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Topological interactions drive the first fate decision in the Drosophila embryo

Nature Physics volume 21, pages 632–643 (2025)Cite this article

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Abstract

During embryogenesis, the first cell fate decision—whether the cell participates in development of the embryo or not—is often linked to the positioning of the nucleus. The cell cycle oscillator and associated cytoskeletal dynamics contribute to the control of nuclear positioning. However, the mechanisms that ensure that the correct number of nuclei move to their appropriate place remain poorly understood. Here we show that the orientation of the mitotic spindle controls the first fate decision, embryonic or yolk cell fate, in Drosophila embryos using light sheet microscopy experiments. Combining computational methods inspired by integral geometry, manipulation of cell cycle genes, and investigation of the relationship between geometry and topology, we show that spindle orientation is controlled by topological interactions with neighbouring nuclei and not by internuclear distance. Leveraging the physics of space-filling systems, we develop a theory for topological dependency in microtubule structures. Our work shows how the topological interplay of microtubule mechanics can ensure robust control of nuclear density and determine cell fate.

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Fig. 1: Symmetry breaking in nuclear positioning underlies embryo–yolk fate choice.
Fig. 2: Spindle orientation drives nuclear positioning.
Fig. 3: Geometry and mechanics of cortical migration via local force balance.
Fig. 4: Theoretical model predicts aster–aster alignment interactions are scale independent and topological.
Fig. 5: Cell cycle manipulations confirm scale-independent and robust aster–aster alignment.
Fig. 6: Local and geometric control of topology and spindle orientation.

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Data availability

All image data are available upon reasonable request to S.D.T. Source data are provided with this paper.

Code availability

Codes are available upon reasonable request to S.D.T.

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Acknowledgements

We acknowledge S. Gunther and L. Hufnagel for discussion and for sharing their original observations of cortical migration. We thank the Bloomington Drosophila Stock Center and the Kyoto Drosophila Stock Center for providing stocks. We thank the Drosophila Genomics Resource Center and J. Gatlin for constructs. We thank C. Field and T. Mitchison for discussions. N.P.M. acknowledges support from NICHD award number K99HD110675. This work was supported by NIH R35-GM153490; R01-GM136763; R01-GM122936 to S.D.T.

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Author notes

  1. These authors contributed equally: Woonyung Hur, Arghyadip Mukherjee.

Authors and Affiliations

  1. Department of Cell Biology, Duke University School of Medicine, Durham, NC, USA

    Woonyung Hur, Luke Hayden, Ziqi Lu, Anna Chao & Stefano Di Talia

  2. Laboratoire de physique de l’Ecole Normale Superieure, CNRS, PSL Research University, Sorbonne Universite, Paris, France

    Arghyadip Mukherjee & Massimo Vergassola

  3. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, Santa Barbara, CA, USA

    Noah P. Mitchell & Sebastian J. Streichan

  4. Department of Physics, University of California, Santa Barbara, Santa Barbara, CA, USA

    Noah P. Mitchell & Sebastian J. Streichan

  5. Department of Physics, University of California, San Diego, La Jolla, CA, USA

    Massimo Vergassola

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Contributions

Conceptualization: W.H., A.M., S.J.S., M.V. and S.D.T. Methodology: W.H., A.M. and S.J.S. Software: W.H., A.M. and S.J.S. Validation: W.H. and A.M. Data processing and preparation: W.H. Formal analysis: A.M. Investigation: W.H., A.M., L.H., Z.L., A.C. and N.P.M. Resources: W.H., A.M. and A.C. Data curation: W.H., A.M. and Z.L. Writing—original draft: W.H., A.M. and S.D.T. Writing—review and editing: all authors. Visualization: W.H., A.M. and Z.L. Supervision: S.J.S., M.V. and S.D.T. Project administration: S.J.S., M.V. and S.D.T. Funding acquisition: A.M., M.V. and S.D.T.

Corresponding authors

Correspondence to Arghyadip Mukherjee, Massimo Vergassola or Stefano Di Talia.

