vanadate as a dynein inhibitor suggests a possible resolution of the seemingly contradictory experimental observations mentioned previously. Low concentrations of vanadate (0.5-5.0 puM) are highly effective in blocking coordinated beating in demembranated cilia/flagella (Gibbons et al., 1978; Sale and Gibbons, 1979; Okuno and Brokaw, 1981; Penningroth, 1989). However, vanadate is considerably less effectual in completely blocking MT sliding or dynein ATPase activity, generally requiring 5-10 times greater concentration than that needed to suppress motility (Gibbons and Gibbons, 1980;

28

CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

Bird et af., 1996). Therefore, in cilia or flagella inhibited with less than 10 pM vanadate, it should be possible to have internal MT translocation and bend formation based on dynein-tubulin sliding. If the triggering mechanism for bridge switching is suppressed by vanadate inhibition, the residual sliding in the vanadate-treated axoneme would move the cilium/ flagellum to one beat end point, at which point the beating process would stall. There is a possible explanation for the aforementioned vanadate effect. If vanadate-complexed dynein heads are rendered dysfunctional at low vanadate concentrations, it would be reasonable to expect that most dynein would be complexed and thereby inhibited. However, some dynein should remain uncomplexed and therefore functional. In vitro studies of dynein-MT translocation demonstrate that high translocation velocities can be obtained with remarkably few dynein arms (Vale et al., 1989). Hence, in motility inhibition utilizing low vanadate concentrations, there may be adequate functional dyneins to translocate doublets and bend the flagellum most of the way to the end of a normal beat cycle. If the switching mechanism requires not only bending but a critical summated force production between the outer doublets, then decreasing the number of contributing dyneins reduces the summated force necessary to activate the switching mechanism. The Geometric Clutch mechanism (Lindemann, 1994a,b) states that the product of force X curvature is a key component of the switching mechanism. In this context, the inability of the internal force to reach the critical level (due to subminimal numbers of functional dyneins) results in the expected switching failure observed in vanadate-treated cilia and flagella. To validate the calcium regulation concept, it is necessary to demonstrate that Ca2+exerts a selective influence over which dyneins will dominate when the flagellum is passive. Studies have implicated Ca2+ in this role, either through direct application of calcium to induce asymmetric dynein sliding (Sale, 1986) or localized asymmetric bending (Okuno, 1986) or by using Ni2' as a probe (Lindemann and Goltz, 1988; Kanous et al., 1993) to block the calcium response. Once again, a key feature of dynein is its propensity to form bridges spontaneously and initiate sliding episodes. As discussed earlier, this capability is necessary to explain observed flagellar behavior, and it must be addressed in any analysis of axonemal functioning. The Geometric Clutch model includes a formulation for giving a bridgeformation advantage to the dynein arms on one side of the axoneme, with Ca2+modifying the bias on that side. Work by Sale (1986) can be viewed as supporting this hypothesis because he demonstrated a calcium-induced selectivity of MT sliding in disintegrating sea urchin sperm axonemes. Additionally, good candidates for Ca2'-sensitive sites have been discovered. Centrin (also known as caltractin), a Ca2'-responsive contractile protein,

FLAGELLAR MOTILITY

29

has been localized to the axoneme (Salisbury et al., 1986; Salisbury, 1989). It has been identified specifically to the D R C in association with the inner arms (Piperno et al., 1992) and affiliated with certain subsets of inner arm dynein heavy chains (LeDizet and Piperno, 1995a). If the distribution of calcium regulatory sites were bilaterally differentiated (with the set of inner arms that bend in one direction being more sensitive to calcium than the opposing set), the very type of bridge biasing predicted by the Geometric Clutch mechanism could exist under calcium concentration control. To date, there are several studies suggesting differences in the dyneins on opposite sides of the axoneme (Kanous et al., 1993; King et al., 1994; Lindemann et al., 1995). However, conclusive evidence to support this view has not yet been obtained. A compilation of studies provides overwhelming experimental testimony that the Ca2+response is subject to modulation by the CAMP-kinase A pathway (Nakaoka and Ooi, 1985; Izumi and Nakaoka, 1987; Bonini and Nelson, 1988; Lindemann et al., 1991a,b). Additionally, exposing Mytilus gill laterofrontal cirri to greater than physiological CAMP levels results in ciliary arrest at the end of the effective stroke, the opposite direction of the calcium-induced arrest (Sanderson et af., 1985). Consequently, it is likely that control via phosphorylation and/or calcium binding is involved in at least two, if not more, functional sites within the axoneme. Possible candidates for regulatory sites include the outer arm dynein light chains (Barkalow et al., 1994; Hamasaki et al., 1995b; Satir et al., 1995; King and Patel-King, 1995), outer arm heavy chains (King and Witman, 1994), the nexin links (Ohnishi et al., 1982), the DRC (Piperno et al., 1992), and the inner arms (LeDizet and Piperno, 1995a).

V. Coordination of the Beat Cycle A. Minimal Requirements for Beating The isolated flagellar axoneme is a self-contained mechanical oscillator. This fact was established by microdissection (Lindemann and Rikmenspoel, 1972a,b), glycerin extraction (Hoffman-Berling, 1955; Brokaw, 1968), and detergent demembranation of intact cells (Gibbons and Gibbons, 1972; Morton, 1973; Lindemann and Gibbons, 1975). Using detergent-extracted flagella, it was possible to define the minimal requirements for axonemal functioning without the interference of a plasma membrane. It was demonstrated that under the proper conditions, using a suitable pH and sufficient Mg-ATP concentration, the isolated flagellar axoneme was still a fully functional motile organelle (Gibbons and Gibbons, 1972). In light of this

30

CHARLES 8. LINDEMANN AND KATHLEEN S. KANOUS

evidence, the search to uncover the underlying mechanisms that generate flagellar beating was directed away from membrane potentialslionic signaling, and toward intrinsic structurallchemical components of the axoneme itself. The simplicity of the basic chemical requirements for beating must be qualified due to a number of observations indicating that the basic oscillator is sensitive to other contributing factors in addition to the Mg-ATP concentration. Most ciliary and flagellar beating will arrest in the presence of a sufficient (10-6-10-5 M ) Ca2+concentration (Satir, 1975; Satir and Reed, 1976; Tsuchiya, 1976, 1977; Walter and Satir, 1978; Wais-Steider and Satir, 1979; Gibbons and Gibbons, 1980; Sale, 1986; Lindemann and Goltz, 1988; Satir et al., 1991). Other reports also implicate increasing the free Mg2' concentration in generating an arrest-like response (Lindemann and Gibbons, 1975; Sale, 1985; Yeung, 1987). However, because it is difficult to control and monitor the effect increased Mg2+has on the free Ca2+concentration, it cannot be ruled out that the magnesium effect is actually due to a cross-interaction of Mg2' on the free Ca2' level. The calcium response itself is well documented and clearly modifies the performance of the flagellar oscillator. In addition to provoking outright arrest, the free Ca2+level can also bias the P and R bend contributions to the beat cycle, thereby altering the flagellarlciliary waveform (Miller and Brokaw, 1970; Naitoh and Kaneko, 1973; Brokaw et al., 1974; Holwill and McGregor, 1976; Brokaw, 1979; Brokaw and Goldstein, 1979; Okuno, 1986; Lindemann and Goltz, 1988). Another interesting avenue of investigation highlights the flagellar oscillator's response to alternate nucleotides, primarily ADP and ATP analogs. Although ATP is undisputively the natural fuel for the axonemal motor, ADP (another physiologically present nucleotide) has a powerful impact on the oscillation mechanism. Lindemann and Rikmenspoel (1973) first noted that the beat cycle of impaled, dissected sperm was facilitated by the inclusion of ADP in the external medium. ADP was observed to reduce the beat frequency of Triton X-100-extracted sperm models while improving the maintenance of a coordinated beat (Lindemann and Gibbons, 1975) and increasing amplitude/bend angle (Okuno and Brokaw, 1979). In recent studies of the dynein-tubulin cross-bridge cycle, accumulated evidence suggests that ADP lengthens the duty cycle of dynein by slowing down the bridge release step (Johnson, 1985; Omoto, 1989,1991). This action results in a slowing of the interdoublet sliding rate (Bird et al., 1996) but also serves to convert the hyperoscillation observed in paralyzed mutant Chlamydomonas to a form of undulation (Yagi and Kamiya, 1995). Additionally, although the presence of either ADP or ATP analogs hampered MT sliding velocity, their addition increased the extent of sliding disintegration possible in demembranated Tetrahymena (Kinoshita et al., 1995). A number of ATP

