Skip to main content

Advertisement

Log in

Multiscale Models of Breast Cancer Progression

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

Breast cancer initiation, invasion and metastasis span multiple length and time scales. Molecular events at short length scales lead to an initial tumorigenic population, which left unchecked by immune action, acts at increasingly longer length scales until eventually the cancer cells escape from the primary tumor site. This series of events is highly complex, involving multiple cell types interacting with (and shaping) the microenvironment. Multiscale mathematical models have emerged as a powerful tool to quantitatively integrate the convective-diffusion-reaction processes occurring on the systemic scale, with the molecular signaling processes occurring on the cellular and subcellular scales. In this study, we reviewed the current state of the art in cancer modeling across multiple length scales, with an emphasis on the integration of intracellular signal transduction models with pro-tumorigenic chemical and mechanical microenvironmental cues. First, we reviewed the underlying biomolecular origin of breast cancer, with a special emphasis on angiogenesis. Then, we summarized the development of tissue engineering platforms which could provide high-fidelity ex vivo experimental models to identify and validate multiscale simulations. Lastly, we reviewed top-down and bottom-up multiscale strategies that integrate subcellular networks with the microenvironment. We present models of a variety of cancers, in addition to breast cancer specific models. Taken together, we expect as the sophistication of the simulations increase, that multiscale modeling and bottom-up agent-based models in particular will become an increasingly important platform technology for basic scientific discovery, as well as the identification and validation of potentially novel therapeutic targets.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1
Figure 2

Similar content being viewed by others

References

  1. Abbott, R. G., S. Forrest, and K.J. Pienta. Simulating the hallmarks of cancer. Artif. Life 12:617–634, 2006.

    Article  PubMed  Google Scholar 

  2. Allinen, M., Beroukhim, R., Cai, L., Brennan, C., Lahti-Domenici, J. et al.: Molecular characterization of the tumor microenvironment in breast cancer. Cancer Cell 6:17–32, 2004.

    Article  PubMed  CAS  Google Scholar 

  3. Ananiadou, S., D. B. Kell, and J. I. Tsujii. Text mining and its potential applications in systems biology. Trends Biotechnol. 24:571–579, 2006.

    Article  PubMed  CAS  Google Scholar 

  4. Andasari, V., R. T. Roper, M. H. Swat, and M. A. J. Chaplain. Integrating intracellular dynamics using CompuCell3D and Bionetsolver: applications to multiscale modelling of cancer cell growth and invasion. PLoS One 7:e33726, 2012.

    Google Scholar 

  5. Anderson, A. R. A., K. A. Rejniak, P. Gerlee, and V. Quaranta. Microenvironment driven invasion: a multiscale multimodel investigation. J. Math. Biol. 58:579–624, 2009.

    Article  PubMed  Google Scholar 

  6. Aoki-Kinoshita, K. F., and M. Kanehisa. Gene annotation and pathway mapping in KEGG. Methods Mol. Biol. 396:71–91, 2007.

    Article  PubMed  CAS  Google Scholar 

  7. Asthagiri, A. R., and D. A. Lauffenburger. A computational study of feedback effects on signal dynamics in a mitogen-activated protein kinase (MAPK) pathway model. Biotechnol. Prog. 17:227–239, 2001.

    Article  PubMed  CAS  Google Scholar 

  8. Athale, C. A., and T. S. Deisboeck. The effects of EGF-receptor density on multiscale tumor growth patterns. J. Theor. Biol. 238:771–779, 2006.

    Article  PubMed  CAS  Google Scholar 

  9. Bailey, A. M., B. C. Thorne, and S. M. Peirce. Multi-cell agent-based simulation of the microvasculature to study the dynamics of circulating inflammatory cell trafficking. Ann. Biomed. Eng. 35:916–936, 2007.

    Article  PubMed  Google Scholar 

  10. Balmain, A., J. Gray, and B. Ponder. The genetics and genomics of cancer. Nat. Genet. 33(Suppl):238–244, 2003.

    Article  PubMed  CAS  Google Scholar 

  11. Bandara, S., J. P. Schlöder, R. Eils, H. G. Bock, and T. Meyer. Optimal experimental design for parameter estimation of a cell signaling model. PLoS Comput. Biol. 5:e1000558, 2009.

    Google Scholar 

  12. Barnes, P. J., and M. Karin. Nuclear factor-kappaB: a pivotal transcription factor in chronic inflammatory diseases. N. Engl. J. Med. 336:1066–1071, 1997.

    Article  PubMed  CAS  Google Scholar 

  13. Battogtokh, D., D. K. Asch, M. E. Case, J. Arnold, and H. B. Schuttler. An ensemble method for identifying regulatory circuits with special reference to the QA gene cluster of Neurospora crassa. Proc. Natl. Acad. Sci. U S A 99:16904–16909, 2002.

    Article  PubMed  CAS  Google Scholar 

  14. Benoy, I. H., R. Salgado, P. Van Dam, K. Geboers, E. Van Marck, et al. Increased serum interleukin-8 in patients with early and metastatic breast cancer correlates with early dissemination and survival. Clin. Cancer Res. 10:7157–7162, 2004.

