Flagellar and ciliary beating: the proven and the possible

Flagella (and cilia) are organelles of eukaryotic cells that produce motility by repetitive episodes of bending. Flagella and cilia are functional in diverse cell types: the beating of cilia in the bronchi of the lungs keeps airways clear of mucus and debris; the flagellum of a sperm cell propels the cell to the egg and is an essential step in the life cycle of humans and most complex organisms; and cilia and flagella are used for feeding and reproduction in animals and plants as diverse as clams and algae. The cycle of bending and bend propagation in a cilium or flagellum is called the flagellar beat, and is the subject of this Commentary.

Cilia and flagella are two forms of the same cell organelle. Historically, they were called flagella when present singly or in pairs, and called cilia when many were present. They both originate through the assembly of proteins onto a centriole-like basal body and they have the same internal arrangement of microtubules, motor proteins and accessory structures.

We already know a great deal about the inner workings of a flagellum. The internal cytoskeletal arrangement of a flagellum is composed of nine doublet microtubules in a ring surrounding a pair of single microtubules [the central pair (CP)]; these structures collectively compose the axoneme. This structural arrangement is illustrated in Fig. 1. Each of the outer doublets is linked to its neighbors by strands of protein called the nexin links. Each doublet also has a series of projections, called the radial spokes, that seem to act as spacers to position the doublets in a circle around the central pair of microtubules. The CP itself is enclosed in a sheath of proteins that form a series of projections that are well positioned to interact with each of the spoke heads. The spokes in turn are anchored onto each outer doublet near a complex of proteins called the dynein regulatory complex (DRC), which in turn is in close contact with the inner row of dynein arms. Both the spokes and the DRC are known to contain calcium-binding proteins (centrin in the DRC and calmodulin in the spokes) and all cilia and flagella respond to free calcium by altering the beating pattern.

In 1965, Gibbons and Rowe identified dynein, the major protein of the arm-like projections found on each of the nine doublet tubules of the axoneme, as the provider of molecular motive force for the flagellar beat (Gibbons and Rowe, 1965). The base of the flagellum, which usually terminates in a centriole-like basal body or in the connecting piece in mammalian sperm, anchors the doublets. The nexin links are elastic and resist the free sliding of the microtubules with respect to each other. Summers and Gibbons showed that sea urchin flagella broken off at their base and subjected to brief tryptic digestion to cut the nexin links would slide apart in the presence of Mg-ATP (Summers and Gibbons, 1971). Therefore, the basic movement-inducing interaction in the flagellar structure is the sliding of the microtubule doublets along each other's length as a result of the action of dynein in the presence of Mg-ATP. This sliding is converted to bending through the restraining influence of the basal anchor and the nexin links, as was first demonstrated by the modeling work of Brokaw (Brokaw, 1971; Brokaw, 1972a; Brokaw, 1972b).

Sale and Satir showed that the direction of sliding is uniform around the axoneme, with the dyneins of each doublet translocating that doublet base-ward by acting on the neighboring doublet (Sale and Satir, 1977). Therefore, the dyneins on one side of the axoneme tend to bend the flagellum in one direction of the beat cycle, and the dyneins on the opposite side contribute to bending in the opposite direction. In most flagella and cilia, the doublets numbered 5 and 6 in the standard numbering convention are permanently linked to one another and cannot slide relative to each other (Afzelius, 1959), and the CP is positioned perpendicularly to the major plane of the beat (Gibbons, 1961; Afzelius, 1961). These structures provide landmarks that define the beat plane, particularly in metazoan flagella. Doublet 1, which is located approximately 90 degrees to the plane of the CP on one side of the axoneme, is the first of the group of doublets 1-4 whose dyneins bend the axoneme in one direction of the beat cycle. The opposing group are the dyneins on doublets 6-9, which bend the flagellum in the opposite direction. Satir (Satir, 1985; Satir, 1989; Satir and Matsuoka, 1989) proposed that the beat consists of alternate episodes of activation of the two opposing dynein-bridge sets, which is regulated by some means of switching one set ‘on’ and the other set ‘off’ at appropriate mechanical set points. This was postulated as the ‘switch-point’ hypothesis and is generally believed to be a valid summary of the known data into an orderly picture of the events in the beat.

Naturally, the next question that needs to be resolved is: what controls the switching of activation of the two dynein-bridge sets? We know that the control must reside within the axoneme. Brokaw demonstrated that a flagellum removed from an intact cell was capable of autonomous functioning (Brokaw, 1961). Later, we (Lindemann and Rikmenspoel, 1972a; Lindemann and Rikmenspoel, 1972b) showed that isolated pieces of flagellum retain the capacity for bend propagation and sustained rhythmic beating if supplied with Mg-ATP and ADP. A fascinating observation of our early studies was that cut pieces of flagella lost coordination and stopped beating, but could be restarted by bending the flagellum with a microprobe (Lindemann and Rikmenspoel, 1972a). This observation seems to be a universal characteristic of the axoneme (Okuno and Hiramoto, 1976; Omoto et al., 1996; Hayashibe et al., 1997).

