Hydrodynamics of the double-wave structure of insect spermatozoa flagella

TL;DR

This paper investigates the hydrodynamics of insect spermatozoa with a double-wave flagellar structure, revealing how superimposed helical waves contribute to swimming, with implications for understanding flagellar propulsion mechanisms.

Contribution

It introduces a hydrodynamic model of superhelical flagella, providing new insights into the propulsion mechanisms of insect sperm with double-wave structures.

Findings

Propulsion mainly driven by the minor wave.

Negligible contribution from the major wave.

Counter-intuitive effects when minor and major waves have opposite chirality.

Abstract

In addition to conventional planar and helical flagellar waves, insect sperm flagella have also been observed to display a double-wave structure characterized by the presence of two superimposed helical waves. In this paper, we present a hydrodynamic investigation of the locomotion of insect spermatozoa exhibiting the double-wave structure, idealized here as superhelical waves. Resolving the hydrodynamic interactions with a non-local slender body theory, we predict the swimming kinematics of these superhelical swimmers based on experimentally collected geometric and kinematic data. Our consideration provides insight into the relative contributions of the major and minor helical waves to swimming; namely, propulsion is due primarily to the minor wave, with negligible contribution from the major wave. We also explore the dependence of the propulsion speed on geometric and kinematic parameters, revealing counter-intuitive results, particularly for the case when the minor and major helical structures are of opposite chirality.