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Laser ablation and fluid flows reveal the mechanism behind spindle and centrosome positioning

Nature Physics volume 20, pages 157–168 (2024)Cite this article

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Abstract

Few techniques are available for studying the nature of forces that drive subcellular dynamics. Here we develop two complementary ones. The first is femtosecond stereotactic laser ablation, which rapidly creates complex cuts of subcellular structures and enables precise dissection of when, where and in what direction forces are generated. The second is an assessment of subcellular fluid flows by comparison of direct flow measurements using microinjected fluorescent nanodiamonds with large-scale fluid-structure simulations of different force transduction models. We apply these techniques to study spindle and centrosome positioning in early Caenorhabditis elegans embryos and to probe the contributions of microtubule pushing, cytoplasmic pulling and cortical pulling upon centrosomal microtubules. Based on our results, we construct a biophysical model to explain the dynamics of centrosomes. We demonstrate that cortical pulling forces provide a general explanation for many behaviours mediated by centrosomes, including pronuclear migration and centration, rotation, metaphase spindle positioning, asymmetric spindle elongation and spindle oscillations. This work establishes methodologies for disentangling the forces responsible for cell biological phenomena.

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Fig. 1: Laser ablation during spindle oscillations in the first mitotic division of C. elegans.
Fig. 2: Open-cylindrical and cup cuts around the posterior centrosomes during spindle oscillations.
Fig. 3: Fluid flows during spindle oscillations.
Fig. 4: Laser ablation and fluid flows in prometaphase and metaphase.
Fig. 5: Laser ablation and fluid flows during migration of the PNC.
Fig. 6: Coarse-grained model of cortical pulling and model predictions.

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Data availability

All data in this study are available from the corresponding authors upon reasonable request.

Code availability

The codes used in this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

Worm strains were provided by M. Delattre and the Caenorhabditis Genetics Center. M.J.S. acknowledges support from the National Science Foundation (NSF) under awards DMR-1420073 (NYU MRSEC) and DMR-2004469. D.J.N. acknowledges NSF grant DBI-1919834, NSF grant 2004380, and the National Institutes of Health grant 1R01GM104976-01. We are grateful to C.-H. Yu who assisted with the optical setup and to C.-Y. Fang for advice on FND surface treatment. We also like to thank R. Farhadifar for helpful discussion over the whole project and advice on modelling, Y.-N. Young for assistance in a technical calculation and J. Howard for helpful discussions.

Author information

Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, MA, USA

    Hai-Yin Wu

  2. Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, USA

    Hai-Yin Wu & Daniel J. Needleman

  3. Center for Computational Biology, Flatiron Institute, Simons Foundation, New York, NY, USA

    Gökberk Kabacaoğlu, Ehssan Nazockdast, Michael J. Shelley & Daniel J. Needleman

  4. Department of Applied Physical Sciences, University of North Carolina, Chapel Hill, NC, USA

    Ehssan Nazockdast

  5. Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan

    Huan-Cheng Chang

  6. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Michael J. Shelley

  7. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Daniel J. Needleman

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  1. Hai-Yin Wu
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Contributions

H.W., D.J.N. and M.J.S. designed the research. H.W. developed the FESLA setup. H.W. conducted all the experiments and data analysis. H.C. provided support for the FND experiments. G.K., E.N. and M.J.S. worked on the large-scale fluid mechanics simulations. M.J.S. and D.J.N. derived and analysed the coarse-grained model. H.W., D.J.N., M.J.S., E.N. and G.K. wrote the paper.

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Correspondence to Hai-Yin Wu.

