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  • Open Access

Physical Modeling of Embryonic Transcriptomes Identifies Collective Modes of Gene Expression

Dominic J. Skinner1,2,*, Patrick Lemaire3, and Madhav Mani2,4,†

  • *Contact author: dskinner@flatironinstitute.org
  • †Contact author: madhav.mani@gmail.com

PRX Life 3, 033028 – Published 29 September, 2025

DOI: https://doi.org/10.1103/7gs5-w48q

Abstract

Starting from one totipotent cell, complex multicellular organisms form through a series of differentiation and morphogenetic events, culminating in a multitude of cell types arranged in a functional and intricate spatial pattern. To do so, cells coordinate with each other, resulting in dynamics which follow a precise developmental trajectory, constraining the space of possible embryo-to-embryo variation. Using recent single-cell sequencing data of early ascidian embryos, we leverage natural variation together with modeling and inference techniques to investigate development at the level of a complete interconnected embryo—an embryonic transcriptome. After developing a robust and biophysically motivated approach to identifying distinct transcriptomic states or cell types, a statistical analysis reveals correlations within embryos and across cell types demonstrating the presence of collective variation. From these intraembryo correlations, we infer minimal networks of cell-cell interactions, which reveal the collective modes of gene expression. Our work demonstrates how the existence and nature of spatial interactions along with the collective modes of expression that they give rise to can be inferred from single-cell gene expression measurements, opening up a wider range of biological questions that can be addressed using sequencing-based modalities.

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References (63)

