Charles B. Lindemann

Advances in imaging at the molecular scale have provided greater detail concerning the three‐dimensional structure of the ciliary/flagellar axoneme. Additionally, it has recently been confirmed that electrostatic forces regulate the dynein‐tubulin interaction at the microtubule binding domain (MTBD) of dynein, and at the junction of the nexin‐dynein regulatory complex (N‐DRC) with the adjacent outer doublet. There is also considerable evidence that radial spokes (RSs) and the central pair (CP) apparatus primarily contribute to the mechanical functioning of the axoneme. These discoveries make it possible to analyze in more detail how stresses are transferred within the three‐dimensional axoneme structure. This report evaluates how stress that is generated when the axoneme bends is distributed to the various structural components. Based on the latest findings, it appears that transverse stress generated during active beating is primarily distributed to the N‐DRC and the MTBDs of the dynein heavy chains. It is the balance of tension between the N‐DRC and inner dynein arms (IDAs) that is the key regulator of dynein switching in the beat cycle. The stress distribution to the IDAs impacts the functioning of the dynein heavy chains by inhibition of stepping. This analysis supports a key tenet of the Geometric Clutch (GC) hypothesis of flagellar beating.

This essay presents a hypothesis which contends that the development of organismic complexity in the eukaryotes depended extensively on propagation via flagellated and ciliated gametes. Organisms utilizing flagellate and ciliate gametes to propagate their germ line have contributed most of the organismic complexity found in the higher animals. The genes of the flagellum and the flagellar assembly system (intraflagellar transport) have played a disproportionately important role in the construction of complex tissues and organs. The hypothesis also proposes that competition between large numbers of haploid flagellated male gametes rigorously conserved the functionality of a key set of flagellar genes for more than 700 million years. This in turn has insured that a large set (>600) of highly functional cytoskeletal and signal pathway genes is always present in the lineage of organisms with flagellated or ciliated gametes to act as a dependable resource, or “toolkit,” for organ elaboration. Also see the video abstract here: https://youtu.be/lC5nC-WOcm8

The mechanism that allows the axoneme of eukaryotic cilia and flagella to produce both helical and planar beating is an enduring puzzle. The nine outer doublets of eukaryotic cilia and flagella are arranged in a circle. Therefore, each doublet pair with its associated dynein motors, should produce torque to bend the flagellum in a different direction. Sequential activation of each doublet pair should, therefore result in a helical bending wave. In reality, most cilia and flagella have a well‐defined bending plane and many exhibit an almost perfectly flat (planar) beating pattern. In this analysis we examine the physics that governs flagellar bending, and arrive at two distinct possibilities that could explain the mechanism of planar beating. Of these, the mechanism with the best observational support is that the flagellum behaves as two ribbons of doublets interacting with a central partition. We also examine the physics of torsion in flagella and conclude that torsion could play a role in transitioning from a planar to a helical beating modality in long flagella. Lastly, we suggest some tests that would provide theoretical and/or experimental evaluation of our proposals.

The eukaryotic flagellum is the organelle responsible for the propulsion of the male gamete in most animals. Without exception, sperm of all mammalian species use a flagellum for swimming. The mammalian sperm has a centrally located 9 + 2 arrangement of microtubule doublets and hundreds of accessory proteins that together constitute an axoneme. However, they also possess several characteristic peri‐axonemal structures that make the mammalian sperm tail function differently. These modifications include nine outer dense fibers (ODFs) that are paired with the nine outer microtubule doublets of the axoneme, and are anchored in a structure called the connecting piece located at the base. The presence of the ODFs and connecting piece, and the absence of a basal body, dictate that physical forces generated by the dynein motors are transmitted to the base of the flagellum through the ODFs. Mammalian sperm flagella also possess a mitochondrial and a fibrous sheath that encircle most of the axoneme. These sheaths and the ODFs add mechanical rigidity to the flagellum creating the functional effect of increasing bend wavelength, which requires the entrainment of more dynein motors in the production of a single wave. The sheaths also act as a retinaculum and maintain the integrity of the central axoneme when large bending torques are generated by dynein. Large torque production is crucial to the process of hyperactivation and the unique motility transitions associated with effective fertilizing capacity. Consequently, these specialized anatomical features are essential for the effective interaction of sperm with the female reproductive tract and ovum.

