Research ArticleBIOPHYSICS

Human sperm uses asymmetric and anisotropic flagellar controls to regulate swimming symmetry and cell steering

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Science Advances  31 Jul 2020:
Vol. 6, no. 31, eaba5168
DOI: 10.1126/sciadv.aba5168
  • Fig. 1 The postulation of symmetry has not changed since Leeuwenhoek’s first observations in the 17th century.

    (Top) The flagellar beat is asymmetric in 3D, characterized by a one-sided stroke in each beating plane that rotates with the flagellum. The out-of-plane motion causes the sperm flagellum to roll around the swimming axis (dark blue axis), causing the sperm to move equally on all sides in 3D. This creates the effect of a precessing spinning top, in which head spinning, ωspin, around the longitudinal axis of the sperm (yellow axis) occurs at the same time as, and independently of, the flagellar rolling, ωroll, around the swimming axis (Supporting Video S2). (Bottom) Planar projection of the 3D beat averages out the one-sided asymmetric stroke and creates the optical illusion of bilateral symmetry in 2D microscopy. Symmetry is thus achieved through asymmetry.

  • Fig. 2 3D flagellar beating of human spermatozoa.

    Sperm swimming near to (A and B) and far from (C and D) the coverslip: (A and C) flagellar waveform relative to the laboratory fixed frame of reference (x, y, z) and (B and D) relative to the comoving frame of reference (xc, yc, zc) (see Materials and Methods). In (A) to (D), color progression of the waveform through the flagellar rolling cycle is indicated by the cyclic color map inset, with periods of 474 ms for (A) and (B) and 285 ms for (C) and (D). The red curves depict the trajectory of the mid-flagellar point, indicated by the red plane cross section in (B) and (D). Light gray areas in (A) to (D) show the flagellar projection highlighting the shadow of the wave envelope in each plane. Note that 2D microscopy can only capture the planar xy projection depicted. The flagellum rotates around the mean swimming axis, i.e., the rolling axis, depicted by the black straight line in (B) and (D) with the arrow indicating the rolling direction. (B) and (D) show highly symmetric beating in both planar (xy) and out-of-plane direction (z), see also movies S2 and S3 showing (A) and (B). (A and B) and (C and D) show results for sperm sp6 and sp23, respectively, as described in Materials and Methods.

  • Fig. 3 Human sperm beats anisotropically and asymmetrically in 3D.

    (A to D) The comoving frame of reference (xc, yc, zc) for spermatozoon sp6 in Fig. 2 (A and B) with rolling axis upright (black line) and arrow showing the rolling direction in (A) and (B). (E to H) The comoving-rolling frame of reference (xcr, ycr, zcr) showing waveform in absence of rotation around the rolling axis (black line) in (E) and (F). Movies S3, S4, and S5 show fixed, comoving, and comoving-rolling frames of reference. (E) Three beating planes are introduced as follows: “b plane” (blue) captures the xy planar projection, “z plane” (red) captures the out-of-plane motion, and “rolling plane” (green) is the plane perpendicular to the rolling axis. (B and F) Principal components analysis (PCA) reconstruction using the first two PCA modes. Inset shows the cyclic color map for (A), (B), (E), and (F) with a period of 474 ms; light-gray areas show flagellar projections highlighting the wave envelope in each plane. (C) and (G) show the time evolution of the first PCA mode (blue) and second PCA mode (orange) for different views [left and right plots in (C) and (G)]. (D and H) Fourier analysis of the waveform. For both (D) and (H): left plot, static (black) and dynamic (red) Fourier modes; middle plot, Fourier reconstruction of the waveform using a superposition of the static mode (black) and dynamic mode (red); and right plot, original data. Frame of references, PCA, and Fourier analyses are detailed in Materials and Methods.

  • Fig. 4 The 3D flagellar beating is a transverse superposition of a traveling wave and a standing wave.

    Fourier analysis of each transverse plane across the free-swimming sperm population for a total of 28 spermatozoa: 20 cells near to the coverslip and 8 cells far from the coverslip, with heights between 0 and 85 μm, as detailed in Materials and Methods. (A and D) The comoving and comoving-rolling frame of references, respectively, for the spermatozoon sp6 depicted in Fig. 3. (B and C) Columns, for the comoving frame coordinates (yc, zc); (E and F) Columns, for the comoving-rolling frame coordinates, (ycr, zcr), denoted, respectively, by b plane (E) and z plane (F). In (B), (C), (E), and (F), top and middle rows show the amplitude of the static and dynamic modes rescaled by 1.6 μm, respectively, as a function of arc length. The bottom row shows the phase of the dynamical mode as a function of arc length. Black curves depict averages in the free-swimming sperm population. The transformations between referential frames and Fourier analysis are detailed in Materials and Methods.

  • Fig. 5 Hydrodynamic modulation of the beat by the coverslip and the logarithmic flagellar helix are anisotropic.

