MultiCell: geometric learning in multicellular development

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  • Keller, R. Shaping the vertebrate body plan by polarized embryonic cell movements. Science 298, 1950–1954 (2002).

    Article  PubMed  Google Scholar 

  • Zhu, M. & Zernicka-Goetz, M. Principles of self-organization of the mammalian embryo. Cell 183, 1467–1478 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  • Liu, Y. et al. Morphogenesis beyond in vivo. Nat. Rev. Phys. 6, 28–44 (2024).

    Article  Google Scholar 

  • Gilmour, D., Rembold, M. & Leptin, M. From morphogen to morphogenesis and back. Nature 541, 311–320 (2017).

    Article  PubMed  Google Scholar 

  • Keller, R. Physical biology returns to morphogenesis. Science 338, 201–203 (2012).

    Article  PubMed  Google Scholar 

  • Trepat, X. & Sahai, E. Mesoscale physical principles of collective cell organization. Nat. Phys. 14, 671–682 (2018).

    Article  Google Scholar 

  • Stern, T., Shvartsman, S. Y. & Wieschaus, E. F. Deconstructing gastrulation at single-cell resolution. Curr. Biol. 32, 1861–1868 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  • Mongera, A. et al. A fluid-to-solid jamming transition underlies vertebrate body axis elongation. Nature 561, 401–405 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  • Zenker, J. et al. Expanding actin rings zipper the mouse embryo for blastocyst formation. Cell 173, 776–791 (2018).

    Article  PubMed  Google Scholar 

  • Lim, H. Y. G. et al. Keratins are asymmetrically inherited fate determinants in the mammalian embryo. Nature 585, 404–409 (2020).

    Article  PubMed  Google Scholar 

  • Rozbicki, E. et al. Myosin-ii-mediated cell shape changes and cell intercalation contribute to primitive streak formation. Nat. Cell Biol. 17, 397–408 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  • Ershov, D. et al. Trackmate 7: integrating state-of-the-art segmentation algorithms into tracking pipelines. Nat. Methods 19, 829–832 (2022).

    Article  PubMed  Google Scholar 

  • Pachitariu, M. & Stringer, C. Cellpose 2.0: how to train your own model. Nat. Methods 19, 1634–1641 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  • Huijben, T. A. P. M. et al. inTRACKtive: a web-based tool for interactive cell tracking visualization. Nat. Methods 22, 2229–2231 (2025).

  • Toulany, N. et al. Uncovering developmental time and tempo using deep learning. Nat. Methods 20, 2000–2010 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  • Mitchell, N. P. & Cislo, D. J. Tubular: tracking in toto deformations of dynamic tissues via constrained maps. Nat. Methods 20, 1980–1988 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  • Noll, N., Streichan, S. J. & Shraiman, B. I. Variational method for image-based inference of internal stress in epithelial tissues. Phys. Rev. X 10, 011072 (2020).

    PubMed  PubMed Central  Google Scholar 

  • Abramson, J. et al. Accurate structure prediction of biomolecular interactions with AlphaFold 3. Nature 630, 493–500 (2024).

  • Jumper, J. et al. Highly accurate protein structure prediction with alphafold. Nature 596, 583–589 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  • Pope, K. L. & Harris, T. J. C. Control of cell flattening and junctional remodeling during squamous epithelial morphogenesis in Drosophila. Development https://doi.org/10.1242/dev.019802 (2008).

  • Serra, M., Streichan, S., Chuai, M., Weijer, C. J. & Mahadevan, L. Dynamic morphoskeletons in development. Proc. Natl Acad. Sci. USA 117, 11444–11449 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  • Butler, L. C. et al. Cell shape changes indicate a role for extrinsic tensile forces in Drosophila germ-band extension. Nat. Cell Biol. 11, 859–864 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  • Irvine, K. D. & Wieschaus, E. Cell intercalation during Drosophila germband extension and its regulation by pair-rule segmentation genes. Development 120, 827–841 (1994).

    Article  PubMed  Google Scholar 

  • Foe, V. E. Mitotic domains reveal early commitment of cells in Drosophila embryos. Development 107, 1–22 (1989).

    Article  PubMed  Google Scholar 

  • Sweeton, D., Parks, S., Costa, M. & Wieschaus, E. Gastrulation in Drosophila: the formation of the ventral furrow and posterior midgut invaginations. Development 112, 775–789 (1991).

    Article  PubMed  Google Scholar 

  • Campàs, O., Noordstra, I. & Yap, A. S. Adherens junctions as molecular regulators of emergent tissue mechanics. Nat. Rev. Mol. Cell Biol. 25, 252–269 (2024).

