An agent-based model of cancer stem cell initiated avascular tumour growth and metastasis: The effect of seeding frequency and location

Journal of the Royal Society Interface

Volumn 11, Issue 100, 2014, Pages

  Norton, Kerri Ann ^a   Popel, Aleksander S ^a,b  

^a Johns Hopkins University   (United States)

^b JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Computational modelling; Metastatic niche; Progenitor cells

Indexed keywords

CELL DEATH; CELL PROLIFERATION; COMPUTATIONAL METHODS; DISEASES; GROWTH RATE; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TUMORS;

AGENT-BASED STOCHASTIC MODEL; CELL DIVISION CYCLE; COMPUTATIONAL MODELLING; IMPORTANT FEATURES; METASTATIC DISEASE; METASTATIC NICHE; PROGENITOR CELL; SPATIAL AND TEMPORAL DISTRIBUTION;

STEM CELLS;

APOPTOSIS; ARTICLE; BREAST METASTASIS; CANCER STEM CELL; CELL AGING; CELL DEATH; CELL DIVISION; CELL MIGRATION; CELL PROLIFERATION; CELL RENEWAL; CELL TYPE; METASTASIS; STOCHASTIC MODEL; TUMOR GROWTH; TUMOR LOCALIZATION; TUMOR SEEDING; BIOLOGICAL MODEL; BREAST TUMOR; FEMALE; HUMAN; METABOLISM; PATHOLOGY;

BREAST NEOPLASMS; FEMALE; HUMANS; MODELS, BIOLOGICAL; NEOPLASM METASTASIS; NEOPLASTIC STEM CELLS;

EID: 84908155302     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2014.0640     Document Type: Article

References (90)

1. Li Y, Laterra J. 2012 Cancer stem cells: Distinct entities or dynamically regulated phenotypes? Cancer Res. 72, 576-580. (doi:10.1158/0008-5472. CAN-11-3070)
2. Visvader JE, Lindeman GJ. 2012 Cancer stem cells: Current status and evolving complexities. Cell Stem Cell 10, 717-728. (doi:10.1016/j.stem.2012. 05.007)
3. Wicha MS, Liu S, Dontu G. 2006 Cancer stem cells: An old idea: A paradigm shift. Cancer Res. 66, 1883-1890; discussion 1895-1896. (doi:10.1158/0008-5472.CAN-05-3153)
4. Zhao Y et al. 2011 Cancer stem cells and angiogenesis. Int. J. Dev. Biol. 55, 477-482. (doi:10.1387/ijdb.103225yz)
5. Alkatout I, Wiedermann M, Bauer M, Wenners A, Jonat W, Klapper W. 2013 Transcription factors associated with epithelial-mesenchymal transition and cancer stem cells in the tumor centre and margin of invasive breast cancer. Exp. Mol. Pathol. 94, 168-173. (doi:10.1016/j.yexmp.2012. 09.003)
6. Liu S et al. 2011 Breast cancer stem cells are regulated by mesenchymal stem cells through cytokine networks. Cancer Res. 71, 614-624. (doi:10.1158/0008-5472.CAN-10-0538)
7. Potten CS, Booth C, Hargreaves D. 2003 The small intestine as a model for evaluating adult tissue stem cell drug targets. Cell Prolif. 36, 115-129. (doi:10.1046/j.1365-2184.2003.00264.x)
8. Schepers AG, Snippert HJ, Stange DE, van den Born M, van Es JH, van de Wetering M, Clevers H. 2012 Lineage tracing reveals Lgr5+ stem cell activity in mouse intestinal adenomas. Science 337, 730-735. (doi:10.1126/science.1224676)
9. Takahashi-Yanaga F, Kahn M. 2010 Targeting Wnt signaling: Can we safely eradicate cancer stem cells? Clin. Cancer Res. 16, 3153-3162. (doi:10.1158/1078-0432.CCR-09-2943)
10. Driessens G, Beck B, Caauwe A, Simons BD, Blanpain C. 2012 Defining the mode of tumour growth by clonal analysis. Nature 488, 527-530. (doi:10.1038/nature11344)
11. Teitz-Tennenbaum S, Wicha MS, Chang AE, Li Q. 2012 Targeting cancer stem cells via dendritic-cell vaccination. Oncoimmunology 1, 1401-1403. (doi:10.4161/onci.21026)
12. Korkaya H, Liu S, Wicha MS. 2011 Breast cancer stem cells, cytokine networks, and the tumor microenvironment. J. Clin. Invest. 121, 3804-3809. (doi:10.1172/JCI57099)
13. Malanchi I, Santamaria-Martinez A, Susanto E, Peng H, Lehr H-A, Delaloye J-F, Huelsken J. 2012 Interactions between cancer stem cells and their niche govern metastatic colonization. Nature 481, 85-89. (doi:10.1038/nature10694)
14. Velasco-Velazquez MA, Popov VM, Lisanti MP, Pestell RG. 2011 The role of breast cancer stem cells in metastasis and therapeutic implications. Am. J. Pathol. 179, 2-11. (doi:10.1016/j.ajpath. 2011.03.005)
15. Nguyen DX, Bos PD, Massague J. 2009 Metastasis: From dissemination to organ-specific colonization. Nat. Rev. Cancer 9, 274-284. (doi:10.1038/nrc2622)
16. Langley RR, Fidler IJ. 2011 The seed and soil hypothesis revisited: The role of tumor-stroma interactions in metastasis to different organs. Int. J. Cancer 128, 2527-2535. (doi:10.1002/ijc.26031)
17. Joyce JA, Pollard JW. 2009 Microenvironmental regulation of metastasis. Nat. Rev. Cancer 9, 239-252. (doi:10.1038/nrc2618)
18. Norton L, Massague J. 2006 Is cancer a disease of self-seeding? Nat. Med. 12, 875-878. (doi:10.1038/nm0806-875)
19. Norton L. 2008 Cancer stem cells, self-seeding, and decremented exponential growth: Theoretical and clinical implications. Breast Dis. 29, 27-36.
20. Comen E, Norton L, Massague J. 2011 Clinical implications of cancer self-seeding. Nat. Rev. Clin. Oncol. 8, 369-377.
21. Kim MY, Oskarsson T, Acharyya S, Nguyen DX, Zhang XH-F, Norton L, Massagué J. 2009 Tumor self-seeding by circulating cancer cells. Cell 139, 1315-1326. (doi:10.1016/j.cell.2009. 11.025)
22. Leung CT, Brugge JS. 2009 Tumor self-seeding: Bidirectional flow of tumor cells. Cell 139, 1226-1228. (doi:10.1016/j.cell.2009.12.013)
23. Michor F. 2008 Mathematical models of cancer stem cells. J. Clin. Oncol. 26, 2854-2861. (doi:10.1200/JCO.2007.15.2421)
24. Agur Z, Kirnasovsky OU, Vasserman G, Tencer-Hershkowicz L, Kogan Y, Harrison H, Lamb R, Clarke RB, Gottardi C. 2011 Dickkopf1 regulates fate decision and drives breast cancer stem cells to differentiation: An experimentally supported mathematical model. PLoS ONE 6, e24225. (doi:10. 1371/journal.pone.0024225)
25. Vainstein V, Kirnasovsky OU, Kogan Y, Agur Z. 2011 Strategies for cancer stem cell elimination: Insights from mathematical modeling. J. Theor. Biol. 298C, 32-41.
26. Molina-Pena R, Alvarez MM. 2012 A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth. PLoS ONE 7, e26233. (doi:10.1371/journal.pone.0026233)
27. Ashkenazi R, Gentry SN, Jackson TL. 2008 Pathways to tumorigenesis: Modeling mutation acquisition in stem cells and their progeny. Neoplasia 10, 1170-1182.
28. Sottoriva A, Vermeulen L, Tavare S. 2011 Modeling evolutionary dynamics of epigenetic mutations in hierarchically organized tumors. PLoS Comput. Biol. 7, e1001132. (doi:10.1371/journal.pcbi.1001132)
29. Foo J, Leder K, Michor F. 2011 Stochastic dynamics of cancer initiation. Phys. Biol. 8, 015002. (doi:10. 1088/1478-3975/8/1/015002)
30. White DE, Kinney MA, McDevitt TC, Kemp ML. 2013 Spatial pattern dynamics of 3D stem cell loss of pluripotency via rules-based computational modeling. PLoS Comput. Biol. 9, e1002952. (doi:10. 1371/journal.pcbi.1002952)
31. Deleyrolle LP et al. 2011 Determination of somatic and cancer stem cell self-renewing symmetric division rate using sphere assays. PLoS ONE 6, e15844. (doi:10.1371/journal.pone.0015844)
32. Scott JG, Basanta D, Anderson AR, Gerlee P. 2013 A mathematical model of tumour self-seeding reveals secondary metastatic deposits as drivers of primary tumour growth. J. R. Soc. Interface 10, 20130011. (doi:10.1098/rsif.2013.0011)
33. Sottoriva A, Sloot PM, Medema JP, Vermeulen L. 2010 Exploring cancer stem cell niche directed tumor growth. Cell Cycle 9, 1472-1479. (doi:10. 4161/cc.9.8.11198)
34. Sottoriva A, Verhoeff JJ, Borovski T, McWeeney SK, Naumov L, Medema JP, Sloot PMA, Vermeulen L. 2010 Cancer stem cell tumor model reveals invasive morphology and increased phenotypical heterogeneity. Cancer Res. 70, 46-56. (doi:10. 1158/0008-5472.CAN-09-3663)
35. Enderling H, Hlatky L, Hahnfeldt P. 2009 Migration rules: Tumours are conglomerates of selfmetastases. Br. J. Cancer 100, 1917-1925. (doi:10. 1038/sj.bjc.6605071)
36. Enderling H, Anderson AR, Chaplain MA, Beheshti A, Hlatky L, Hahnfeldt P. 2009 Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res. 69, 8814-8821. (doi:10.1158/0008-5472.CAN-09-2115)
37. Hillen T, Enderling H, Hahnfeldt P. 2012 The tumor growth paradox and immune system-mediated selection for cancer stem cells. Bull. Math. Biol. 75, 161-184. (doi:10.1007/s11538-012-9798-x)
38. Enderling H, Hlatky L, Hahnfeldt P. 2010 Tumor morphological evolution: Directed migration and gain and loss of the self-metastatic phenotype. Biol. Direct. 5, 23. (doi:10.1186/1745-6150-5-23)
39. Weekes SL, Barker B, Bober S, Cisneros K, Cline J, Thompson A, Hlatky L, Hahnfeidt P, Enderling H. 2014 A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics. Bull. Math. Biol. (doi:10.1007/s11538-014-9976-0)
40. Qutub AA, Mac Gabhann F, Karagiannis ED, Vempati P, Popel AS. 2009 Multiscale models of angiogenesis. IEEE Eng. Med. Biol. Mag. 28, 14-31. (doi:10.1109/MEMB.2009.931791)
41. Chakrabarti A, Verbridge S, Stroock AD, Fischbach C, Varner JD. 2012 Multiscale models of breast cancer progression. Ann. Biomed. Eng. 40, 2488-2500. (doi:10.1007/s10439-012-0655-8)
42. Norton KA, Wininger M, Bhanot G, Ganesan S, Barnard N, Shinbrot T. 2010 A 2D mechanistic model of breast ductal carcinoma in situ (DCIS) morphology and progression. J. Theor. Biol. 263, 393-406. (doi:10.1016/j.jtbi.2009.11.024)
43. Mac Gabhann F, Stefanini MO, Popel AS. 2012 Simulating therapeutics using multiscale models of the VEGF receptor system in cancer. In Modeling tumor vasculature: Molecular, cellular, and tissue level aspects and implications (ed. TL Jackson), pp. 37-53. New York, NY: Springer.
44. Qutub AA, Liu G, Vempati P, Popel AS. 2009 Integration of angiogenesis modules at multiple scales: From molecular to tissue. Pac. Symp. Biocomput. 2009, 316-327.
45. Qutub AA, Popel AS. 2009 Elongation, proliferation and migration differentiate endothelial cell phenotypes and determine capillary sprouting. BMC Syst. Biol. 3, 13. (doi:10.1186/1752-0509-3-13)
46. Hatzikirou H, Chauviere A, Bauer AL, Leier A, Lewis MT, Macklin P, Marquez-Lago TT, Bearer EL, Cristini V. 2012 Integrative physical oncology. Wiley Interdiscip. Rev. Syst. Biol. Med. 4, 1-14. (doi:10. 1002/wsbm.158)
47. Rejniak KA, Anderson ARA. 2010 Hybrid models of tumor growth. Wiley Interdiscip. Rev. Syst. Biol. Med. 3, 115-125. (doi:10.1002/wsbm.102)
48. Sanga S, Frieboes HB, Zheng X, Gatenby R, Bearer EL, Cristini V. 2007 Predictive oncology: A review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth. Neuroimage 37(Suppl. 1), S120-S134. (doi:10. 1016/j.neuroimage.2007.05.043)
49. Enderling H, Chaplain MA, Anderson AR, Vaidya JS. 2007 A mathematical model of breast cancer development, local treatment and recurrence. J. Theor Biol. 246, 245-259. (doi:10.1016/j.jtbi. 2006.12.010)
50. Kim U, Shu CW, Dane KY, Daugherty PS, Wang JY, Soh HT. 2007 Selection of mammalian cells based on their cell-cycle phase using dielectrophoresis. Proc. Natl Acad. Sci. USA 104, 20 708-20 712. (doi:10.1073/pnas.0708760104)
51. Korkaya H, Wicha MS. 2013 Breast cancer stem cells: We've got them surrounded. Clin. Cancer Res. 19, 511-513. (doi:10.1158/1078-0432.CCR-12-3450)
52. Wicha MS. 2012 Migratory gene expression signature predicts poor patient outcome: Are cancer stem cells to blame? Breast Cancer Res. 14, 114. (doi:10.1186/bcr3338)
53. Gudjonsson T, Villadsen R, Nielsen HL, Ronnov-Jessen L, Bissell MJ, Petersen OW. 2002 Isolation, immortalization, and characterization of a human breast epithelial cell line with stem cell properties. Genes Dev. 16, 693-706. (doi:10.1101/gad.952602)
54. Sieburg HB, Rezner BD, Muller-Sieburg CE. 2011 Predicting clonal self-renewal and extinction of hematopoietic stem cells. Proc. Natl Acad. Sci. USA 108, 4370-4375. (doi:10.1073/pnas.1011414108)
55. Harmes DC, DiRenzo J. 2009 Cellular quiescence in mammary stem cells and breast tumor stem cells: Got testable hypotheses? J. Mamm. Gland Biol. Neoplasia 14, 19-27. (doi:10.1007/s10911-009-9111-2)
56. Stoletov K, Kato H, Zardouzian E, Kelber J, Yang J, Shattil S, Klemke R. 2010 Visualizing extravasation dynamics of metastatic tumor cells. J. Cell Sci. 123, 2332-2341. (doi:10.1242/jcs.069443)
57. Huang Y, Song N, Ding Y, Yuan S, Li X, Cai H, Shi H, Luo Y. 2009 Pulmonary vascular destabilization in the premetastatic phase facilitates lung metastasis. Cancer Res. 69, 7529-7537. (doi:10.1158/0008-5472.CAN-08-4382)
58. Kuilman T, Michaloglou C, Mooi WJ, Peeper DS. 2010 The essence of senescence. Genes Dev. 24, 2463-2479. (doi:10.1101/gad.1971610)
59. Lagadec C, Dekmezian C, Bauche L, Pajonk F. 2012 Oxygen levels do not determine radiation survival of breast cancer stem cells. PLoS ONE 7, e34545. (doi:10.1371/journal.pone.0034545)
60. Li C, Heidt DG, Dalerba P, Burant CF, Zhang L, Adsay V, Wicha M, Clarke MF, Simeone DM. 2007 Identification of pancreatic cancer stem cells. Cancer Res. 67, 1030-1037. (doi:10.1158/0008-5472.CAN-06-2030)
61. Hsu CS, Tung CY, Yang CY, Lin CH. 2013 Response to stress in early tumor colonization modulates switching of CD133-positive and CD133-negative subpopulations in a human metastatic colon cancer cell line, SW620. PLoS ONE 8, e61133. (doi:10.1371/journal.pone.0061133)
62. Todaro M et al. 2007 Colon cancer stem cells dictate tumor growth and resist cell death by production of interleukin-4. Cell Stem Cell 1, 389-402. (doi:10. 1016/j.stem.2007.08.001)
63. Buehring GC, Williams RR. 1976 Growth rates of normal and abnormal human mammary epithelia in cell culture. Cancer Res. 36, 3742-3747.
64. Friberg S, Mattson S. 1997 On the growth rates of human malignant tumors: Implications for medical decision making. J. Surg. Oncol. 65, 284-297. (doi:10.1002/(SICI)1096-9098(199708)65:4,284:: AID-JSO11.3.0.CO;2-2)
65. Skipper HE. 1971 Kinetics of mammary tumor cell growth and implications for therapy. Cancer 28, 1479-1499. (doi:10.1002/1097-0142(197112) 28:6,1479::AID-CNCR2820280622.3.0.CO;2-M)
66. Tubiana M. 1989 Tumor cell proliferation kinetics and tumor growth rate. Acta Oncol. 28, 113-121. (doi:10.3109/02841868909111193)
67. Aktas B, Tewes M, Fehm T, Hauch S, Kimmig R, Kasimir-Bauer S. 2009 Stem cell and epithelial-mesenchymal transition markers are frequently overexpressed in circulating tumor cells of metastatic breast cancer patients. Breast Cancer Res. 11, R46. (doi:10.1186/bcr2333)
68. Mani SA et al. 2008 The epithelial-mesenchymal transition generates cells with properties of stem cells. Cell 133, 704-715. (doi:10.1016/j.cell.2008. 03.027)
69. Monteiro J, Fodde R. 2010 Cancer stemness and metastasis: Therapeutic consequences and perspectives. Eur. J. Cancer 46, 1198-1203. (doi:10. 1016/j.ejca.2010.02.030)
70. Morel AP, Lievre M, Thomas C, Hinkal G, Ansieau S, Puisieux A. 2008 Generation of breast cancer stem cells through epithelial-mesenchymal transition. PLoS ONE 3, e2888. (doi:10.1371/journal.pone. 0002888)
71. Turner C, Kohandel M. 2010 Investigating the link between epithelial-mesenchymal transition and the cancer stem cell phenotype: A mathematical approach. J. Theor. Biol. 265, 329-335. (doi:10. 1016/j.jtbi.2010.05.024)
72. Norton L. 2005 Conceptual and practical implications of breast tissue geometry: Toward a more effective, less toxic therapy. Oncologist 10, 370-381. (doi:10.1634/theoncologist.10-6-370)
73. Norton L, Simon R, Brereton HD, Bogden AE. 1976 Predicting the course of Gompertzian growth. Nature 264, 542-545. (doi:10.1038/264542a0)
74. Norton L. 1988 A Gompertzian model of human breast cancer growth. Cancer Res. 48, 7067-7071.
75. Rodriguez-Brenes IA, Wodarz D, Komarova NL. 2013 Stem cell control, oscillations, and tissue regeneration in spatial and non-spatial models. Front. Oncol. 3, 82. (doi:10.3389/fonc.2013.00082)
76. Cheung KJ, Gabrielson E, Werb Z, Ewald AJ. 2013 Collective invasion in breast cancer requires a conserved basal epithelial program. Cell 155, 1639-1651. (doi:10.1016/j.cell.2013.11.029)
77. Debnath J, Brugge JS. 2005 Modelling glandular epithelial cancers in three-dimensional cultures. Nat. Rev. Cancer 5, 675-688. (doi:10.1038/nrc1695)
78. Jaffer S, Bleiweiss IJ. 2002 Histologic classification of ductal carcinoma in situ. Microsc. Res. Tech. 59, 92-101. (doi:10.1002/jemt.10180)
79. Anderson AR, Quaranta V. 2008 Integrative mathematical oncology. Nat. Rev. Cancer 8, 227-234. (doi:10.1038/nrc2329)
80. Tanei T, Morimoto K, Shimazu K, Kim SJ, Tanji Y, Taguchi T, Tamaki Y, Noguchi S. 2009 Association of breast cancer stem cells identified by aldehyde dehydrogenase 1 expression with resistance to sequential paclitaxel and epirubicin-based chemotherapy for breast cancers. Clin. Cancer Res. 15, 4234-4241. (doi:10.1158/1078-0432.CCR-08-1479)
81. Gottschalk A, Sharma S, Ford J, Durieux ME, Tiouririne M. 2010 Review article: The role of the perioperative period in recurrence after cancer surgery. Anesth. Analg. 110, 1636-1643. (doi:10. 1213/ANE.0b013e3181de0ab6)
82. Bhise NS, Shmueli RB, Sunshine JC, Tzeng SY, Green JJ. 2011 Drug delivery strategies for therapeutic angiogenesis and antiangiogenesis. Expert Opin. Drug Deliv. 8, 485-504. (doi:10.1517/17425247. 2011.558082)
83. Liu S, Korkaya H, Wicha MS. 2012 Are cancer stem cells ready for prime time? The Scientist 26, 33-37.
84. Poleszczuk J, Hahnfeldt P, Enderling H. 2014 Biphasic modulation of cancer stem cell-driven solid tumour dynamics in response to reactivated replicative senescence. Cell Prolif. 47, 267-276. (doi:10.1111/cpr.12101)
85. Tang Y, Wang Y, Chen L, Pan Y, Weintraub N. 2012 Cross talk between the Notch signaling and noncoding RNA on the fate of stem cells. Prog. Mol. Biol. Transl. Sci. 111, 175-193. (doi:10.1016/B978-0-12-398459-3.00008-3)
86. Hanahan D, Weinberg RA. 2011 Hallmarks of cancer: The next generation. Cell 144, 646-674. (doi:10.1016/j.cell.2011.02.013)
87. Greenberg RA et al. 1999 Telomerase reverse transcriptase gene is a direct target of c-Myc but is not functionally equivalent in cellular transformation. Oncogene 18, 1219-1226. (doi:10. 1038/sj.onc.1202669)
88. Gupta PB, Onder TT, Jiang G, Tao K, Kuperwasser C, Weinberg RA, Lander ES. 2009 Identification of selective inhibitors of cancer stem cells by highthroughput screening. Cell 138, 645-659. (doi:10. 1016/j.cell.2009.06.034)
89. Enderling H, Hlatky L, Hahnfeldt P. 2013 Cancer stem cells: A minor cancer subpopulation that redefines global cancer features. Front. Oncol. 3, 76. (doi:10.3389/fonc.2013.00076)
90. Rodriguez-Brenes IA, Komarova NL, Wodarz D. 2011 Evolutionary dynamics of feedback escape and the development of stem-cell-driven cancers. Proc. Natl Acad. Sci. USA 108, 18 983-18 988. (doi:10.1073/pnas.1107621108)