    Each column (A to D), from top to bottom, respectively, the averages for spermatozoa swimming near to (blue; 20 cells) and far from (red; 8 cells) the coverslip of the static and dynamic modes and phase of yc (A), zc (B), ycr (C), and zcr (D) from Fig. 4. Sperm swimming far from the coverslip ranged their heights between 20 and 85 μm, as detailed in Materials and Methods. The static mode is a logarithmic-like helix that dictates the sperm rolling direction in (E) to (H). (E) The averaged static mode of the coordinates ycr0 and zcr0 across the population, shown in the top row of Fig. 4 (C and D) by the black curves, defines a right-handed helix in 3D (black curve), denoted by h(s). The helix projection at the rolling plane (green plane) is an asymmetric, counterclockwise spiral (gray curve). The b plane and z plane are shown, respectively, by the blue and red planes. Arrows depict the Frenet basis (normal and binormal vectors) showing that the helix is right handed (see Materials and Methods). The dashed straight line is the rolling axis; (F) radius of the spiral r in polar coordinates (r, α) as a function of arclength s (black curve); (H) radius squared of the spiral, r2, in function the polar angle α (black curve), with blue squares showing the linear regression before and after the maximum at α = 0, denoted by rmax. The red curve and blue squares in (F) show, respectively, the Gaussian fit and the linear regression, as in (H), but only for the first half before rmax ; (G) pitch of the helix, p(s), as a function of arc length s (black curve) and its exponential fit (red curve), see main text for details.

  • Fig. 6 Helical waves of flagellar perversion.

    (A) Typical flagellar bending around the rolling axis (black line) with ribbon’s color showing the torsion intensity as in (C). (B) Time series of the 3D waveform with ribbon’s color showing the magnitude in curvature κ in units of μm−1. (C) Torsional waves in the absence of bending deformation with ribbon colors showing the torsion τ in units of μm−1. All twisted ribbons in (A) to (C) show the torsional angle of rotation along the flagellum (see Materials and Methods). (D to G) Kymographs of the curvature κ, torsion τ, spiral’s curvature κs (projection in the rolling plane), and the chirality ψ in radians as a function of arc length s and time t (see Materials and Methods). Overlaid black line indicates that the speed of propagation in (D) to (G) is the same. The dashed lines in (D) to (G) show the time duration depicted in (B) and (C). (H and I) Top to bottom is as follows: amplitude of the static and dynamic modes and phase, respectively, for (H) column the curvature κ and (I) column the absolute torsion ∣τ∣, with black curves depicting averages across all free-swimming spermatozoa (see Materials and Methods). (D to I) Curvature and torsion are in units of μm−1. (A) to (G) show results for sperm sp8 (see Materials and Methods). The waveform parameters and Fourier analysis are detailed in Materials and Methods.

  • Fig. 7 Flagellar rolling and head spinning, hydrodynamic modulation, and 2D microscope projections.

    (A) Correlation between the beating frequency, defined by the first peak of the Fourier spectrum of the 3D curvature [red curve in (F)], ωκ, and the torsion’s frequency, ωτ. (B) Strong correlations between torsion ωτ and the head spinning frequency ωspin and (C) between curvature ωκ and flagellar rolling frequency ωroll. (D) No correlation exists between head spinning, ωspin, and flagellar rolling frequency around the swimming axis, ωroll. (E) From top to bottom, respectively, the averages across the population of the static and dynamic modes and phase of the curvature κ, for the sperm near to (blue; 20 cells) and far from (red; 8 cells) the coverslip. Sperm swimming far from the coverslip ranged their heights between 20 and 85 μm, as detailed in Materials and Methods. (F and G) 2D microscopy fails to capture beating asymmetry: (F) Typical Fourier spectrum of the 3D curvature (red) and the 2D curvature κ2D (black), obtained by projecting the 3D waveform in the xy plane (gray curves in Fig. 2, B and D and Materials and Methods). The first peak in κ (red) defines the beating frequency ωκ. κ2D is characterized instead by two frequency peaks (black markers), denoted by ωκ2D1,2, while zeroth mode (static mode) is zero. (G) No correlation exist between the first frequency peak of the 2D curvature ωκ2D1 and the head spinning ωspin.

  • Fig. 8 Ultrastructural and molecular origin of the flagellar anisotropy.

    (A) The flagellar beating anisotropy in 3D, as in Fig. 4D, showing the b plane and z plane. (B) Representation of a mammalian sperm flagellum showing the tapering of the reinforcing ultrastructure along the flagellar length (blue), with the axoneme depicted in yellow. (C) The cross section of a mammalian sperm flagellum [rectangle in (B)] showing that the 9 + 9 + 2 ultrastructure (2) is anisotropic. The 9 + 2 axoneme is surrounded by nine outer dense fibers (gray); however, the outer dense fibers 8 and 3 are replaced by two diagonally opposite LC. The LCs constrain the beating to the weaker side of the flagellum (blue double arrow), thus potentially coaligned with the b plane in (A). The reduced amplitudes of the z plane (red) in (A) are likely to be suppressed by the stronger side of the flagellum and thus aligned with the plane defined by the LCs (red double arrow). (D) Anisotropic bilateral localization of Hv1 proton channels (blue eclipses) compared with the symmetrical, quadrilateral localization of CatSper ion channels (red ellipses) reported by Lishko’s group (34), in a flagellar cross section. Dashed circular region (light blue) shows the CatSper channel mostly affected by one of the Hv1 channels in close proximity, which is also located near to one of the LCs, thus affecting molecular motors anisotropically along the stronger side of the flagellum.

Supplementary Materials

  • Supplementary Materials

    Human sperm uses asymmetric and anisotropic flagellar controls to regulate swimming symmetry and cell steering

    Hermes Gadêlha, Paul Hernández-Herrera, Fernando Montoya, Alberto Darszon, Gabriel Corkidi

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