FLAGELLAR MOTILITY

31

analogs have been investigated to determine their effect on dynein activity (Shimizu, 1987; Inaba ef al., 1989; Omoto and Brokaw, 1989; Omoto and Nakamaye, 1989; Shimizu et af., 1989, 1991; Omoto, 1992). Some analogs found to be capable of inducing in v i m dynein-driven MT translocation (ATP,S and formycin 5’-triphosphate) could not elicit ciliary reactivation (Shimizu et a/., 1991). This suggests a number of possible differences between the dynein-mediated processes of MT translocation and axonemal motility, including a stricter substrate specificity for initiation of beating, a requirement of multiple motor participation (each with its own substrate specificity), or a greater sliding velocity/force production necessary than the analogs are capable of supplying (Shimizu ef al., 1991). Omoto et al. (1996) demonstrated that ribose-modified ATP analogs, as well as ADP, were capable of restoring motility to paralyzed Chlamydomonas mutants in the presence of millimolar ATP concentrations (motility could also be induced if the ATP levels were reduced below 50 p M ) . All the above results implicate cross-bridge cycle dynamics as having an impact on the oscillation mechanism. If the interpretation of ADP’s action is correct, a prolongation of the force-producing step (bridge attachment) facilitates the events that coordinate the beat cycle.

B. Mechanics of the Beat Cycle One of the most compelling features of the isolated flagellar axoneme is its sensitivity to mechanical stimulation. Isolated distal sections of bull or starfish sperm flagellum will not beat spontaneously, even if supplied with Mg-ATP. Nonetheless, if the isolated fragment is bent, using a microprobe, a pattern of repetitive beating can be triggered, which persists as long as the imposed bend is mechanically maintained (Lindemann and Rikmenspoel, 1972a; Okuno and Hiramoto, 1976). This behavior in isolated flagellar pieces can be explained if the imposed bend activates the dynein bridges that act to bend the flagellum in the direction opposite t o the imposed bend. Naturally, when the dynein-tubulin sliding episode terminates, the flagellum will snap back to its original position. If the equilibrium (original) position is controlled by the microprobe, then this original bend (which provoked the initial flagellar response) will again develop, and the events will repeat. This scheme can only explain the observed phenomenon if the episode of dynein-tubulin sliding can self-terminate. Kamiya and Okagaki (1986) demonstrated just such a self-terminating mechanism, a result of two adjacent MTs undergoing sliding in an axoneme bent beyond a critical limit. In an intact beating flagellum, it is likely that the action of one set of dynein bridges is sufficient to bend the flagellum beyond the activation trigger point of the opposing set. Therefore, action termination of the

32

CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

first set would relinquish control to the newly activated second set, and reciprocation could proceed without the need for external triggering. Ni2+ inhibits sliding of the doublets on one side of the axoneme (Kanous et af., 1993) and also blocks spontaneous flagellar/ciliary beating. The nickelinhibited cells retain the ability to reinstate a beat in response to micromanipulatory bending (Lindemann et af., 1980, 1995), but only if a microprobe is used to impose a bend in the direction normally produced by the inactivated bridges (see Fig. 7B). Based on experimental observations, Satir and co-workers proposed that each phase of the beat cycle is initiated or terminated by activation of a switch point to activate the opposing set of bridges (Wais-Steider and Satir, 1979; Satir, 1985; Satir and Matsuoka, 1989). The beat cycle of most cilia can be subdivided into two opposing phases, referred to as the effective and recovery strokes, each possessing fairly well-defined characteristics. The effective stroke is rapid and powerful (Rikmenspoel and Rudd, 1973) and often described as stiff or “oar-like.’’ The recovery stroke, on the other hand, is more of a rolling wave of bending that propagates along the cilium. Satir’s laboratory demonstrated that the ciliary beat could be arrested at opposite extremes of the beat cycle by Ca2+ and vanadate ( Wais-Steider and Satir, 1979; Satir, 1985; Satir and Matsuoka, 1989; Satir et aL, 1991). Nickel ion has also been used to produce ciliary/flagellar arrest (Naitoh and Kaneko, 1973; Lindemann et af., 1980, 1995; Larsen and Satir, 1991). Apparently, any of these inhibitory agents prevent the switching to the next phase of the beating cycle. The parallel of the Ca2+ and Ni2+ arrest phenomena between MytiZus cilia and rat sperm has been noted, along with the similarities in arrest positions (Satir etaZ., 1991). These arrest patterns, in both cilia and sperm flagella, involve the maintenance of a unidirectionally curved configuration, suggesting the continued dominance of a one-sided episode of dynein-tubulin engagement (implying that the capability of switching dominance to the other side is somehow impaired). Although open to more than one interpretation, it is important to note that the ciliary switch point hypothesis can be reconciled with the results of bull sperm micromanipulation studies presented here. If the basic beat mechanism requires a degree of reciprocation between the dynein bridges on the two opposing sides of the axoneme, and if the action of each set normally triggers the activation of the opposite set, this proposal is still lacking several important details. First and foremost, no mechanism is provided to explain how a nonbeating flagellum/cilium could assume a coordinated beat without an external push. A crucial factor in the initiation of spontaneous flagellarkiliary beating is the presence of a basal anchor. An early study (Douglas and Holwill, 1972) of isolated, reactivated Crithidia flagella, and flagellar fragments, revealed that freely suspended flagella did not demonstrate wave propaga-

33 tion. However, fragments that became attached by one end t o aglass surface were observed to generate waves originating from the attached end. A later study examining the effect of mechanically reanchoring clipped sperm flagella using a microprobe discovered that creating an anchor could restore beating (Woolley and Bozkurt, 1995). This information specifically points to anchoring as a requirement for normal beat production. Although the bending wave of most flagella travels from base to tip, it is interesting that some flagella are capable of a reversed wave propagation direction. The sperm of certain rotifers maintain an axonemal basal body at the distal tip of the flagellum; undulations originate there to pull the cell along (Melone and Ferraguti, 1994). In addition, certain eukaryotic protozoa can reverse wave propagation direction during flagellar beating (Walker, 1961; Holwill, 1965). A protein was immunologically localized to both the basal body and the flagellar tip of Trypanosoma brucei (Woodward et af., 1995), pointing to the possibility of a common structure at both ends of the flagella. Micromanipulation studies of Crithidia oncopelti revealed that microprobe dissection of the flagellum allowed continuation of tip to base wave propagation in severed portions of the flagellum (Holwill and McGregor, 1974), whereas laser irradiation usually resulted in a base t o tip direction reversal (Goldstein et af., 1970). It was speculated that laser irradiation welded the components of the newly formed base together, whereas microprobe cutting probably left the axonemal elements free from each other (eliminating an anchoring device at that end). Fractionated distal fragments of flagella given Mg-ATP do not beat (Brokaw and Benedict, 1968; Lindemann and Rikmenspoel, 1972a; Summers, 1975; Woolley and Bozkurt, 1995). Close examination of some “immotile” fragments reveals that they are no1 completely inactive but actually exhibit small-amplitude “jittering” all along the flagellar shaft (Lindemann and Rikmenspoel, 1972a). Lindemann and Gibbons (1975) also demonstrated the same type of small-amplitude, uncoordinated “twitching” in reactivated bull sperm exposed to Mg-ATP concentrations outside the range established to support spontaneous beating. Close examination of isolated sea urchin sperm (Kamimura and Kamiya, 1989, 1992) or Chfamydomonas (Yagi ef af., 1994: Yagi and Kamiya, 1995) axonemes in later studies revealed “nanometer-scale’’ high-frequency oscillations in nonbeating flagella. Mutant Chlamydomonas specimens lacking various axonemal components were also observed to vibrate, although in a slightly different manner (Yagi et af., 1994). Vanadate was shown to decrease the amplitude of oscillation with no effect on frequency (Yagi et af., 1994), whereas the addition of high concentrations of ADP ( 3 mM) increased the amplitude of these oscillations and (at high enough ATP concentrations) could result in a kind of beating (Yagi and Kamiya, 1995). This concurs with the earlier results of Lindemann and Rikmenspoel(1972b) who converted the jittering FLAGELLAR MOTILITY

