Counterbend of Tapered Elastic Filament-Bundles #

Natasha Avery, Alan Champneys, Hermes Bloomfield-Gadelha

10:50 Wednesday in 4Q08.

Part of the Filaments, membranes, and shells session.

Abstract #

In this talk we will discuss a static, geometrically exact, sliding filament model, allowing only for varying rates of taper in the filament-bundles. This is an attempt to explain the diversity of counterbend observed in the sperm flagella of different species, specifically sea urchin and rat. Rat sperm possess outer dense fibers surrounding the axoneme which taper along the length of the flagella, whereas, sea urchin sperm lacks such structures meaning they do not have a tapered structure. Four different rates of tapering are considered by varying the bend modulus of the filament-bundles, in order to discern the effect on the post-buckled geometry. It is found that counterbend positively correlates to the rate of taper, which is most easily observed when the basal compliance is low, and sliding resistance through the filament is high. Post-buckled geometry for sea urchin sperm flagella has been qualitatively recreated, both here and in previous works. Given the results obtained by studying various tapered filament bundles, it would appear that there are other factors relating to structure of rat sperm flagella which are not accounted for in the model.