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Generation of fate patterns via intercellular forces

Hayden Nunley1,*,†, Xufeng Xue2,‡, Jianping Fu2,3,4, and David K. Lubensky1,5,§

  • *Contact author: nunley@umich.edu
  • †Present address: Center for Computational Biology, Flatiron Institute– Simons Foundation, New York, NY 10010, USA.
  • ‡Present address: Center for Stem Cell & Organoid Medicine (CuSTOM), Cincinnati Children’s Hospital Medical Center, 3333 Burnet Avenue, Cincinnati, Ohio 45229-3026, USA.
  • §Contact author: dkluben@umich.edu
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Phys. Rev. Research 7, L022051 – Published 4 June, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022051

Abstract

Studies of fate patterning during development typically emphasize cell-cell communication via diffusible chemical signals. Recent experiments on stem cell colonies, however, suggest that in some cases mechanical stresses, rather than secreted chemicals, enable long-ranged cell-cell interactions that specify positional information and pattern cell fates. These findings inspire a model of mechanical patterning: fate affects cell contractility, and pressure in the cell layer biases fate. Cells at the colony edge, more contractile than cells at the center, seed a pattern that propagates via force transmission. Strikingly, our model implies that the width of the outer fate domain varies nonmonotonically with substrate stiffness, a prediction that we confirm experimentally; we argue that a similar dependence on substrate stiffness can be achieved by a chemical morphogen only if strong constraints on the signaling pathway's mechanobiology are met. Our findings thus support the idea that mechanical stress can mediate patterning in the complete absence of chemical morphogens, even in nonmotile cell layers, thus expanding the repertoire of possible roles for mechanical signals in development and morphogenesis. Future tests of additional model predictions, like the effect of anisotropic substrate rigidity, will further broaden the range of achievable fate patterns.

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References (64)

