Planar Beating Research Articles

Human sperm accumulation near surfaces: a simulation study

A hybrid boundary integral/slender body algorithm for modelling flagellar cell motility is presented. The algorithm uses the boundary element method to represent the ‘wedge-shaped’ head of the human sperm cell and a slender body theory representation of the flagellum. The head morphology is specified carefully due to its significant effect on the force and torque balance and hence movement of the free-swimming cell. The technique is used to investigate the mechanisms for the accumulation of human spermatozoa near surfaces. Sperm swimming in an infinite fluid, and near a plane boundary, with prescribed planar and three-dimensional flagellar waveforms are simulated. Both planar and ‘elliptical helicoid’ beating cells are predicted to accumulate at distances of approximately 8.5–22 μm from surfaces, for flagellar beating with angular wavenumber of 3π to 4π. Planar beating cells with wavenumber of approximately 2.4π or greater are predicted to accumulate at a finite distance, while cells with wavenumber of approximately 2π or less are predicted to escape from the surface, likely due to the breakdown of the stable swimming configuration. In the stable swimming trajectory the cell has a small angle of inclination away from the surface, no greater than approximately 0.5°. The trapping effect need not depend on specialized non-planar components of the flagellar beat but rather is a consequence of force and torque balance and the physical effect of the image systems in a no-slip plane boundary. The effect is relatively weak, so that a cell initially one body length from the surface and inclined at an angle of 4°–6° towards the surface will not be trapped but will rather be deflected from the surface. Cells performing rolling motility, where the flagellum sweeps out a ‘conical envelope’, are predicted to align with the surface provided that they approach with sufficiently steep angle. However simulation of cells swimming against a surface in such a configuration is not possible in the present framework. Simulated human sperm cells performing a planar beat with inclination between the beat plane and the plane-of-flattening of the head were not predicted to glide along surfaces, as has been observed in mouse sperm. Instead, cells initially with the head approximately 1.5–3 μm from the surface were predicted to turn away and escape. The simulation model was also used to examine rolling motility due to elliptical helicoid flagellar beating. The head was found to rotate by approximately 240° over one beat cycle and due to the time-varying torques associated with the flagellar beat was found to exhibit ‘looping’ as has been observed in cells swimming against coverslips.

3D structure of eukaryotic flagella in a quiescent state revealed by cryo-electron tomography

We have used cryo-electron tomography to investigate the 3D structure and macromolecular organization of intact, frozen-hydrated sea urchin sperm flagella in a quiescent state. The tomographic reconstructions provide information at a resolution better than 6 nm about the in situ arrangements of macromolecules that are key for flagellar motility. We have visualized the heptameric rings of the motor domains in the outer dynein arm complex and determined that they lie parallel to the plane that contains the axes of neighboring flagellar microtubules. Both the material associated with the central pair of microtubules and the radial spokes display a plane of symmetry that helps to explain the planar beat pattern of these flagella. Cryo-electron tomography has proven to be a powerful technique for helping us understand the relationships between flagellar structure and function and the design of macromolecular machines in situ.

The flagellar beat of rat sperm is organized by the interaction of two functionally distinct populations of dynein bridges with a stable central axonemal partition.

Two distinct patterns of microtubular sliding were observed in rat sperm flagellar axonemes. The particular pattern of sliding was determined by the extraction conditions used to prepare the sperm for axoneme disintegration. Sperm prepared by incubating concentrated suspensions of Triton X-100-extracted sperm at pH 9.0 disintegrated by extruding the doublets and outer dense fibers numbered 4 through 7 in response to Mg-ATP. Sperm prepared by incubating motile Triton X-100-extracted models at 37 degrees C for 1 to 3 hours extruded doublets and outer dense fibers 9, 1 and 2. Axonemes disintegrated by both regimens tended to have doublets 3 and 8 (with their corresponding outer dense fibers), as well as the central pair, in place. In numerous instances, the 3-central-8 complex with outer dense fibers 3 and 8 could be found isolated in midpiece sections prepared from both methods. The 3-central-8 partition was also sometimes seen in isolation in cross-sections of the principal piece where it remained attached to the fibrous sheath. The flagellar remnant produced by extrusion of fibers 4 through 7 under high pH conditions was generally straight or randomly curved. In contrast, the flagellar remnant produced by extrusion of the 9-1-2 bundle of fibers was most often curved into a hook in the midpiece region. While the hook-like configuration was not Ca(2+)-dependent, it may be based on a related mechanism. The sliding of the 9-1-2 group of fibers is a consequence of dynein-tubulin sliding between the 2 and 3 doublets. This sliding pattern appears to be preferentially activated in the motile sperm models in EGTA, but seldom if ever produced sliding in the high-pH-extracted models. We conclude that the 3-central pair-8 complex and associated outer dense fibers form an I-beam-like partition that does not participate in sliding, but acts as a structural foundation for organizing a planar beat. In addition, it is clear that preferential activation of certain dynein arms can be evoked, depending on the treatment regimen employed. This shows definitively that the types of microtubule sliding in the two bend directions are not identical.