Abstract
We demonstrate a technique for investigating the energetics of flagella or cilia. We record the planar beating of tethered mouse sperm at high resolution. Beating waveforms are reconstructed using proper orthogonal decomposition of the centerline tangent-angle profiles. Energy conservation is employed to obtain the mechanical power exerted by the dynein motors from the observed kinematics. A large proportion of the mechanical power exerted by the dynein motors is dissipated internally by the motors themselves. There could also be significant dissipation within the passive structures of the flagellum. The total internal dissipation is considerably greater than the hydrodynamic dissipation in the aqueous medium outside. The net power input from the dynein motors in sperm from Crisp2-knockout mice is significantly smaller than in wildtype samples, indicating that ion-channel regulation by cysteine-rich secretory proteins controls energy flows powering the axoneme.
Highlights
In their journey towards the oocyte, sperm propel themselves by beating a whip-like flagellum
In all the results presented here, the arc-length coordinate s along the centerline is normalized by the maximum observable length of the whole flagellum in the entire duration of a sample video
Our observation that the mean shape is curved with an anti-hook concave shape is consistent with the observations of Woolley, 2003 that, in mouse sperm, the flagellum bends at the neck more on the ventral side than on the other
Summary
In their journey towards the oocyte, sperm propel themselves by beating a whip-like flagellum. Despite the vast body of work on the structure and function of different parts of the axoneme – the internal ‘engine’ powering the flagellum (Brokaw and Kamiya, 1987; Okagaki and Kamiya, 1986; Yagi et al, 2005) – and other accessory structures that surround the axoneme, such as the outer dense fibers (Zhao et al, 2018) and the fibrous sheath (Eddy et al, 2003), the mechanisms that control the complex beating patterns observed in flagella remain poorly understood (Brokaw, 2009; Lehti and Sironen, 2017; Lindemann and Lesich, 2016; Lin and Nicastro, 2018) It is, recognized that mechanical properties of the flagellum and its surroundings play a crucial role in determining sperm motility (Gaffney et al, 2011). Measurements of the mechanical behavior of single flagella in living sperm have remained a critical bottleneck
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