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Multifocal imaging for precise, label-free tracking of fast biological processes in 3D.
Hansen JN
,
Gong A
,
Wachten D
,
Pascal R
,
Turpin A
,
Jikeli JF
,
Kaupp UB
,
Alvarez L
.
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Many biological processes happen on a nano- to millimeter scale and within milliseconds. Established methods such as confocal microscopy are suitable for precise 3D recordings but lack the temporal or spatial resolution to resolve fast 3D processes and require labeled samples. Multifocal imaging (MFI) allows high-speed 3D imaging but is limited by the compromise between high spatial resolution and large field-of-view (FOV), and the requirement for bright fluorescent labels. Here, we provide an open-source 3D reconstruction algorithm for multi-focal images that allows using MFI for fast, precise, label-free tracking spherical and filamentous structures in a large FOV and across a high depth. We characterize fluid flow and flagellar beating of human and sea urchin sperm with a z-precision of 0.15 µm, in a volume of 240 × 260 × 21 µm, and at high speed (500 Hz). The sampling volume allowed to follow sperm trajectories while simultaneously recording their flagellar beat. Our MFI concept is cost-effective, can be easily implemented, and does not rely on object labeling, which renders it broadly applicable.
Fig. 1. Multifocal imaging enables high-speed, extended depth-of-field visualization.a Multifocal images, acquired with the MFI system at various scales, demonstrate that MFI can be used to simultaneously image fast-moving objects at different depths. Left to right: grooming Drosophila melanogaster (1×; scale bar 1 mm, bright-field microscopy), foraging Hydra vulgaris (4×; scale bar 200 µm, dark-field microscopy), crawling Amoeba proteus (10×; scale bar 100 µm, dark-field microscopy), and swimming human sperm cell (32×; scale bar 20 µm, dark-field microscopy). b Extended depth-of-field (EDOF) images produced from multifocal images shown in a. c Max-variance maps showing for specific pixel positions the planes (color-coded) wherein the specimen appeared most sharp (sharpness determined as pixel variance), revealing a coarse feature localization of the object in z. Experiments replicated three times with similar results.
Fig. 2. Localizing latex beads in z using four focal planes.a–c Characterizing the relationship between the image and the z-position of a latex bead (diameter 500 nm) in the MFI setup, equipped with a ×20 objective (NA 0.5) and a ×1.6 magnification changer. a Bead radius determined by a circle fit as a function of z-position; mean ± standard deviation of n = 7 beads (left). MF images of a latex bead at an exemplary z-position (right). b Maximum intensity of the bead image as a function of the bead’s z-position in the four focal planes for one exemplary bead. c Difference between the measured bead radius and the calibrated relationship between bead radius and z-position (from panel a) reveals two possible bead z-positions as minima (arrows) for each imaging plane. The overlay of the difference functions from two planes determines the bead’s z-position unequivocally. d Predicted z-precision at different z-positions and e mean z-precision of all z-positions using plane 1 only, planes 1 and 2, planes 1 to 3, or planes 1 to 4. For comparison, the relationship between bead radius and z-position for plane 1 is overlaid in d (red). The range of z-positions with a z-precision better than 0.5 µm is overlaid in e (red). The z-precision was predicted based on the calibrated relationship shown in a (see Methods). f
z-position of a nonmoving bead inferred from MF images based on the calibrated relationship between bead radius and z-position during modulation of the objective z-position with a piezo (step size: 0.1 µm). A linear curve with a unity slope was fit to the data. g
z-precision measured as the standard deviation of the residuals of linear curve fits with unity slope to the inferred z-positions during modulation of the objective z-position (gray), determined from n = 5 beads. The z-precision predicted as in d was overlayed (red). h Representative 3D trajectories of freely diffusing latex beads, displaying a characteristic Brownian motion. Magnified view of an individual trajectory on the right. The z-positions of the beads were inferred by multifocal image analysis. Arrows indicate 10 µm. i Characterization of bead displacement between consecutive frames (n = 81 beads), demonstrating that the displacement of the bead is normally distributed in x, y, and z. j From the variance \documentclass[12pt]{minimal}
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\begin{document}$${\sigma }_{M}^{2}$$\end{document}σM2 of the measured bead displacement and that predicted by diffusion \documentclass[12pt]{minimal}
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\begin{document}$${\sigma }_{D}^{2}$$\end{document}σD2 of the 500 nm beads (standard deviation shown as red dotted line) a localization precision of 45, 37, and 154 in x, y, and z, respectively, can be estimated (see Methods). Data points represent individual beads tracked for a mean duration of 3.3 s. n = 81 beads. Bars indicate mean ± standard deviation. Source Data are available as a source data file.