    Article  PubMed  Google Scholar 

  • Bi, D., Lopez, J. H., Schwarz, J. M. & Manning, M. L. A density-independent rigidity transition in biological tissues. Nat. Phys. 11, 1074–1079 (2015).

    Article  Google Scholar 

  • Kim, S., Pochitaloff, M., Stooke-Vaughan, G. A. & Campàs, O. Embryonic tissues as active foams. Nat. Phys. 17, 859–866 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  • Mongera, A. et al. Mechanics of the cellular microenvironment as probed by cells in vivo during zebrafish presomitic mesoderm differentiation. Nat. Mater. 22, 135–143 (2023).

    Article  PubMed  Google Scholar 

  • Bertet, C., Sulak, L. & Lecuit, T. Myosin-dependent junction remodelling controls planar cell intercalation and axis elongation. Nature 429, 667–671 (2004).

    Article  PubMed  Google Scholar 

  • Blanchard, G. B. et al. Tissue tectonics: morphogenetic strain rates, cell shape change and intercalation. Nat. Methods 6, 458–464 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  • Rauzi, M., Verant, P., Lecuit, T. & Lenne, P.-F. Nature and anisotropy of cortical forces orienting Drosophila tissue morphogenesis. Nat. Cell Biol. 10, 1401–1410 (2008).

    Article  PubMed  Google Scholar 

  • Wang, X. et al. Anisotropy links cell shapes to tissue flow during convergent extension. Proc. Natl Acad. Sci. USA 117, 13541–13551 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  • Etournay, R. et al. Interplay of cell dynamics and epithelial tension during morphogenesis of the Drosophila pupal wing. Elife 4, e07090 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  • Herrera-Perez, R. M., Cupo, C., Allan, C., Dagle, A. B. & Kasza, K. E. Tissue flows are tuned by actomyosin-dependent mechanics in developing embryos. PRX Life 1, 013004 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  • Cupo, C., Allan, C., Ailiani, V. & Kasza, K. E. Signatures of structural disorder in the developing Drosophila germband epithelium. PRX Life 2, 043004 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  • Walck-Shannon, E. & Hardin, J. Cell intercalation from top to bottom. Nat. Rev. Mol. Cell Biol. 15, 34–48 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  • Brauns, F., Claussen, N. H., Lefebvre, M. F., Wieschaus, E. F. & Shraiman, B. I. The geometric basis of epithelial convergent extension. Elife https://doi.org/10.7554/eLife.95521.3 (2024).

  • Campàs, O. et al. Quantifying cell-generated mechanical forces within living embryonic tissues. Nat. Methods 11, 183–189 (2014).

    Article  PubMed  Google Scholar 

  • Di Talia, S. & Wieschaus, E. F. Short-term integration of cdc25 dynamics controls mitotic entry during Drosophila gastrulation. Dev. Cell 22, 763–774 (2012).

    Article  PubMed  PubMed Central  Google Scholar 

  • Ferree, P. L. Temporal Regulation of Cell Divisions in the Embryo of Drosophila melanogaster. PhD thesis, Duke Univ. (2022).

  • Claussen, N. H., Brauns, F. & Shraiman, B. I. A geometric-tension-dynamics model of epithelial convergent extension. Proc. Natl Acad. Sci. USA 121, e2321928121 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  • Yamamoto, T., Cockburn, K., Greco, V. & Kawaguchi, K. Probing the rules of cell coordination in live tissues by interpretable machine learning based on graph neural networks. PLoS Comput. Biol. 18, e1010477 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  • Yang, H. et al. Learning collective cell migratory dynamics from a static snapshot with graph neural networks. PRX Life 2, 043010 (2024).

    Article  Google Scholar 

  • Supekar, R. et al. Learning hydrodynamic equations for active matter from particle simulations and experiments. Proc. Natl Acad. Sci. USA 120, e2206994120 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  • Lefebvre, M. F. et al. Learning a conserved mechanism for early neuroectoderm morphogenesis. Preprint at bioRxiv https://doi.org/10.1101/2023.12.22.573058 (2023).

  • LaChance, J., Suh, K., Clausen, J. & Cohen, D. J. Learning the rules of collective cell migration using deep attention networks. PLoS Comput. Biol. 18, e1009293 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  • Brückner, D. B., Ronceray, P. & Broedersz, C. P. Inferring the dynamics of underdamped stochastic systems. Phys. Rev. Lett. 125, 058103 (2020).