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Extended data

Extended Data Fig. 1 Orientation terminology, image analysis and centrosome motion quantification.

a, The configuration and the terminology of embryo orientation used in this study. The mitotic spindle is simply illustrated by the green dumbbell, while astral MTs illustrated by slender green sticks. The confocal imaging plane, which is parallel to the coverslip, is defined as the x-y plane, with the z = 0 plane falling at the centre of the spindle or the PNC. The embryo’s A–P direction is assigned as the longitudinal direction (x axis), with the embryo’s posterior end facing the positive x direction. And the transverse direction refers to the y direction. b,c, An example of the centrosome-tracking image. b, The two-colour merged image of an C. elegans embryo expressing mCherry-tagged γ-tubulin (red) and GFP-tagged β-tubulin (green). The two separate images of the dashed-line region are shown in the right panel. The upper one is a γ-tubulin-labeling image with its labeled centrosome locations derived by MATLAB Particle Tracking Code Repository by Daniel Blair and Eric Dufresne. The lower one is a β-tubulin-labeling image, while its centrosome information is derived from the particle tracking code plus the second-step correlation method. c, Top, the square image patch with the artificial ring structure mimicking a centrosome. Bottom, an example of the post-processed (background-subtraction and thresholding) β-tubulin-labeling image used for correlation calculation. (The top and bottom images are displayed on the same scale.) d,e, The information of the embryo long axis (or longitudinal direction) can be extracted automatically in two ways: d, through linear fitting on the trajectory data of the anterior and posterior centrosomes, or e, through fitting the automatic detected embryo contour with a simple ellipse. f, An example of the automatic detected embryo contour and the embryo anterior/posterior ends. g, An example of oscillation peak detection. The crests/troughs (or the peak points) of the transverse oscillations were calculated by (1) first finding the local maxima/minima from the smoothed amplitude data, and then (2) fitting the raw amplitude data, which fall within the 15-second windows around the above detected maxima/minima, by Gaussian function (see the enlargements). The derived peak points are marked by pink asterisks. All scale bars on images are 10 μm.

Extended Data Fig. 2 Dimensions of laser ablations performed during transverse spindle oscillations and the results quantifications.

In 3D schematics a, e, f, and i, centrosomes are represented by two green balls and the spindle body is simplified into the green dashed line. The A–P direction (embryo polarity) is indicated by the brown arrow. The orange and blue arrows displayed on the centrosomes imply the transverse oscillations of the anterior and posterior centrosomes respectively. The posterior part of the corresponding x-y imaging midplane (2D view from the top) is exhibited on the right of each 3D schematic, with the spindle and astral MTs sketched in green and chromosomes in magenta. All ablation geometrics are portrayed in red for both 2D and 3D schematics. a, Dimensions of the arc cuts in Fig. 1e,f, and h,i (all performed with the same angular span stated here). b,c, Calculation of centrosome velocity change (Δvy) for arc cuts. b, Definition of Δvy at timing Tm and Tp respectively. And τw is the sandwiched window (for ablated embryos: this window is the ablation execution time) between the two intervals Δt used for calculating centrosome transverse velocity vy(before) and vy(after). c, The raw data of centrosome position falling within the interval Δt are used to calculate transverse (y) velocity by linear fitting. d, The Δvy data for uncut (control) and arc-cut embryos. Left, the data for Fig. 1e,f (Tm). Right, the data for Fig. 1h,i (Tp). e, A schematic of the double rectangular (y-z) plane cut and the detailed dimensions. f, Dimensions of the open-cylindrical cuts in Fig. 2a–e. g, Measurement on oscillation amplitude change by calculating the amplitude ratio Aafter /Abefore (mentioned in Fig. 2e). The notation A means oscillation transverse amplitude, and D stands for peak-to-valley transverse amplitude/displacement. The oscillation example (pink curve) is the one from Fig. 2d (open-cylindrical cut). The ablation execution is highlighted by the light pink vertical strip. h, The comparison of the amplitude ratios among uncut, double-plane-cut, and open-cylindrical-cut embryos. We found that the more perpendicular MTs that were ablated, the more the oscillation amplitude increased. This is consistent with the perpendicular MTs being subject to pulling forces, and hence constraining centrosome motion. i, Dimensions of the cup cuts in Fig. 2f–i. j, An example image of calculating the minimum distance to the cell cortex (mentioned in Fig. 2i). The minimum distance, from the posterior centrosome to the cell cortex, of each embryo, is extracted from the time frame with minimal dmin (scale bar, 10 μm). All P values were calculated by two-tailed Student’s t-tests (error bars, SEM).