  1. C. J. Chan, C.-P. Heisenberg, and T. Hiiragi, Coordination of morphogenesis and cell-fate specification in development, Curr. Biol. 27, R1024 (2017).
  2. W. Driever and C. Nüsslein-Volhard, The bicoid protein determines position in the Drosophila embryo in a concentration-dependent manner, Cell 54, 95 (1988).
  3. T. Gregor, D. W. Tank, E. F. Wieschaus, and W. Bialek, Probing the limits to positional information, Cell 130, 153 (2007).
  4. E. Hannezo and C.-P. Heisenberg, Mechanochemical feedback loops in development and disease, Cell 178, 12 (2019).
  5. A. M. Turing, The chemical basis of morphogenesis. 1953, Bull. Math. Biol. 52, 153 (1990).
  6. K. D. Gallagher, M. Mani, and R. W. Carthew, Emergence of a geometric pattern of cell fates from tissue-scale mechanics in the Drosophila eye, eLife 11, e72806 (2022).
  7. D. K. Lubensky, M. W. Pennington, B. I. Shraiman, and N. E. Baker, A dynamical model of ommatidial crystal formation, Proc. Natl. Acad. Sci. USA 108, 11145 (2011).
  8. F. Corson, L. Couturier, H. Rouault, K. Mazouni, and F. Schweisguth, Self-organized Notch dynamics generate stereotyped sensory organ patterns in Drosophila, Science 356, eaai7407 (2017).
  9. M. Bauer, M. D. Petkova, T. Gregor, E. F. Wieschaus, and W. Bialek, Trading bits in the readout from a genetic network, Proc. Natl. Acad. Sci. USA 118, e2109011118 (2021).
  10. C. D. Stern, Neural induction: Old problem, new findings, yet more questions, Development 132, 2007 (2005).
  11. G. Britton, I. Heemskerk, R. Hodge, A. A. Qutub, and A. Warmflash, A novel self-organizing embryonic stem cell system reveals signaling logic underlying the patterning of human ectoderm, Development 146, 179093 (2019).
  12. E. Karzbrun, A. H. Khankhel, H. C. Megale, S. M. K. Glasauer, Y. Wyle, G. Britton, A. Warmflash, K. S. Kosik, E. D. Siggia, B. I. Shraiman, and S. J. Streichan, Human neural tube morphogenesis in vitro by geometric constraints, Nature (London) 599, 268 (2021).
  13. L. Wolpert, Positional information and the spatial pattern of cellular differentiation, J. Theor. Biol. 25, 1 (1969).
  14. K. Dasbiswas, E. Hannezo, and N. S. Gov, Theory of epithelial cell shape transitions induced by mechanoactive chemical gradients, Biophys. J. 114, 968 (2018).
  15. F. Brinkmann, M. Mercker, T. Richter, and A. Marciniak-Czochra, Post-Turing tissue pattern formation: Advent of mechanochemistry, PLoS Comput. Biol. 14, e1006259 (2018).
  16. S. Okuda, T. Miura, Y. Inoue, T. Adachi, and M. Eiraku, Combining Turing and 3D vertex models reproduces autonomous multicellular morphogenesis with undulation, tubulation, and branching, Sci. Rep. 8, 2386 (2018).
  17. P. Recho, A. Hallou, and E. Hannezo, Theory of mechanochemical patterning in biphasic biological tissues, Proc. Natl. Acad. Sci. USA 116, 5344 (2019).
  18. J. S. Bois, F. Jülicher, and S. W. Grill, Pattern formation in active fluids, Phys. Rev. Lett. 106, 028103 (2011).
  19. C. Parada, S. P. Banavar, P. Khalilian, S. Rigaud, A. Michaut, Y. Liu, D. M. Joshy, O. Campàs, and J. Gros, Mechanical feedback defines organizing centers to drive digit emergence, Dev. Cell 57, 854 (2022).
  20. A. J. Engler, S. Sen, H. L. Sweeney, and D. E. Discher, Matrix elasticity directs stem cell lineage specification, Cell 126, 677 (2006).
  21. E. Farge, Mechanical induction of twist in the drosophila foregut/stomodeal primordium, Curr. Biol. 13, 1365 (2003).
  22. N. Desprat, W. Supatto, P.-A. Pouille, E. Beaurepaire, and E. Farge, Tissue deformation modulates twist expression to determine anterior midgut differentiation in drosophila embryos, Dev. Cell 15, 470 (2008).
  23. G. F. Oster, J. D. Murray, and A. K. Harris, Mechanical aspects of mesenchymal morphogenesis, Development 78, 83 (1983).
  24. A. E. Shyer, A. R. Rodrigues, G. G. Schroeder, E. Kassianidou, S. Kumar, and R. M. Harland, Emergent cellular self-organization and mechanosensation initiate follicle pattern in the avian skin, Science 357, 811 (2017).
  25. K. H. Palmquist, S. F. Tiemann, F. L. Ezzeddine, S. Yang, C. R. Pfeifer, A. Erzberger, A. R. Rodrigues, and A. E. Shyer, Reciprocal cell-ECM dynamics generate supracellular fluidity underlying spontaneous follicle patterning, Cell 185, 1960 (2022).
  26. T. R. Huycke, T. J. Häkkinen, H. Miyazaki, V. Srivastava, E. Barruet, C. S. McGinnis, A. Kalantari, J. Cornwall-Scoones, D. Vaka, Q. Zhu, H. Jo, R. Oria, V. M. Weaver, W. F. DeGrado, M. Thomson, K. Garikipati, D. Boffelli, O. D. Klein, and Z. J. Gartner, Patterning and folding of intestinal villi by active mesenchymal dewetting, Cell 187, 3072 (2024).
  27. J. D. Murray and G. F. Oster, Generation of biological pattern and form, IMA J. Math. Appl. Med. Biol. 1, 51 (1984).
  28. G. M. Odell, G. Oster, P. Alberch, and B. Burnside, The mechanical basis of morphogenesis. I. Epithelial folding and invagination, Dev. Biol. 85, 446 (1981).
  29. X. Xue, Y. Sun, A. M. Resto-Irizarry, Y. Yuan, K. M. Aw Yong, Y. Zheng, S. Weng, Y. Shao, Y. Chai, L. Studer, and J. Fu, Mechanics-guided embryonic patterning of neuroectoderm tissue from human pluripotent stem cells, Nat. Mater. 17, 633 (2018).
  30. S. M. Chambers, C. A. Fasano, E. P. Papapetrou, M. Tomishima, M. Sadelain, and L. Studer, Highly efficient neural conversion of human ES and iPS cells by dual inhibition of SMAD signaling, Nat. Biotechnol. 27, 275 (2009).
  31. Y. Mica, G. Lee, S. M. Chambers, M. J. Tomishima, and L. Studer, Modeling neural crest induction, melanocyte specification, and disease-related pigmentation defects in hESCs and patient-specific iPSCs, Cell Rep. 3, 1140 (2013).
  32. J. Tchieu, B. Zimmer, F. Fattahi, S. Amin, N. Zeltner, S. Chen, and L. Studer, A modular platform for differentiation of human PSCs into all major ectodermal lineages, Cell Stem Cell 21, 399 (2017).
  33. I. Muñoz-Sanjuán and A. H. Brivanlou, Neural induction, the default model and embryonic stem cells, Nat. Rev. Neurosci. 3, 271 (2002).
  34. E. Bier and E. M. De Robertis, BMP gradients: A paradigm for morphogen-mediated developmental patterning, Science 348, aaa5838 (2015).
  35. S. Banerjee and M. C. Marchetti, Substrate rigidity deforms and polarizes active gels, Europhys. Lett. 96, 28003 (2011).
  36. C. M. Edwards and U. S. Schwarz, Force localization in contracting cell layers, Phys. Rev. Lett. 107, 128101 (2011).
  37. S. Banerjee and M. C. Marchetti, Contractile stresses in cohesive cell layers on finite-thickness substrates, Phys. Rev. Lett. 109, 108101 (2012).
  38. M. Tewary, J. Ostblom, L. Prochazka, T. Zulueta-Coarasa, N. Shakiba, R. Fernandez-Gonzalez, and P. W. Zandstra, A stepwise model of reaction-diffusion and positional information governs self-organized human peri-gastrulation-like patterning, Development (Cambridge, England) 144, 4298 (2017).
  39. F. Etoc, J. Metzger, A. Ruzo, C. Kirst, A. Yoney, M. Z. Ozair, A. H. Brivanlou, and E. D. Siggia, A balance between secreted inhibitors and edge sensing controls gastruloid self-organization, Dev. Cell 39, 302 (2016).
  40. H. Nunley, X. Xue, Y. Sun, A. M. Resto-Irizarry, Y. Yuan, K. M. A. Yong, Y. Zheng, S. Weng, Y. Shao, D. K. Lubensky, L. Studer, and J. Fu, Dataset of cell layers on micro-patterned substrates composed of posts [Data set], University of Michigan - Deep Blue Data (2025), https://doi.org/10.7302/2kbj-1y73.
  41. J. Fu, Y.-K. Wang, M. T. Yang, R. A. Desai, X. Yu, Z. Liu, and C. S. Chen, Mechanical regulation of cell function with geometrically modulated elastomeric substrates, Nat. Methods 7, 733 (2010).
  42. A. Saez, A. Buguin, P. Silberzan, and B. Ladoux, Is the mechanical activity of epithelial cells controlled by deformations or forces? Biophys. J. 89, L52 (2005).
  43. Y. Sun, K. M. A. Yong, L. G. Villa-Diaz, X. Zhang, W. Chen, R. Philson, S. Weng, H. Xu, P. H. Krebsbach, and J. Fu, Hippo/YAP-mediated rigidity-dependent motor neuron differentiation of human pluripotent stem cells, Nat. Mater. 13, 599 (2014).
  44. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022051 for estimation of in-plane stress in colonies, estimation of cellular mechanical properties, simulations of tissue patterning on substrates of finite thickness, calculations based on the domain-wall approximation, and a more complete discussion of constraints on alternative models that rely on an unidentified chemical signal.
  45. F. Corson and E. D. Siggia, Geometry, epistasis, and developmental patterning, Proc. Natl. Acad. Sci. USA 109, 5568 (2012).
  46. A. Raju and E. D. Siggia, A geometrical perspective on development, Dev. Growth Differ. 65, 245 (2023), .
  47. M. Cross and H. Greenside, Pattern Formation and Dynamics in Nonequilibrium Systems (Cambridge University Press, Cambridge, 2009).
  48. E. Närvä, A. Stubb, C. Guzmán, M. Blomqvist, D. Balboa, M. Lerche, M. Saari, T. Otonkoski, and J. Ivaska, A strong contractile actin fence and large adhesions direct human pluripotent colony morphology and adhesion, Stem Cell Rep. 9, 67 (2017).
  49. K. A. Rosowski, A. F. Mertz, S. Norcross, E. R. Dufresne, and V. Horsley, Edges of human embryonic stem cell colonies display distinct mechanical properties and differentiation potential, Sci. Rep. 5, 14218 (2015).
  50. H. Nunley, X. Xue, J. Fu, and D. K. Lubensky, Dataset on cell areas and nuclear densities in differentiating stem cell colonies [Data set], University of Michigan - Deep Blue Data (2025), https://doi.org/10.7302/0n9v-6397.
  51. H. Nunley and D. K. Lubensky, Code for simulating the formation of a binary fate pattern in response to mechanical stresses [Data set], University of Michigan - Deep Blue Data (2025), https://doi.org/10.7302/44wm-j668.
  52. C. B. Muratov and S. Y. Shvartsman, An asymptotic study of the inductive pattern formation mechanism in Drosophila egg development, Physica D 186, 93 (2003).
  53. C. B. Muratov and V. V. Osipov, General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems, Phys. Rev. E 53, 3101 (1996).
  54. W. v. Saarloos, Three basic issues concerning interface dynamics in nonequilibrium pattern formation, Phys. Rep. 301, 9 (1998).
  55. A. F. Mertz, Y. Che, S. Banerjee, J. M. Goldstein, K. A. Rosowski, S. F. Revilla, C. M. Niessen, M. C. Marchetti, E. R. Dufresne, and V. Horsley, Cadherin-based intercellular adhesions organize epithelial cell–matrix traction forces, Proc. Natl. Acad. Sci. USA 110, 842 (2013).
  56. H. Nunley, X. Xue, Y. Sun, A. M. Resto-Irizarry, Y. Yuan, K. M. A. Yong, Y. Zheng, S. Weng, Y. Shao, D. K. Lubensky, L. Studer, and J. Fu, Dataset of stem cell colonies differentiating in neural induction medium and code for analysis of resulting fate pattern [Data set], University of Michigan - Deep Blue Data (2025), https://doi.org/10.7302/axdw-zm41.
  57. A. Saez, M. Ghibaudo, A. Buguin, P. Silberzan, and B. Ladoux, Rigidity-driven growth and migration of epithelial cells on microstructured anisotropic substrates, Proc. Natl. Acad. Sci. USA 104, 8281 (2007).
  58. J. L. Tan, J. Tien, D. M. Pirone, D. S. Gray, K. Bhadriraju, and C. S. Chen, Cells lying on a bed of microneedles: An approach to isolate mechanical force, Proc. Natl. Acad. Sci. USA 100, 1484 (2003).
  59. P. Caldarelli, A. Chamolly, A. Villedieu, O. Alegria-Prévot, C. Phan, J. Gros, and F. Corson, Self-organized tissue mechanics underlie embryonic regulation, Nature (London) 633, 887 (2024).
  60. T. Das, K. Safferling, S. Rausch, N. Grabe, H. Boehm, and J. P. Spatz, A molecular mechanotransduction pathway regulates collective migration of epithelial cells, Nat. Cell Biol. 17, 276 (2015).
  61. P. E. Farahani, S. B. Lemke, E. Dine, G. Uribe, J. E. Toettcher, and C. M. Nelson, Substratum stiffness regulates Erk signaling dynamics through receptor-level control, Cell Rep. 37, 110181 (2021).
  62. I. Martyn, T. Y. Kanno, A. Ruzo, E. D. Siggia, and A. H. Brivanlou, Self-organization of a human organizer by combined Wnt and Nodal signalling, Nature (London) 558, 132 (2018).
  63. H. Spemann and H. Mangold, Induction of embryonic primordia by implantation of organizers from a different species. 1923, Int. J. Dev. Biol. 45, 13 (2001).
  64. P. Wilson, G. Lagna, A. Suzuki, and A. Hemmati-Brivanlou, Concentration-dependent patterning of the Xenopus ectoderm by BMP4 and its signal transducer Smad1, Development 124, 3177 (1997).

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Phys. Rev. Research 7, L022051– Published 4 June, 2025
  • Received 30 April 2021
  • Accepted 15 April 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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