Fig. 3. Reconstructing flagellar z-positions of human sperm using four focal planes.a, b Characterizing the relationship between image and z-position of human sperm flagella in the MFI setup. a Flagellar width (color-coded), determined by a Gaussian curve fit on a normal to the flagellum, as a function of the flagellar position (arc length) and the z-distance to the respective plane (mean image of n = 12 sperm from five different donors). b Maximum flagellar intensity (color-coded) as a function of the flagellar position (arc length) and the z-position relative to the four planes. c
z-position (color-coded) along the flagellum (arc length) of an immotile human sperm cell inferred from MF images based on the calibrated relationship between the flagellar width, position on the flagellum, and z-distance to the respective plane during modulation of the objective z-position with a piezo (steps 0.1 µm; left). Colored ticks on the arc-length axis mark flagellar positions that are further analyzed by a linear curve fit (right), revealing a linear relationship between the objective z-position and the z-position determined by MF image analysis (m: slope). d Standard deviation (SD) of the residuals of linear curve fits to data as exemplified in c. Mean ± standard deviation of n = 3 sperm of different donors. Source Data are available as a source data file.
Fig. 4. 3D reconstruction of the flagellar beat from a swimming human sperm cell.a 3D visualization of the four planes (depicted in different colors) acquired by MFI and the flagellum reconstructed using SpermQ-MF and the calibrated relationship between flagellar width, position along the flagellum, and z-distance to the respective plane (Fig. 3a). Overlay of three exemplary timepoints. Flagella indicated in blue. Positions of sperm heads indicated as yellow spheres. Arrows indicate 20 µm. b Kymographic representation of flagellar 3D coordinates (color-coded) in a reference system defined by the head-midpiece axis (see sketch on top). For better visualization, only the first second was plotted (reconstructed time span: 2.2 s). c 3D visualization of one beat cycle (time is color-coded). Arrows indicate 10 µm. Shadow indicates a projection of the flagellar beat to the xy-plane. Source Data are available as a source data file.
Fig. 5. Relating flagellar beat pattern and swimming trajectory of human and sea urchin sperm.a, b 3D-tracked flagella from exemplary free swimming, a human and b sea urchin sperm. Views for visualizing the trajectory (left, only every 4th frame plotted for better visualization), the flagellar beat (middle), or sperm rolling (right, a yz-projection of a flagellar point at arc length 20 µm, view in swimming direction). Bars and arrows indicate 10 µm. Additional tracked sperm are displayed in Supplementary Fig. 6–8). c–l Quantification of the swimming and flagellar beating of all tracked sperm (n = 7 human sperm from two different donors and n = 10 sea urchin sperm). c, d 3D swim speed, calculated as described in Supplementary Fig. 5. Each line (c) or point (d) corresponds to one tracked sperm cell. e, f Nonplanarity ratio. Exemplary time courses (e) and median over time (f) of the nonplanarity ratio. The nonplanarity ratio is determined as the ratio of the two minor Eigenvectors of the flagellar inertial ellipsoid29. Dark lines in e show the median over time for the entire time course. Each datapoint in f corresponds to the single-sperm median. g, h Rolling velocity. Exemplary time courses (g) and median over time (h) of the rolling velocity. Positive values indicate clockwise rotation when viewing the sperm from the head to the tail. Dark lines show the median obtained from the whole time series. Each datapoint in h corresponds to the single-sperm median. i–l Frequency spectrum of the flagellar beat in the distal flagellum of human and sea urchin sperm (determined at arc length 33 and 34 µm, respectively) i Frequency spectra for an exemplary human and an exemplary sea urchin sperm. j Frequency of the highest peak in the frequency spectra of all human and sea urchin sperm analysed. Individual data points represent individual sperm. k Frequency spectra of all human and sea urchin sperm analysed after normalization of the frequency axis in each spectrum to the frequency of the highest peak. l Frequency of the highest peak in the frequency spectrum as a function of the time (mean frequency of arc lengths 20–30 µm shown). Each datapoint represents the analysis of the time span from 0.2 s before to 0.2 s after the indicated timepoint. Bars indicate mean ± standard deviation. Source Data are available as a source data file.
Fig. 6. 3D particle imaging velocimetry around a sperm cell.a, b Exemplary 3D trajectories of latex beads flowing around a human sperm cell tethered to the cover glass at the head. Each trajectory is depicted in a different color. Arrows indicate 20 µm. Perspective (a) and top (b) views are shown. The bead trajectories have been projected onto an image of the tracked sperm cell (intensity inverted for better visualization, beads removed by image processing). Arrows indicate 20 µm. c Trajectories (color-coded by time) of few exemplary beads from b. Beads that are remote from the flagellum show Brownian motion; close to the sperm flagellum the beads display a 3D spiraling motion. Time color-coded as indicated. Black arrows mark trajectories magnified in d and e. The other trajectories shown are magnified in Supplementary Fig. 11. d Trajectory of a bead that is attracted to the sperm cell. e Trajectory of a bead that moves away from the flagellum. f Averaging z-projection of the 3D flow profile obtained from the bead motion, for which exemplary trajectories are shown in a–e. The cyan and red arrows indicate a new coordinate system, which is used as a reference to show the 3D flow profile in g. Black arrows are normalized. Flow speed is color-coded. g Flow profile sections in the vicinity of the sperm flagellum, extracted from the 3D flow at the positions marked with cyan and red lines/rectangles in (f). Cross-section (bottom) and top view (top) are shown. Scale bar: 5 µm. Arrow on bottom left indicates 125 µm s−1. Source Data are available as a source data file.
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