34

CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

of bull sperm flagellar fragments to a regular form of beating at high ADP concentrations. The significance of these observations resides in the concept that, when the flagellum fails to coordinate the activity of the dyneins into regular beating under suboptimal conditions, there is still spontaneous force production. This disorganized development of force is insufficient to supply the initial bending necessary to trigger reciprocal activation. The meager level of stochastic dynein bridge formation is below the threshold level necessary to initiate substantial multiple dynein activation. However, the presence of a basal anchor helps convert this sporadic bridging force into an effective bend. This was demonstrated when reanchoring the cut end of a flagellar fragment reestablished beating (Douglas and Holwill, 1972; Woolley and Bozkurt, 1995). The addition of A D P also has a facilitating effect by increasing the amplitude of the nanometer-scale vibrations (Lindemann and Rikmenspoel, 1972b; Yagi and Kamiya, 1995). This may be due to the previously mentioned supposition that high concentrations of A D P alter the duty cycle of dynein by prolonging the force-producing stroke of the bridge cycle (Johnson, 1985; Omoto, 1989, 1991). The concepts that emerge from the results of these studies can be summarized as follows: 1. Bending the flagellum in one direction activates the dynein bridges acting to bend the axoneme in the opposite direction. 2. When a flagellum is beating, each episode of dynein-driven sliding acts as the stimulus to activate the opposing bridge set. 3. The dynein bridges exhibit spontaneous, random (stochastic) subthreshold bridging, even when the flagellum is not beating. 4. The random bridge activity can self-organize into coordinated beating if a basal anchor is present to assemble the summated forces from random bridging into a bend sufficient to activate a whole group of dyneins.

VI. Modeling the Flagellum

A. Physical Parameters of Flagellar Movement The flagellum is nature’s answer to the need for a biological propeller. It is an organelle that, in most of its applications, is providing motive force in a fluid environment. Not surprisingly, it has drawn the attention of biophysicists interested in an intriguing problem of interfacing hydrodynamics and biology. Some of the earliest studies attempting to understand the propulsive mechanism of flagellar motility were conducted by biophysicists

35

FLAGELLAR MOTILITY

who had to find methods of dealing with the complex problem of a flexible, thin beam (the flagellum) interacting with a viscous fluid. The first hurdle was to address the effect of fluid (viscous) drag on the generation of propulsive force. As a flagellum moves through its fluid surroundings, the movement is countered by viscous drag. Because the flagellum is a long, thin, flexible structure, all the viscous drag encountered by the flagellum as it moves must be opposed by active forces produced within the structure and conveyed to the areas of viscous resistance. This force transmission must occur through the long, thin shaft of the flagellum itself. Perhaps the first significant headway into a practical evaluation of the drag on a flexible beam moving in sinusoidal waves comes from Taylor (1952). Gray and Hancock (1955) used a somewhat different approach by segregating the drag into two categories, components transverse to or parallel to the long flagellar axis. They concluded that the flagellum creates twice as much drag moving transversely (like an oar) as when it moves longitudinally (like a dragging rope). This difference in drag is the basic source of flagellarkiliary propulsion, making possible both the swimming of sperm and the fluid transport of cilia (Fig. 8). This relationship between drag and propulsion, derived by hydrodynamic theory, was experimentally confirmed (Brokaw, 1965; Rikmenspoel, 1965). The physics of viscous drag sufficiently explains why a flagellum can do its job as a propeller of fluid. Biophysics can also tell us something about the internal forces needed to push the flagellum. By Newton’s laws, viscous drag must be countered by equal and opposite force contributed by the flagellum. Machin (1958,1963) further elaborated on the description of the Newtonian balance of forces, expressed as moments (force times lever arm). He divided the internal forces that balance the viscous drag (Mviscous or M y )into those derived from the contractile machinery (Mactiveor Ma) and those forces created by bending the elastic structures in the flagellum (Melastic or M e ) . Consequently, the basic equation of flagellar motion actually and an has three parts; an active term (Ma), a viscous drag term (My), elastic bending term ( M e ) , the sum of which must equal the Newtonian balance at any point along the flagellum:

M, + M ,

+ Ma = 0.

(1)

This equation, and its derivative forms, has become the basis of flagellar motility analysis. It is reasonable to expect that solving for both the viscous drag and the elastic term at each point along the flagellum would reveal the internal forces. Using this approach, Machin made a major conceptual contribution by showing that force applied only to one end of a passive elastic rod could not reproduce the beating patterns observed in live flagella. This led to the conclusion that the active forces must somehow be locally produced along the flagellar length (Machin, 1958, 1963).

36

CHARLES B. LINDEMANN AND KATHLEEN

S. KANOUS

A \

net

FIG. 8 Fluid propulsion in cilia and flagella. Stylized renderings of both ciliary (A) and flagellar (B) beating are displayed. The trajectory of a specific point on each of the cilium and flagellum is followed and indicated by the dotted lines. Note that the ciliary axis along the path traversed by a point on a distal segment is mainly perpendicular to the direction of movement during the effective stroke while being predominantly parallel to the direction of motion during the recovery stroke. Because the drag on a cylindrical structure is approximately twice as great when the structure passes through the fluid perpendicular to its long axis, there is a net propulsive drag that moves the external fluid in the direction indicated by the arrows. In the case of the flagellar beat, points on the flagellum follow a figure eight-like trajectory. Movement of each point is proximally directed at the upper and lower extremes of the “8”shaped pattern. During this proximally directed movement, the flagellar shaft is roughly parallel to the direction of motion. Distally directed motion is generated at the center portion of the 8-pattern, and the perpendicular component of motion is greatest there. Because the perpendicular component of the fluid drag is mainly limited to the distally directed part of the beat path, the net fluid drag is distally directed. If the flagellum is on a free (unanchored) cell, this net drag provides the propulsion necessary for swimming.

Rikmenspoel also adopted Machin’s approach. If a rigorous specification of the two physical terms of the equation of motion could be reached, the active term should then become apparent and open to examination. Deducing the Ma term by analyzing the motion of a number of different cilia and flagella might be conducive to understanding the underlying function. In a series of progressively more rigorous approximations, Rikmenspoel(l965, 1966a, 1971; Rikmenspoel and Rudd, 1973) produced computed simulations in an effort to duplicate the motion of cilia and flagella, as observed in nature. In the process of developing his computer model, he did some of

