The elastic rigidity (stiffness) of impaled motionless bull sperm flagella has been determined by a manipulatory technique which permitted direct analytical treatment of the experimental system. The effects of external ATP and ADP were measured. It was found that ATP acts as a plasticizing agent, while ADP does not. The stiffness measured for flagella in a medium without ATP was 15 times greater than the value measured with 10 mM ATP present. The rigor-like stiffness measured with no ATP present is reversible with ATP and seems to be correlated to a transition in the state of the contractile system.

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Detailed observations of the tail movement of non-rotating and rotating bull spermatozoa have been carried out. For rotating sperm a helical tail wave was found with a ratio of the amplitudes of the two perpendicular components of approximately 3 to 1. For both types of cells the variation of the amplitude and the phase shift of the wave as it travels from the proximal to the distal part are reported. Model calculations indicate that the stiffness of the tail originates in the fibrous sheath, which has a Young's modulus of 3 x 10(7) dynes/cm(2). Active contractile elements distributed continuously along the tail are found necessary to maintain the amplitude of the tail wave against damping by the fluid drag. If the longitudinal fibers are identified with the contractile elements the maximum tension to be developed by these fibers is 4 x 10(6) dynes/cm(2). The energy dissipated by the "active" part of the tail wave is at least approximately 70 percent of the total dissipation.

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The motion of the sea urchin sperm flagellum was analyzed from high-speed cinemicrographs. At all locations on the flagellum the transversal motion and the curvature were found to vary sinusoidally in time. The curvatures of the flagella increase strongly near the proximal junction. Two sperm are described in transient from rest to normal motion. The full wave motion developed in both sperm within 40 ms.KEY WORDS sea urchin sperm 9 flagellum motion high-speed film -transientsIn recent years the understanding of the forceproducing mechanisms in sea urchin sperm flagella has advanced greatly. A sliding filament mechanism, in which cross bridges between the longitudinal fibers are formed by the dynein arms, has been shown to operate in these flagella (23, 10). The molecular understanding of the force-producing mechanisms has led several investigators to develop theoretical models for the processes that control and coordinate the attachment and breakage of the dynein cross bridges (3,4,16,17,19,21). The aim of these models is to reproduce the characteristics of the flagellar movements from an equation of motion that contains a prescription for the attachment and detachment of the dynein cross bridges. The somewhat surprising situation exists, however, that a detailed description of the sea urchin sperm flagellar motion has not been presented in the literature. The best data available are from "multiple flash" photographs (1, 6), in which three to five positions of a flagellum are registered on a single still frame. The time interval between the successive positions is of the order of one full period of the flagellar beat. The shape of the flagellar wave is well shown in these photographs, but the time resolution is not sufficient to provide an accurate description of the course of events within a cycle of the flagellar beat. In this paper a description of the motion of the sea urchin sperm flagellum is given, based on data from high-speed cinemicrographs at 400 frames/s. The filming speed was made possible by the application of a very highqntensity illumination of the specimens. MATERIALS AND METHODS Experimental MethodsSea urchins (Arbacia and Lytechinus) were obtained from N.E. Marine Supply Co. (Woods Hole, Mass.) (Arbacia) and Pacific BioMarine Laboratories, Inc.(Venice, Calif.) (Lytechinus). Sperm shedding was induced by injecting the sea urchins with 1-2 ml of 0.5 M KCt. The spermatozoa were collected and suspended in artificial seawater (Aquarium Systems, Inc., Eastlake, Ohio) to a concentration of approx. 2 x 107/ml. Several hundred sea urchin eggs were added per milliliter of the suspension to prolong the life of the sperm. When the spermatozoa were stored at room temperature, their motility in the suspension was, by visual estimate, approximately constant for a period of several hours. The pH of the artificial seawater was kept at 7.9. All specimen handling and observations were carried out at a room temperature of 22 _+ I~ A few drops of sperm suspension were placed on a microscope slide and co...