Structural-functional relationships of the dynein, spokes, and central-pair projections predicted from an analysis of the forces acting within a flagellum

Abstract

In the axoneme of eukaryotic flagella the dynein motor proteins form crossbridges between the outer doublet microtubules. These motor proteins generate force that accumulates as linear tension, or compression, on the doublets. When tension or compression is present on a curved microtubule, a force per unit length develops in the plane of bending and is transverse to the long axis of the microtubule. This transverse force (t-force) is evaluated here using available experimental evidence from sea urchin sperm and bull sperm. At or near the switch point for beat reversal, the t-force is in the range of 0.25-1.0 nN/ micro m, with 0.5 nN/ micro m the most likely value. This is the case in both beating and arrested bull sperm and in beating sea urchin sperm. The total force that can be generated (or resisted) by all the dyneins on one micron of outer doublet is also approximately 0.5 nN. The equivalence of the maximum dynein force/ micro m and t-force/ micro m at the switch point may have important consequences. Firstly, the t-force acting on the doublets near the switch point of the flagellar beat is sufficiently strong that it could terminate the action of the dyneins directly by strongly favoring the detached state and precipitating a cascade of detachment from the adjacent doublet. Secondly, after dynein release occurs, the radial spokes and central-pair apparatus are the structures that must carry the t-force. The spokes attached to the central-pair projections will bear most of the load. The central-pair projections are well-positioned for this role, and they are suitably configured to regulate the amount of axoneme distortion that occurs during switching. However, to fulfill this role without preventing flagellar bend formation, moveable attachments that behave like processive motor proteins must mediate the attachment between the spoke heads and the central-pair structure.

FIGURE 1

Force transfer in the flagellar axoneme. (a) The proposed configuration of the axoneme during the active formation of a new bend. The dyneins on the left side of the axoneme (doublets 6–9) are engaged and pulling, whereas those on the opposite side (doublets 1–4) are inactive. The force from each engaged set of dyneins is relayed to the first and last outer doublet in the active group as indicated by the doubleheaded arrow, in this case doublets 1 and 5–6. In the case illustrated, doublet 1 is pulled tipward and is under tension, whereas the 5–6 complex is pushed baseward and is under compression. (b) When a bend has formed and reached the critical curvature for switching, the t-force becomes large enough to disengage the dyneins on the active side as illustrated. At this crucial instant the t-force is transferred to the spokes and central-pair projections as indicated by the outwardly directed arrows. The central-pair projections not only flex outward bearing the t-force, but also limit the distortion of the axoneme. The increased spacing of the doublets on the active side, coupled with the restraining action of the spoke and central-pair projections, makes it possible for dynein arms on the inactive side to begin to engage. (c) This illustration shows the putative condition of Chlamydomonas spoke-head deficient mutants. In the absence of the spoke heads, the nexin links bear the full t-force, exerted in the direction of the arrows, as the dyneins on the active side disengage. Based on estimates of nexin elasticity (see text), the t-force causes a major distortion of the axoneme preventing reengagement of dyneins on either side of the axoneme. This interrupts the beat cycle until the t-force diminishes sufficiently to allow reengagement.

FIGURE 2

The balance of t-force and dynein bearing force in the axoneme. (a) A beating sperm flagellum is illustrated showing the method of finding the radius of curvature (r) for a newly formed bend. The length of flagellum that is contributing to the formation of the bend (interbend distance) is indicated and is the segment where the curvature is actively changing. It starts at the end of the circularly curved portion of the previous bend and extends to the crest of the new bend. (b) In a simplified representation of the forces acting in the bend, the contributing interbend dyneins push and pull on the doublets to create linear tension and compression. Arrows indicate the tension that develops on the concave side of the bend and the compression that develops on the convex side. In the curved bend, tension and compression lead to the development of outwardly directed t-force, as indicated by the paired arrows. The t-force that develops in the fully formed bend is equal to, or greater than, the holding capacity of the dyneins in the region of maximal curvature.

FIGURE 3

The relationship of dynein force to t-force in a flagellar bend. The figure schematically represents two doublets bridged by active dyneins in a region of active bending. The arrows on the doublets indicate the direction of sliding. The dynein force is transmitted from one doublet to the neighboring doublet through the stalks (or B-links), which are slender α-helical extensions of the dynein molecule. The axis of the stalk (Dynein Axis) defines the direction of the dynein force (DF). The stretched nexin links also contribute an elastic force (NF) in the axis defined by the nexin links (Nexin Axis). The vector diagram above the schematic breaks down the DF and NF into the longitudinal (DF_L/NF_L) and transverse (DF_T/NF_T) components. In the vector analysis, the t-force vector (TF) is balanced by the DF_T and NF_T vectors . The text provides an analysis of the magnitude of the nexin elastic force. This force component is ∼1% of the total t-force magnitude. Therefore, there is a close equivalence between the magnitude of t-force and the transverse component of the dynein force (DF_T), and they are balanced in a Newtonian equilibrium. The relationship of the total dynein force exerted along the dynein stalk to the t-force can therefore be found by application of the Pythagorean theorem, as shown below the schematic.