FLAGELLAR MOTILITY

37

the most thorough analyses of the physical parameters of flagellar and ciliary systems (Rikmenspoel, 1965, 1966a, 1971, 1978). Rikmenspoel and Rudd (1973) produced a rigorous, large-amplitude solution to the equation of motion that allowed virtually any ciliary or flagellar waveform to be analyzed. A number of intriguing findings that pertain to the nature of the active forces emerged. Rikmenspoel(1965, 1966a) demonstrated that the traveling waves normally observed in bull sperm flagella could be produced using a standing waveform of the active moment, without complex timing functions or wave phase dependency. The ciliary effective and recovery strokes could be modeled only if forces producing the effective stroke were activated very abruptly (simultaneously) along most of the axonemal length. The active forces producing the recovery stroke were much more localized, propagating along with the physical bend (Rikmenspoel and Rudd, 1973). The flagellar beat in both bull and sea urchin sperm appears more evenly distributed in the two bending directions. Nevertheless, there is a dominant bending direction (referred to as the principle bend) and a subdominant (reverse) bend. Rikmenspoel (1971) found a component of M ain flagella that had a more broadly distributed onset. Naturally, any successful mechanistic explanation of the beating cycle will, of necessity, have to be capable of reproducing these characteristics of M,derived from live cilia and flagella. Based on his deduction that active forces must be produced all along the length of the flagellum, Machin (1958,1963) hypothesized that flagellar bending participates in the activation of the localized force production mechanism (which at the time was considered to be a contractile event). This concept, that the local curvature in some way activates a local forceproducing mechanism, led to later curvature control theories. In order to “push” a bending wave effectively down the flagellum, the control function must turn on the flagellar motor apparatus somewhat out of phase with the mechanical wave. Consequently, in the curvature control models, the control function requires the incorporation of a phase delay (time delay) from the current curvature. This line of reasoning precipitated a number of models, and the basic underlying assumptions still play a dominant role in conceptual analysis involving the axoneme. Brokaw (1972a) experimented with curvature control functions that could activate force production by providing the necessary time delay from the current state. Miles and Holwill (1971) devised a control function based on drag and elastic strain transmitted along the flagellum to provide the phase delay necessary for curvature control. Lubliner and Blum (1971) developed a model capable of modifying the timing of curvature activation by incorporating external viscosity and internal shear information into the timing function. This method corrected the problems of eliciting appropriate responses to viscosity changes (increased viscous drag) in previous curva-

38

CHARLES 6. LINDEMANN AND KATHLEEN

S. KANOUS

ture control models. Rikmenspoel (1971) insisted that waveform and wave propagation rate were largely governed by external viscosity and flagellar elasticity. He believed that correct viscous load responses could be obtained, even with a standing wave mode of active moment that had no propagating component. His models of bull and sea urchin sperm were able to automatically adjust both waveform and wave propagation to increased viscosity in a life-like way (Rikmenspoel, 1971). However, Rikmenspoel later realized that the ciliary recovery stroke could not be modeled without a substantial traveling component in the Ma term (Rikmenspoel and Rudd, 1973). Also, using a nontraveling Ma did not allow the duplication of the sea urchin sperm response to cold or low ATP concentrations, in which the waveform remains relatively unchanged while the beat frequency drops substantially. Straightforward curvature control also fails to reproduce realistic results under many experimental conditions. In particular, it is nearly impossible to elicit the clear-cut, simultaneous initialization of Ma over the ciliary length (necessary for effective stroke production) without a totally separate control function that can explain the two phases of the ciliary beat. The deviations from observed behavior led Brokaw (1985) to conclude that all schemes based strictly on curvature control were “incompletely specified.” A successful explanation of the force-producing mechanism must be able to reconcile experimental observations that appear on first examination to be contradictory. As experimental investigations continue to fill in more of the details pertaining to axonemal structure and function, flagelladciliary model creators have been quick to incorporate these new concepts into their computer models. Brokaw (1971, 1972b) was the first to convert the treatment of force production into a computable sliding doublet formulation. Lubliner and Blum (1971) expanded this sliding doublet treatment into a model that included a more complete set of the axonemal components. Sugino and Naitoh (1983) produced a three-dimensional model that successfully explored the geometry and timing of the sliding interactions necessary for the helical beat of many cilia. Others have produced detailed descriptions of the three-dimensional operation of cilialflagella (Holwill et al., 1979; Hines and Blum, 1983, 1984, 1985; Woolley and Osborn, 1984; Sugino and Machemer, 1987; Machemer, 1990; Mogami et al., 1992; Teunis and Machemer, 1994). Holwill and Satir (1990) produced the most structurally complete model, incorporating all the known structural details into a threedimensional computer representation that can be used as a basis for functional modeling. Because dynein is the motor of the axoneme, a complete understanding of axonemal functioning demands that close attention be paid to the role of the cross-bridge cycle. Brokaw (1976a,b) pioneered the efforts in this direction by introducing a two-state stochastic treatment of individual

FLAGELLAR MOTILITY

39

dyneins into his flagellar sliding doublet model. The recognition that bridge attachment is a stochastic process at the molecular level that must be treated by alterations in the probability of cross-bridge formation was a novel concept in treating motor protein behavior. Brokaw used curvature control with a time delay function as the basis for modulating the probability of bridge formation in his model of dynein bridge regulation. Murase and Shimizu (1986) proposed that the control of the beat cycle could come from cooperative dynamics of a number of dyneins, resulting in an activation scheme in which dynein exhibits excitable properties in a three-stage crossbridge activation cycle without curvature feedback control. Several elaborations of this view (Murase et al., 1989; Murase, 1990, 1991, 1992) propose that it is the excitable properties of the dynein cross-bridge cycle that lead to coordination of the multiple bridge actions that organize the beat. This represents a novel alternative model concept in which macroscopic behavior is depicted as a direct outcome of cross-bridge cycle dynamics. A conceptually interesting possibility, as currently postulated, this mechanism involving cooperative dynein excitability has thus far had limited success in replicating the natural beat cycle of cilia or flagella.

6.A Physical Model Based on a New/Old Perspective As we have seen, extensive information defining the structural and functional properties of the eukaryotic axoneme has been painstakingly gathered through experimentation. A successful explanation of axonemal functioning must be compatible with this existing body of knowledge. To be of use to the community of scholars currently exploring cilia/flagella, a workable interpretation of axonemal operation must also be detailed enough to have predictive value. Recently, a plausible hypothesis to explain the beating of cilia and flagella has been advanced that is compatible with much of the accumulated experimental data. This concept is based on relatively simple underlying assumptions and has been dubbed the “Geometric Clutch.” It is based on a long-standing observation that spacing between the outer doublets in the circle of nine is somewhat more than that which will permit easy cross-bridging by the dynein arms (Gibbons and Grimstone, 1960; Allen, 1968; Gibbons and Gibbons, 1973; Warner, 1978; Zanetti et al., 1979).The Geometric Clutch hypothesis adopts the simplest assumption; dynein-tubulin cross-bridge formation is limited by the interdoublet spacing. When cross-bridges form, they produce interdoublet force, and some of this force (strain) between the doublets is directed transverse to their longitudinal axis. This transverse force (t-force), which can move doublets closer together or further apart, controls the probability of cross-bridge formation. Two major sources contribute to the development of t-force:

CHARLES B. LINDEMANN AND KATHLEEN S. KANOUS

40

1. The formation of dynein-tubulin cross-bridges contributes some force pulling adjacent doublets together. When a single dynein head acquires sufficient kinetic energy, through Brownian motion, it bridges the gap between doublets and attaches to the binding site on the adjacent doublet. This stretched bridge contributes a small amount of force, pulling the doublets together, as illustrated in Fig. 9, which increases the probability of additional bridge formation. This is supported by the observation that interdoublet spacing and axonemal diameter are decreased in axonemes

R

Actively bent

Transfer FIG. 9 The transfer of force across the axoneme. As depicted in A, when a dynein bridge forms in a resting axoneme, the interdoublet spacing is greater than the length of the inactive dynein arms. Initially, kinetic energy must contribute to dynein stretching to allow random bridge attachment. As an individual dynein gains sufficient energy to form a bridge, it spans the interdoublet space, attaching to the adjacent doublet. The force contributed by each connection acts to pull the doublets closer together, increasing the probability of additional bridge formation. This initiates a cascade of bridge attachments on this side of the axoneme while providing an adhesive force between neighboring doublets. A strong negative t-force is necessary to overcome these resultant adhesive forces. This one-sided dynein bridge attachment impacts the entire axoneme as demonstrated in B. As bridges form on one side, the probability of bridge formation on the opposite side decreases. This is due to the increase in interdoublet spacings on the passive side resulting from the transfer of forces through the interdoublet linkages acting to separate those doublets. Reproduced from Lindemann (1994b) with permission.