    Article  PubMed  CAS  Google Scholar 

  15. Bergers, G., and D. Hanahan. Modes of resistance to anti-angiogenic therapy. Nat. Rev. Cancer 8:592–603, 2008.

    Article  PubMed  CAS  Google Scholar 

  16. Bertos, N. R., and M. Park. Breast cancer—one term, many entities. J. Clin. Invest. 121:3789–3796, 2011.

    Article  PubMed  CAS  Google Scholar 

  17. Bonabeau, E. Agent-based modeling: methods and techniques for simulating human systems. Proc. Natl. Acad. Sci. U S A 99(Suppl 3):7280–7287, 2002.

  18. Brahimi-Horn, M. C., J. Chiche, and J. Pouysségur. Hypoxia and cancer. J. Mol. Med. (Berl.) 85:1301–1307, 2007.

    Article  Google Scholar 

  19. Brown, K. S., and J. P. Sethna. Statistical mechanical approaches to models with many poorly known parameters. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68:021904, 2003.

    Google Scholar 

  20. Brown, K. S., C. C. Hill, G. A. Calero, C. R. Myers, K. H. Lee et al. The statistical mechanics of complex signaling networks: nerve growth factor signaling. Phys. Biol. 1:184–195, 2004.

    Article  PubMed  CAS  Google Scholar 

  21. Cabodi, M., N. W. Choi, J. P. Gleghorn, C. S. D. Lee, L. J. Bonassar, et al. A microfluidic biomaterial. J. Am. Chem. Soc. 127:13788–13789, 2005.

    Article  PubMed  CAS  Google Scholar 

  22. Chao, D. L., M. E. Halloran, V. J. Obenchain, Longini, I. M., Jr. Flute, a publicly available stochastic influenza epidemic simulation model. PLoS Comput. Biol. 6: e1000656, 2010.

  23. Chavali, A. K., E. P. Gianchandani, K. S. Tung, M. B. Lawrence, S. M. Peirce, et al. Characterizing emergent properties of immunological systems with multi-cellular rule-based computational modeling. Trends Immunol. 29:589–599, 2008.

    Article  PubMed  CAS  Google Scholar 

  24. Chen, W. W., B. Schoeberl, P. J. Jasper, M. Niepel, U. B. Nielsen, et al. Input–output behavior of ERBB signaling pathways as revealed by a mass action model trained against dynamic data. Mol. Syst. Biol. 5:239, 2009.

    Google Scholar 

  25. Chin, K., C. O. de Solorzano, D. Knowles, A. Jones, W. Chou, et al. In situ analyses of genome instability in breast cancer. Nat. Genet. 36:984–988, 2004.

    Article  PubMed  CAS  Google Scholar 

  26. Choi, N. W., M. Cabodi, B. Held, J. P. Gleghorn, L. J. Bonassar, et al. Microfluidic scaffolds for tissue engineering. Nat. Mater. 6:908–915, 2007.

    Article  PubMed  CAS  Google Scholar 

  27. Choueiri, T. K., E. L. Mayer, Y. Je, J. E. Rosenberg, P. L. Nguyen, et al. Congestive heart failure risk in patients with breast cancer treated with bevacizumab. J. Clin. Oncol. 29:632–638, 2011.

    Article  PubMed  CAS  Google Scholar 

  28. Chrobak, K. M., D. R. Potter, J. Tien. Formation of perfused, functional microvascular tubes in vitro. Microvasc. Res. 71:185–196, 2006.

    Article  PubMed  CAS  Google Scholar 

  29. Correia, A. L., and M. J. Bissell. The tumor microenvironment is a dominant force in multidrug resistance. Drug. Resist. Updat. 15:39–49, 2012.

    Article  PubMed  CAS  Google Scholar 

  30. Das, A., D. Lauffenburger, H. Asada, and R. D. Kamm. A hybrid continuum-discrete modelling approach to predict and control angiogenesis: analysis of combinatorial growth factor and matrix effects on vessel-sprouting morphology. Philos. Trans. A Math. Phys. Eng. Sci. 368:2937–2960, 2010.

    CAS  Google Scholar 

  31. Deisboeck, T. S., and G. S. Stamatakos (eds.). Multiscale Cancer Modeling. Boca Raton, FL: CRC Press, 2010.

  32. Deisboeck, T. S., Z. Wang, P. Macklin, V. Cristini. Multiscale cancer modeling. Annu. Rev. Biomed. Eng. 13:127–155, 2011.

    Article  PubMed  CAS  Google Scholar 

  33. Dittrich, P. S., and A. Manz. Lab-on-a-chip: microfluidics in drug discovery. Nat. Rev. Drug Discov. 5:210–218, 2006.

    Article  PubMed  CAS  Google Scholar 

  34. Dvorak, H. F. Tumors: wounds that do not heal. similarities between tumor stroma generation and wound healing. N. Engl. J. Med. 315:1650–1659, 1986.