    Article  PubMed  Google Scholar 

  • Frishman, A. & Ronceray, P. Learning force fields from stochastic trajectories. Phys. Rev. X 10, 021009 (2020).

    Google Scholar 

  • Angelini, T. E. et al. Glass-like dynamics of collective cell migration. Proc. Natl Acad. Sci. USA 108, 4714–4719 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  • Atia, L. et al. Geometric constraints during epithelial jamming. Nat. Phys. 14, 613–620 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  • Brandstätter, T. et al. Curvature induces active velocity waves in rotating spherical tissues. Nat. Commun. 14, 1643 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  • Tang, W. et al. Topology and nuclear size determine cell packing on growing lung spheroids. Phys. Rev. X 15, 011067 (2025).

    PubMed  PubMed Central  Google Scholar 

  • Hu, Y. et al. Unsupervised and supervised discovery of tissue cellular neighborhoods from cell phenotypes. Nat. Methods 21, 267–278 (2024).

  • Lecuit, T. & Lenne, P.-F. Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis. Nat. Rev. Mol. Cell Biol. 8, 633–644 (2007).

    Article  PubMed  Google Scholar 

  • Rozman, J., Krajnc, M. & Ziherl, P. Collective cell mechanics of epithelial shells with organoid-like morphologies. Nat. Commun. 11, 3805 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  • Wang, X., Cupo, C. M., Ostvar, S., Countryman, A. D. & Kasza, K. E. E-cadherin tunes tissue mechanical behavior before and during morphogenetic tissue flows. Curr. Biol. https://doi.org/10.1016/j.cub.2024.06.038 (2024).

  • Thomson, D. W. On Growth and Form (Cambridge Univ. Press, 1917).

  • Firmin, J. et al. Mechanics of human embryo compaction. Nature 629, 646–651 (2024).

  • Martin, A. C., Kaschube, M. & Wieschaus, E. F. Pulsed contractions of an actin–myosin network drive apical constriction. Nature 457, 495–499 (2009).

    Article  PubMed  Google Scholar 

  • Yevick, H. G., Miller, P. W., Dunkel, J. & Martin, A. C. Structural redundancy in supracellular actomyosin networks enables robust tissue folding. Dev. Cell 50, 586–598 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  • Wang, H. et al. Scientific discovery in the age of artificial intelligence. Nature 620, 47–60 (2023).

    Article  PubMed  Google Scholar 

  • Kipf, T.N. & Welling, M. Semi-supervised classification with graph convolutional networks. In International Conference on Learning Representations 2017 https://openreview.net/pdf?id=SJU4ayYgl (ICLR, 2017).

  • Kipf, T. N. & Welling, M. Variational graph auto-encoders. In Bayesian Deep Learning Workshop https://www.bayesiandeeplearning.org/2016/papers/BDL_16.pdf (2016).

  • Corso, G., Cavalleri, L., Beaini, D., Liò, P. & Veličković, P. Principal neighbourhood aggregation for graph nets. In 34th Conference on Neural Information Processing Systems (NeurIPS 2020) https://proceedings.neurips.cc/paper/2020/file/99cad265a1768cc2dd013f0e740300ae-Paper.pdf (2020).

  • Veličković, P. et al. Graph attention networks. In International Conference on Learning Representations 2018 https://openreview.net/forum?id=rJXMpikCZ (ICLR, 2018).

  • Shi, Y. et al. Masked label prediction: unified message passing model for semi-supervised classification. In Proc. Thirtieth International Joint Conference on Artificial Intelligence (IJCAI-21) https://www.ijcai.org/proceedings/2021/0214.pdf (IJCAI, 2021).

  • Bapst, V. et al. Unveiling the predictive power of static structure in glassy systems. Nat. Phys. 16, 448–454 (2020).

    Article  Google Scholar 

  • Yang, Z. & Buehler, M. J. Linking atomic structural defects to mesoscale properties in crystalline solids using graph neural networks. NPJ Comput. Mater. 8, 198 (2022).

    Article  Google Scholar 

  • Pineda, J. et al. Geometric deep learning reveals the spatiotemporal features of microscopic motion. Nat. Mach. Intell. 5, 71–82 (2023).

    Article  Google Scholar 

  • Viñas, R. et al. Hypergraph factorization for multi-tissue gene expression imputation. Nat. Mach. Intell. 5, 739–753 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  • Baker, E. A. G., Schapiro, D., Dumitrascu, B., Vickovic, S. & Regev, A. In silico tissue generation and power analysis for spatial omics. Nat. Methods 20, 424–431 (2023).

