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Data-Driven Theory Reveals Protrusion and Polarity Interactions Governing Collision Behavior of Distinct Motile Cells

Tom Brandstätter1,2,*, Emily Brieger3,*, David B. Brückner4,5, Georg Ladurner3,6, Joachim O. Rädler3, and Chase P. Broedersz1,2,†

  • *These authors contributed equally to this work.
  • †Contact author: c.p.broedersz@vu.nl
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PRX Life 3, 033015 – Published 26 August, 2025

DOI: https://doi.org/10.1103/3hhj-rt1n

Abstract

The migration behavior of colliding cells is critically determined by transient contact interactions. During these interactions, the motility machinery, including the front-rear polarization of the cell, dynamically responds to surface protein-mediated transmission of forces and biochemical signals between cells. While biomolecular details of such contact interactions are increasingly well understood, it remains unclear what biophysical interaction mechanisms govern the cell-level dynamics of colliding cells and how these mechanisms vary across cell types. Here we develop a phenomenological theory based on 14 candidate contact-interaction mechanisms coupling cell position, protrusion, and polarity. Using high-throughput micropattern experiments, we detect which of these phenomenological contact interactions captures the interaction behaviors of cells. We find that various cell types—ranging from mesenchymal to epithelial cells—are accurately captured by a single model with only two interaction mechanisms: polarity-protrusion coupling and polarity-polarity coupling. Remarkably, the qualitatively different interaction behaviors of distinct cells, as well as cells subject to molecular perturbations of surface protein-mediated signaling, can all be quantitatively captured by varying the strength and sign of the polarity-polarity coupling mechanism. Altogether, our data-driven phenomenological theory of cell-cell interactions reveals polarity-polarity coupling as a versatile and general contact-interaction mechanism, which may underlie diverse collective migration behaviors of motile cells.

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References (83)

  1. A. Haeger, K. Wolf, M. M. Zegers, and P. Friedl, Collective cell migration: Guidance principles and hierarchies, Trends Cell Biol. 25, 556 (2015).
  2. E. Scarpa and R. Mayor, Collective cell migration in development, J. Cell Biol. 212, 143 (2016).
  3. M. Poujade, E. Grasland-Mongrain, A. Hertzog, J. Jouanneau, P. Chavrier, B. Ladoux, A. Buguin, and P. Silberzan, Collective migration of an epithelial monolayer in response to a model wound, Proc. Natl. Acad. Sci. USA 104, 15988 (2007).
  4. P. Friedl and D. Gilmour, Collective cell migration in morphogenesis, regeneration and cancer, Nat. Rev. Mol. Cell Biol. 10, 445 (2009).
  5. S. Vedel, S. Tay, D. M. Johnston, H. Bruus, and S. R. Quake, Migration of cells in a social context, Proc. Natl. Acad. Sci. USA 110, 129 (2013).
  6. M. Abercrombie, Contact inhibition and malignancy, Nature (London) 281, 259 (1979).
  7. E. Scarpa, A. Roycroft, E. Theveneau, E. Terriac, M. Piel, R. Mayor, E. Scarpa, A. Roycroft, E. Theveneau, E. Terriac, M. Piel, and R. Mayor, A novel method to study contact inhibition of locomotion using micropatterned substrates, Biol. Open 5, 1553 (2016).
  8. D. B. Brückner, N. Arlt, A. Fink, P. Ronceray, J. O. Rädler, and C. P. Broedersz, Learning the dynamics of cell–cell interactions in confined cell migration, Proc. Natl. Acad. Sci. USA 118, e2016602118 (2021).
  9. A. Roycroft and R. Mayor, Molecular basis of contact inhibition of locomotion, Cell. Mol. Life Sci. 73, 1119 (2016).
  10. C. Collins and W. J. Nelson, Running with neighbors: Coordinating cell migration and cell-cell adhesion, Curr. Opin. Cell Biol. 36, 62 (2015).
  11. B. Ladoux and R. M. Mège, Mechanobiology of collective cell behaviours, Nat. Rev. Mol. Cell Biol. 18, 743 (2017).
  12. A. J. Ridley, Life at the leading edge, Cell 145, 1012 (2011).
  13. W. J. Rappel and L. Edelstein-Keshet, Mechanisms of cell polarization, Curr. Opin. Syst. Biol. 3, 43 (2017).
  14. G. Danuser, J. Allard, and A. Mogilner, Mathematical modeling of eukaryotic cell migration: Insights beyond experiments, Annu. Rev. Cell Dev. Biol. 29, 501 (2013).