    Article  PubMed  CAS  Google Scholar 

  35. Ebos, J. M. L., C. R. Lee, J. G. Christensen, A. J. Mutsaers, and R. S. Kerbel. Multiple circulating proangiogenic factors induced by sunitinib malate are tumor-independent and correlate with antitumor efficacy. Proc. Natl Acad. Sci. U S A 104:17069–17074, 2007.

    Article  PubMed  CAS  Google Scholar 

  36. Ebos, J. M. L., C. R. Lee, W. Cruz-Munoz, G. A. Bjarnason, J. G. Christensen, et al. Accelerated metastasis after short-term treatment with a potent inhibitor of tumor angiogenesis. Cancer Cell 15:232–239, 2009.

    Article  PubMed  CAS  Google Scholar 

  37. Engler, A. J., P. O. Humbert, B. Wehrle-Haller, and V. M. Weaver. Multiscale modeling of form and function. Science 324:208–212, 2009.

    Article  PubMed  CAS  Google Scholar 

  38. Faro, A., D. Giordano, and C. Spampinato. Combining literature text mining with microarray data: advances for system biology modeling. Brief Bioinform. 13:61–82, 2012.

    Article  PubMed  Google Scholar 

  39. Ferrara, N., H. P. Gerber, and J. LeCouter. The biology of VEGF and its receptors. Nat. Med. 9:669–676, 2003.

    Article  PubMed  CAS  Google Scholar 

  40. Ferrara, N., K. J. Hillan, H. P. Gerber, and W. Novotny. Discovery and development of bevacizumab, an anti-VEGF antibody for treating cancer. Nat. Rev. Drug Discov. 3:391–400, 2004.

    Article  PubMed  CAS  Google Scholar 

  41. Fields, S., and R. Sternglanz. The two-hybrid system: an assay for protein–protein interactions. Trends Genet. 10:282–292, 1994.

    Article  Google Scholar 

  42. Fischbach, C., R. Chen, T. Matsumoto, T. Schmelzle, J. S. Brugge, et al. Engineering tumors with 3D scaffolds. Nat. Methods 4:855–860, 2007.

    Article  PubMed  CAS  Google Scholar 

  43. Fischbach, C., H. J. Kong, S. X. Hsiong, M. B. Evangelista, W. Yuen, et al. Cancer cell angiogenic capability is regulated by 3D culture and integrin engagement. Proc. Natl Acad. Sci. U S A 106:399–404, 2009.

    Article  PubMed  CAS  Google Scholar 

  44. Flohé, L., R. Brigelius-Flohé, C. Saliou, M. G. Traber, and L. Packer. Redox regulation of NF-kappa B activation. Free Radic. Biol. Med. 22:1115–1126, 1997.

    Article  PubMed  Google Scholar 

  45. Frieboes, H. B., M. E. Edgerton, J. P. Fruehauf, F. R. A. J. Rose, L. K. Worrall, et al. Prediction of drug response in breast cancer using integrative experimental/computational modeling. Cancer Res. 69:4484–4492, 2009.

    Article  PubMed  CAS  Google Scholar 

  46. Gadkar, K. G., J. Varner, and F. J. Doyle. Model identification of signal transduction networks from data using a state regulator problem. Syst. Biol. (Stevenage) 2:17–30, 2005.

    Article  CAS  Google Scholar 

  47. Gennemark, P., and D. Wedelin. Benchmarks for identification of ordinary differential equations from time series data. Bioinformatics 25:780–786, 2009.

    Article  PubMed  CAS  Google Scholar 

  48. Gerlee, P., and A. R. A. Anderson. Modelling evolutionary cell behaviour using neural networks: application to tumour growth. Biosystems 95:166–174, 2009.

    Article  PubMed  CAS  Google Scholar 

  49. Gerlee, P., and A. R. A. Anderson. Evolution of cell motility in an individual-based model of tumour growth. J. Theor. Biol. 259:67–83, 2009.

    Article  PubMed  CAS  Google Scholar 

  50. Grant, M. R., K. E. Mostov, T. D. Tlsty, and C. A. Hunt. Simulating properties of in vitro epithelial cell morphogenesis. PLoS Comput. Biol. 2:e129, 2006.

    Google Scholar 

  51. Grimm, V., E. Revilla, U. Berger, F. Jeltsch, W. M. Mooij, et al. Pattern-oriented modeling of agent-based complex systems: lessons from ecology. Science 310:987–991, 2005.

    Article  PubMed  CAS  Google Scholar 

  52. Grunewald, M., I. Avraham, Y. Dor, E. Bachar-Lustig, A. Itin, et al. VEGF-induced adult neovascularization: recruitment, retention, and role of accessory cells. Cell 24:175–189, 2006.

    Article  PubMed  CAS  Google Scholar 

  53. Gupta, A., J. Varner, and C. Maranas. Large-scale inference of the transcriptional regulation of Bacillus subtilis. Comput. Chem. Eng. 29:565–576, 2005.

    Google Scholar 

  54. Gutenkunst, R. N., J. J. Waterfall, F. P. Casey, K. S. Brown, C. R. Myers, et al. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol. 3:1871–1878, 2007.

