Mechanical properties of the passive sea urchin sperm flagellum

In this study we used Triton X-100 extracted sea urchin spermatozoa to investigate the mechanical behavior of the basic 9+2 axoneme. The dynein motors were disabled by vanadate so that the flagellum is rendered a passive structure. We find that when a proximal portion of the flagellum is bent with a glass microprobe, the remainder of the flagellum distal to the probe exhibits a bend in the opposite direction (a counterbend). The counterbend can be understood from the prevailing sliding doublet model of axoneme mechanics, but does require the existence of elastic linkages between the outer doublets. Analysis of the shapes of counterbends provides a consensus value of 0.03-0.08/µm^2 for the ratio of the interdoublet shear resistance (E_S) to the bending resistance (E_B) and we find that the ratio E_S/E_B is relatively conserved for both passive flagella and transiently quiescent live flagella. This ratio expresses a fundamental mechanical property of the eukaryotic axoneme. It defines the contributions to total bending resistance derived from bending the microtubules and from stretching the interdoublet linkages, respectively. Using this ratio, and computer simulations of earlier experiments that measured the total stiffness of the flagellum, we obtain estimates of approximately 1 × 10^8 pN nm^2/rad for E_B and 6 pN/rad for E_S, assuming that both elasticities are linear. Our results indicate that the behavior of the flagellum is close to that predicted by a linear model for shear elasticity