  15. S. Kadir, J. W. Astin, L. Tahtamouni, P. Martin, and C. D. Nobes, Microtubule remodelling is required for the front-rear polarity switch during contact inhibition of locomotion, J. Cell Sci. 124, 2642 (2011).
  16. E. Theveneau and R. Mayor, Collective cell migration of epithelial and mesenchymal cells, Cell. Mol. Life Sci. 70, 3481 (2013).
  17. S. Jain, V. M. Cachoux, G. H. Narayana, S. de Beco, J. D'Alessandro, V. Cellerin, T. Chen, M. L. Heuzé, P. Marcq, R. M. Mège, A. J. Kabla, C. T. Lim, and B. Ladoux, The role of single-cell mechanical behaviour and polarity in driving collective cell migration, Nat. Phys. 16, 802 (2020).
  18. C. Carmona-Fontaine, H. K. Matthews, S. Kuriyama, M. Moreno, G. A. Dunn, M. Parsons, C. D. Stern, and R. Mayor, Contact inhibition of locomotion in vivo controls neural crest directional migration, Nature (London) 456, 957 (2008).
  19. E. Theveneau, L. Marchant, S. Kuriyama, M. Gull, B. Moepps, M. Parsons, and R. Mayor, Collective Chemotaxis Requires Contact-Dependent Cell Polarity, Develop. Cell 19, 39 (2010).
  20. J. R. Davis, C. Y. Huang, J. Zanet, S. Harrison, E. Rosten, S. Cox, D. Y. Soong, G. A. Dunn, and B. M. Stramer, Emergence of embryonic pattern through contact inhibition of locomotion, Development 139, 4555 (2012).
  21. V. Villar-Cerviño, M. Molano-Mazón, T. Catchpole, M. Valdeolmillos, M. Henkemeyer, L. M. Martínez, V. Borrell, and O. Marín, Contact Repulsion Controls the Dispersion and Final Distribution of Cajal-Retzius cells, Neuron 77, 457 (2013).
  22. R. Mayor and C. Carmona-Fontaine, Keeping in touch with contact inhibition of locomotion, Trends Cell Biol. 20, 319 (2010).
  23. J. D'alessandro, A. P. Solon, Y. Hayakawa, C. Anjard, F. Detcheverry, J. P. Rieu, and C. Rivière, Contact enhancement of locomotion in spreading cell colonies, Nat. Phys. 13, 999 (2017).
  24. M. Hayakawa, T. Hiraiwa, Y. Wada, H. Kuwayama, and T. Shibata, Polar pattern formation induced by contact following locomotion in a multicellular system, eLife 9, e53609 (2020).
  25. A. M. Mendonsa, T. Y. Na, and B. M. Gumbiner, E-cadherin in contact inhibition and cancer, Oncogene 37, 4769 (2018).
  26. J. L. Maître and C. P. Heisenberg, Three functions of cadherins in cell adhesion, Curr. Biol. 23, R626 (2013).
  27. B. Stramer and R. Mayor, Mechanisms and in vivo functions of contact inhibition of locomotion, Nat. Rev. Mol. Cell Biol. 18, 43 (2017).
  28. J. W. Astin, J. Batson, S. Kadir, J. Charlet, R. A. Persad, D. Gillatt, J. D. Oxley, and C. D. Nobes, Competition amongst Eph receptors regulates contact inhibition of locomotion and invasiveness in prostate cancer cells, Nat. Cell Biol. 12, 1194 (2010).
  29. N. K. Noren and E. B. Pasquale, Eph receptor-ephrin bidirectional signals that target Ras and Rho proteins, Cell. Signal. 16, 655 (2004).
  30. R. A. Desai, L. Gao, S. Raghavan, W. F. Liu, and C. S. Chen, Cell polarity triggered by cell-cell adhesion via E-cadherin, J. Cell Sci. 122, 905 (2009).
  31. E. Scarpa, A. Szabó, A. Bibonne, E. Theveneau, M. Parsons, and R. Mayor, Cadherin switch during EMT in neural crest cells leads to contact inhibition of locomotion via repolarization of forces, Develop. Cell 34, 421 (2015).
  32. I. Y. Wong, S. Javaid, E. A. Wong, S. Perk, D. A. Haber, M. Toner, and D. Irimia, Collective and individual migration following the epithelial–mesenchymal transition, Nat. Mater. 13, 1063 (2014).