FLAGELLAR MOTILITY

41

demonstrating the presence of cross-bridges in electron micrographs (Gibbons and Gibbons, 1973; Warner, 1978; Zanetti er al., 1979). 2. When dyneins induce sliding (and bending) by exerting force on a pair of doublets, the cumulative tension (or compression) creates a transverse force between the two doublets. This force is proportional to the total longitudinal tension (or compression) times the curvature of the flagellum at that location. This component of the transverse force must be countered by the local dynein bridges and/or the structural interdoublet connectors (spokes and nexin links). The cumulative nature of this element of the t-force enables it to become very large, especially near the basal anchor (basal body). This force can either pry doublets apart or move them together, depending on the direction of the curvature. Kamiya and Okagaki (1986) elegantly demonstrated the premise that an episode of cross-bridge activity can be terminated by the resulting interdoublet t-force. Two individual doublets from a frayed Chlamydomonas axoneme were able to set up a repetitive cycle of bending and straightening. The doublets were observed to associate, forming a bend that reached a critical curvature (1 radlpm). This was followed by unbending and splitting into two separate doublets, one forming a loop against the other. Upon straightening, the two doublets again became associated and repeated the cycle. The best explanation for the termination of the sliding episodes in this experiment is that the t-force mechanism acts to pull the doublets apart as the bend develops beyond a critical degree. Elaboration of this very simple idea, that the t-force between doublets coordinates the action of the dynein motors in the axoneme, is the basis of the Geometric Clutch hypothesis. In fact, the possibility that axonemal distortion might be involved in beat coordination has been alluded to in the literature for decades (Summers and Gibbons, 1971; Summers, 1975; Warner, 1978). However, systematic detailed examination of this idea has been neglected until recently. Using this basic conception, it has been possible to construct computer simulations controlling bridge activation/ deactivation by the t-force principle (using the conventions shown in Fig. 10). In its most rudimentary form, the Geometric Clutch mechanism has shown that t-force resulting from tension on the doublets can initiate a complete beat cycle in a simulated flagellum (Lindemann, 1994a). The resultant beat can be made cilium-like if the bridges on one side of the axoneme are designated as easier to engage, and harder to disengage, than those on the opposite side. The modeling mechanism can produce both recovery stroke-like traveling bends and effective stroke-like simultaneous bridge activation over much of the axonemal length. Bends are observed to initiate automatically near the basal end of the simulation and propagate distally.

42

CHARLES B. LINDEMANN AND KATHLEEN

S. KANOUS

Trans. force =

a

Trans. force =

a

-d0= @ ds

Tension =

@

Trans. force =

a

-d0= @ ds

Tension =

0

Trans. force =

L -

I

a

~

Dynein arms FIG. 10 The t-force of passively and actively bent flagella. Triplets are displayed corresponding to three outer doublets in the process of flagellar bending. Both A and C depict doublets in passively bent flagella (bends imposed by an external force), whereas B and D portray doublets induced to bend by dynein action. The longitudinal force on the outer elements is displayed, along with the resultant t-force (bold arrows). Although passive (imposed) bending compresses the axoneme in the plane of bending, active (dynein-induced) bending leads to axonemal distention. Inwardly directed t-forces (resulting in compression) are assigned a "+," whereas outwardly directed t-forces (causing distention) are designated by a " -." The curvature (dOld.7) multiplied by the tension yields the t-force. The corresponding signs of the curvature and tension are shown for each condition to demonstrate the convention used in modeling the flagellum. Reproduced from Lindemann (1YY4a) with permission.

43

FLAGELLAR MOTILITY

A more advanced formulation of the model incorporated a two-state stochastic treatment of individual dynein bridges (Lindemann, 1994b). This improved version was also scaled to cgs units, allowing the simulation to utilize measured values for dynein force, flagellar stiffness, viscous drag, and flagellar dimensions. The stochastic approach enabled those dynein bridges already formed to influence the probability of future bridge attachment. This permits bridge formation to occur in a spontaneous cascade, starting with a straight, passive flagellum. The model can both initiate spontaneous motility and maintain oscillations using physical parameters appropriate for an actual flagellum. Figure 11 displays the computer output for modeling both a 10-pm cilium and a 30-pm flagellum. Figure 12 displays the progression of events occurring during a beat cycle as envisioned in the Geometric Clutch hypothesis. Each individual diagram represents three adjacent outer doublets (corresponding to doublet set 2,3, and 4 or set 7, 8, and 9). The P bridge set consists of bridges forming the

2231 2387

FIG. 11 Computed simulations of a flagellum and a cilium. The output from the Geometric Clutch simulations of both a flagellar and a ciliary beat cycle are displayed. A 30-fim long “flagellum” with a freely pivoting base is displayed in A, showing every 12th iteration of a cycle divided into intervals of 0.0001 s per iteration. A 10-pm “cilium” with an anchored base is exhibited in B, showing every eighth iteration, utilizing the same iteration intervals as that used in the flagellar model. The numbers printed on the output denote the iteration number of the indicated beat position, corresponding to the first and last elements displayed. Note that the cilium clearly exhibits a two-phased heat cycle, with well-defined effective and recovery strokes. The flagellum shows wave propagation tipward from the base in both bending directions. The Geometric Clutch program was capable of producing both patterns of beating without any fundamental change in the switching algorithm. The main determinants of the resultant beat included base anchoring, axonemal length, and assignment of base-level bridge attachment probability of the P and R bridges on opposing sides of the axoneme. From Lindemann (1994b) with permission (The complete modeling parameters for the figure are given in that original report).

44

CHARLES 6. LINDEMANN AND KATHLEEN S. KANOUS P-Bridges Random bridge attachment

Cascade of bridge attachment due to adhesion A

Initiation of detachment

R- Bridges

,

Random bridge attachment

Inhibition due to force transfer from P side

3 ,

L

Delayed attachment due to force transfer

Propagation of detachment

Initiation of attachment

( i j

Propagation of attachment P I A (+>

Delayed initiation due to force transfer

New eDisode of

,

6

,,

Initiation of detachment

FIG. 12 The beat cycle of the axoneme. In this simplified schematic, the events on the P and R sides of the axoneme are illustrated to present, in a stepwise format, the hypothetical mechanism by which the axoneme develops oscillations. I, Starting in the straight position, both bridge sets have a base level of random bridge attachments. 2, A cascade of attachments on one side (usually the side with the higher base level of attachment probability) begins an episode of sliding and (due to force transfer) simultaneously inhibits bridge attachment on the opposing side. 3, As bending increases, a negative t-force develops on the active side of the axoneme and is strongest near the base. Force transfer continues to inhibit the opposite side but becomes weaker as detachment of dynein bridges proceeds. 4, A propagating area of bridge detachment on the P bridge side is accompanied by a positive t-force from passive bending on the R bridge side. and this ensures a cascade of bridge activation on the R side.

FLAGELLAR MOTILITY

45

principal (or dominant) bend, which have the higher initial probability of attachment. On the opposite side, the R bridge set acts to form the reverse bend. The P arrows signify the passive force of stretching elastic interdoublet links, whereas the A arrows represent the active forces of dynein bridges, and the A* arrows depict active force transferred from the opposing side through the nexin links. The events progress in the following stepwise fashion: (i) Both bridge sets undergo random, sporadic bridge formation while the axoneme is initially straight. (ii) A cascade of P bridges are formed due to the higher probability of attachment on that side. This inhibits R bridge formation due to force transfer through the interdoublet links. (iii) As the bending increases, the P bridges experience a negative t-force that is greatest in the basal region. P bridge detachment ensues, whereas the inhibition of R bridge formation decreases. (iv) P-bridge detachment continues, resulting in a positive t-force effecton the R bridges and a subsequent cascade of R bridge attachments. (v) The P bridges become inhibited through interdoublet-link force transfer as the R bridge formations reverse the axonemal curvature. (vi) The increased bending in the reverse direction exerts negative t-force in the flagellar basal end that initiates a chain reaction of R bridge detachment. Simultaneously, the passive links and residual active bridges exert a positive t-force on the P bridges, activating bridge attachment on that side. This sets in motion the events in the initial steps, and all steps then repeat themselves in a cyclical fashion, propagating stable flagellar oscillations. This hypothetical mechanism is dependent on certain crucial axonemal properties. There must exist a small propensity for random bridge attachment, in the absence o f t force,to initiate the oscillatory cycle in a straight, immotile axoneme. In addition, elastic linkages must exist to contribute to bridge engagement during oscillation while acting to restrict the axonemal splaying during bridge detachment. Lastly, longitudinal force must be transferred from opposite sides of the axoneme. Otherwise, bridge attachment probability would increase on the opposing side as soon as the curvature increased (see R bridge Step 2), and bridges would attach simultaneously on both sides of the axoneme. This would restrict the developing bend from reaching the crucial curvature necessary to instigate bridge detachment. The t-force concept illustrates the need

5, Curvature is now reversing due to the R bridge forces. P bridges are temporarily inhibited by force transfer from the R bridge side. 6, The curvature is now favorable for production of a negative t-force near the base on the R bridge side. and deactivation begins there. Meanwhile. a new cycle is beginning on the P bridge side, as positive t-force from passive links and residual active bridges contribute to activation. Arrows labeled P are passive force contributions originating from stretching the passive interdoublet links. Arrows labeled A are active forces from bridges, and A* indicates active force transferred from the opposite side. Reproduced with permission from Lindemann (1994b).

