Elastic properties of the sea urchin sperm flagellum

The theory of flexural vibrations in thin rods, applied to the movement of flagella, has been extended to include an investigation of the influence of the boundary conditions on the theoretical waveforms. It was found that for flagella which are flexible enough, the flexibility can be estimated solely from the wavelength of the wave traveling in it. This can be expected to hold for those flagella which do not possess a fibrous sheath. The bending moment in flagella in which the ampitude of the wave is maintained as the wave travels distally is almost completely produced by active contractile elements. This means that the active bending moment can be estimated from the radius of curvature of the flagellum and the stiffness. The above findings were applied to the case of the sea urchin sperm flagellum. One finds that the stiffness of the flagellum is caused mainly by the nine longitudinal fibers which must have a Young's modulus of slightly less than 10(8)dyne/cm(2). The longitudinal fibers need to develop a tension of 1.6 x 10(8)dyne/cm(2) to account for the bending moment in the flagellum. These two figures are in line with those found for muscle fibers.