  33. D. B. Brückner, M. Schmitt, A. Fink, G. Ladurner, J. Flommersfeld, N. Arlt, E. Hannezo, J. O. Rädler, and C. P. Broedersz, Geometry adaptation of protrusion and polarity dynamics in confined cell migration, Phys. Rev. X 12, 031041 (2022).
  34. J. Flommersfeld, S. Stöberl, O. Shah, J. O. Rädler, and C. P. Broedersz, Geometry-sensitive protrusion growth directs confined cell migration, Phys. Rev. Lett. 132, 098401 (2024).
  35. L. Edelstein-Keshet, W. R. Holmes, M. Zajac, and M. Dutot, From simple to detailed models for cell polarization, Phil. Trans. R. Soc. B 368, 20130003 (2013).
  36. P. Sens, Stick-slip model for actin-driven cell protrusions, cell polarization, and crawling, Proc. Natl. Acad. Sci. USA 117, 24670 (2020).
  37. B. A. Camley, Y. Zhang, Y. Zhao, B. Li, E. Ben-Jacob, H. Levine, and W. J. Rappel, Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns, Proc. Natl. Acad. Sci. USA 111, 14770 (2014).
  38. B. Smeets, R. Alert, J. Pešek, I. Pagonabarraga, H. Ramon, and R. Vincent, Emergent structures and dynamics of cell colonies by contact inhibition of locomotion, Proc. Natl. Acad. Sci. USA 113, 14621 (2016).
  39. N. Sepúlveda, L. Petitjean, O. Cochet, E. Grasland-Mongrain, P. Silberzan, and V. Hakim, Collective cell motion in an epithelial sheet can be quantitatively described by a stochastic interacting particle model, PLoS Comput. Biol. 9, e1002944 (2013).
  40. J. E. Ron, J. d'Alessandro, V. Cellerin, R. Voituriez, B. Ladoux, and N. S. Gov, Polarization and motility of one-dimensional multi-cellular trains, Biophys. J. 122, 4598 (2023).
  41. K. Copenhagen, G. Malet-Engra, W. Yu, G. Scita, N. Gov, and A. Gopinathan, Frustration-induced phases in migrating cell clusters, Sci. Adv. 4, eaar8483 (2018).
  42. E. Vercruysse, D. B. Brückner, M. Gómez-González, A. Remson, M. Luciano, Y. Kalukula, L. Rossetti, X. Trepat, E. Hannezo, and S. Gabriele, Geometry-driven migration efficiency of autonomous epithelial cell clusters, Nat. Phys. 20, 1492 (2024).
  43. D. A. Kulawiak, B. A. Camley, and W. J. Rappel, Modeling contact inhibition of locomotion of colliding cells migrating on micropatterned substrates, PLoS Comput. Biol. 12, e1005239 (2016).
  44. R. A. Desai, S. B. Gopal, S. Chen, and C. S. Chen, Contact inhibition of locomotion probabilities drive solitary versus collective cell migration, J. R. Soc. Interface 10, 20130717 (2013).
  45. T. Zisis, D. B. Brückner, T. Brandstätter, W. X. Siow, J. d'Alessandro, A. M. Vollmar, C. P. Broedersz, and S. Zahler, Disentangling cadherin-mediated cell-cell interactions in collective cancer cell migration, Biophys. J. 121, 44 (2022).
  46. R. Alert and X. Trepat, Physical models of collective cell migration, Annu. Rev. Condens. Matter Phys. 11, 77 (2020).
  47. J. Löber, F. Ziebert, and I. S. Aranson, Collisions of deformable cells lead to collective migration, Sci. Rep. 5, 9172 (2015).
  48. T. Bertrand, J. D'Alessandro, A. Maitra, S. Jain, B. Mercier, R. M. Mège, B. Ladoux, and R. Voituriez, Clustering and ordering in cell assemblies with generic asymmetric aligning interactions, Phys. Rev. Res. 6, 023022 (2024).
  49. D. B. Brückner and C. P. Broedersz, Learning dynamical models of single and collective cell migration: A review, Rep. Prog. Phys. 87, 056601 (2024).
  50. D. B. Brückner, P. Ronceray, and C. P. Broedersz, Inferring the dynamics of underdamped stochastic systems, Phys. Rev. Lett. 125, 058103 (2020).