    Article  PubMed  CAS  Google Scholar 

  55. Hanahan, D., and R. A. Weinberg. The hallmarks of cancer. Cell 100:57–70, 2000.

    Article  PubMed  CAS  Google Scholar 

  56. Harris, A. L. Hypoxia—a key regulatory factor in tumour growth. Nat Rev. Cancer 2:38–47, 2002.

    Article  PubMed  CAS  Google Scholar 

  57. Hattne, J., D. Fange, and J. Elf. Stochastic reaction-diffusion simulation with MesoRD. Bioinformatics 21:2923–2924, 2005.

    Article  PubMed  CAS  Google Scholar 

  58. Higgins, M. J., and J. Baselga. Targeted therapies for breast cancer. J. Clin. Invest. 121:3797–3803, 2011.

    Article  PubMed  CAS  Google Scholar 

  59. Hinow, P., P. Gerlee, L. J. McCawley, V. Quaranta, M. Ciobanu, et al. A spatial model of tumor-host interaction: application of chemotherapy. Math. Biosci. Eng. 6:521–546, 2009.

    Article  PubMed  Google Scholar 

  60. Hornbeck, P. V., J. M. Kornhauser, S. Tkachev, B. Zhang, E. Skrzypek, et al. Phosphositeplus: a comprehensive resource for investigating the structure and function of experimentally determined post-translational modifications in man and mouse. Nucleic Acids Res. 40:D261–D70, 2012.

  61. Hornberg, J. J., B. Binder, F. J. Bruggeman, B. Schoeberl, R. Heinrich, et al. Control of MAPK signalling: from complexity to what really matters. Oncogene 24:5533–5542, 2005.

    Article  PubMed  CAS  Google Scholar 

  62. Huang, Y., B. Agrawal, D. Sun, J. S. Kuo, and J. C. Williams. Microfluidics-based devices: new tools for studying cancer and cancer stem cell migration. Biomicrofluidics 5:13412, 2011.

    Article  PubMed  CAS  Google Scholar 

  63. Huh, D., Y. S. Torisawa, G. A. Hamilton, H. J. Kim, and D. E. Ingber. Microengineered physiological biomimicry: organs-on-chips. Lab Chip 12:2156–2164, 2012.

    Article  PubMed  CAS  Google Scholar 

  64. Iliopoulos, D., H. A. Hirsch, and K. Struhl. An epigenetic switch involving NF-kappaB, Lin28, Let-7 MicroRNA, and IL6 links inflammation to cell transformation. Cell 139:693–706, 2009.

    Article  PubMed  CAS  Google Scholar 

  65. Jain, R. K., and L. T. Baxter. Mechanisms of heterogeneous distribution of monoclonal antibodies and other macromolecules in tumors: significance of elevated interstitial pressure. Cancer Res. 48:7022–7032, 1988.

    PubMed  CAS  Google Scholar 

  66. Jemal, A., F. Bray, M. M. Center, J. Ferlay, E. Ward, et al. Global cancer statistics. CA Cancer J. Clin. 61:69–90, 2011.

    Article  PubMed  Google Scholar 

  67. Jensen, L. J., M. Kuhn, M. Stark, S. Chaffron, C. Creevey, et al. String 8—a global view on proteins and their functional interactions in 630 organisms. Nucleic Acids Res. 37: D412–D416, 2009.

  68. Jeong, G. S., S. Han, Y. Shin, G. H. Kwon, R. D. Kamm, et al. Sprouting angiogenesis under a chemical gradient regulated by interactions with an endothelial monolayer in a microfluidic platform. Anal. Chem. 83:8454–8459, 2011.

    Article  PubMed  CAS  Google Scholar 

  69. Jones, S., X. Zhang, D. W. Parsons, J. C. H. Lin, R. J. Leary, et al. Core signaling pathways in human pancreatic cancers revealed by global genomic analyses. Science 321:1801–1806, 2008.

    Article  PubMed  CAS  Google Scholar 

  70. Kaplan, R. N., R. D. Riba, S. Zacharoulis, A. H. Bramley, L. Vincent, et al. VEGFR1-positive haematopoietic bone marrow progenitors initiate the pre-metastatic niche. Nature 438:820–827, 2005.

    Article  PubMed  CAS  Google Scholar 

  71. Karlebach, G., and R. Shamir. Modelling and analysis of gene regulatory networks. Nat. Rev. Mol. Cell Biol. 9:770–780, 2008.

    Article  PubMed  CAS  Google Scholar 

  72. Kerbel, R. S.: Tumor angiogenesis. N. Engl. J. Med. 358:2039–2049, 2008.

    Article  PubMed  CAS  Google Scholar 

  73. Korkaya, H., S. Liu, and M. S. Wicha. Breast cancer stem cells, cytokine networks, and the tumor microenvironment. J. Clin. Invest. 121:3804–3809, 2011.

    Article  PubMed  CAS  Google Scholar 

  74. Kuepfer, L., M. Peter, U. Sauer, and J. Stelling. Ensemble modeling for analysis of cell signaling dynamics. Nat. Biotechnol. 25:1001–1006, 2007.