46

CHARLES B. LINDEMANN AND KATHLEEN

S. KANOUS

for side-to-side force transfer between opposing dynein bridges. The probable mechanism for this side-to-side transfer is illustrated in Fig. 9B.

C. t-Force The key to the Geometric Clutch design is the t-force, which acts as the main regulator of dynein-tubulin interaction in this hypothesis. So, what exactly is t-force? Whenever a flexible structure is under tension or compression, it requires some externally applied force to maintain a curved configuration. In the axoneme, flexible rods of tubulin (forming the doublets) are collectively connected at the basal attachment. To help visualize this structural arrangement, imagine two flexible wooden reeds fastened together at one end, as shown in Fig. 13A. If force is exerted from the unattached ends by pushing on one and pulling on the other, the result is that depicted in Fig. 13B. Instead of the two elements bending smoothly,

FIG.13 The mechanism of flagellar bending. A visual demonstration of the principle behind

flagellar bend formation is presented. In A, two flexible reeds, anchored at one end to a small wooden spacer with a mechanical clamp, are each held at equal distances from the clamped end. When one reed is pushed baseward (toward the clamp) while the other is pulled tipward (as would be the case in outer doublet sliding), the pushed element buckles outward into an arch and the pulled element remains fairly straight, as shown in B. This separation of the two elements results from the development of t-forces acting to pull the two reeds apart. However, if rubber "linkers" are provided (represented by small rubber bands), these links can bear the outwardly directed t-force such that the same push/pull movement results in the formation of a smooth bend, as can be seen in C . This principle of balancing the t-forces between axonemal doublets using interdoublet linkers is what makes flagellar bending possible.

FLAGELLAR MOTILITY

47

one bows away from the other. A smooth bend of the entire structure can be produced from the applied force only if the two elements arc “linked” together. These connections arc then capable of bearing the outward t-force that would normally cause one of the elements to bow outward, counterbalancing it with the inward t-force developed on the other element, in a kind of force-sharing equilibrium (demonstrated in Fig. 13C). This same stratagem exists in the axoneme. The translocation of one doublet in relation to another can generate bending only if the doublets are linked and share the t-forces in a compensatory manner. Coincidentally, the axoneme contains interdoublet protein connections called nexin “links.” If these links are broken, or digested away, MT sliding within the axoneme produces an effect very similar to that shown in Fig. 13B. This experimentally induced flagellar disintegration has been called axonemal splitting (Satir and Matsuoka, 1989). In fact, it is the removal of the interdoublet connections with trypsin that disrupts the t-force balance, causing splitting due to the weakened axonemal structure. The role of the nexin links in bearing and distributing the t-force in the Geometric Clutch model sets rather specific limitations on nexin’s elastic properties. Life-like simulations of ciliary and flagellar beating are achieved when the nexin elasticity is specified to be within certain limits (0.010.03 dynkm), values given in a recent analysis of predictions derived through the Geometric Clutch model (Lindemann and Kanous, 1995). Within months, Yagi and Kamiya (1995) published an experimentally determined estimate for nexin elasticity, which when converted to cgs units equaled 0.02 dynkm. Although the basic idea of the t-force is conceptually very simple, the interplay between the t-force and the dynein-tubulin motor in the context of a complete axoneme is much more difficult to analyze and predict. The computer simulation is beneficial in revealing the necessary steps to creating the beat cycle, as displayed in Fig. 12. When the model is operating, the t-force can be analyzed through the beat cycle to examine the form the t-force takes in the working simulation with a printout as shown in Fig. 14. Note that the t-force itself develops a traveling component that propagates along the flagellum due to the summation of force from dynein bridges along the doublets. The t-force was observed to reach its maximum amplitude at the flagellar base. The t-force can be designated as positive (favoring bridge formation) simultaneously over a fairly long stretch of the flagellum. This would provide the needed mechanism to create the effective (power) stroke of the ciliary beat cycle, aphenomenon difficult to accommodate with more direct curvature control-based models of dynein activation (Brokaw, 1985). Consequently, the Geometric Clutch mechanism is capable of producing both propagated bending waves and near-simultaneous bridge activation, both using one common switching algorithm.

48

CHARLES 6. LINDEMANN AND KATHLEEN

A 2.OE-5 1.OE-5 .w

J

S. KANOUS

1

0.0 -

a2

k

d -1.OE-53

% -2.OE-5-

0

-3.OE-5

-4.OE-5

B

1

1 0

5

10

5

10

15 20 POSITION

I

25

30

25

30

T

2*0E-5 1 .OE-5

B

- 1.OE-5 --2.OE-5 -3.OE-5

0

15

20

POSITION FIG. 14 The t-force profiles of the cilium simulation. These graphs are created by plotting the t-force values at six intervals during the beat cycle versus their position along the axoneme. In A, the P bridge side t-forces are displayed, whereas B presents the R bridge side. Each numbered plot represents the values at one 2.6-ms iteration interval of the complete beat cycle. Note the organized t-force propagation, particularly of the negative bridge-terminating effect. This figure graphically explains the location of bridge activity initiation and termination because it is obvious that the t-force values are greatest near the axonemal base and travel tipward. Reproduced from Lindemann (1994b) with permission.

D. The Oscillator An interesting outcome of the Geometric Clutch simulation is the production of stable oscillations with propagating waves by a mechanism that does not specify a phase delay, a timing constant, or a propagation velocity. The t-force algorithm, responsible for organizing the beat, might be considered

FLAGELLAR MOTILITY

49

a subform of a curvature control design based on the curvature term utilized in calculating the t-force. However, because it also includes a force term (equal to the summation of tension on the doublet) there is no absolute curvature threshold necessary for bridge switching in this mechanism. In addition, a fundamental difference exists in the complete departure from the harmonic oscillator concept utilized in most earlier models. This focused on rhythmic, sinusoidal, or periodic application of the Ma driving force. In the Geometric Clutch simulation, the oscillation mechanism can best be described as a relaxation oscillator. There is no mass or inertial term in the equations of flagellar motion because the dissipation due to drag is very high relative to the inertial energy (Hancock, 1953; Machin, 1963; Rikmenspoel, 1966b). However, an inertial mass is a necessary basic component of harmonic oscillations. By contrast, relaxation oscillators develop a cycle of oscillation through two or more cascade events that exhibit hysteresis. That means the events have a different threshold level to start the cascade than to terminate it. In actuality, dynein bridge formation requires only a small t-force to initiate an episode of interdoublet sliding. In fact, just a few randomly attaching dynein heads can start a cascade of additional bridge attachment. Once an episode of sliding has begun, a much stronger t-force is necessary to pry apart the doublets and make the dynein arms release from the binding sites. What contributes to this hysteresis? Most likely it is the adhesive contribution of the dynein bridges themselves! Therefore, a bend must grow fairly large before the curvature and resulting t-force reach the much higher threshold level needed to pull the doublets apart. The feedback to terminate the sliding comes from the force generated by the bridges via the t-force mechanism. Hysteresis in the bridge attachmeddetachment thresholds causes the episode of sliding to proceed far enough to ensure activation of a cascade on the opposing side of the axoneme. Because forces exerted on each doublet will summate toward the basal anchor, Ma is greatest near the flagellar base, and bends will originate there. Consequently, the t-force in the basal region will reach the critical threshold for dynein disengagement first (see Fig. 12). Once these basal dyneins release, the threshold for their more distal neighbors is reduced, sending a wave of dynein disengagement toward the flagellar tip. These events provide the necessary basis for base-to-tip wave propagation in the Geometric Clutch mechanism. The absence of a basal anchor severely affects the key events of the beat cycle. Not only is the formation of a basal bend inhibited but the coordination mechanism to establish repetitive cycles of reciprocation between the two sides of the axoneme is suppressed. Dissected or fractionated axonemal fragments will not typically reactivate to produce coordinated beating (Brokaw and Benedict, 1968; Lindemann and Rikmenspoel, 1972a; Summers, 1975; Woolley and Bozkurt, 1995). How-