  1. J. M. W. Slack, From Egg to Embryo: Regional Specification in Early Development, 2nd ed., Developmental and Cell Biology Series (Cambridge University Press, Cambridge, UK, 1991).
  2. C. H. Waddington, The Strategy of the Genes (Allen & Unwin, Sydney, 1957).
  3. V. Alba, J. E. Carthew, R. W. Carthew, and M. Mani, Global constraints within the developmental program of the Drosophila wing, eLife 10, e66750 (2021).
  4. S. R. Quake, The cell as a bag of RNA, Trends Genet. 37, 1064 (2021).
  5. J. Cao, J. S. Packer, V. Ramani, D. A. Cusanovich, C. Huynh, R. Daza, X. Qiu, C. Lee, S. N. Furlan, F. J. Steemers, A. Adey, R. H. Waterston, C. Trapnell, and J. Shendure, Comprehensive single-cell transcriptional profiling of a multicellular organism, Science 357, 661 (2017).
  6. Tabula Sapiens Consortium, The tabula sapiens: A multiple-organ, single-cell transcriptomic atlas of humans, Science 376, eabl4896 (2022).
  7. Tabula Muris Consortium, Single-cell transcriptomics of 20 mouse organs creates a tabula muris, Nature (London) 562, 367 (2018).
  8. G. La Manno, R. Soldatov, A. Zeisel, E. Braun, H. Hochgerner, V. Petukhov, K. Lidschreiber, M. E. Kastriti, P. Lönnerberg, A. Furlan, J. Fan, L. E. Borm, Z. Liu, D. van Bruggen, J. Guo, X. He, R. Barker, E. Sundström, G. Castelo-Branco, P. Cramer, I. Adameyko, S. Linnarsson, and P. V. Kharchenko, RNA velocity of single cells, Nature (London) 560, 494 (2018).
  9. C. Weinreb, A. Rodriguez-Fraticelli, F. D. Camargo, and A. M. Klein, Lineage tracing on transcriptional landscapes links state to fate during differentiation, Science 367, eaaw3381 (2020).
  10. S. L. Freedman, B. Xu, S. Goyal, and M. Mani, A dynamical systems treatment of transcriptomic trajectories in hematopoiesis, Development 150, dev201280 (2023).
  11. A. Alemany, M. Florescu, C. Baron, J. Peterson-Maduro, and A. van Oudenaarden, Whole-organism clone tracing using single-cell sequencing, Nature (London) 556, 108 (2018).
  12. S. Jin, C. F. Guerrero-Juarez, L. Zhang, I. Chang, R. Ramos, C.-H. Kuan, P. Myung, M. V. Plikus, and Q. Nie, Inference and analysis of cell-cell communication using cellchat, Nat. Commun. 12, 1088 (2021).
  13. S. Kirkpatrick and D. Sherrington, Infinite-ranged models of spin-glasses, Phys. Rev. B 17, 4384 (1978).
  14. W. Bialek, A. Cavagna, I. Giardina, T. Mora, E. Silvestri, M. Viale, and A. M. Walczak, Statistical mechanics for natural flocks of birds, Proc. Natl. Acad. Sci. USA 109, 4786 (2012).
  15. T. R. Lezon, J. R. Banavar, M. Cieplak, A. Maritan, and N. V. Fedoroff, Using the principle of entropy maximization to infer genetic interaction networks from gene expression patterns, Proc. Natl. Acad. Sci. USA 103, 19033 (2006).
  16. J. Jiang, S. Chen, T. Tsou, C. S. McGinnis, T. Khazaei, Q. Zhu, J. H. Park, I.-M. Strazhnik, J. Hanna, E. D. Chow, D. A. Sivak, Z. J. Gartner, and M. Thomson, D-SPIN constructs gene regulatory network models from multiplexed scRNA-seq data revealing organizing principles of cellular perturbation response, bioRxiv: 10.1101/2023.04.19.537364 (2023).
  17. Y. Roudi, E. Aurell, and J. Hertz, Statistical physics of pairwise probability models, Front. Comput. Neuro. 3, 22 (2009).
  18. E. G. Conklin, Mosaic development in ascidian eggs, J. Exp. Zool. 2, 145 (1905).
  19. H. M. Funakoshi, T. T. Shito, K. Oka, and K. Hotta, Developmental table and three-dimensional embryological image resource of the ascidian ascidiella aspersa, Front. Cell Dev. Biol. 9, 789046 (2021).
  20. G. Kumano and H. Nishida, Ascidian embryonic development: An emerging model system for the study of cell fate specification in chordates, Dev. Dynamics 236, 1732 (2007).
  21. K. Hotta, K. Mitsuhara, H. Takahashi, K. Inaba, K. Oka, T. Gojobori, and K. Ikeo, A web-based interactive developmental table for the ascidian ciona intestinalis, including 3d real-image embryo reconstructions: I. From fertilized egg to hatching larva, Dev. Dynam. 236, 1790 (2007).