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Extended data

Extended Data Fig. 1 Symmetry breaking in nuclear positioning underlies embryo-yolk fate choice.

A, Lineage tracing of segmented and tracked nuclei are shown along their relative position in the anterior posterior axis from cycle 8 to cycle 11. Different colours indicate each unique lineage trace that is, same colour means it originated from the same nucleus. A=anterior, P=posterior. B, A schematic depiction of a nucleus with respect to the embryo cortex is shown. The nuclear velocity \(\overrightarrow{v_{i}}\), the unit orientation vector \(\hat{u_{c}}\) pointing to the closest plane in the cortex is marked. The dashed line connects to the approximated closest plane indicated. C-D, Frequency distributions of movement direction of the nuclei during cycle 8 and cycle 9 is shown. The movement direction is defined as the dot product of unit nuclear velocity and orientation vector. E, Nuclear speed towards the embryo cortex is shown as a function of time. Black lines=outer shell nuclei, red lines=nuclei in bulk (yolk), vertical dashed line=chromosome separation event. F, Enrichment score for the top 25 expressed genes in the yolk nuclei (with respect to the rest of the nuclei) are shown in rank order. Genes sisA, serp and spo are highlighted.

Source data

Extended Data Fig. 2 Orientational dynamics and its effect on nuclear trajectories.

A, Frequency distribution of tilt angle ψ is shown for an embryo during cycle 10 when they have already reached the embryo cortex. Vertical dashed line indicates 45 degrees in angle. B, Temporal traces of tilt angle ψ is shown from mid-interphase to onset of metaphase during cycle 8. Different colours indicate each unique trace of the spindle. C, The average change in tilt angle Δψ is shown for cycles 7,8 and 9. Shaded region marks the standard deviation. D, The probability distribution function of tilt angles is shown for cycle 8 and cycle 9. E, Left- The probability distribution function of tilt angles is shown for a randomized reference state. To derive the distribution one can assume a neamtic object inside a sphere oriented randomly and measure the latitude. Right- Comparison of the random distribution of angles is shown with cycle 8 and cycle 9. Measured Kullback-Leibler divergence between the random state and data from cycle 8 and cycle 9 is ~ 0.08 while between data from the two cycles is <0.01. F, Individual (grey) and average (red dots with errorbars representing 95% confidence interval of the mean) trajectories are shown for nuclei that show >45 degree with respect to the cortex at the onset of nuclear division. A clear bifurcation is indicated just after 2 min timepoint. G, Individual (gray) and average (blue dots with errorbars representing 95% confidence interval of the mean) trajectories are shown for nuclei that show <45 degree with respect to the cortex at the onset of nuclear division. A collective migration is found in the trajectories. H, A two dimensional count density map is shown for tilt angle ψ and location along the normalized anterior posterior (AP) axis for pooled 8 wild type (WT) embryos during cycle 9. Colorbar indicates the bin counts. I, Probability density function of tilt angle ψ is plotted for spindles belonging to binned locations along the AP axis with 5 equally sized bins (every 20% along the AP axis). Color indicates location along the normalized AP axis (see colorbar).

Source data

Extended Data Fig. 3 Dynamics of nuclear shell expansion.

A, A hemispherical view of the nuclear shell/boundary is shown during cycle 7-10 for wildtype (WT) and cul-5 mutants. Inflation and differences in morphology is noted. B, Average nuclear speed towards the embryo cortex is plotted for wildtype and cul-5 mutants (for different embryos), during the transition from cycle 7 to cycle 8 (left) and from cycle 8 to cycle 9 (right). Vertical dashed line=chromosome separation. C, Distance of the nuclei from the cortex is shown as a function of time for a cul-5 mutant embryo. Temporal traces (dots) and average trajectories are shown for different anterior-posterior regions (color coded shown as in the inset image). c=cycle. D, Lineage tracing of segmented and tracked nuclei are shown along their relative position in the anterior posterior axis from cycle 7 to cycle 10 for a cul-5 mutant embryo. Note that the axial spread is smaller than a WT embryo (Extended Data Fig. 1A). Different colors indicate each unique lineage trace that is, same color means it originated from the same nucleus. A=anterior, P=posterior. E, Nuclei shell area A(t) from cycle 7 to cycle 10 (A(t)–A0, with A0 = 1.2*104 μm2 for WT and A0 = 0 for cul-5 mutant) is plotted against predicted shell area from the pushing model based on nuclei number N(t) on the shell as a0N(t), where a0 = 700μm2 is the extracted domain area. Colorbar indicates time with respect to end of cycle 10. y= x line indicates the excellent agreement of the prediction while the flat dashed line indicates the saturation as the nuclear shell reaches the cortex at cycle 10.