    Article  PubMed  PubMed Central  Google Scholar 

  • Cubuk, E. D. et al. Identifying structural flow defects in disordered solids using machine-learning methods. Phys. Rev. Lett. 114, 108001 (2015).

    Article  PubMed  Google Scholar 

  • Cubuk, E. D. et al. Structure-property relationships from universal signatures of plasticity in disordered solids. Science 358, 1033–1037 (2017).

  • Jung, G. et al. Roadmap on machine learning glassy dynamics. Nat. Rev. Phys. 7, 91–104 (2025).

    Article  Google Scholar 

  • Mitchell, N. P. et al. Morphodynamic atlas for Drosophila development. Preprint at bioRxiv https://doi.org/10.1101/2022.05.26.493584 (2022).

  • Zhou, B., Khosla, A., Lapedriza, A. Oliva, A. & Torralba, A. Learning deep features for discriminative localization. In Proc. IEEE Conference on Computer Vision and Pattern Recognition https://openaccess.thecvf.com/content_cvpr_2016/papers/Zhou_Learning_Deep_Features_CVPR_2016_paper.pdf (IEEE, 2016).

  • Tanay, A. & Regev, A. Scaling single-cell genomics from phenomenology to mechanism. Nature 541, 331–338 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  • Rodriques, S. G. et al. Slide-seq: a scalable technology for measuring genome-wide expression at high spatial resolution. Science 363, 1463–1467 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  • Ståhl, P. L. et al. Visualization and analysis of gene expression in tissue sections by spatial transcriptomics. Science 353, 78–82 (2016).

    Article  PubMed  Google Scholar 

  • Lohoff, T. et al. Integration of spatial and single-cell transcriptomic data elucidates mouse organogenesis. Nat. Biotechnol. 40, 74–85 (2022).

    Article  PubMed  Google Scholar 

  • Hallou, A., He, R., Simons, B. D. & Dumitrascu, B. A computational pipeline for spatial mechano-transcriptomics. Nat. Methods https://doi.org/10.1038/s41592-025-02618-1 (2025).

  • Martin, A. C., Gelbart, M., Fernandez-Gonzalez, R., Kaschube, M. & Wieschaus, E. F. Integration of contractile forces during tissue invagination. J. Cell Biol. 188, 735–749 (2010).

    Article  PubMed  PubMed Central  Google Scholar 

  • Zallen, J. A. & Wieschaus, E. Patterned gene expression directs bipolar planar polarity in Drosophila. Dev. Cell 6, 343–355 (2004).

    Article  PubMed  Google Scholar 

  • Popović, M., Druelle, V., Dye, N. A., Jülicher, F. & Wyart, M. Inferring the flow properties of epithelial tissues from their geometry. N. J. Phys. 23, 033004 (2021).

    Article  Google Scholar 

  • Falk, M. L. & Langer, J. S. Deformation and failure of amorphous, solidlike materials. Annu. Rev. Condens. Matter Phys. 2, 353–373 (2011).

    Article  Google Scholar 

  • Richard, D., Elgailani, A., Vandembroucq, D., Manning, M. L. & Maloney, C. E. Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids. Phys. Rev. E 107, 034902 (2023).

    Article  PubMed  Google Scholar 

  • Huang, J., Cochran, J. O., Fielding, S. M., Marchetti, M. C. & Bi, D. Shear-driven solidification and nonlinear elasticity in epithelial tissues. Phys. Rev. Lett. 128, 178001 (2022).

    Article  PubMed  Google Scholar 

  • Rados, T. et al. Tissue-like multicellular development triggered by mechanical compression in archaea. Science 388, 109–115 (2025).

    Article  PubMed  PubMed Central  Google Scholar 

  • Shah, H. et al. Life-cycle-coupled evolution of mitosis in close relatives of animals. Nature 630, 116–122 (2024).

    Article  PubMed  PubMed Central  Google Scholar 

  • Park, J.-A. et al. Unjamming and cell shape in the asthmatic airway epithelium. Nat. Mater. 14, 1040–1048 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  • Yang, H. et al. Configurational fingerprints of multicellular living systems. Proc. Natl Acad. Sci. USA 118, e2109168118 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  • Hörl, D. et al. Bigstitcher: reconstructing high-resolution image datasets of cleared and expanded samples. Nat. Methods 16, 870–874 (2019).

    Article  PubMed  Google Scholar 

  • Schindelin, J. et al. Fiji: an open-source platform for biological-image analysis. Nat. Methods 9, 676–682 (2012).

    Article  PubMed  Google Scholar 

  • Yang, H. et al. Zenodo https://doi.org/10.5281/zenodo.17605530 (2025).