    Article  PubMed  CAS  Google Scholar 

  75. LaBarge, M. A., C. M. Nelson, R. Villadsen, A. Fridriksdottir, J. R. Ruth, et al. Human mammary progenitor cell fate decisions are products of interactions with combinatorial microenvironments. Integr. Biol. (Camb.) 1:70–79, 2009.

    Article  CAS  Google Scholar 

  76. Lazzara, M. J., and D. A. Lauffenburger. Quantitative modeling perspectives on the ERBB system of cell regulatory processes. Exp. Cell Res. 315:717–725, 2009.

    Article  PubMed  CAS  Google Scholar 

  77. Lequieu, J., A. Chakrabarti, S. Nayak, and J. D. Varner. Computational modeling and analysis of insulin induced eukaryotic translation initiation. PLoS Comput. Biol. 7:e1002263, 2011.

    Google Scholar 

  78. Li, C., M. Donizelli, N. Rodriguez, H. Dharuri, L. Endler, et al. Biomodels database: an enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst. Biol. 4:92, 2010.

    Google Scholar 

  79. Liao, D., C. Corle, T. N. Seagroves, and R. S. Johnson. Hypoxia-inducible factor-1alpha is a key regulator of metastasis in a transgenic model of cancer initiation and progression. Cancer Res. 67:563–72, 2007.

    Article  PubMed  CAS  Google Scholar 

  80. Linding, R., L. J. Jensen, G. J. Ostheimer, M. A. T. M. van Vugt, C. Jørgensen, et al. Systematic discovery of in vivo phosphorylation networks. Cell 129, 1415–1426, 2007.

    Article  PubMed  CAS  Google Scholar 

  81. Liu, G., A. A. Qutub, P. Vempati, F. Mac Gabhann, and A. S. Popel. Module-based multiscale simulation of angiogenesis in skeletal muscle. Theor. Biol. Med. Model. 8:6, 2011.

  82. Liu, S., C. Ginestier, S. J. Ou, S. G. Clouthier, S. H. Patel, et al. Breast cancer stem cells are regulated by mesenchymal stem cells through cytokine networks. Cancer Res. 71:614–624, 2011.

    Article  PubMed  CAS  Google Scholar 

  83. Locasale, J. W., and A. Wolf-Yadlin. Maximum entropy reconstructions of dynamic signaling networks from quantitative proteomics data. PLoS One 4: e6522, 2009.

  84. Loges, S., T. Schmidt, and P. Carmeliet. “Antimyeloangiogenic” therapy for cancer by inhibiting PLGF. Clin. Cancer Res. 15:3648–3653, 2009.

    Article  PubMed  CAS  Google Scholar 

  85. Lu, L., and S. Pope. An improved algorithm for in situ adaptive tabula tion. J. Comput. Phys. 228:361–386, 2009.

    Article  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  87. Luan, D., F. Szlam, K. A. Tanaka, P. S. Barie, and J. D. Varner. Ensembles of uncertain mathematical models can identify network response to therapeutic interventions. Mol. Biosyst. 6:2272–2286, 2010.

    Article  PubMed  CAS  Google Scholar 

  88. Lutolf, M. P., and J. A. Hubbell. Synthetic biomaterials as instructive extracellular microenvironments for morphogenesis in tissue engineering. Nat. Biotechnol. 23:47–55, 2005.

    Article  PubMed  CAS  Google Scholar 

  89. Ma, X. J., S. Dahiya, E. Richardson, M. Erlander, and D. C. Sgroi. Gene expression profiling of the tumor microenvironment during breast cancer progression. Breast Cancer Res. 11:R7, 2009.

    Google Scholar 

  90. Macklin, P., J. Kim, G. Tomaiuolo, M. Edgerton, and V. Cristini. Agent-based modeling of ductal carcinoma in situ: application to patient-specific breast cancer modeling. In: Computational Biology Issues and Applications in Oncology, edited by T. D. Pharm. New York: Springer, 2010, pp. 77–111.

  91. Macklin, P., S. McDougall, A. R. A. Anderson, M. A. J. Chaplain, V. Cristini, et al. Multiscale modelling and nonlinear simulation of vascular tumour growth. J. Math. Biol. 58:765–798, 2009.

    Article  PubMed  Google Scholar 

  92. MacQuarrie, K. L., A. P. Fong, R. H. Morse, S. J. Tapscott. Genome-wide transcription factor binding: beyond direct target regulation. Trends Genet. 27:141–148, 2011.

    Article  PubMed  CAS  Google Scholar 

  93. Mantovani, A., P. Allavena, A. Sica, and F. Balkwill. Cancer-related inflammation. Nature 454:436–44, 2008.

    Article  PubMed  CAS  Google Scholar 

  94. Massey, S. C., M. C. Assanah, K. A. Lopez, P. Canoll, and K. R. Swanson. Glial progenitor cell recruitment drives aggressive glioma growth: mathematical and experimental modelling. J. R. Soc. Interface 9(73):1757–1766, 2012.