In this Commentary, we examine some of the ideas that have been advanced to explain how the flagellar axoneme works as an organelle of motility. Rather than providing a general review of the subject, we will focus on recent experimental findings that lend new insight into the nature of the beating mechanism.

The first mechanistic proposal for the control of switching was the ‘curvature control’ hypothesis of Brokaw (Brokaw, 1971; Brokaw, 1972a; Brokaw, 1972b). Curvature is a mechanical parameter of the axoneme. The curvature control hypothesis maintains that, when the flagellum bends to a sufficient curvature, it triggers the inactivation of one set of dyneins and the activation of the opposite set. To make such a scheme work, a time delay is required between reaching the triggering curvature and switching the two sets of motors. Flagellar bending waves appear to maintain a nearly constant curvature, especially in very long flagella (>200 μm) such as those of quail sperm (Woolley, 2007). However, Brokaw surmised that ‘simple curvature-controlled models are incompletely specified’ to be able to account for many flagellar behaviors (Brokaw, 1985).

Cibert suggested a geometric mechanism that might serve as a regulator in a curvature control scheme. When a bend forms on a flagellum, the periodicity (spacing) of the motor proteins relative to the periodicity of the binding sites on the adjacent doublets must be altered by curvature (Cibert, 2008). This periodicity relationship might serve as a cue for initiation and termination of dynein action. This is an interesting proposal, although no plausible mechanism has yet been elaborated to link the periodicity relationship to the control of dynein function. The geometric-clutch hypothesis, which can be thought of as a type of curvature control, is discussed in detail in the following section.

The ‘geometric clutch’ hypothesis (Lindemann, 1994a; Lindemann, 1994b) is based on the mechanics of the axonemal scaffold. The idea resulted from our studies of the behavior of wooden models of the axoneme (for details, see Lindemann, 2004). The hypothesis is predicated on the following idea: in an intact axoneme, motor proteins are positioned just far enough from their binding sites on the adjacent doublet that, when the flagellum is straight and at rest, the dynein heads have a very small, but finite, probability of forming a bridge to the next doublet. The probability of forming a bridge increases as the interdoublet distance decreases. Thus, a bend in the flagellum stretches the nexin links that hold the nine outer doublets in a ring and results in the development of a force transverse to the bend (the t-force) that squeezes certain doublets towards each other. Moving the doublets together increases the likelihood that a dynein bridge will be formed. This idea is illustrated in Fig. 2.

When dynein bridges attach in the presence of Mg-ATP, they translocate upon the adjacent doublet and apply a longitudinal force to both of the doublets involved. The longitudinal force exerted across the diameter of the axoneme provides the torque that is required to actively bend the flagellum, and generates a t-force that prises the doublets apart. When this t-force component is sufficiently large, the dynein motors no longer function in a processive manner because they are pulled away from their binding sites on the adjacent doublet. This is the switching mechanism that, according to the geometric-clutch hypothesis, terminates dynein action (Fig. 2).

The main component of the transverse force acting on the axoneme is defined by multiplying the longitudinal force on the active doublets by the local curvature (Lindemann, 1994a). Thus, in the geometric-clutch mechanism, curvature is a primary control parameter in switching, and one can consider the geometric-clutch mechanism as a mechanistically more specified type of curvature control. This mechanism has the advantage over other curvature control schemes in that switching can occur over a range of curvatures, depending on the amount of total tension on the doublets. This allows considerable variation in the appearance of the beat, as is found in nature.

The switching mechanism of the geometric clutch utilizes the dynamic balance between t-force and dynein binding affinity. Consequently, such factors as the adhesiveness of the dynein stalks to their binding sites on the adjacent doublet will alter the switch-point (the point at which dynein bridges are inactivated). Also, because the switching mechanism depends on the total stress acting across the axonemal scaffold, imposed external forces that stress the axoneme will also alter the switch-point. Cibert and Heck have suggested that, when the doublets are bent, they also experience a torsional force because they are not radially symmetric (Cibert and Heck, 2004). They suggested that the torsional force might play a role in breaking the dynein attachments and in terminating episodes of activity in a geometric-clutch-type stress-based regulatory scheme. Stress-based models have the advantage that they automatically provide an explanation for the intrinsic mechanical sensitivity of flagella and cilia.