It has been 20 years since the geometric clutch (GC) hypothesis was first proposed. The core principle of the GC mechanism is fairly simple. When the axoneme of a eukaryotic flagellum is bent, mechanical stress generates forces transverse to the outer doublets (t-forces). These t-forces can push doublets closer together or pry them apart. The GC hypothesis asserts that changes in the inter-doublet spacing caused by t-forces are responsible for the activation and deactivation of the dynein motors, that creates the beat cycle. A series of computer models utilizing the clutch mechanism has shown that it can simulate ciliary and flagellar beating. The objective of the present review is to assess where things stand with the GC hypothesis in the clarifying light of new information. There is considerable new evidence to support the hypothesis. However, it is also clear that it is necessary to modify some of the original conceptions of the hypothesis so that it can be consistent with the results of recent experimental and ultrastructural studies. In particular, dynein deactivation by t-forces must be able to occur with dyneins that remain attached to the B-subtubule of the adjacent doublet.

Sperm flagella derive their motive power from the motor protein dynein. In this study, we show that maintenance of the flagellar beat cycle in detergent‐extracted bull sperm models is highly dependent on the ratio of Mg²⁺ to adenosine triphosphate (ATP). An excess of either ATP un‐complexed with Mg²⁺, or an excess of Mg²⁺ without an equivalent concentration of ATP, results in the loss of beat amplitude and a reduced curvature development in the beat cycle. In addition, we find that adenosine diphosphate (ADP) can stabilize the beat cycle and permit rhythmic beating across a broader range of ATP and Mg²⁺ concentrations. We provide evidence that suggests that when ATP is un‐complexed with Mg²⁺, it disrupts the beat cycle by reducing dynein adhesion and thereby, reduces the transmission of dynein‐generated force between the doublets. Excess Mg²⁺ does not act by the same mechanism and induces a condition where the flagellum is more resistant to bending. This is consistent with the idea that high Mg²⁺ stabilizes rigor bridges, and ATP reduces the microtubule binding affinity of dynein. Our results may explain how intact sperm are able to sustain coordinated flagellar beating under a wide range of metabolic conditions, as intact sperm produce ADP in direct proportion to their consumption of ATP.

We report the results of an ultrastructural study of Triton X‐100‐extracted, Mg‐adenosine triphosphate (ATP)‐reactivated bull sperm. We utilized a rapid fixation method to look for differences in the flagellar apparatus that correlate to the state of motility of reactivated sperm models. In a companion article, we examined the motility characteristics induced in bull sperm models by varying the concentration ratio of ATP and Mg²⁺ and the stabilizing effect of adenosine diphosphate (ADP) on coordinated beating. Based on the results of that report, we selected four dissimilar states that appeared to represent extremes. One reactivation condition produces vigorous motility similar to live sperm, another produces large amplitude, low frequency beating while the remaining two conditions produce small amplitude vibrations of the flagellum with little coordinated beating. Morphometric analysis of transmission electron micrographs of sperm from these four treatment conditions revealed statistically significant differences between the samples in regard to axoneme diameter, inter‐microtubule doublet spacing, and outer dense fiber (ODF) spacing. Our results show that Mg²⁺ decreases the axoneme diameter and reduces interdoublet spacing, while ATP, uncomplexed with Mg²⁺, had the opposite effect. We also provide supporting evidence that this may be due to Mg²⁺ increasing, and ATP decreasing, the interdoublet adhesion of dynein. We also found that 4 mM ADP significantly increases the separation between the ODFs and the space between the ODFs and the central axoneme within the middle piece. We present a hypothetical explanation that is consistent with our results to explain how ATP, ADP, and Mg²⁺ act to regulate the beat cycle.

Calcium regulation of flagellar motility is the basis for chemotaxis, phototaxis, and hyperactivation responses in eukaryotic flagellates and spermatozoa. Ca²⁺is the internal messenger for these responses, but the coupling between Ca²⁺and the motor mechanism that generates the flagellar beat is incompletely understood. We examined the effects of Ca²⁺on the flagellar curvature at the switch‐points of the beat cycle in bull sperm. The sperm were detergent extracted and reactivated with 0.1 mM adenosine triphosphate (ATP). With their heads immobilized and their tails beating freely it is possible to calculate the bending torque and the transverse force acting on the flagellum at the switch‐points. An increase in the free Ca²⁺concentration (pCa 8 to pCa 4) significantly decreased the development of torque and t‐force in the principal bending direction, while having negligible effect on the reverse bend. The action of Ca²⁺was more pronounced when the sperm were also treated with 4 mM adenosine diphosphate (ADP); it was sufficient to change the direction of bending that reaches the greater curvature. We also observed that the curvature of the distal half of the flagellum became locked in one direction in the presence of Ca²⁺. This indicates that a subset of the dynein becomes continuously activated by Ca²⁺and fails to switch with the beat cycle. Our evidence suggests this subset of dyneins is localized to doublets #1–4 of the axoneme.