    Google Scholar 

  95. Mayawala, K., C. A. Gelmi, and J. S. Edwards. MAPK cascade possesses decoupled controllability of signal amplification and duration. Biophys. J. 87:L01–L02, 2004.

    Article  PubMed  CAS  Google Scholar 

  96. Meng, X., J. Zhong, S. Liu, M. Murray, and A. M. Gonzalez-Angulo. A new hypothesis for the cancer mechanism. Cancer Metastasis Rev. 31(1–2):247–268, 2011.

    Google Scholar 

  97. Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller. Equation of state calculations by fast computing machines. J. Chem. Phys. 21:1087–1093, 1953.

    Article  CAS  Google Scholar 

  98. Miles, D. W., A. Chan, L.Y. Dirix, J. Cortés, X. Pivot, et al. Phase III study of bevacizumab plus docetaxel compared with placebo plus docetaxel for the first-line treatment of human epidermal growth factor receptor 2-negative metastatic breast cancer. J. Clin. Oncol. 28:3239–3247, 2010.

    Article  PubMed  CAS  Google Scholar 

  99. Milo, R., S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, et al. Network motifs: simple building blocks of complex networks. Science 298:824–827, 2002.

    Article  PubMed  CAS  Google Scholar 

  100. Mizukami, Y., Y. Kohgo, and D. C. Chung. Hypoxia inducible factor-1 independent pathways in tumor angiogenesis. Clin. Cancer Res. 13:5670–5674, 2007.

    Article  PubMed  CAS  Google Scholar 

  101. Mori, H., N. Gjorevski, J. L. Inman, M. J. Bissell, C. M. Nelson. Self-organization of engineered epithelial tubules by differential cellular motility. Proc. Natl Acad. Sci. U S A 106:14890–14895, 2009.

    Article  PubMed  CAS  Google Scholar 

  102. Moussaïd, M., E. G. Guillot, M. Moreau, J. Fehrenbach, O. Chabiron, et al. Traffic instabilities in self-organized pedestrian crowds. PLoS Comput. Biol. 8:e1002442, 2012.

    Google Scholar 

  103. Nakatsu, M. N., J. Davis, and C. C. W. Hughes. Optimized fibrin gel bead assay for the study of angiogenesis. J. Vis. Exp. 3:186, 2007.

    Google Scholar 

  104. Navin, N., J. Kendall, J. Troge, P. Andrews, L. Rodgers, et al. Tumour evolution inferred by single-cell sequencing. Nature 472:90–94, 2011.

    Article  PubMed  CAS  Google Scholar 

  105. Nelson, C. M., J. L. Inman, and M. J. Bissell. Three-dimensional lithographically defined organotypic tissue arrays for quantitative analysis of morphogenesis and neoplastic progression. Nat Protoc. 3:674–678, 2008.

    Article  PubMed  CAS  Google Scholar 

  106. Nguyen, L. V., R. Vanner, P. Dirks, and C. J. Eaves. Cancer stem cells: an evolving concept. Nat. Rev. Cancer 12:133–143, 2012.

    PubMed  CAS  Google Scholar 

  107. Owen, M. R., T. Alarcón, P. K. Maini, and H. M. Byrne. Angiogenesis and vascular remodelling in normal and cancerous tissues. J. Math. Biol. 58:689–721, 2009

    Article  PubMed  Google Scholar 

  108. Pà àez-Ribes, M., E. Allen, J. Hudock, T. Takeda, H. Okuyama, et al. Antiangiogenic therapy elicits malignant progression of tumors to increased local invasion and distant metastasis. Cancer Cell 15:220–231, 2009.

    Article  CAS  Google Scholar 

  109. Palmer, T., G. Shutts, R. Hagedorn, F. Doblas-Reyes, Y. Jung, et al. Representing model uncertainty in weather and climate prediction. Annu. Rev Earth Planetary Sci. 33:163–193, 2005.

    Article  CAS  Google Scholar 

  110. Patocs, A., L. Zhang, Y. Xu, F. Weber, T. Caldes, et al. Breast-cancer stromal cells with TP53 mutations and nodal metastases. N. Engl. J. Med. 357:2543–2551, 2007.

    Article  PubMed  CAS  Google Scholar 

  111. Peirce, S. M., F. M. Gabhann, and V. L. Bautch. Integration of experimental and computational approaches to sprouting angiogenesis. Curr. Opin. Hematol. 19(3):184–191, 2012.

    Google Scholar 

  112. Peirce, S. M., E. J. Van Gieson, and T. C. Skalak. Multicellular simulation predicts microvascular patterning and in silico tissue assembly. FASEB J. 18:731–733, 2004.

    PubMed  CAS  Google Scholar 

  113. Perfahl, H., H. M. Byrne, T. Chen, V. Estrella, T. Alarcón, et al. Multiscale modelling of vascular tumour growth in 3D: the roles of domain size and boundary conditions. PLoS One 6:e14790, 2011.

    Google Scholar 

  114. Perou, C. M., T. Sørlie, M. B. Eisen, M. van de Rijn, S. S. Jeffrey, et al. Molecular portraits of human breast tumours. Nature 406:747–752, 2000.