The most widely held conception of axonemal coordination is that it is controlled through the CP-spoke apparatus. In the earliest version of this hypothesis (Omoto and Kung, 1980), the CP acts as a rotor that, during its rotation, is the trigger for switching selected sets of outer doublet pairs into action (as illustrated in Fig. 3A). There is evidence that, in some cilia and flagella, the CP does rotate during the beat cycle (Omoto and Kung, 1979; Omoto and Kung, 1980; Omoto and Witman, 1981; Kamiya et al., 1982). The most direct demonstration of the rotation of the CP was presented by Mitchell (Mitchell, 2003b). In this report, the author looked at the orientation of the CP in Chlamydomonas flagella that had been rapidly fixed to preserve the waveform of the beat. However, Mitchell and Nakatsugawa analyzed the mechanism of CP rotation and concluded that the CP is a helically curved structure in Chlamydomonas, and that its orientation follows the beat, rather than being the driver for the beat (Mitchell and Nakatsugawa, 2004).

It is well established that the CP does not rotate in metazoans (Gibbons, 1961; Tamm and Horridge, 1970; Tamm and Tamm, 1981; Sale, 1986), which have functional flagella and cilia. This makes the postulate that CP rotation is the main element of beat coordination untenable as a universal mechanism. In mammalian sperm, the CP is rather solidly anchored in a partition that traverses the axoneme from doublets 3 to 8. This partition is so sturdy that it is often the last structure that remains intact when the axoneme disintegrates by partial digestion and ATP-induced sliding (Olson and Linck, 1977; Lindemann et al., 1992; Kanous et al., 1993). This is most probably the case in other metazoan flagella as well, as shown in elastase digestion studies in sea urchin sperm (Shingyoji and Takahashi, 1995). In bull sperm, when flagellar motion of the proximal part of the flagellum is stalled by an obstacle, the unobstructed distal part of the flagellum continues to beat (Holcomb-Wygle et al., 1999; Schmitz et al., 2000). This is an impossible result in a CP-regulated beat cycle because the CP is continuous along the length of the flagellum and cannot be both stopped and rotating.

The major contributors to the rotating CP hypothesis also concluded that there are many instances in which coordinated movement is produced without the CP. In a review in 1999, they state: “Thus we propose that the nine outer doublets exhibit a default movement in the absence of the central pair-radial spoke complex” (Omoto et al., 1999). Nonetheless, the idea that the spokes are the regulators of the beat cycle presently holds favor with many researchers in the field. This is because of the accumulated evidence for spoke-mediated regulation of microtubule sliding (Wargo and Smith, 2003; Smith and Yang, 2004; Yang et al., 2006; Dymek and Smith, 2007).

Smith and Sale produced convincing evidence that the spoke apparatus can modulate doublet sliding and therefore might mediate coordinated sliding, possibly through interaction with the CP (Smith and Sale, 1992). The action of the spokes in wild-type Chlamydomonas appears to be an inhibitory action that the paralyzed flagella (pf) suppressor mutations can override (Porter et al., 1992; Piperno et al., 1994). Nakano and colleagues provide similar evidence for an inhibitory action of the CP complex when associated with the spokes in sea-urchin sperm flagella, so the effect might be universal (Nakano et al., 2003). If so, the CP-spoke axis would keep the doublet it controls inactive until some de-inhibiting mechanical or chemical signal is produced, either through CP rotation or a related mechanism.

The most recent candidate for a mechanical trigger is the phenomenon of spoke tilting. Spoke tilting is induced by interaction of the spoke heads with the CP, and occurs when shear is present as a result of flagellar bending. It was proposed that this might be the trigger mechanism that initiates a signalling pathway acting via the kinase assemblage that resides on the spokes (Porter and Sale, 2000; Smith and Yang, 2004; Yang et al., 2006). In the overview of this control, interaction of the spoke heads with the CP projections [including, most importantly, hydin on C2 (Lechtreck and Witman, 2007)] leads to the activation of elements of this kinase assembly that control the activation state of the dyneins on the associated doublet. Consequently, this mechano-chemical view, which is illustrated in Fig. 3B, is now a contending mechanism for beat control. In contrast to direct control through CP rotation, spoke tilting incorporates a bending-dependent step in the control sequence that is more compatible with the mechanical feedback that all cilia and flagella are known to exhibit. It is an attractive and plausible hypothesis in that it is consistent with the many studies (Piperno et al., 1994; Piperno, 1995; Porter and Sale, 2004; Smith and Yang, 2004; Yang et al., 2006; Yang et al., 2008; Lechtreck and Witman, 2007) that implicate individual protein constituents on the CP, spokes and DRC as being essential to flagellar beating. In this view, beating depends on an enzymatic regulatory cascade that begins with the spoke-CP interaction and sends a signal through the spoke-DRC linkage to the inner-arm dynein.

Of the other mechanistic proposals to explain the beat cycle, the most noteworthy are those that can generally be grouped as being dependent on the dynein cross-bridge cycle (that is, the cycle of dynein attachment to microtubules, power stroke and detachment). This control scheme, which has been proposed in somewhat different forms by Sugino and Naitoh (Sugino and Naitoh, 1982) and by Murase and Shimizu (Murase and Shimizu, 1986), holds that the beat cycle of the cilium or flagellum is fundamentally a direct outcome of the dynein cross-bridge cycle. In other words, each dynein undergoes one cycle of attachment, power stroke and detachment as the cilium undergoes one effective and recovery stroke (illustrated in its simplest form in Fig. 4).

