Flagellar energetics from high-resolution imaging of beating patterns in tethered mouse sperm

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.

CRISPs Function to Boost Sperm Power Output and Motility

“…1.5 glass coverslip (Thermo Fisher Scientific). Head tethered sperm with free beating flagellum were imaged at room temperature (25°C) within 10–15 min of collection from the cauda epididymis at 400 fps for 10 s of which the first 1,000 frames were used in the analysis as described previously ( Nandagiri et al, 2021 ). N = 25–30 sperm/genotype from at least 5–6 mice were imaged and analyzed.…”

“…The best-case blur free motion capture of the system using 400 fps allowed element point velocities of 130 microns per second at Nyquist-Shannon frequency sampling to be measured. Mouse sperm are 110 μm in length and were divided into three parts: mid-piece (24 μm), principal piece (80 μm) and end piece (∼6 μm) for analysis ( Nandagiri et al, 2021 ).…”

“…Image-analysis protocols are used to extract smooth centerlines of sperm in every frame of the recorded image sequence ( Nandagiri et al, 2021 ). The tangent angle at any point on the centerline is the angle made by the tangent at that point with the horizontal axis.…”

“…The tangent-angle data is obtained at discrete locations, s 1 , s 2 , …, s M , and at times, τ 1 , τ 2 , …, τ N . The proper orthogonal decomposition of the tangent angle profile has been described previously by Werner et al (2014) and Nandagiri et al (2021) . With this technique, the tangent angle data is resolved into a weighted sum of time-independent tangent angle profiles known as the shape modes:…”

“…These knowledge gaps are due in large part to the challenges of imaging sperm flagellar motion and the absence of analytical processes to unravel the subtle changes in sperm flagellum function required to achieve optimal fertility. Recently, we have solved this challenge through the development of an imaging and analysis pipeline capable of mathematically quantifying the flagellar waveform with sufficient resolution to enable the measurement of kinematic characteristics such as the beat frequency and flagellar velocities and the spatiotemporal distribution of the hydrodynamic power dissipated along the tail ( Nandagiri et al, 2021 ). Our approach takes advantage of the fact that many mammalian sperm are known to swim close to walls with their flagella beating in a plane that is parallel to the surfaces ( Nosrati et al, 2015 ; Raveshi et al, 2021 ).…”