- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

How does the extracellular matrix affect the rigidity of an embedded spheroid?

Amanda Parker1, M. Cristina Marchetti2, M. Lisa Manning1, and J. M. Schwarz1,3

PDF

Phys. Rev. E 111, 044410 – Published 22 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.044410

Abstract

Cellularized tissue and polymer networks can both transition from floppy to rigid as a function of their control parameters, and, yet, the two systems often mechanically interact, which could affect their respective rigidities. To study this interaction, we consider a vertex model with surface tension embedded in a spring network in two dimensions. We identify two regimes with different global spheroid shapes and governed by the pressure resulting from competition between surface tension and tension in the network. In the first regime, the tissue remains compact, while in the second, a cavitation-like instability leads to the emergence of gaps at the tissue-network interface. Intriguingly, compression of the tissue promotes fluidization, while tension promotes cellular alignment and rigidification with the mechanisms driving rigidification differing on either side of the instability.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (53)

  1. G.M. Cooper, The Cell: A Molecular Approach, 2nd ed. (Sunderland, MA: Sinauer Associates, 2000).
  2. C. M. Niessen, D. Leckband, and A. S. Yap, Tissue organization by cadherin adhesion molecules: Dynamic molecular and cellular mechanisms of morphogenetic regulation, Physiol. Rev. 91, 691 (2011).
  3. L. Li, Y. He, M. Zhao, and J. Jiang, Collective cell migration: Implications for wound healing and cancer invasion, Burn Trauma 1, 21 (2013).
  4. M. A. Garcia, W. J. Nelson, and N. Chavez, Cell-cell junctions organize structural and signaling networks, Cold Spring Harbor Perspect. Biol. 10, a029181 (2018).
  5. B. R. Bruckner and A. Janshoff, Importance of integrity of cell-cell junctions for the mechanics of confluent MDCK II cells, Sci. Reps. 8, 14117 (2018).
  6. C. G. Galbraith and M. P. Sheetz, Forces on adhesive contacts affect cell function, Curr. Opin. Cell Biol. 10, 566 (1998).
  7. C. M. Lo, H. B. Wang et al., Cell movement is guided by the rigidity of the substrate, Biophys. J. 79, 144 (2000).
  8. A. P. Liu, O. Chaudhuri, and S. H. Parekh, New advances in probing cell–extracellular matrix interactions, Integrat. Biol. 9, 383 (2017).
  9. J. D. Humphrey, E. R. Dufresne, and M. A. Schwartz, Mechanotransduction and extracellular matrix homeostasis, Nat. Rev. Mol. Cell Biol. 15, 802 (2014).
  10. C. Frantz, K. M. Stewart, and V. M. Weaver, The extracellular matrix at a glance, J. Cell Sci. 123, 4195 (2010).
  11. C. Walker, E. Mojares, and A. Del Río Hernández, Role of extracellular matrix in development and cancer progression, Int. J. Mol. Sci. 19, 3028 (2018).
  12. M. Giussani, G. Merlino, V. Cappelletti, E. Tagliabue, and M. G. Daidone, Tumor-extracellular matrix interactions: Identification of tools associated with breast cancer progression, Semin. Cancer Biol. 35, 3 (2015).
  13. I. Acerbi, L. Cassereau, I. Dean, Q. Shi, A. Au, C. Park, Y. Y. Chen, J. Liphardt, E. S. Hwang, and V. M. Weaver, Human breast cancer invasion and aggression correlates with ECM stiffening and immune cell infiltration, Int. Biol. 7, 1120 (2015).