Extended Data Fig. 3 Averaging operations for experimental flow measurements and fluid results.

a, The fluid flow vector field is displayed by 2D vectors (magenta arrows) plotted on grid points with 2.5 μm x spacing and 2.5 μm y spacing (the bottom enlargement). After proper alignment and data grouping, each velocity vector represents the mean x-y velocity of the FNDs located within the averaging domain surrounding the centre grid point (the purple square frame surrounding the purple dot, further described in b and c). b,c, Schematics of the averaging cuboid domain (purple transparent cuboid) with the grid point located at the centre of the cuboid. Centrosomes are illustrated by green balls, and the magenta particles inside the cuboids represent tracked FNDs. The A–P direction is indicated by the brown arrow. b, For prometaphase to late anaphase, the averaging domain is a 5 μm (x) by 5 μm (y) by 6 μm (z) cuboid. Spindles are aligned onto the x-y midplane (z = 0), at which plane the mean 2D projection vector field is plotted. And the purple frame (3D view) is the purple square frame in a. c, An exception for the PNC stage, the averaging cuboid measures 5 μm (x) by 5 μm (y) by 9 μm (z) (larger size in the z direction). The purple square in the upper panel is the purple frame (3D view) in the bottom panel. d,e, The simulated fluid flows (in the x-y plane of spindle motion) at the peak of the oscillations, time Tp, under (d) the cytoplasmic pulling or (e) the cortical pulling models. f, The experimental flow vector field derived from averaging the movements of tracked FNDs in 17 embryos at time Tp. g, Left, definition of pronuclear migration/centration and rotation progression. Middle, the averaged pronuclear experimental fluid data with migration ratio R = 0.35 ~ 0.5 (the same data as Fig. 5e). Right, the data with rotation angle A = 33° ~ 66°. For all experimental fluid data, the statistical significance of the velocity vectors is indicated by their colour scale (P-value colour bar) (see Methods for details). Arrows on centrosomes indicate mean measured centrosome velocities.

Extended Data Fig. 4 Dimensions of laser ablation experiments performed in metaphase and the PNC stage.

Centrosomes are presented by green balls in all 3D schematics. Centrosomes and astral MTs are sketched in green and chromosomes in magenta in all 2D schematics. All ablation geometrics are portrayed in red. The A–P directions are indicated by brown arrows. a,b, Metaphase: dimensions of the rectangular plane cuts in Fig. 4a,b respectively. c,d, Metaphase: dimensions of the cup cuts in Fig. 4c,d respectively. e, The PNC stage: dimensions of the rectangular plane cuts in Fig. 5a,b. f,g, The PNC stage: the plane cuts near the anterior or leading centrosomes (f), and the plane cuts near the posterior or trailing centrosomes (g). Both upper parts are the schematics showing the definition of centrosome centre displacement d, which is the relative orthogonal (away from the plane cut) displacement from the locus right before cutting. The black arrows indicate the progression of pronuclear migration and rotation. The mean displacement results with SEM error bars, including uncut and cut embryos, are shown in both lower parts. Their raw data are plotted semi-transparently in the back layer. Sample numbers are f, n = 25 (uncut), n = 25 (with cut) and g, n = 23 (uncut), n = 23 (with cut). And the data in Fig. 5b is the combination of these two data sets (f and g), including both plane cuts near the leading and the trailing centrosomes. h, The PNC stage: dimensions of the large semicircular arc cuts (near anterior cortices) in Fig. 5f–h. All scale bars on images are 10 μm.

