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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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
Tracqui P. Biophysical models of tumour growth. Rep Prog Phys, 2009, 72: 056701
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
Lu P, Weaver V M, Werb Z. The extracellular matrix: A dynamic niche in cancer progression. J Cell Biol, 2012, 196: 395–406
Frantz C, Stewart K M, Weaver V M. The extracellular matrix at a glance. J Cell Sci, 2010, 123: 4195–4200
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
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
Montel F, Delarue M, Elgeti J, et al. Isotropic stress reduces cell proliferation in tumor spheroids. New J Phys, 2012, 14: 055008
Montel F, Delarue M, Elgeti J, et al. Stress clamp experiments on multicellular tumor spheroids. Phys Rev Lett, 2011, 107: 188102
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
Levayer R, Dupont C, Moreno E. Tissue crowding induces caspase-dependent competition for space. Curr Biol, 2016, 26: 670–677
Fidler I J. The pathogenesis of cancer metastasis: The “seed and soil” hypothesis revisited. Nat Rev Cancer, 2003, 3: 453–458
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
Friedl P, Locker J, Sahai E, et al. Classifying collective cancer cell invasion. Nat Cell Biol, 2012, 14: 777–783
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
Hanahan D, Coussens L M. Accessories to the crime: Functions of cells recruited to the tumor microenvironment. Cancer Cell, 2012, 21: 309–322
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
Condeelis J, Pollard J W. Macrophages: Obligate partners for tumor cell migration, invasion, and metastasis. Cell, 2006, 124: 263–266
Roose T, Chapman S J, Maini P K. Mathematical models of avascular tumor growth. SIAM Rev, 2007, 49: 179–208
Szabó A, Merks R M H. Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution. Front Oncol, 2013, 3: 87
Lin S Z, Li B, Feng X Q. A dynamic cellular vertex model of growing epithelial tissues. Acta Mech Sin, 2017, 33: 250–259
Li B, Sun S X. Coherent motions in confluent cell monolayer sheets. Biophys J, 2014, 107: 1532–1541
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
Drasdo D, Höhme S. A single-cell-based model of tumor growth in vitro: Monolayers and spheroids. Phys Biol, 2005, 2: 133–147
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
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
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
Cross S E, Jin Y S, Rao J, et al. Nanomechanical analysis of cells from cancer patients. Nat Nanotech, 2007, 2: 780–783
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
Lee G Y H, Lim C T. Biomechanics approaches to studying human diseases. Trends Biotech, 2007, 25: 111–118
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
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
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
Schaller G, Meyer-Hermann M. Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model. Phys Rev E, 2005, 71: 051910
Ladoux B, Mège R M. Mechanobiology of collective cell behaviours. Nat Rev Mol Cell Biol, 2017, 18: 743–757
Frixen U H. E-cadherin-mediated cell-cell adhesion prevents invasiveness of human carcinoma cells. J Cell Biol, 1991, 113: 173–185
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
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
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
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
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
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
Chesla S E, Selvaraj P, Zhu C. Measuring two-dimensional receptorligand binding kinetics by micropipette. Biophys J, 1998, 75: 1553–1572
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
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
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
Ambrosi D, Preziosi L, Vitale G. The interplay between stress and growth in solid tumors. Mech Res Commun, 2012, 42: 87–91
Durian D J. Bubble-scale model of foam mechanics: Melting, nonlinear behavior, and avalanches. Phys Rev E, 1997, 55: 1739–1751
Yilmaz M, Christofori G, Lehembre F. Distinct mechanisms of tumor invasion and metastasis. Trends Mol Med, 2007, 13: 535–541
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
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
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
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
Alexander N R, Branch K M, Parekh A, et al. Extracellular matrix rigidity promotes invadopodia activity. Curr Biol, 2008, 18: 1295–1299
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
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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