Sperm motility analyses

Mouse sperm were collected by cutting off the cauda epididymites followed by a swim-out process in modified TYH medium (10 mM HEPES pH 7.4, 135 mM NaCl, 4.8 mM KCl, 2 mM CaCl₂, 1.2 mM KH₂PO₄, 1 mM MgSO₄, 5.6 mM glucose, 0.5 mM Na-pyruvate, 10 mM l-lactate) for 30 min at 37°C. Sperm were collected carefully without touching oil and tissue fragments.

Freely swimming and tethered sperm were studied in TYH medium containing 3 and 0.3 mg/ml BSA, respectively. Images were recorded using a high-speed camera (pco.dimax; PCO AG) and an inverted microscope (IX 71; Olympus). The temperature of the microscope was adjusted to 37°C using an incubator (Life Imaging Services, Switzerland). Wide-field images were recorded at 50 FPS using a 4× objective (UPLanFLN; Olympus) and custom-made observation chambers with a 100-μm depth. Illumination was achieved using a 660-nm LED. Dark-field and holographic recordings were achieved using a 10× objective (UPLSAPO10X; Olympus) and an additional 1.6× magnifying lens.

Dark-field images were recorded at 250 FPS using a M730L4 LED light source. For analysis, images were processed by a Gaussian blur (sigma: 0.5 pixels) and the Subtract Background method (radius: 5 pixels) in ImageJ. Next, the flagellar analysis was performed using SpermQ (20). Positive curvature refers to bending in the direction of the hook-shaped sperm head. The peak frequency was determined from the Fast Fourier Transform of the curvature values. Individual values for all the analyses are provided in table S3.

Three-dimensional holographic images were recorded at 500 or 1000 FPS in observation chambers with a 150-μm depth. Coherent illumination was produced by a 510-nm laser (LDH-D-C serials, PicoQuant GmbH) and the corresponding controller (Sepia II Multichannel Processor, PicoQuant GmbH). Holograms were analyzed as previously described (25). In brief: The background was calculated by averaging all the holograms from each recording, and a background-free hologram was obtained by dividing the original hologram by the background. The Rayleigh-Sommerfeld back-propagation method (59) was used to numerically refocus each background-free hologram, resulting in a refocused stack. A filter based on the Gouy phase anomaly (60) was applied on the refocused stack, and the 3D coordinates of the sperm flagellum were extracted by localizing the brightest shape in the refocused stack. The head x and y coordinates were estimated by calculating the center of mass of the scattering pattern from the sperm head. To determine robustly the z head coordinates, we fitted a plane to the basal end of the flagellum (about 11 μm from the head center). The head z coordinate was obtained by substituting the head x and y coordinates into the plane equation. All the analysis was done in the open-source software ImageJ combined with custom-made Java plugins.

Three-dimensional trajectories predicted from flagellar beat patterns were computed using resistive-force theory, as previously described (25, 29), using the 2D flagellar beat pattern from tethered sperm (Fig. 3A) and assuming a constant z = z(s) component characterized by an arc of curvature κ_z = 5 × 10⁻³ μm⁻¹ along the full flagellar arc length s.

Color-coded videos and projections were generated using custom ImageJ macros. The macros and code are open source and freely available at https://github.com/hansenjn/ColorStackByTimeAndProject.