Sperm trajectories form chiral ribbons

Abstract

We report the discovery of an entirely new three-dimensional (3D) swimming pattern observed in human and horse sperms. This motion is in the form of 'chiral ribbons', where the planar swing of the sperm head occurs on an osculating plane creating in some cases a helical ribbon and in some others a twisted ribbon. The latter, i.e., the twisted ribbon trajectory, also defines a minimal surface, exhibiting zero mean curvature for all the points on its surface. These chiral ribbon swimming patterns cannot be represented or understood by already known patterns of sperms or other micro-swimmers. The discovery of these unique patterns is enabled by holographic on-chip imaging of >33,700 sperm trajectories at >90-140 frames/sec, which revealed that only ~1.7% of human sperms exhibit chiral ribbons, whereas it increases to ~27.3% for horse sperms. These results might shed more light onto the statistics and biophysics of various micro-swimmers' 3D motion.

Figure 1. Schematics which illustrate the 3D structures of chiral ribbons.

(a) A helical ribbon. (b) A twisted ribbon.

Figure 2. Dual-view and dual-wavelength lensfree 3D tracking of sperms on a chip.

(a) The picture of the imaging system. Two partially-coherent light sources (LED-coupled multimode fibers, core size: 400 μm) illuminate the observation chamber from two different angles with two different wavelengths (vertical one: 625 nm; oblique one at 45°: 470 nm; bandwidth ~20 nm). A CMOS image sensor records the dual-view lensfree holograms that encode the position information of each sperm. (b) The close-up image of an observation chamber that is placed on the top of the CMOS image sensor. (c) The reconstructed 3D spatio-temporal trajectories of 998 horse sperms that were tracked inside a volume of ~9.0 μL at a frame rate of 143 FPS. The inset in (c) shows the trajectories reconstructed inside a sub-volume of the lensfree imaging system. The time position of each track point is encoded by its color (see the color bar).

Figure 3. The chiral ribbon patterns displayed by horse sperm trajectories.

(a) and (d) are two chiral ribbon trajectories recorded over a duration of 4.6 sec. (b) and (e) are digitally zoomed segments (~0.7-sec long each) of the two ribbon trajectories shown in (a) and (d), respectively. Both of the trajectories in (a) and (d) have left-handed twisting and form left-handed helical ribbons. (c) and (f) are two simulated trajectories that were generated by equation 2 to match the measured chiral ribbon trajectories shown in (a) and (d), respectively (see Table 1 for the simulation parameters). The magenta ribbon surfaces in (b) and (e) designate the osculating planes of the twisting ribbon trajectories. The inset in each panel represents the lateral displacement of the straightened sperm trajectory (front view). The arrows indicate the directions of the sperms' forward movement. The time position of each track point is encoded by its color (see the color bar). See Supplementary Movies S1 and S2 for the spatio-temporal evolution of the ribbon trajectories shown in (a) and (d), respectively.

Figure 4. A 5.0-sec long 3D trajectory showing the transitions between different swimming patterns of a horse sperm.

This trajectory switched from a right-handed chiral ribbon pattern to a simple planar swimming pattern when the sperm encountered the bottom glass surface of the observation chamber. (b), (c), and (d) illustrate digitally zoomed segments (~0.7-sec long each) of the whole sperm trajectory shown in (a). The inset in each panel represents the lateral displacement of the straightened sperm track segment (front view). The arrows indicate the directions of the sperm's forward movement. The time position of each track point is encoded by its color (see the color bar). See Supplementary Movie S3 for the spatio-temporal evolution of this trajectory.

Figure 5. Dynamic swimming parameters of 2,625 chiral ribbon trajectories (out of a total of 9,625 motile horse sperms, each ~0.7 sec long).

Color bar represents the relative density of data points in each graph. Magenta lines enclose 90% of the chiral ribbon trajectories presented in each panel. VSL: straight-line velocity. VCL: curvilinear velocity. ALH: amplitude of lateral head displacement. LIN: linearity. RTW: rate of twisting. A chiral ribbon trajectory with RTW > 0 (RTW < 0) is defined as right-handed (left-handed). These measurements were all made with horse sperms suspended in equine semen extender (BotuSemen) after >30 min of incubation.

Figure 6

(a) A 4.4-sec long human sperm trajectory that forms a twisted ribbon.The magenta ribbon surface in (b) designates the right-handed osculating plane of the trajectory. The insets in the panels represent the lateral displacement of the straightened sperm trajectories (front view). The arrows indicate the directions of the sperms' forward movement. The time position of each track point is encoded by its color (see the color bar). See Supplementary Movie S4 for the spatio-temporal evolution of the sperm trajectory shown in (a).

Figure 7. The statistics of human sperm chiral ribbon swimming patterns compared to other swimming patterns observed in human sperms.

The right-handed and left-handed chiral ribbon patterns (excluding hyperactivated ribbons) account for 1.1% and 0.6% of all the 24,090 human sperm trajectories that we reconstructed, respectively. These measurements were made in human sperm baseline medium (artificial HTF) after >2 h of incubation.