Axoneme distortion in sea urchin sperm flagella evaluated by a geometric analysis of bending and shear.


C. B. Lindemann, T. G. dePinho, D. W. Pelle and K. A. Lesich


Biological Sciences, Oakland University, Rochester, MI


When the axoneme of a flagellum or cilium bends, it is an accepted maxim that the resulting interdoublet shear can be found by multiplying the interdoublet spacing in the bending plane by the shear angle. Shear angle is the difference in angle of the flagellum (radians) from the flagellar base to the point of interest. This relationship rests on the assumption that the outer doublet microtubules of the axoneme are relatively inextensible and incompressible under physiological loading; an assumption that was tested by Brokaw (1991, J. Cell Biol. 114: 1201-1215) and found to be essentially correct. Due to the presence of interdoublet elastic linkages (nexin links) in an intact sea urchin flagellum, the unrestrained passive flagellum can only be straight when the interdoublet shear is zero. Sea urchin sperm that are treated with 50 μM sodium metavandate in the presence of 0.1 mM Mg-ATP are rendered passive by inactivation of the dyneins. When sperm in this condition are bent with a glass microprobe, the flagellum distal to the probe develops a “counterbend”, which is a bend of opposite curvature to the imposed bend (Pelle et al., 2009, Cell Motil. Cytoskeleton 66: 721-735). When bends were imposed on passive sea urchin flagella, the resulting counterbend was generally insufficient to bring the tip of the flagellum back to the shear angle of the flagellar base. Most often, when the flagellum was bent in the middle or basal region, the tip of the flagellum was straight; this indicates that there is no residual interdoublet shear at the tip. At the same time, the shear angle of the tip was as often as much as one radian different from the base angle.Under these circumstances, either the assumption that the doublets are incompressible and inextensible is incorrect, or the interdoublet spacing must be reduced in the bent region. Since the imposed bends were similar in magnitude to normal physiological bending during the beat cycle, the assumption of incompressibility/inextensibility of the doublets is likely valid. Therefore, we must conclude that the interdoublet spacing of the axoneme distorts appreciably (as much as 40%) under physiological loading. Supported by grant MCB-0918294 from the National Science Foundation.