50

CHARLES 6. LINDEMANN AND KATHLEEN S. KANOUS

ever, when the cut end of the fragment is manually “reanchored” (Douglas and Holwill, 1972; Woolley and Bozkurt, 1995) beating can be restored. Studies utilizing Ni2’ graphically illustrate the importance of force reciprocation between the two opposing halves of the axoneme in creating a beat cycle. Nickel ion selectively impairs the functioning of certain dynein arms more than others (Larsen and Satir, 1991; Kanous et al., 1993; Lindemann et al., 1995). In bull sperm, Ni2’ blocks the sliding of doublets 1-4 on one side of the axoneme (Kanous et al., 1993). The beating of reactivated bull sperm exposed to a perfusate containing Ni2’ becomes progressively more asymmetric until the flagella ultimately arrest at one extreme curvature of the beat cycle (Lindemann et al., 1995). According to the Geometric Clutch hypothesis, these cells have arrested at the point where the disengagement of the dominant bridge set has initiated in the basal region but has only propagated part way down the flagellum. This is the point where the opposing bridge set would normally start a cascade of attachment to reverse the prevailing curvature, thus completing the beat cycle. However, the cycle stalls because that set of dynein arms has been rendered dysfunctional by nickel ion inhibition. Theoretically, normal beating should resume if the missing motive force is manually supplied in the direction necessary to reverse the prevailing curvature. Experimental examination of Ni2+inhibited bull sperm demonstrated that micromanipulatory bending of the flagellum in the direction opposite to the sustained curvature direction will restore flagellar oscillation as shown in Fig. 7 (Lindemann et al., 1995). This resumption of beating occurs as the imposed bend becomes sufficient to compensate for the force normally supplied by the nickel-inhibited bridges, thus triggering the activation of the functional bridge set. This onesided bridge set induced oscillation fits well within the premises of the Geometric Clutch mechanism. The microprobe substitutes for the dysfunctional bridges, bringing the flagellar curvature to the end point normally controlled by those bridges. This position creates a positive (compressing) t-force that strongly activates the functioning bridges on the opposing side. These working bridges then rebend the flagellum until they reach their own t-force release point. Once they release, the flagellum snaps back to the induced position elastically, and the cycle repeats. The Geometric Clutch mechanism is not only compatible with the observed behavior but it actually predicts this response and explains how the beat is restored.

E. Reflections on the Experimental Data At this point, the Geometric Clutch hypothesis is a rudimentary framework, but one that unifies a large number of experimental observations into one orderly scheme. The conserved geometry of the axoneme might be

FLAGELLAR MOTILITY

51

explained by the need to provide just the right spacing to permit dynein bridge formation in response to distortion of the mechanical framework. Elastic interdoublet linkages are vital to the basic organization of the Geometric Clutch and are conserved along with the spacing requirements, even when the axoneme is modified to its most extreme. The necessity of force summation to produce directional dynein attachment episodes is consistent with the universal presence of a basal anchoring structure. In cases in which nature has eliminated the basal centriole, as in mammalian sperm, a replacement anchoring structure (the connecting piece) has been incorporated. The potential for reciprocal activation of two (or more) opposing dynein bridge sets also seems to be vigorously conserved, as would be expected if reciprocation were key to maintaining the oscillatory mechanism. This may define one role of the central partition as organizing the beat through entraining force reciprocation, thereby coordinating opposing bridges over longer distances. Perhaps this is why the partition is sturdiest and most easily observed in mammalian sperm (Lindemann et al., 1992; Kanous et al., 1993), compound cilia (Afzelius, 1959; Tamm and Tamm, 1984), and sea urchin sperm (Sale, 1986), all of which have a long working length. In shorter cilia, the axonemal torsion producing a more helical beat would interfere less with beat cycle coordination, as long as there was still sufficient reciprocation to provide the necessary activation trigger for the opposing bridges. Although axonemal division into two opposing bridge sets is not an absolute requirement of the Geometric Clutch mechanism, activation of particular bridges leading to the subsequent reciprocal activation of opposing bridges is necessary. This is achievable if the t-force resulting from each episode of bridge activity favors the activation of opposing bridge sites. If the axoneme is not bisected by a partition, the result is a more helical beat pattern. The extensive work of Sugino and Naitoh (1983) and Sugino and Machemer (1987, 1988) consistently demonstrates that, even in cilia that beat with a very three-dimensional waveform, there is still a general pattern of reciprocation between two opposed bridge sites. The fundamental nature of the dynein motor also seems particularly well suited for a geometrically gated coordination mechanism. When allowed to directly engage MTs, dynein arms translocate the MTs in a free-run reaction. Nothing like the locally imposed troponin-tropomyosin gating mechanism of skeletal muscle has been identified yet for dynein. The dynein motor is a fast translocator, allowing the rapid sliding rates necessary to power the 10- to 60-Hz beating of most cilia and flagella. Sliding rate modulation has been observed directly in in vitro assays and can be attributed to the axonemal functions controlling the speed or frequency of the beat but not the coordination mechanism (Hamasaki et al., 1991; Satir et al., 1995).

52

CHARLES 8. LINDEMANN AND KATHLEEN S. KANOUS

Given the nature of the isolated motor, understanding the arrest response and calcium response of cilia and flagella may only be possible in the context of the intact axoneme. In the Geometric Clutch mechanism template, the shape of the beat and failure to complete the beat cycle is likely a result of changes in the probability of bridge attachment between the two opposing sets and failure to reach the t-force thresholds necessary for bridge attachment/detachment during beating. In the Geometric Clutch simulation of a cilium (Lindemann, 1994a,b), the asymmetry of the ciliary beat can be greatly enhanced by setting the t-force necessary for bridge engagement lower for the P-bend bridges while setting the t-force cutoff for bridge disengagement more negative. In other words, the dynein bridges on that side are easier to attach and harder to detach. In the intact axoneme, this could be accomplished by any change that increases the likelihood of bridge formation on one side of the axoneme. This could include the presence of a Ca2+-sensitive contractile protein in the nexin (Ohnishi et al., 1982) or dynein stalk/DRC complex (Piperno et al., 1992; LeDizet and Piperno, 1995a). Okuno (1980) analyzed the vanadate arrest of sea urchin sperm, deducing that the partially bent final configuration was due to the flagellum stopping just prior to the commencement of active sliding in the opposite direction. Satir and co-workers ( Wais-Steider and Satir, 1979; Satir, 1985; Satir and Matsuoka, 1989) first hypothesized that arrest responses are logically attributable to switching failure in the reciprocation mechanism of the two bridge sets. In terms of the Geometric Clutch mechanism, this switching failure occurs if (i) the dynein activation cascade is not initiated at the end point of the sliding episode of the opposing bridges or (ii) the generated t-force is insufficient to terminate a sliding episode. The first condition is probably the key in Ni2+-induced flagellar arrest because it has been shown that one set of dynein bridges is selectively impaired (Kanous et al., 1993; Lindemann et al., 1995). The second condition may describe the calcium and vanadate arrest circumstances. It has long been surmised that the flagellum remains under tension during calcium arrest, as if the bridges on one side of the axoneme are locked “on” (Gibbons and Gibbons, 1980). In the case of vanadate arrest, the tension necessary to reach the critical t-force level necessary for switching is probably compromised. Additionally, the ability to initiate a cascade of bridge attachment is negatively affected because vanadate interferes with the dynein cross-bridge cycle, leading to an accumulation of dynein in the unattached state (Sale and Gibbons, 1979;Mitchell and Warner, 1980; Okuno, 1980). If a sliding episode is already in progress, vanadate would be expected to weaken force production. Because t-force switching depends on the product of cumulative force X curvature, vanadate could impair the switching mechanism by interfering with both bridge detachment and reattachment.

FLAGELLAR MOTILITY

53

If the arrest patterns observed with Ca2+and Ni2+are a result of switching failure, then manipulation of arrested flagella to help trigger the switching event should induce an active flagellar response. This has been demonstrated in Ni2+-arrested bull sperm (Lindemann et al., 1980, 1995) and Ca2+-arrested Mytilus gill cilia (Stommel, 1986), resulting in a resumption of bend propagation. The defining principle of the Geometric Clutch hypothesis is the role of t-force, which is directly and predictably modified by mechanically repositioning the flagellum/cilium. Therefore, mechanosensitivity is an innate and unavoidable property of the axoneme in the Geometric Clutch paradigm. Disturbing the natural flagellar curvature with imposed vibrations (Gibbons et al., 1987; Eshel and Gibbons, 1989), mechanically imposedhestricted bends (Holwill and McGregor, 1974; Okuno and Hiramoto, 1976), or external fluid flow of sufficient strength and speed (Murase, 1990) all result in adjustments in the phase of beating. This is exactly the expected response if the t-force is responsible for coordinating the switching events in the beat cycle. The curvature of the flagellum is one of the two key determinants of the t-force magnitude. In long flagella with a simple axoneme, such as those of sea urchin sperm, the wave of active bending seems to be defined by a traveling region of uniform curvature. This observation undoubtedly played a key role in the efforts to develop a dynein regulatory model based on curvature control. The Geometric Clutch hypothesis predicts that this curvature uniformity is a result of a consistent switching threshold along the flagellar length, with each traveling bend powered by approximately equal numbers of active bridges. In contrast to sea urchin sperm, mammalian sperm are much stiffer near their base, thereby requiring the development of a greater cumulative force on the doublets to bend these flagella. Therefore, because the product of force times curvature determines the switching threshold, it should be reached at a lesser curvature in these axonemes. Not only do large mammalian sperm exhibit just such a reduced-curvature form of flagellar beating but the propagating bends increase in curvature as they move toward the flagellar tip where the stiffness is reduced (Gray, 1958). The mystery of the simultaneous and traveling components of M a highlighted previously (Rikmenspoel, 1971) becomes less enigmatic in light of the Geometric Clutch concept. The ciliary computer simulation demonstrates that bridge activation along most of the axonemal length can occur almost simultaneously when the t-force algorithm is used to control switching. This requires that the bridges controlling the P bend engage substantially easier than those forming the R bend. If this is the case, then nearsimultaneous activation of the P-bend bridges occurs spontaneously as the R-bend bridges disengage. The events mediating this trick of nature can

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be explained by the peculiar dynamics of t-force. The ciliary recovery stroke is dominated by the P-bend propagation created by the bridges on that side. R-bend bridge activation follows the propagating P bend, reversing the basal curvature. As R-bend bridge action terminates on reaching their switching threshold, there are still working P-bend bridges near the flagellar tip and these contribute a t-force that favors P-bend bridge attachment in the basal region of the flagellum. Normally, the action of one set of bridges works to disengage those bridges (self-terminating). However, because the R-bend bridges have reversed the curvature in the basal half of the flagellum (as can be seen at the end of the recovery stroke in Fig. l l ) , the force contributed by the P-bend bridges at the flagellar tip now promotes, rather than terminates, the engagement of more P-bend bridges near the flagellar base. This simultaneously snaps “on” the P-bend bridges along most of the cilium. This is the only currently devised bridge-switching scheme that logically explains both the ciliary and flagellar beat cycles with one consistent mechanism.

F. Caveats Although the Geometric Clutch idea can accommodate a great many experimental observations into one conceptual framework, it must be noted that it is still in a rudimentary form. The computed simulations are not yet sufficiently detailed to address certain important questions. As pointed out in a previous minireview (Lindemann and Kanous, 1995), the magnitude of the determined t-force is too large to be compensated for by the nexin links alone. Additional structures must also distribute and bear some of the t-force to prevent the axoneme from distorting greatly, or even rupturing, during normal operation. Goodenough and Heuser’s (1985) extensive microscopic reconstruction of the axoneme gives evidence for a set of transient linkages that move along with each dynein head as the doublets translocate. These “B-links” may be the structures that bear some of the t-force as the ATPase sites of the dynein head disengage from the adjacent doublet. The spokes may also serve to bear a considerable share of the t-force in an intact axoneme. The original Geometric Clutch simulations simplified the axonemal structure down to two opposing bridge sets (2,3,4 and 7,8,9) on opposite sides of the axoneme. In actuality, some of the force is also transferred to doublets 5-6 and 1 through the dynein bridges present in a complete axoneme. The spokes would be largely responsible for bearing the t-force acting on these doublets. Like the B-links, spokes have been observed to move along (or jump) as axonemal bending progresses. If the spokes and B-links are assumed to be the axonemal components designed to

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withstand and redistribute t-force, it becomes obvious that no hypothetical switching mechanism would be entirely satisfactory unless the influence of these structures has been incorporated. The intricacy of the organization of the inner arms and dynein regulatory complex suggests that further clarification of the function of these components is necessary. As discussed previously, a flagellum without outer dynein arms can still coordinate a normal (although slower) beat (Kamiya and Okamoto, 1985; Mitchell and Rosenbaum, 1985; Kurimoto and Kamiya, 1991; Hard et al., 1992). This indicates that the inner arms play a key role in the beat cycle events. The inner arms are positioned such that they are closest to bridging the interdoublet gap, and it is likely that they initiate the cascade of bridge attachment required for normal oscillation. Their location also makes the inner arms the ideal site for waveform modification and arrest. Although much more information will be needed to fully understand how the DRC and spokes are involved in beat modulation, a possible explanation is suggested by the Geometric Clutch mechanism. Changes in the configuration of accessory proteins at or near the attachment of the crucial inner arms may influence the ease o r difficulty of dynein bridge engagement and disengagement. This could be accomplished either by changing the orientation of the dynein head to the adjacent doublet or by changing the interdoublet spacing. At present, the Geometric Clutch model incorporates the known traits of the dynein motor in a simplified manner. Refinement of the model will involve a continued demonstration of compatibility with the best functional descriptions of all the axonemal components.

VII. Concluding Remarks The major strength of the Geometric Clutch hypothesis is its ability to make sense of a wide variety of experimental observations on cilia/flagella, consolidating them through one well-defined functional mechanism. The strict conservation of certain geometric and structural axonemal traits, such as interdoublet spacing and nexin links, can be identified as necessary in the axonemal conversion of dynein activity into flagellarkiliary beating. The action of the t-force in orchestrating the beat demonstrates that mechanical sensitivity, curvature control, and arrest phenomena are not exclusive of one another. In addition, simple rules of the Geometric Clutch mechanism allow small differences in t-force thresholds (necessary for bridge attachment/detachment) on opposite sides of the axoneme to have dramatic effects in modifying thc beat. This could form the basis for variations in beating observed in living cilia and flagella, including an explanation for the mechanism

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underlying the calcium response. This view of axonemal functioning is still formative (at present), but further exploration of this hypothesis, including additional experimental evaluation of its predictions, may provide a key to unlocking the mysteries of eukaryotic flagellar motility.

Acknowledgments The authors thank Dr. Esther Goudsmit for valuable input in the preparation of the manuscript. This work was supported by Grant MCB-9220910 from the National Science Foundation.

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