  22. H. L. Sladitschek, U.-M. Fiuza, D. Pavlinic, V. Benes, L. Hufnagel, and P. A. Neveu, Morphoseq: Full single-cell transcriptome dynamics up to gastrulation in a chordate, Cell 181, 922.e21 (2020).
  23. L. Guignard, U.-M. Fiúza, B. Leggio, J. Laussu, E. Faure, G. Michelin, K. Biasuz, L. Hufnagel, G. Malandain, C. Godin, and P. Lemaire, Contact area-dependent cell communication and the morphological invariance of ascidian embryogenesis, Science 369, eaar5663 (2020).
  24. J. Wei, W. Zhang, A. Jiang, H. Peng, Q. Zhang, Y. Li, J. Bi, L. Wang, P. Liu, J. Wang, Y. Ge, L. Zhang, H. Yu, L. Li, S. Wang, L. Leng, K. Chen, and B. Dong, Temporospatial hierarchy and allele-specific expression of zygotic genome activation revealed by distant interspecific urochordate hybrids, Nat. Commun. 15, 2395 (2024).
  25. H. Nishida and K. Sawada, macho-1 encodes a localized mRNA in ascidian eggs that specifies muscle fate during embryogenesis, Nature (London) 409, 724 (2001).
  26. V. Bertrand, C. Hudson, D. Caillol, C. Popovici, and P. Lemaire, Neural tissue in ascidian embryos is induced by fgf9/16/20, acting via a combination of maternal gata and ets transcription factors, Cell 115, 615 (2003).
  27. K. Imai, N. Takada, N. Satoh, and Y. Satou, β-catenin mediates the specification of endoderm cells in ascidian embryos, Development 127, 3009 (2000).
  28. T. Negishi and H. Nishida, Asymmetric and unequal cell divisions in ascidian embryos, in Asymmetric Cell Division in Development, Differentiation and Cancer, edited by J.-P. Tassan and J. Z. Kubiak (Springer International, Cham, 2017), pp. 261–284.
  29. S. Picelli, O. R. Faridani, Å. K. Björklund, G. Winberg, S. Sagasser, and R. Sandberg, Full-length RNA-seq from single cells using Smart-seq2, Nat. Prot. 9, 171 (2014).
  30. C. Ziegenhain, B. Vieth, S. Parekh, B. Reinius, A. Guillaumet-Adkins, M. Smets, H. Leonhardt, H. Heyn, I. Hellmann, and W. Enard, Comparative analysis of single-cell rna sequencing methods, Mol. Cell 65, 631 (2017).
  31. N. Treen, T. Heist, W. Wang, and M. Levine, Depletion of maternal cyclin b3 contributes to zygotic genome activation in the ciona embryo, Cur. Biol. 28, 1150 (2018).
  32. R. Satija, J. A. Farrell, D. Gennert, A. F. Schier, and A. Regev, Spatial reconstruction of single-cell gene expression data, Nat. Biotech. 33, 495 (2015).
  33. M. D. Robinson and A. Oshlack, A scaling normalization method for differential expression analysis of RNA-seq data, Genome Biol. 11, R25 (2010).
  34. J. Breda, M. Zavolan, and E. van Nimwegen, Bayesian inference of gene expression states from single-cell RNA-seq data, Nat. Biotech. 39, 1008 (2021).
  35. J. Lause, C. Ziegenhain, L. Hartmanis, P. Berens, and D. Kobak, Compound models and pearson residuals for normalization of single-cell RNA-seq data without UMIs, bioRxiv 10.1101/2023.08.02.551637 (2023).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/7gs5-w48q for additional algorithmic and numerical details, Figs. S1–S25, and Tables S1–S3.
  37. P. Grobecker, T. Sakoparnig, and E. van Nimwegen, Identifying cell states in single-cell RNA-seq data at statistically maximal resolution, PLoS Comput. Biol. 20, e1012224 (2024).
  38. S. M. Lundberg, G. Erion, H. Chen, A. DeGrave, J. M. Prutkin, B. Nair, R. Katz, J. Himmelfarb, N. Bansal, and S.-I. Lee, From local explanations to global understanding with explainable ai for trees, Nat. Mach. Intel. 2, 56 (2020).
  39. S. Melton and S. Ramanathan, Discovering a sparse set of pairwise discriminating features in high-dimensional data, Bioinformatics 37, 202 (2021).
  40. Y. Cheng and G. M. Church, Biclustering of expression data, in Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology, Vol. 8 (AAAI Press, 2000), pp. 93–103.
  41. J. Xie, A. Ma, A. Fennell, Q. Ma, and J. Zhao, It is time to apply biclustering: A comprehensive review of biclustering applications in biological and biomedical data, Brief. Bioinform. 20, 1450 (2019).
  42. S. Monti, P. Tamayo, J. Mesirov, and T. Golub, Consensus clustering: A resampling-based method for class discovery and visualization of gene expression microarray data, Mach. Learn. 52, 91 (2003).