  14. J. L. Leight, A. P. Drain, and V. M. Weaver, Extracellular matrix remodeling and stiffening modulate tumor phenotype and treatment response, Annu. Rev. Cancer Biol. 1, 313 (2017).
  15. A. J. McKenzie, S. R. Hicks, K. V. Svec et al., The mechanical microenvironment regulates ovarian cancer cell morphology, migration, and spheroid disaggregation, Sci. Rep. 8, 7228 (2018).
  16. K. S. Kopanska, Y. Alcheikh, R. Staneva, D. Vignjevic, and T. Betz, Tensile forces originating from cancer spheroids facilitate tumor invasion, PLoS ONE 11, e0156442 (2016).
  17. Y. J. Suh, M. S. Hall, Y. L. Huang, S. Y. Moon, W. Song, M. Ma, L. J. Bonassar, J. E. Segall, and M. Wu, Glycation of collagen matrices promotes breast tumor cell invasion, Integrat. Biol. 11, 109 (2019).
  18. J. P. Baskaran, A. Weldy, J. Guarin, G. Munoz, M. Kotlik, N. Subbiah, A. Wishart, Y. Peng, M. A. Miller, L. Cowen, and M. J. Oudin, Cell shape, and not 2D migration, predicts ECM-driven 3D cell invasion in breast cancer, bioRxiv (2020).
  19. Y. Zheng, H. Nan, Y. Liu, Q. Fan, X. Wang, R. Liu, L. Liu, F. Ye, B. Sun, and Y. Jiao, Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling, Phys. Rev. E 100, 043303 (2019).
  20. M.-C. Kim, Y. R. Silberberg, R. Abeyaratne, R. D. Kamm, and H. H. Asada, Computational modeling of three-dimensional ECM-rigidity sensing to guide directed cell migration, Proc. Natl. Acad. Sci. USA 115, E390 (2018).
  21. Y. L. Han, P. Ronceray, G. Xu, A. Malandrino, R. D. Kamm, M. Lenz, C. P. Broedersz, and M. Guo, Cell contraction induces long-ranged stress stiffening in the extracellular matrix, Proc. Natl. Acad. Sci. USA 115, 4075 (2018).
  22. T. Nagai and H. Honda, A dynamic cell model for the formation of epithelial tissues, Philos. Mag. B 81, 699 (2001).
  23. R. Farhadifar, J.-C. Roper et al., The influence of cell mechanics, cell-cell interactions, and proliferation on epithelial packing, Curr. Biol. 17, 2095 (2007).
  24. D. Bi, J. Lopez, J. M. Schwarz, and M. L. Manning, A density-independent rigidity transition in biological tissues, Nat. Phys. 11, 1074 (2015).
  25. M. Merkel and M. L. Manning, A geometrically controlled rigidity transition in a model for confluent 3D tissues, New J. Phys. 20, 022002 (2018).
  26. P. Sahu et al., Small-scale demixing in confluent biological tissues, Soft Matter 16, 3325 (2020).
  27. J. Park, J. Kim, D. Bi et al., Unjamming and cell shape in the asthmatic airway epithelium, Nat. Mater. 14, 1040 (2015).
  28. C. Malinverno et al., Endocytic reawakening of motility in jammed epithelia, Nat. Mater. 16, 587 (2017).
  29. A. J. Licup et al., Stress controls the mechanics of collagen networks, Proc. Natl. Acad. Sci. USA 112, 9573 (2015).
  30. A. Sharma, A. Licup, K. Jansen et al., train-controlled criticality governs the nonlinear mechanics of fibre networks, Nat. Phys. 12, 584 (2016).
  31. K. A. Jansen, A. J. Licup, A. Sharma, R. Rens, F. C. MacKintosh, and G. H. Koenderink, The role of network architecture in collagen mechanics, Biophys. J. 114, 2665 (2018).
  32. M. Merkel, K. Baumgarten, B. P. Tighe, and M. L. Manning, A minimal-length approach unifies rigidity in underconstrained materials, Proc. Natl. Acad. Sci. USA 116, 6560 (2019).
  33. G. W. Brodland, The differential interfacial tension hypothesis (DITH): A comprehensive theory for the self-rearrangement of embryonic cells and tissues, J. Biomech. Eng. 124, 188 (2002).