Extended Data Fig. 5 Parameter sweeping simulations of the cortical pulling model.

a-c, The examples of simulated centrosome movements while parameter sweeping. a, How varying the pulling force f0 per force generator affects the PNC centration and the corresponding exponential fitting of τc. b, How varying the motor number M in metaphase affects the stable centring behavior under the condition of exerting an external force for 150 seconds and releasing. The centrosome motion is shown with the corresponding exponential fitting of τf and the spring constant ks calculated from the theory. c, How changing the cortical motor detachment rate κ affects the spindle oscillations. The corresponding Mc were derived from the theory and we adopted the same motor number (above all Mc) to simulate the oscillations. The averaged oscillation frequencies and amplitudes are specified. d-h, The results of PNC centration (τc), metaphase stable centring (τf and spring constant ks), and anaphase oscillation (Mc, and oscillation frequency and amplitude) under different parameters.

Extended Data Fig. 6 Quantification of astral MTs intensity during transverse oscillations.

a, One snapshot from the example GFP::β-tubulin time-series with the assigned transverse and lateral annular-sector regions shown (scale bar, 10 μm). The dimensions of the annular sectors are depicted on the top. b, Detailed information about data alignment for intensity measurement. Please refer to Methods for detailed operations.

Extended Data Fig. 7 Models of the force transduction mechanisms and initial position values in computational fluid dynamics simulations.

a,b, Schematics for the computational models of the force transduction mechanisms. The figure shows the PNC stage (see Fig. 5e for the corresponding experiment). Our simulations have five structural elements: the cell cortex (gray purple ellipses), the spindle/pronuclei (light green circles), the centrosomes (green circles), elastic MTs (green lines) and the cytoplasm, the fluid filling inside the cortex. a, Cortical pulling. Due to the cortical pulling forces, MTs remain straight and the forces directly act on the PNC without any loss for the MT bending. Hence, in a short time horizon, the cytoplasmic flow arises from the translation and rotation of the pronuclei-centrosome- MT complex. We model that mechanism by applying an external force Fext and torque Lext on the PNC. b, Cytoplasmic pulling. Cytoplasmic dynein motors attach to the MTs and walk towards the centrosomes with velocity v (black arrow). As they do so, they apply a pulling force on the MTs in the opposite direction to their motion. We model the force applied by the motors by a continuum model: fmotor (s). c, The initial (x,y) positions (in μm) of the spindle’s (or pronuclei’s) and the centrosomes’ centres in the simulations. All objects are at z = 0. We decided on those values based on the experiments (see Fig. 3e for oscillation, Fig. 4g for prometaphase, Fig. 4j for metaphase elongation, and Fig. 5e for the pronuclear migration).

Extended Data Table 1 Simulation parameters for the cortical pulling coarse-grained model
Full size table

Supplementary information

Supplementary Information

Supplementary Methods (computational fluid dynamics simulations) and Notes (coarse-grained model of cortical pulling).

Supplementary Video 1

Centrosome-positioning events in an early Caenorhabditis elegans embryo and the transverse spindle oscillations. (The anterior end of the embryo is on the left, while the posterior end is on the right.)

Supplementary Video 2

Arc cuts on transverse astral microtubules (MTs) of the posterior centrosomes at two different times of spindle oscillations.

Supplementary Video 3

An open-cylindrical cut and a cup cut around the posterior centrosomes during spindle oscillations.

Supplementary Video 4

Microinjected passivated fluorescent nanodiamonds (FNDs) in an early Caenorhabditis elegans embryo.

Supplementary Video 5

Rectangular plane cuts and cup cuts around the posterior centrosomes in metaphase.

Supplementary Video 6

Rectangular plane cuts around centrosomes and a large semicircular arc cut close to the anterior cortex during pronuclear migration and rotation.

Supplementary Video 7

Measurement of astral microtubules (MTs) intensity within the annular-sector regions during spindle oscillations.

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Wu, HY., Kabacaoğlu, G., Nazockdast, E. et al. Laser ablation and fluid flows reveal the mechanism behind spindle and centrosome positioning. Nat. Phys. 20, 157–168 (2024). https://doi.org/10.1038/s41567-023-02223-z

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