  51. E. Agliari, P. J. Sáez, A. Barra, M. Piel, P. Vargas, and M. Castellana, A statistical inference approach to reconstruct intercellular interactions in cell migration experiments, Sci. Adv. 6, eaay2103 (2020).
  52. C. Joshi, S. Ray, L. M. Lemma, M. Varghese, G. Sharp, Z. Dogic, A. Baskaran, and M. F. Hagan, Data-driven discovery of active nematic hydrodynamics, Phys. Rev. Lett. 129, 258001 (2022).
  53. N. Romeo, A. D. Hastewell, A. Mietke, and J. Dunkel, Learning developmental mode dynamics from single-cell trajectories, eLife 10, e68679 (2021).
  54. See Supplemental Material at http://link.aps.org/supplemental/10.1103/3hhj-rt1n for additional experimental analysis and theoretical results, which also contains Refs. [8, 33, 48, 55, 81].
  55. D. B. Brückner, A. Fink, C. Schreiber, P. J. Röttgermann, J. O. Rädler, and C. P. Broedersz, Stochastic nonlinear dynamics of confined cell migration in two-state systems, Nat. Phys. 15, 595 (2019).
  56. Y. Kalukula, M. Luciano, G. Charras, D. B. Brückner, and S. Gabriele, The actin cortex acts as a mechanical memory of morphology in confined migrating cells, bioRxiv:2024.08.05.606589.
  57. J. E. Ron, P. Monzo, N. C. Gauthier, R. Voituriez, and N. S. Gov, One-dimensional cell motility patterns, Phys. Rev. Res. 2, 033237 (2020).
  58. I. C. Fortunato, D. B. Brückner, S. Grosser, L. Rossetti, M. Bosch-Padrós, J. Trebicka, P. Roca-Cusachs, R. Sunyer, E. Hannezo, and X. Trepat, Single cell migration along and against confined haptotactic gradients, bioRxiv (2024).
  59. T. D. Pollard, The cytoskeleton, cellular motility and the reductionist agenda, Nature (London) 422, 741 (2003).
  60. R. M. Lee, M. I. Vitolo, W. Losert, and S. S. Martin, Distinct roles of tumor associated mutations in collective cell migration, Sci. Rep. 11, 10291 (2021).
  61. T. Blick, E. Widodo, H. Hugo, M. Waltham, M. E. Lenburg, R. M. Neve, and E. W. Thompson, Epithelial mesenchymal transition traits in human breast cancer cell lines, Clin. Exp. Metastasis 25, 629 (2008).
  62. D. Selmeczi, S. Mosler, P. H. Hagedorn, N. B. Larsen, and H. Flyvbjerg, Cell motility as persistent random motion: Theories from experiments, Biophys. J. 89, 912 (2005).
  63. D. F. Milano, N. A. Ngai, S. K. Muthuswamy, and A. R. Asthagiri, Regulators of metastasis modulate the migratory response to cell contact under spatial confinement, Biophys. J. 110, 1886 (2016).
  64. L. Lu, T. Guyomar, Q. Vagne, R. Berthoz, A. Torres-Sánchez, M. Lieb, C. Martin-Lemaitre, K. van Unen, A. Honigmann, O. Pertz, D. Riveline, and G. Salbreux, Polarity-driven three-dimensional spontaneous rotation of a cell doublet, Nat. Phys. 20, 1194 (2024).
  65. Y. L. Chao, C. R. Shepard, and A. Wells, Breast carcinoma cells re-express E-cadherin during mesenchymal to epithelial reverting transition, Mol. Cancer 9, 179 (2010).
  66. X. Serra-Picamal, V. Conte, R. Vincent, E. Anon, D. T. Tambe, E. Bazellieres, J. P. Butler, J. J. Fredberg, and X. Trepat, Mechanical waves during tissue expansion, Nat. Phys. 8, 628 (2012).
  67. D. T. Tambe, C. Corey Hardin, T. E. Angelini, K. Rajendran, C. Y. Park, X. Serra-Picamal, E. H. Zhou, M. H. Zaman, J. P. Butler, D. A. Weitz, J. J. Fredberg, and X. Trepat, Collective cell guidance by cooperative intercellular forces, Nat. Mater. 10, 469 (2011).
  68. S. Lo Vecchio, O. Pertz, M. Szopos, L. Navoret, and D. Riveline, Spontaneous rotations in epithelia as an interplay between cell polarity and boundaries, Nat. Phys. 20, 322 (2024).