Source data

Extended Data Fig. 4 Morphometric analysis of the nuclear shell.

A, An example of a mesh reconstruction is shown for a nuclear point cloud data from a wildtype embryo during cycle 9. B, Dual/Voronoi mesh is shown for the reconstructed mesh. Facecolor indicates isoperimetric quotient (Perimeter/√Area), a measure of shape for astral domains. C, Probability density is shown for isoperimetric quotient for an example embryo (same as Extended Data Fig. 4B), with numerically associated regular polygons/circle to emphasize an intuition of the shape. D, Correlation coefficient is calculated between tilt ψ and negative strain ϵ < 0 (see Fig. 3a) after randomization. A probability distribution is plotted for the correlation coefficients upon randomization. Standard deviation of the randomization σr is shown in orange. The correlation of the experimental data is found to be ~ 2σr. E, Binscatter plots for experimental data (left) of tilt angle ψ and strain ϵ and a randomized sample of the experimental data (right) is shown. A and \(\overline{A}\) indicate domain area and its’ average. F, Scatter plots are shown for tilt angle ψ vs rescaled distance with the closest neighbour (right) and the average distance to the three closesr neighbours (left). No significant correlation is found. Pearson correlation is reported in the legend. Pooled data over n=8 WT cycle 9 embryos.

Source data

Extended Data Fig. 5 Scaling of microtubule density.

A, Rescaled microtubule radial intensity profile is shows for wild type (WT) and mutants (legend) in a log-log plot. The tail can be well-captured by a power law with exponent of − 2.1, shown by a dashed line. Measurements are performed on intensity profiles of tau-mCherry around the centrosome as in Fig. 2b. Different conditions are annotated in the fig. B, Rescaling factor/maxmimal microtubule intensity at the centrosome is plotted across genetic backgrounds for comparison (see inset). CycB 1x and CycB 6x show clear differences.

Source data

Extended Data Table 1 Resources used in the study
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Supplementary information

Supplementary Information

Supplementary Note.

Reporting Summary

Supplementary Video 1

Time-lapse imaging with maximum intensity projection of an exemplary Drosophila embryo from cycle 7 to cycle 10 is shown with mRFP-Nup107 (red). Scale bar, 100 μm.

Supplementary Video 2

Tracing of three-dimensional segmented nuclei (marked in variety of colours) is shown during cycle 7 to cycle 10. As the video progresses, expansion of the nuclear shell can be seen. Scale bar, 100 μm.

Supplementary Video 3

Segmented spindles are rendered and visualized in three dimensions. Spindles with tilt angle <45° are marked in gold, while spindles with tilt angle ≥45° are marked in red.

Supplementary Video 4

A typical simulation of expansion is shown where the system starts with 20 particles that divide/double and relaxes the forces by pushing on each other. This leads to inflation as well increase in eccentricity. After relaxation, the number is again doubled and the process is repeated until interaction with the boundary.

Supplementary Video 5

Tracking of nuclei are shown, colour-coded for initial tilt angle with respect to the embryo cortex. Perpendicular nuclei >45° are marked in red and parallel ones in yellow. Side and polar views are shown, which reveal a significant number of red daughter nuclei moving inwards while most yellow nuclei move towards the cortex.

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Hur, W., Mukherjee, A., Hayden, L. et al. Topological interactions drive the first fate decision in the Drosophila embryo. Nat. Phys. 21, 632–643 (2025). https://doi.org/10.1038/s41567-025-02796-x

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