    Article  PubMed  CAS  Google Scholar 

  115. Polyak, K. Breast cancer: origins and evolution. J. Clin. Invest. 117:3155–3163, 2007.

    Article  PubMed  CAS  Google Scholar 

  116. Polyak, K., I. Haviv, I. G. Campbell. Co-evolution of tumor cells and their microenvironment. Trends Genet. 25:30–38, 2009.

    Article  PubMed  CAS  Google Scholar 

  117. Pugh, C. W., and P. J. Ratcliffe. Regulation of angiogenesis by hypoxia: role of the HIF system. Nat. Med. 9:677–684, 2003.

    Article  PubMed  CAS  Google Scholar 

  118. Quo, C. F., C. Kaddi, J. H. Phan, A. Zollanvari, M. Xu, et al. Reverse engineering biomolecular systems using -omic data: challenges, progress and opportunities. Brief Bioinform. 13:430–445, 2012.

    Article  PubMed  CAS  Google Scholar 

  119. Qutub, A. A., F. Mac Gabhann, E. D. Karagiannis, P. Vempati, A. S. Popel. Multiscale models of angiogenesis. IEEE Eng. Med. Biol. Mag. 28:14–31, 2009.

    Article  PubMed  Google Scholar 

  120. Rao, B. M., D. A. Lauffenburger, and K. D. Wittrup. Integrating cell-level kinetic modeling into the design of engineered protein therapeutics. Nat. Biotechnol. 23:191–194, 2005.

    Article  PubMed  CAS  Google Scholar 

  121. Rejniak, K. A., and A. R. A. Anderson. State of the art in computational modelling of cancer. Math. Med. Biol. 29:1–2, 2012.

    Article  PubMed  Google Scholar 

  122. Rejniak, K. A., S. E. Wang, N. S. Bryce, H. Chang, B. Parvin, et al. Linking changes in epithelial morphogenesis to cancer mutations using computational modeling. PLoS Comput. Biol. 6:e1000900, 2010.

    Google Scholar 

  123. Saez-Rodriguez, J., L. G. Alexopoulos, J. Epperlein, R. Samaga, and D. A. Lauffenburger, et al. Discrete logic modelling as a means to link protein signalling networks with functional analysis of mammalian signal transduction. Mol. Syst. Biol. 5:331, 2009.

    Google Scholar 

  124. Salgado, R., S. Junius, I. Benoy, P. Van Dam, P. Vermeulen, et al. Circulating interleukin-6 predicts survival in patients with metastatic breast cancer. Int. J. Cancer 103:642–646, 2003.

    Article  PubMed  CAS  Google Scholar 

  125. Sansone, P., G. Storci, S. Tavolari, T. Guarnieri, C. Giovannini, et al. IL-6 triggers malignant features in mammospheres from human ductal breast carcinoma and normal mammary gland. J. Clin. Invest. 117:3988–4002, 2007.

    Article  PubMed  CAS  Google Scholar 

  126. Schafer, Z. T., and J. S. Brugge. IL-6 involvement in epithelial cancers. J. Clin. Invest. 117:3660–3663, 2007.

    Article  PubMed  CAS  Google Scholar 

  127. Shieh, A. C. Biomechanical forces shape the tumor microenvironment. Ann. Biomed. Eng. 39:1379–1389, 2011.

    Article  PubMed  Google Scholar 

  128. Shin, Y., J. S. Jeon, S. Han, G. S. Jung, S. Shin, et al. In vitro 3D collective sprouting angiogenesis under orchestrated ANG-1 and VEGF gradients. Lab Chip 11:2175–2181, 2011.

    Article  PubMed  CAS  Google Scholar 

  129. Sklar, E.: Netlogo, a multi-agent simulation environment. Artif. Life 13:303–311, 2007.

    Article  PubMed  Google Scholar 

  130. Song, S. O., A. Chakrabarti, and J. D. Varner. Ensembles of signal transduction models using pareto optimal ensemble techniques (POETs). Biotechnol. J. 5:768–780, 2010.

    Article  PubMed  CAS  Google Scholar 

  131. Song, S. O., and J. Varner. Modeling and analysis of the molecular basis of pain in sensory neurons. PLoS One 4:e6758, 2009.

    Google Scholar 

  132. Song, S. O. K., J. Hogg, Z. Y. Peng, R. Parker, J. A. Kellum, et al. Ensemble models of neutrophil trafficking in severe sepsis. PLoS Comput. Biol. 8:e1002422, 2012.

    Google Scholar 

  133. Sørlie, T., C. M. Perou, R. Tibshirani, T. Aas, S. Geisler, et al. Gene expression patterns of breast carcinomas distinguish tumor subclasses with clinical implications. Proc. Natl Acad. Sci. U S A 98:10869–10874, 2001.

    Article  PubMed  Google Scholar 

  134. Spencer, S. L., R. A. Gerety, K. J. Pienta, and S. Forrest. Modeling somatic evolution in tumorigenesis. PLoS Comput. Biol. 2:e108, 2006.