  69. M. Basan, J. Elgeti, E. Hannezo, W. J. Rappel, and H. Levine, Alignment of cellular motility forces with tissue flow as a mechanism for efficient wound healing, Proc. Natl. Acad. Sci. USA 110, 2452 (2013).
  70. B. D. Hoffman, C. Grashoff, and M. A. Schwartz, Dynamic molecular processes mediate cellular mechanotransduction, Nature (London) 475, 316 (2011).
  71. G. F. Weber, M. A. Bjerke, and D. W. DeSimone, A mechanoresponsive cadherin-keratin complex directs polarized protrusive behavior and collective cell migration, Develop. Cell 22, 104 (2012).
  72. B. R. Acharya, A. Nestor-Bergmann, X. Liang, S. Gupta, K. Duszyc, E. Gauquelin, G. A. Gomez, S. Budnar, P. Marcq, O. E. Jensen, Z. Bryant, and A. S. Yap, A mechanosensitive RhoA pathway that protects epithelia against acute tensile stress, Develop. Cell 47, 439 (2018).
  73. M. Nakagawa, M. Fukata, M. Yamaga, N. Itoh, and K. Kaibuchi, Recruitment and activation of Rac1 by the formation of E-cadherin-mediated cell-cell adhesion sites, J. Cell Sci. 114, 1829 (2001).
  74. T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett. 75, 1226 (1995).
  75. S. J. Streichan, M. F. Lefebvre, N. Noll, E. F. Wieschaus, and B. I. Shraiman, Global morphogenetic flow is accurately predicted by the spatial distribution of myosin motors, eLife 7, e27454 (2018).
  76. G. Peyret, R. Mueller, J. d'Alessandro, S. Begnaud, P. Marcq, R. M. Mège, J. M. Yeomans, A. Doostmohammadi, and B. Ladoux, Sustained oscillations of epithelial cell sheets, Biophys. J. 117, 464 (2019).
  77. T. Brandstätter, D. B. Brückner, Y. L. Han, R. Alert, M. Guo, and C. P. Broedersz, Curvature induces active velocity waves in rotating multicellular spheroids, Nat. Commun. 14, 1643 (2023).
  78. C. Malinverno, S. Corallino, F. Giavazzi, M. Bergert, Q. Li, M. Leoni, A. Disanza, E. Frittoli, A. Oldani, E. Martini, T. Lendenmann, G. Deflorian, G. V. Beznoussenko, D. Poulikakos, K. H. Ong, M. Uroz, X. Trepat, D. Parazzoli, P. Maiuri, W. Yu et al., Endocytic reawakening of motility in jammed epithelia, Nat. Mater. 16, 587 (2017).
  79. W. Kang, J. Ferruzzi, C. P. Spatarelu, Y. L. Han, Y. Sharma, S. A. Koehler, J. A. Mitchel, A. Khan, J. P. Butler, D. Roblyer, M. H. Zaman, J. A. Park, M. Guo, Z. Chen, A. F. Pegoraro, and J. J. Fredberg, A novel jamming phase diagram links tumor invasion to non-equilibrium phase separation, iScience 24, 103252 (2021).
  80. A. Palamidessi, C. Malinverno, E. Frittoli, S. Corallino, E. Barbieri, S. Sigismund, G. V. Beznoussenko, E. Martini, M. Garre, I. Ferrara, C. Tripodo, F. Ascione, E. A. Cavalcanti-Adam, Q. Li, P. P. Di Fiore, D. Parazzoli, F. Giavazzi, R. Cerbino, and G. Scita, Unjamming overcomes kinetic and proliferation arrest in terminally differentiated cells and promotes collective motility of carcinoma, Nat. Mater. 18, 1252 (2019).
  81. H. Aragaki, K. Ogoh, Y. Kondo, and K. Aoki, LIM Tracker: a software package for cell tracking and analysis with advanced interactivity, Sci. Rep. 12, 2702 (2023) .
  82. A. Szabó, M. Melchionda, G. Nastasi, M. L. Woods, S. Campo, R. Perris, and R. Mayor, In vivo confinement promotes collective migration of neural crest cells, J. Cell Biol. 213, 543 (2016).
  83. J. M. Belmonte, G. L. Thomas, L. G. Brunnet, R. M. De Almeida, and H. Chaté, Self-propelled particle model for cell-sorting phenomena, Phys. Rev. Lett. 100, 248702 (2008).

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PRX Life 3, 033015– Published 26 August, 2025
  • Received 9 August 2024
  • Accepted 1 August 2025
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