The proposal of Sugino and Naito suggested a metachronal (sequential) scheme of dynein activation, in which every dynein is activated in succession to produce the beat (Sugino and Naitoh, 1982). Consequently, the beat reflects a collective dynein cross-bridge cycle, but dyneins activate in sequence rather than simultaneously. A recent synthesis developed by Seetharam and Satir provides support for this model (Seetharam and Satir, 2008). In such a metachronal scheme, the number of dyneins that simultaneously contribute force is small; therefore, the dyneins must be very powerful. However, unless such a metachronal scheme is used, the amplitude of the beat is limited by the step-length of the dynein cross-bridge cycle, which is not more than 16 nm, and yields a beat that is too shallow to correspond to those that are found in nature. Modifications of the idea have been proposed to overcome this limitation. In one modified form of the hypothesis, the ‘one bridge cycle, one beat’ idea is replaced with multiple cycles that terminate when shear velocity falls to zero against a bending resistance (Murase, 1991).

A similar idea has been carried further by Camelet and colleagues, who treated whole groups of dyneins as tuned oscillators in which a harmonic-like resonance of the group results when the action of the group is resisted by elastic stress (Camelet et al., 1999). The beat of the whole flagellum results as an emergent behavior of an excitable ensemble of interacting dyneins (Kruse and Julicher, 2005). Energy from the power stroke of many dyneins is transferred into storage in an elastic resistance, which, when it accumulates sufficiently, acts to terminate the action of the group (reviewed by Riedel-Kruse et al., 2007). Consequently, this view incorporates elements of both an excitable-dynein cross-bridge cycle and stress-mediated inactivation. The inactivation by the accumulated stress renders the switching shear dependent, in a way that is somewhat similar to the inactivation by zero shear velocity in the modified excitable-dynein proposal of Murase (Murase, 1991). The idea of inactivation of dynein by a threshold of accumulated stress also has something in common with the geometric-clutch hypothesis, although the vector direction of the stress is not transverse but longitudinal with respect to the direction of dynein translocation.

In summary, there are currently three quite different views of how the axoneme might work as an organ of motility. The first view is that the structure of the axoneme is itself a mechanical device that regulates the operation of the dynein motor proteins by changing the spacing of the doublets. The second view is that the motors are enzymatically regulated through a cascade of molecular and mechanical events that originate at the CP and are transmitted through the spokes and DRC to the inner-arm dyneins. The third view is that the beating is the result of an intrinsic oscillatory property of the dynein motors, which is expressed as the flagellar beat when the motors act in cooperative groups.

The inner row of dynein arms (see Fig. 1) consists of seven different dynein heavy chains arranged in a linear pattern that repeats along each outer doublet every 96 nm. One of the inner-arm dyneins, called I1 or dynein f, has two motor domains and therefore is referred to as double headed. The inner-arm dyneins, especially I1, seem to occupy a special place in the regulation of the flagellar beat. Inner-arm-dynein mutations of Chlamydomonas result in either complete or partial loss of coordinated beating. The 138 kD intermediate chain (IC138) is a protein that is associated with the inner-arm dyneins (Habermacher and Sale, 1997) and is actively phosphorylated by casein kinase 1 (Yang and Sale, 2000). Wirschell and colleagues state: ‘The current model for regulation of I1-dynein is that chemical and/or mechanical signals from the central pair are transmitted through the radial spokes to affect IC138 phosphorylation on specific outer doublets (e.g. outer doublets N, N+1, N−1). Thus, phosphorylation of IC138 in an asymmetrical manner is predicted to result in local inhibition of sliding’ (Wirschell et al., 2007). Their view of the importance of dynein I1 is based on reports that indicate that dynein activity is modulated by the presence or absence of spokes (Smith and Sale, 1992), that phosphorylation of the IC138 component of I1 can inhibit doublet sliding (Smith, 2007), and that the phosphorylation is controlled by the action of the CP-associated protein hydin (see Fig. 3) that is crucial for motility (Lechtreck and Witman, 2007; Smith, 2007).

To make the IC138 phosphorylation site doublet specific, so that it can produce alternation of dynein action in the beat, requires some form of control. In species such as Chlamydomonas, in which the CP is known to rotate, this might be accomplished through the CP-spoke interaction (see above). However, to propose this mechanism as the universal coordination mechanism that regulates beating, even in organisms in which the CP apparently does not rotate, would require the operation of another selection criterion, such as the mechanical tilting of the spokes during interdoublet sliding (see below). Such a view has been proposed, and assigns to the spokes the role of stress transducers (Smith and Yang, 2004).