  43. Y. Senbabaoğlu, G. Michailidis, and J. Z. Li, Critical limitations of consensus clustering in class discovery, Sci. Rep. 4, 6207 (2014).
  44. E. Levine and E. Domany, Resampling method for unsupervised estimation of cluster validity, Neural Comput. 13, 2573 (2001).
  45. S. Jang, S. Choubey, L. Furchtgott, L.-N. Zou, A. Doyle, V. Menon, E. B. Loew, A.-R. Krostag, R. A. Martinez, L. Madisen, B. P. Levi, and S. Ramanathan, Dynamics of embryonic stem cell differentiation inferred from single-cell transcriptomics show a series of transitions through discrete cell states, eLife 6, e20487 (2017).
  46. J. Dardaillon, D. Dauga, P. Simion, E. Faure, T. A. Onuma, M. B. DeBiasse, A. Louis, K. R. Nitta, M. Naville, L. Besnardeau, W. Reeves, K. Wang, M. Fagotto, M. Guéroult-Bellone, S. Fujiwara, R. Dumollard, M. Veeman, J.-N. Volff, H. Roest-Crollius, E. Douzery, J. F. Ryan, B. Davidson, H. Nishida, C. Dantec, and P. Lemaire, ANISEED 2019: 4D exploration of genetic data for an extended range of tunicates, Nucl. Ac. Res. 48, D668 (2019).
  47. A. Madgwick, M. S. Magri, C. Dantec, D. Gailly, U.-M. Fiuza, L. Guignard, S. Hettinger, J. L. Gomez-Skarmeta, and P. Lemaire, Evolution of embryonic cis-regulatory landscapes between divergent phallusia and ciona ascidians, Dev. Biol. 448, 71 (2019).
  48. L. Aparicio, M. Bordyuh, A. J. Blumberg, and R. Rabadan, A random matrix theory approach to denoise single-cell data, Patterns 1, 100035 (2020).
  49. M. Nitzan and M. P. Brenner, Revealing lineage-related signals in single-cell gene expression using random matrix theory, Proc. Natl. Acad. Sci. USA 118, e1913931118 (2021).
  50. S. Pressé, K. Ghosh, J. Lee, and K. A. Dill, Principles of maximum entropy and maximum caliber in statistical physics, Rev. Mod. Phys. 85, 1115 (2013).
  51. J. Shore and R. Johnson, Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy, IEEE Trans. Inform. Theory 26, 26 (1980).
  52. Y. Kleeorin, W. P. Russ, O. Rivoire, and R. Ranganathan, Undersampling and the inference of coevolution in proteins, Cell Syst. 14, 210 (2023).
  53. G. Stepaniants, A. D. Hastewell, D. J. Skinner, J. F. Totz, and J. Dunkel, Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations, Phys. Rev. Res. 6, 043062 (2024).
  54. M. Schulze, A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method, Soc. Choice Welfare 36, 267 (2011).
  55. N. Ohta and Y. Satou, Multiple signaling pathways coordinate to induce a threshold response in a chordate embryo, PLoS Genet. 9, e1003818 (2013).
  56. Y. Rosen, Y. Roohani, A. Agarwal, L. Samotorčan, T. S. Consortium, S. R. Quake, and J. Leskovec, Universal cell embeddings: A foundation model for cell biology, bioRxiv: 10.1101/2023.11.28.568918 (2023).
  57. M. Smart and A. Zilman, Emergent properties of collective gene-expression patterns in multicellular systems, Cell Rep. Phys. Sci. 4, 101247 (2023).
  58. A. J. Dear, G. A. Garcia, G. Meisl, G. A. Collins, T. P. J. Knowles, and A. L. Goldberg, Maximum entropy determination of mammalian proteome dynamics, Proc. Natl. Acad. Sci. USA 121, e2313107121 (2024).
  59. T. Mora, A. M. Walczak, W. Bialek, and C. G. Callan, Maximum entropy models for antibody diversity, Proc. Natl. Acad. Sci. USA 107, 5405 (2010).
  60. C. Sarra, L. Sarra, L. Di Carlo, T. GrandPre, Y. Zhang, C. G. Callan, and W. Bialek, Maximum entropy models for patterns of gene expression, Phys. Rev. E 112, 014408 (2025).
  61. A. Dobin, C. A. Davis, F. Schlesinger, J. Drenkow, C. Zaleski, S. Jha, P. Batut, M. Chaisson, and T. R. Gingeras, STAR: Ultrafast universal RNA-seq aligner, Bioinformatics 29, 15 (2013).
  62. G. C. Tseng, D. Ghosh, and E. Feingold, Comprehensive literature review and statistical considerations for microarray meta-analysis, Nucl. Ac. Res. 40, 3785 (2012).
  63. D. Skinner, P. Lemaire, and M. Mani, Physical modeling of embryonic transcriptomes identifies collective modes of gene expression [Data set], Zenodo (2025), doi:10.5281/zenodo.16782577.

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