# Human sperm steer with second harmonics of the flagellar beat

## TL;DR

This study reveals that human sperm steer by modulating the second harmonic of their flagellar beat, a mechanism that involves temporal asymmetry and is influenced by progesterone, offering new insights into microswimmer navigation.

## Contribution

The paper demonstrates that second harmonic superposition causes temporal asymmetry in flagellar beating, providing a novel mechanism for sperm steering distinct from previous models.

## Key findings

- Second harmonic superposition breaks beat symmetry temporally.
- Progesterone enhances second harmonic contribution.
- Sperm rotation is controlled by second harmonic amplitude and phase.

## Abstract

Sperm are propelled by bending waves travelling along the flagellum. During steering in gradients of sensory cues, sperm adjust the flagellar beat waveform. Symmetric and asymmetric beat waveforms produce straight and curved swimming paths, respectively. Two different mechanisms controlling the flagellar beat have been proposed: average intrinsic curvature and dynamic buckling instability. Both mechanisms create spatially asymmetric waveforms that could be modulated for steering. Using video microscopy, we image the flagellar waveform of human sperm tethered with the head to a glass surface. The waveform is characterized by a fundamental beat frequency and its second harmonic. We show that superposition of first and second harmonics breaks the beat symmetry temporally rather than spatially. As a result, sperm rotate around the tethering point. The rotation velocity is determined by the amplitude and phase of the second harmonic. Sperm stimulation with the female sex hormone progesterone enhances the second-harmonic contribution, modulates the flagellar beat, and ultimately sperm rotation. The temporal breaking of beat symmetry represents a new mechanism of sperm steering. Higher-frequency components were also reported for the flagellar beat of other cells; therefore, this steering mechanism might by quite general and could inspire the design of synthetic microswimmers.

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Source: https://tomesphere.com/paper/1703.07705