  34. N. B. Ouchi, J. A. Glazier, J.-P. Rieu, A. Upadhyaya, and Y. Sawada, Improving the realism of the cellular Potts model in simulations of biological cells, Physica A 329, 451 (2003).
  35. T. Lecuit and P.-F. Lenne, Cell surface mechanics and the control of cell shape, tissue patterns and morphogenesis, Nat. Rev. Mol. Cell Biol. 8, 633 (2007).
  36. K. Kim, J. M. Schwarz, and M. Ben Amar, A two-dimensional vertex model for curvy cell–cell interfaces at the subcellular scale, J. R. Soc. Interface. 21, 20240193 (2024).
  37. S. Kim, M. Pochitaloff, G. A. Stooke-Vaughan, and O. Campàs, Embryonic tissues as active foams, Nat. Phys. 17, 859 (2021).
  38. A. Mongera et al., A fluid-to-solid jamming transition underlies vertebrate body axis elongation, Nature (London) 561, 401 (2018).
  39. J. C. Maxwell, L. on the calculation of the equilibrium and stiffness of frames, London Edinburgh Dublin Philos. Mag, J. Sci. 27, 294 (1864).
  40. R. C. Arevalo, J. S. Urbach, and D. L. Blair, Size-dependent rheology of type-I collagen networks. Biophys. J. 99, L65 (2010).
  41. D. Weaire and N. Rivier, Soap, cells and statistics—Random patterns in two dimensions, Contemp. Phys. 25, 59 (1984).
  42. D. M. Sussman, cellGPU: Massively parallel simulations of dynamic vertex models, Comput. Phys. Commun. 219, 400 (2017).
  43. E. Bitzek, P. Koskinen, F. Gähler, M. Moseler, and P. Gumbsch, Structural relaxation made simple, Phys. Rev. Lett. 97, 170201 (2006).
  44. W. C. Graustein, On the average number of sides of polygons of a net, Ann. Math. 32, 149 (1931).
  45. X. Wang, M. Merkel, L. B. Sutter, G. Erdemci-Tandogan, M. L. Manning, and K. E. Kasza, Anisotropy links cell shapes to a solid-to-fluid transition during convergent extension, bioRxiv (2019).
  46. X. Li, A. Das, and D. Bi, Mechanical heterogeneity in tissues promotes rigidity and controls cellular invasion, Phys. Rev. Lett. 123, 058101 (2019).
  47. W. Wang et al., Tumor invasion as non-equilibrium phase separation, bioRxiv (2020).
  48. T. Zhang, S. Ameen, S. Ghosh, K. Kim, M. Thanh, A. E. Patteson, M. Wu, and J. M. Schwarz, Enhanced extracellular matrix remodeling due to embedded spheroid fluidization, bioRxiv (2024).
  49. M. T. H. Thanh, A. Poudel, S. Ameen, B. Carroll, M. Wu, P. Soman, T. Zhang, J. M. Schwarz, and A. E. Patteson, Vimentin promotes collective cell migration through collagen networks via increased matrix remodeling and spheroid fluidity, bioRxiv (2024).
  50. K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon et al., Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro, Proc. Natl. Acad. Sci. USA 110, 14843 (2013).
  51. T. Fuhs, F. Wetzel, A. W. Fritsch, X. Li, R. Stange, S. Pawlizak, T. R. Kießling, E. Morawetz, S. Grosser, F. Sauer et al., Rigid tumours contain soft cancer cells, Nat. Phys. 18, 1510 (2022).
  52. R. Etournay, M. Popović, M. Merkel, A. Nandi, C. Blasse, B. Aigouy, H. Brandl, G. Myers, G. Salbreux, F. Jülicher et al., Interplay of cell dynamics and epithelial tension during morphogenesis of the Drosophila pupal wing, eLife 4, e07090 (2015).
  53. D. Bi, J. H. Lopez, J. M. Schwarz, and M. L. Manning, Energy barriers and cell migration in densely packed tissues, Soft Matter 10, 1885 (2014).

Outline

Information

Phys. Rev. E 111, 044410– Published 22 April, 2025
  • Received 3 November 2022
  • Revised 2 October 2023
  • Accepted 21 March 2025
Article part of CHORUS
Crossmark - Check for updates button

©2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation