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A cell-based model for analyzing growth and invasion of tumor spheroids

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Abstract

Both chemical and mechanical determinants adapt and react throughout the process of tumor invasion. In this study, a cell-based model is used to uncover the growth and invasion of a three-dimensional solid tumor confined within normal cells. Each cell is treated as a spheroid that can deform, migrate, and proliferate. Some fundamental aspects of tumor development are considered, including normal tissue constraints, active cellular motility, homotypic and heterotypic intercellular interactions, and pressure-regulated cell division as well. It is found that differential motility between cancerous and normal cells tends to break the spheroidal symmetry, leading to a finger instability at the tumor rim, while stiff normal cells inhibit tumor branching and favor uniform tumor expansion. The heterotypic cell-cell adhesion is revealed to affect the branching geometry. Our results explain many experimental observations, such as fingering invasion during tumor growth, stiffness inhibition of tumor invasion, and facilitation of tumor invasion through cancerous-normal cell adhesion. This study helps understand how cellular events are coordinated in tumor morphogenesis at the tissue level.

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References

  1. Xue S L, Li B, Feng X Q, et al. Biochemomechanical poroelastic theory of avascular tumor growth. J Mech Phys Solids, 2016, 94: 409–432

    Article  MathSciNet  Google Scholar 

  2. Tracqui P. Biophysical models of tumour growth. Rep Prog Phys, 2009, 72: 056701

    Article  Google Scholar 

  3. Lin S Z, Li B, Xu G K, et al. Collective dynamics of cancer cells confined in a confluent monolayer of normal cells. J Biomech, 2017, 52: 140–147

    Article  Google Scholar 

  4. Lu P, Weaver V M, Werb Z. The extracellular matrix: A dynamic niche in cancer progression. J Cell Biol, 2012, 196: 395–406

    Article  Google Scholar 

  5. Frantz C, Stewart K M, Weaver V M. The extracellular matrix at a glance. J Cell Sci, 2010, 123: 4195–4200

    Article  Google Scholar 

  6. Delarue M, Montel F, Vignjevic D, et al. Compressive stress inhibits proliferation in tumor spheroids through a volume limitation. Biophys J, 2014, 107: 1821–1828

    Article  Google Scholar 

  7. Helmlinger G, Netti P A, Lichtenbeld H C, et al. Solid stress inhibits the growth of multicellular tumor spheroids. Nat Biotechnol, 1997, 15: 778–783

    Article  Google Scholar 

  8. Montel F, Delarue M, Elgeti J, et al. Isotropic stress reduces cell proliferation in tumor spheroids. New J Phys, 2012, 14: 055008

    Article  Google Scholar 

  9. Montel F, Delarue M, Elgeti J, et al. Stress clamp experiments on multicellular tumor spheroids. Phys Rev Lett, 2011, 107: 188102

    Article  Google Scholar 

  10. Alessandri K, Sarangi B R, Gurchenkov V V, 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, 2013, 110: 14843–14848

    Article  Google Scholar 

  11. Levayer R, Dupont C, Moreno E. Tissue crowding induces caspase-dependent competition for space. Curr Biol, 2016, 26: 670–677

    Article  Google Scholar 

  12. Fidler I J. The pathogenesis of cancer metastasis: The “seed and soil” hypothesis revisited. Nat Rev Cancer, 2003, 3: 453–458

    Article  Google Scholar 

  13. Haeger A, Krause M, Wolf K, et al. Cell jamming: Collective invasion of mesenchymal tumor cells imposed by tissue confinement. Biochim Biophysica Acta (BBA)-General Subjects, 2014, 1840: 2386–2395

    Article  Google Scholar 

  14. Friedl P, Locker J, Sahai E, et al. Classifying collective cancer cell invasion. Nat Cell Biol, 2012, 14: 777–783

    Article  Google Scholar 

  15. Turner S, Sherratt J A. Intercellular adhesion and cancer invasion: A discrete simulation using the extended Potts model. J Theor Biol, 2002, 216: 85–100

    Article  MathSciNet  Google Scholar 

  16. Hanahan D, Coussens L M. Accessories to the crime: Functions of cells recruited to the tumor microenvironment. Cancer Cell, 2012, 21: 309–322

    Article  Google Scholar 

  17. Labernadie A, Kato T, Brugués A, et al. A mechanically active heterotypic E-cadherin/N-cadherin adhesion enables fibroblasts to drive cancer cell invasion. Nat Cell Biol, 2017, 19: 224–237

    Article  Google Scholar 

  18. Condeelis J, Pollard J W. Macrophages: Obligate partners for tumor cell migration, invasion, and metastasis. Cell, 2006, 124: 263–266

    Article  Google Scholar 

  19. Roose T, Chapman S J, Maini P K. Mathematical models of avascular tumor growth. SIAM Rev, 2007, 49: 179–208

    Article  MathSciNet  MATH  Google Scholar 

  20. Szabó A, Merks R M H. Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution. Front Oncol, 2013, 3: 87

    Article  Google Scholar 

  21. Lin S Z, Li B, Feng X Q. A dynamic cellular vertex model of growing epithelial tissues. Acta Mech Sin, 2017, 33: 250–259

    Article  MathSciNet  MATH  Google Scholar 

  22. Li B, Sun S X. Coherent motions in confluent cell monolayer sheets. Biophys J, 2014, 107: 1532–1541

    Article  Google Scholar 

  23. Honda H, Tanemura M, Nagai T. A three-dimensional vertex dynamics cell model of space-filling polyhedra simulating cell behavior in a cell aggregate. J Theor Biol, 2004, 226: 439–453

    Article  MathSciNet  Google Scholar 

  24. Drasdo D, Höhme S. A single-cell-based model of tumor growth in vitro: Monolayers and spheroids. Phys Biol, 2005, 2: 133–147

    Article  Google Scholar 

  25. Drasdo D, Hoehme S. Modeling the impact of granular embedding media, and pulling versus pushing cells on growing cell clones. New J Phys, 2012, 14: 055025

    Article  Google Scholar 

  26. Lin S Z, Li B, Lan G, et al. Activation and synchronization of the oscillatory morphodynamics in multicellular monolayer. Proc Natl Acad Sci USA, 2017, 114: 8157–8162

    Article  Google Scholar 

  27. Lin S Z, Xue S L, Li B, et al. An oscillating dynamic model of collective cells in a monolayer. J Mech Phys Solids, 2018, 112: 650–666

    Article  MathSciNet  Google Scholar 

  28. Cross S E, Jin Y S, Rao J, et al. Nanomechanical analysis of cells from cancer patients. Nat Nanotech, 2007, 2: 780–783

    Article  Google Scholar 

  29. Hou H W, Li Q S, Lee G Y H, et al. Deformability study of breast cancer cells using microfluidics. Biomed Microdevices, 2009, 11: 557–564

    Article  Google Scholar 

  30. Lee G Y H, Lim C T. Biomechanics approaches to studying human diseases. Trends Biotech, 2007, 25: 111–118

    Article  Google Scholar 

  31. Li Q S, Lee G Y H, Ong C N, et al. AFM indentation study of breast cancer cells. Biochem Biophys Res Commun, 2008, 374: 609–613

    Article  Google Scholar 

  32. Chen P C, Lin S Z, Xu G K, et al. Three-dimensional collective cell motions in an acinus-like lumen. J Biomech, 2019, 84: 234–242

    Article  Google Scholar 

  33. Carey S P, Starchenko A, McGregor A L, et al. Leading malignant cells initiate collective epithelial cell invasion in a three-dimensional heterotypic tumor spheroid model. Clin Exp Metastasis, 2013, 30: 615–630

    Article  Google Scholar 

  34. Schaller G, Meyer-Hermann M. Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model. Phys Rev E, 2005, 71: 051910

    Article  MathSciNet  Google Scholar 

  35. Ladoux B, Mège R M. Mechanobiology of collective cell behaviours. Nat Rev Mol Cell Biol, 2017, 18: 743–757

    Article  Google Scholar 

  36. Frixen U H. E-cadherin-mediated cell-cell adhesion prevents invasiveness of human carcinoma cells. J Cell Biol, 1991, 113: 173–185

    Article  Google Scholar 

  37. Smith P G, Deng L, Fredberg J J, et al. Mechanical strain increases cell stiffness through cytoskeletal filament reorganization. Am J Physiol-Lung Cellular Mol Physiol, 2003, 285: L456–L463

    Article  Google Scholar 

  38. Johnson K L, Kendall K, Roberts A D. Surface energy and the contact of elastic solids. Proc R Soc A-Math Phys Eng Sci, 1971, 324: 301–313

    Article  Google Scholar 

  39. Li K W, Falcovitz Y H, Nagrampa J P, et al. Mechanical compression modulates proliferation of transplanted chondrocytes. J Orthop Res, 2000, 18: 374–382

    Article  Google Scholar 

  40. Malmi-Kakkada A N, Li X, Samanta H S, et al. Cell growth rate dictates the onset of glass to fluidlike transition and long time superdiffusion in an evolving cell colony. Phys Rev X, 2018, 8: 021025

    Google Scholar 

  41. Davidson L A, Koehl M, Keller R, et al. How do sea urchins invaginate? Using biomechanics to distinguish between mechanisms of primary invagination. Development, 1995, 121: 2005–2018

    Google Scholar 

  42. Mahaffy R E, Shih C K, MacKintosh F C, et al. Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells. Phys Rev Lett, 2000, 85: 880–883

    Article  Google Scholar 

  43. Chesla S E, Selvaraj P, Zhu C. Measuring two-dimensional receptorligand binding kinetics by micropipette. Biophys J, 1998, 75: 1553–1572

    Article  Google Scholar 

  44. Beysens D A, Forgacs G, Glazier J A. Cell sorting is analogous to phase ordering in fluids. Proc Natl Acad Sci USA, 2000, 97: 9467–9471

    Article  Google Scholar 

  45. Vintermyr O K, Døskeland S O. Cell cycle parameters of adult rat hepatocytes in a defined medium. A note on the timing of nucleolar DNA replication. J Cell Physiol, 1987, 132: 12–21

    Google Scholar 

  46. Cheng G, Tse J, Jain R K, et al. Micro-environmental mechanical stress controls tumor spheroid size and morphology by suppressing proliferation and inducing apoptosis in cancer cells. PLoS ONE, 2009, 4: e4632

    Article  Google Scholar 

  47. Ambrosi D, Preziosi L, Vitale G. The interplay between stress and growth in solid tumors. Mech Res Commun, 2012, 42: 87–91

    Article  Google Scholar 

  48. Durian D J. Bubble-scale model of foam mechanics: Melting, nonlinear behavior, and avalanches. Phys Rev E, 1997, 55: 1739–1751

    Article  Google Scholar 

  49. Yilmaz M, Christofori G, Lehembre F. Distinct mechanisms of tumor invasion and metastasis. Trends Mol Med, 2007, 13: 535–541

    Article  Google Scholar 

  50. Kaufman L J, Brangwynne C P, Kasza K E, et al. Glioma expansion in collagen I matrices: Analyzing collagen concentration-dependent growth and motility patterns. Biophys J, 2005, 89: 635–650

    Article  Google Scholar 

  51. Ahmadzadeh H, Webster M R, Behera R, et al. Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion. Proc Natl Acad Sci USA, 2017, 114: E1617–E1626

    Article  Google Scholar 

  52. Jimenez Valencia A M, Wu P H, Yogurtcu O N, et al. Collective cancer cell invasion induced by coordinated contractile stresses. Oncotarget, 2015, 6: 43438–43451

    Google Scholar 

  53. Ulrich T A, de Juan Pardo E M, Kumar S. The mechanical rigidity of the extracellular matrix regulates the structure, motility, and proliferation of glioma cells. Cancer Res, 2009, 69: 4167–4174

    Article  Google Scholar 

  54. Alexander N R, Branch K M, Parekh A, et al. Extracellular matrix rigidity promotes invadopodia activity. Curr Biol, 2008, 18: 1295–1299

    Article  Google Scholar 

  55. Parekh A, Ruppender N S, Branch K M, et al. Sensing and modulation of invadopodia across a wide range of rigidities. Biophys J, 2011, 100: 573–582

    Article  Google Scholar 

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Correspondence to Bo Li or XiQiao Feng.

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Chen, P., Li, B. & Feng, X. A cell-based model for analyzing growth and invasion of tumor spheroids. Sci. China Technol. Sci. 62, 1341–1348 (2019). https://doi.org/10.1007/s11431-018-9483-7

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  • DOI: https://doi.org/10.1007/s11431-018-9483-7

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