Several important observations run counter to the hypothesis that the CP-spoke axis controls the activation and deactivation of the dyneins to produce the beat cycle. In nature, there are functionally motile flagella that have no CP or spoke apparatus (Woolley, 1998; Mencarelli et al., 2001). As discussed above, Chlamydomonas pf mutants, which lack the spokes and/or CP, are motile if they also carry a suppressor mutation (Brokaw et al., 1982; Huang et al., 1982; Porter et al., 1992). Some of the suppressor mutations lead to defects in the regulatory chains of both inner and outer dyneins (Porter et al., 1992; Porter et al., 1994; Rupp et al., 1996). Other mutations cause the absence of regulatory proteins and/or dynein subsets (Piperno et al., 1994; Piperno, 1995; Rupp et al., 1996). Therefore, we must conclude that the absence of regulatory components of the hypothetical beating mechanism actually restores a beat. Furthermore, IC138 is hyperphosphorylated in the CP-spoke-defective pf mutants (Hendrickson et al., 2004). As phosphorylation of IC138 blocks sliding, the suppressor mutations must overcome this inhibition of sliding.

The suppressor mutation data pose a serious problem to the contention that the CP-spoke axis is the fundamental mechanism responsible for beating. They indicate that, as long as the dyneins are not actively inhibited, another mechanism can take over in the absence of the CP-spoke control and institute a complete beat cycle. The question then becomes: is this other mechanism a default back-up mechanism, or is it the normal mechanism for coordinating beating, which is fine-tuned by CP-spoke-dependent regulation?

It is possible that control by the CP-spoke axis is part of an on-off switch that has a global effect on all axonemal dyneins. This would allow a complex organism such as Chlamydomonas to turn its flagella on and off, which it is known to do. Yang and colleagues have presented evidence to show that control by radial spokes plays a role in pausing flagellar beating to maintain coordination between the two flagella of Chlamydomonas (Yang et al., 2008). In this way, control by the CP-spoke axis might act to limit or terminate the action of selected dyneins, shaping the beat and altering the waveform for the different modes of swimming that are observed in Chlamydomonas. This might explain the role of Ca²⁺-binding elements on the spoke shafts (Yang et al., 2001) in controlling dynein activity (Dymek and Smith, 2007), as Ca²⁺ can alter the waveform of the Chlamydomonas beat and change the swimming pattern. The results obtained by Nakano and colleagues using sea urchin sperm show that Ca²⁺ can alter which specific dyneins are inhibited by association with the CP-spoke system (Nakano et al., 2003), and fit nicely with the interpretation that the CP-linked regulation of sliding is an element of the Ca²⁺ response pathway.

Spoke tilting and spoke-head—CP interactions are topics that deserve serious investigation because so little is known about the functions of the spokes and CP. The dyneins that do most of the work of the beat cycle are those attached to doublets 2, 3 and 4 on one side of the axoneme and doublets 7, 8 and 9 on the opposing side. Most of the shear developed in the beat (~80%) results from active sliding between these doublets. The kind of spoke tilting that is the result of inter-doublet sliding, as observed by Warner and Satir (Warner and Satir, 1974), has a minimal influence on the spokes of these doublets because their spokes project nearly perpendicularly to the beat plane. Instead, spoke tilting is greatest on doublets 1, 5 and 6, in which the spokes project from their doublets in a direction that is nearly parallel to the beat plane. It is these doublets that would reach a crucial threshold of spoke-tilt first, and would therefore be the probable site of regulation.

To invoke spoke tilting as the principal coordinating mechanism of the beat requires a better understanding of how such an activation scheme could control the dyneins on doublets 2, 3, 4, 7, 8 and 9, which contribute most of the motive force of the beat. Perhaps a system for signal transfer through the CP proteins is possible. In any case, better information is needed on the functional interactions of the spokes and CP.

A special role of the inner arms and dynein I1 is compatible with the geometric-clutch model and possibly with dynein-cycle-based models as well. Experiments in a number of systems have shown that extraction of the outer dynein arms reduces the beating frequency but leaves the waveform of the beat relatively unaltered (Brokaw and Kamiya, 1987). The latest version of the geometric-clutch model (Lindemann, 2002) can duplicate the results of the outer-arm extraction experiment, but only if inner arms contribute almost all of the interdoublet adhesion at low sliding velocity. This is consistent with the idea put forward by Brokaw that the inner arms contribute most of the force at low sliding velocity (Brokaw, 1999). There is good experimental support for the idea that the inner arms are more processive and can hang on more securely to an adjacent doublet (Shingyoji et al., 1998; Sakakibara et al., 1999). In the case of dynein I1, this has been specifically investigated by Oiwa's laboratory, who have shown that dynein I1 might be specially designed to hold on rather than to translocate (Kotani et al., 2007). This is exactly the property that would give it a special role in the beat cycle, as viewed from the perspective of the geometric-clutch model. The inner arms would provide the interdoublet adhesion to keep an active group of dyneins attached and resistant to the t-force until a sufficient bend develops.

The experiments of Oiwa and co-workers showed that isolated dynein I1 also provided a resistance that slowed down the rate of microtubule translocation by other dyneins (Kotani et al., 2007). This might provide the linear resistive element that the model (dyneins as tuned oscillators; see above) proposed by Camelet and colleagues (Camelet et al., 1999) requires. Consequently, the special role of dynein I1 is not very hypothesis selective; all of the mechanistic hypotheses for control of the beat cycle seem to require that a dynein-I1-like function exists.

There are numerous molecular studies that dissect the functions of the AAA (ATPases associated with diverse cellular activities) domain of the dynein motor (Silanovich et al., 2003; Kon et al., 2004; Reck-Peterson and Vale, 2004; Sakato and King, 2004; Cho et al., 2008; Numata et al., 2008). These experimental studies have revealed the functional complexity of the AAA ring and have provided evidence that the multiple ATP-binding sites play a role in nucleotide regulation of dynein, as proposed by Kinoshita and colleagues (Kinoshita et al., 1995). They also support the idea that dynein-ADP is the force-generating intermediate in the power stroke, as proposed by Tani and Kamimura (Tani and Kamimura, 1999).

We have demonstrated that reactivated, de-membranated bull sperm show a significant increase in the t-force at the switch-point of the beat in the presence of ADP (Lesich et al., 2008). This is in agreement with experimental studies on the nucleotide regulation of dynein, which assert that the binding affinity of dynein for tubulin is directly regulated through a long-residence ADP-binding site on the dynein head (Inoue and Shingyoji, 2007; Cho et al., 2008). Our result is consistent with the geometric-clutch hypothesis, in that the switch-point of the beat should depend on the balance between dynein-microtubule binding affinity and t-force. Our study with reactivated bull sperm shows that an independently identified discrete factor (ADP) alters the dynein-binding affinity and changes the dynamics of switching. The change in switching curvature is easily observable (Fig. 5) and is predicted by the geometric-clutch model. The result can also be seen as compatible with the dynein-cycle group of hypotheses because a distinct change in the dynein cross-bridge cycle results in a distinct change in the beat cycle. It is difficult to reconcile the data with beat-coordination schemes that rely on CP rotation or the degree of spoke tilting because these parameters should not be directly influenced by a change in dynein-binding affinity (if the switching event is regulated by a threshold of spoke tilt, then the switching event should take place at a conserved interdoublet shear).

The increase in t-force in the presence of ADP shows that each episode of dynein engagement is terminated at a higher t-force threshold when the dynein-binding affinity is increased by ADP. This directly supports the concept that dynein-tubulin affinity must be overcome by t-force at the switch-point of the beat (as illustrated in Fig. 5). At the same time, the interdoublet shear (which should determine spoke tilting) is not conserved but increases substantially at the switch-point. These results provide an explanation for observations that ADP (in the presence of low ATP concentrations) can reinstitute a beat in some pf Chlamydomonas mutants (Frey et al., 1997). It is not the basic coordination mechanism that is defective in those pf mutants, but the binding properties of the remaining active dynein. Increasing the processive behavior of the functional dyneins that remain restores the capacity for coordinated beating.

In conclusion, it appears that the nucleotide regulation of the dynein-tubulin binding affinity is directly connected to the mechanism of switching in the beat cycle. As we gather a more complete understanding of the parameters that govern the tubulin-binding affinity of the dynein molecule, it will be possible to see how changes in the binding affinity produce predictable changes in the observable characteristics of the flagellar beat cycle. In this way, the nucleotide regulation of dynein might provide a touchstone for linking theory and experimental results.

The observation that bending isolated pieces of bull sperm flagella can re-institute a beat cycle (Lindemann and Rikmenspoel, 1972a) supports the idea that a passive (externally imposed) bend can assist in the engagement of the dynein motors. To invoke a mechanical mechanism such as the geometric clutch to explain the complete beat cycle there must also be a mechanism to disengage the action of the dyneins. Kamiya and Okagaki provided a proof of principle for the assertion that the dyneins can act to terminate their own action (Kamiya and Okagaki, 1986). By looking at individual doublet pairs sticking out from the frayed end of a Chlamydomonas flagellum, they showed that the pairs of doublets set up a limited beat of their own by sliding and bending to a critical bend angle and then separating near the base where the t-force is greatest.

Recent important studies have demonstrated that imposed bending can initiate and reverse episodes of sliding in sea urchin sperm flagella when the doublets have been freed to slide by enzymatically cutting the nexin links with elastase (Morita and Shingyoji, 2004; Hayashi and Shingyoji, 2008); moreover, imposed bending can initiate beating at very low ATP concentrations (Ishikawa and Shingyoji, 2007). These results demonstrated that the curvature imposed on the partially digested structure controls the direction of dynein-driven sliding as the axoneme disintegrates. This is a direct confirmation of the hypothesis that initial curvature plays a role in governing the pattern of dynein engagement.

These observations are generally consistent with the idea that curvature control or some modified form of curvature control, such as the geometric-clutch mechanism, is responsible for activating a select group of dyneins. It can also be viewed as consistent with a centrally mediated mechanism, spoke tilt or spoke-CP interaction (as proposed by the authors). Presently, there is no easy discriminator to decide between these possibilities because the elastase-digested system is of necessity mechanically compromised in order to make it possible to view the sliding event. It might represent normal control in the intact flagellum, but it might also be an artifact of a partially incapacitated regulation system.

What is the flagellar mechanism for dynein engagement in these experiments? It might be as simple as activation of the first pair of doublets that is forced together by the stress imposed on the axoneme. Although the axonemes in these studies are structurally compromised and probably lack most of the interdoublet elastic linkages, there is still no way to bend the nine-fold ring without imposing a distortion that will push certain doublets together. The doublet microtubules are known to be fairly resistant to stretch or compression (Brokaw, 1991). Conservation of length, combined with the fact that enough interdoublet attachments must remain to keep the axoneme intact, requires that the axoneme will compress in the bending plane (Fig. 6A,B). If all the doublets that are initially forced together are activated, there is an immediate leverage disadvantage to the dyneins on one side, as compared with those on the other. The action of one group will create a transverse stress that pushes those doublets tighter together and ensures continuation of the activity, whereas the action of those on the opposite side will create a transverse stress that immediately moves the doublets apart from each other and inhibits further attachment (Fig. 6C). Consequently, the selection of the dyneins on one side by the bending event could be viewed as a direct outcome of the sign of the t-force that is generated by the action of the dyneins on the two sides of the axoneme. This is not only consistent with the geometric-clutch mechanism but can be viewed as a demonstration of the t-force switching principle, which maintains that dyneins will become activated when the doublets are pushed together and be deactivated when the doublets are prised apart.

It is equally possible that the action of the bending is mediated through a mechanism that senses the direction and degree of spoke tilting and relays an activating signal to the dyneins on one side, and an inhibitory signal to those on the other side, through the spoke-DRC enzymatic linkage. This is an attractive hypothesis, given all of the indisputable discoveries of the control-element-like component proteins associated with the spokes and DRC. It might be that an inhibition of certain doublets is mediated when the spokes and CP are pressed together by bending stress. The same conceptual issue as addressed earlier remains applicable here: there still must be a coordinating mechanism that can explain how beating is possible in the absence of the spokes and CP. Even the more limited interpretation that the spokes and CP, when present, select and inhibit certain dyneins requires a much better understanding of the CP-spoke interaction. At this point, it is not possible to say with absolute certainty that the spoke heads actually have a physical binding interaction at the CP apparatus.

The structural arrangement of the microtubules and proteins that make up the axoneme is a marvel of natural engineering. To convert the action of thousands of molecular motors into useful work, the outer doublets must be strong, yet flexible, and they must be anchored solidly at the base of the flagellum or cilium in order to generate the torque to bend it. In this section we examine some revealing work that has aided understanding of the role of the basal anchor in the beat, the forces that the axoneme must carry, and the ingenious tektin fiber system that reinforces the load-carrying structures.

In the geometric-clutch hypothesis, the basal body of the flagellum has a dual role. In addition to providing an anchor for the development of torque, it also allows the accumulation of tension on the doublets at the basal end of the flagellum, which is crucial for generating a large t-force for switching the dyneins (Lindemann and Kanous, 1995; Lindemann and Kanous, 1997). Fujimura and Okuno recently showed, by photochemical cross-linking, that forming an artificial anchor at either end of a cut sea urchin sperm flagellum restores spontaneous beating to fragments of flagella (Fujimura and Okuno, 2006), consistent with the proposed role of the basal anchor in the coordination of the beat.

The magnitude of the t-force at the switch-point of the beat in sea urchin and bull sperm flagella is about 0.5-1.0 nN/micron (Lindemann, 2003). This magnitude of force is consistent with the idea that switching might occur when the magnitude of the t-force is approximately equal to the aggregate tension that the dyneins can carry (Lindemann, 2003).

Such a large t-force is also likely to produce substantial distortion of the axoneme during the beat. Distortion of the axonemal ring during the beat is a necessary tenet of the geometric-clutch hypothesis and has been elusive to demonstrate. Sakakibara and colleagues provided direct measurement of diameter oscillations in sea urchin flagella that correlated with dynein activity (Sakakibara et al., 2004). Other evidence that the diameter of the flagellum distorts during the beat comes from David Mitchell's transmission electron microscopy (TEM) images of Chlamydomonas flagella that were rapidly fixed while beating (Mitchell, 2003b). In a collaborative study using Mitchell's TEM plates, we quantified the degree of distortion of axoneme diameter in the fixed Chlamydomonas beat cycle and compared it to predictions of the geometric-clutch model (Lindemann and Mitchell, 2007). The data allowed us to derive a preliminary estimate of 0.02 MPa for the trans-axonemal Young's modulus (the ratio of stress to strain that defines how a structure will distort under tension). If this estimate can be confirmed by direct measurement on intact axonemes, it will mean that the axoneme must always experience considerable distortion during the beat cycle.

Before concluding, we note with special interest that a more detailed picture of the mechanical construction of the axoneme is emerging. It is known that axonemes are reinforced by a network of tektin protofilaments that, together with the nexin links, maintain the ninefold integrity of the axoneme, even when tubulin is solubilised (Stephens et al., 1989). A recent synthesis of the data on the tektin network provides a convincing case that the nexin links, spokes and inner-arm dyneins are all located so as to be strategically supported by the tektin network (Setter et al., 2006). Thus, these proteins all appear to be anchored to an embedded cable system that is strategically arranged to redistribute the tension that results from the action of the dyneins. This makes the tektin skeleton of the axoneme the major system for carrying and redistributing the forces generated in the beat.

The nexin links are ideally positioned to sense and react to interdoublet shear. If interdoublet shear and reactive elastic resistance are the key elements in dynein switching, as in the model proposed by Camelet and colleagues (Camelet et al., 1999), then it is imperative to learn more about the regulatory components of the nexin link complex. The recent structural work on the axoneme using cryoelectron tomography does show a large aggregate of protein with the correct periodicity and placement for the nexin links (Nicastro et al., 2006). The identity of the proteins in this complex and their mechanical properties need to be examined.

The spokes are optimally positioned to carry a large component of the transverse stress across the center of the axoneme. This tension would be redistributed differently according to whether the spoke heads bind to, or are free of, the elements of the CP apparatus. Consequently, this is an important point for investigation. The details of the mechanical interaction of the spoke heads at the CP might significantly impact the feasibility of both the geometric-clutch mechanism and the CP-spoke control of dynein. Therefore, this issue is pivotal in discriminating between possibilities. It might well be that the t-force determines the interaction of the spokes with the CP apparatus, and that only when the axoneme is ‘pinched’ by t-force acting across the axoneme diameter do the spokes interact strongly enough with the CP to engage the CP-spoke axis. After all, nature is not constrained to pick from only one of our hypotheses.

At present, there are three contending views of how the axoneme might generate the flagellar beat cycle: the mechanical view, which is elaborated in the geometric-clutch hypothesis; the enzymatic view, which relies on the action of components of the CP-spoke axis; and the view that it is the behavior of the dynein motors that contributes spontaneous oscillatory behavior. Each view has considerable conceptual merit and all have at least some observational support.

The control of dynein function and microtubule sliding by means of axoneme components located on the CP, spokes and DRC has the largest base of experimental support. We think it is certain that this regulatory pathway is a key mediator of the calcium response of cilia and flagella. It is also likely that it can act to turn the motility off by rendering a subset of the inner-arm dyneins inactive, particularly I1. From the available experimental evidence it is considerably less certain that the CP-spoke axis is fundamental to the mechanism that generates repetitive beating.

There is strong evidence for the position that the primary mechanism that underlies the beat cycle is bending activated and mechanical, and is intrinsic to the axoneme structure and to the dyneins themselves. The exact mechanism that imposes this control is still inconclusive, but many of the recent experimental observations are consistent with the geometric-clutch hypothesis. Yet, there are several specific points that still need to be resolved. First, to what extent does the axoneme distort during the beat cycle, and does the observed distortion support the geometric-clutch interpretation, which maintains that interdoublet spacing is the principal modulator of dynein activity? Second, what is the nature of the spoke-CP interaction? (Do the spoke heads actually bind to the CP projections? Does spoke-CP binding directly alter the activation state of the associated dyneins, and does this process have a means of reciprocation between the two dynein sets that bend the flagellum in opposite directions?) These are the key issues if the CP-spoke axis hypothesis is to be considered part of the primary mechanism that generates the beat cycle.

Finally, the dynamics of the dynein motor itself need to be better understood. The latest experimental evidence from our laboratory (Lesich et al., 2008) suggests that the microtubule-binding affinity of the dynein motors is crucial to the switch-point of the beat cycle. This supports the idea that the load-bearing capacity of the dynein-tubulin bridges is essential to the mechanism of beat-cycle generation. However, it does not discriminate between a beat-cycle mechanism based on a t-force load limit (i.e. the geometric clutch) and models based on the dynein cross-bridge cycle, especially if loading is invoked as the mechanism that turns the dyneins ‘off’ [as proposed by Camelet et al. (Camelet et al., 1999)]. Ultimately, experimental investigation of the response of the dynein motor to external loading might be able to settle this issue.

Our thanks to David Mitchell for the excellent micrograph used in Fig. 6 and to Mary Porter for helpful consultation on pf mutants. This work was supported by grant MCB-0516181 from the National Science Foundation.