    Google Scholar 

  135. Swanson, K. R., E. C. Alvord, Jr., and J. D. Murray. Quantifying efficacy of chemotherapy of brain tumors with homogeneous and heterogeneous drug delivery. Acta Biotheor. 50:223–237, 2002.

    Article  PubMed  Google Scholar 

  136. Swanson, K. R., C. Bridge, J. D. Murray, and E. C. Alvord, Jr. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J. Neurol. Sci. 216:1–10, 2003.

    Article  PubMed  Google Scholar 

  137. Swanson, K. R., L. D. True, and J. D. Murray. On the use of quantitative modeling to help understand prostate-specific antigen dynamics and other medical problems. Am. J. Clin. Pathol. 119:14–17, 2003.

    Article  PubMed  Google Scholar 

  138. Tasseff, R., S. Nayak, S. Salim, P. Kaushik, N. Rizvi, et al. Analysis of the molecular networks in androgen dependent and independent prostate cancer revealed fragile and robust subsystems. PLoS One 5:e8864, 2010.

    Google Scholar 

  139. Tasseff, R., S. Nayak, S. O. Song, A. Yen, and D. Varner. Modeling and analysis of retinoic acid induced differentiation of uncommitted precursor cells. Integr. Biol. (Camb.) 3:578–591, 2011.

    Article  CAS  Google Scholar 

  140. Thiery, J. P. Epithelial-mesenchymal transitions in tumour progression. Nat. Rev. Cancer 2:442–454, 2002.

    Article  PubMed  CAS  Google Scholar 

  141. Thorne, B. C., A. M. Bailey, and S. M. Peirce. Combining experiments with multi-cell agent-based modeling to study biological tissue patterning. Brief Bioinform. 8:245–257, 2007.

    Article  PubMed  CAS  Google Scholar 

  142. Varner, J. D. Systems biology and the mathematical modelling of antibody-directed enzyme prodrug therapy (ADEPT). Syst. Biol. (Stevenage) 152:291–302, 2005.

    Article  CAS  Google Scholar 

  143. Wang, Z., V. Bordas, and T. S. Deisboeck. Discovering molecular targets in cancer with multiscale modeling. Drug. Dev. Res. 72:45–52, 2011.

    Article  PubMed  CAS  Google Scholar 

  144. Wang, Z., V. Bordas, J. Sagotsky, and T. S. Deisboeck. Identifying therapeutic targets in a combined EGFR-TGFBR signalling cascade using a multiscale agent-based cancer model. Math. Med. Biol. 29:95–108, 2012.

    Article  PubMed  Google Scholar 

  145. Wang, J., Y. Zhang, C. Marian, and H. W. Ressom. Identification of aberrant pathways and network activities from high-throughput data. Brief Bioinform. 13:406–419, 2012.

    Article  PubMed  CAS  Google Scholar 

  146. Waugh, D. J. J., and C. Wilson. The interleukin-8 pathway in cancer. Clin. Cancer Res. 14:6735–6741, 2008.

    Article  PubMed  CAS  Google Scholar 

  147. Yao, J., S. Weremowicz, B. Feng, R. C. Gentleman, J. R. Marks, et al. Combined CDNA array comparative genomic hybridization and serial analysis of gene expression analysis of breast tumor progression. Cancer Res. 66:4065–4078, 2006.

    Article  PubMed  CAS  Google Scholar 

  148. Yarden, Y., and M. X. Sliwkowski. Untangling the erbb signalling network. Nat. Rev. Mol. Cell Biol. 2:127–137, 2001.

    Article  PubMed  CAS  Google Scholar 

  149. Yeung, M. K. S., J. Tegnér, and J. J. Collins. Reverse engineering gene networks using singular value decomposition and robust regression. Proc. Natl Acad. Sci. U S A 99:6163–6168, 2002.

    Article  PubMed  CAS  Google Scholar 

  150. You, X., A. W. Nguyen, A. Jabaiah, M. A. Sheff, K. S. Thorn, et al. Intracellular protein interaction mapping with FRET hybrids. Proc. Natl Acad. Sci. USA 103:18458–18463, 2006.

    Article  PubMed  CAS  Google Scholar 

  151. Zhang, L., C. A. Athale, and T. S. Deisboeck. Development of a three-dimensional multiscale agent-based tumor model: simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer. J. Theor. Biol. 244:96–107, 2007.

    Article  PubMed  CAS  Google Scholar 

  152. Zhang, L., C. G. Strouthos, Z. Wang, and T. S. Deisboeck. Simulating brain tumor heterogeneity with a multiscale agent-based model: Linking molecular signatures, phenotypes and expansion rate. Math. Comput. Model. 49:307–319, 2009.

    Article  PubMed  Google Scholar 

  153. Zheng, Y., J. Chen, M. Craven, N. W. Choi, S. Totorica, et al. In vitro microvessels for the study of angiogenesis and thrombosis. Proc. Natl Acad. Sci. U S A 109:9342–9347, 2012.

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

I apologize to the investigators whose work I was unable to discuss in this focused review. This study was supported by Award Number #U54CA143876 from the National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute or the National Institutes of Health.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jeffrey D. Varner.

Additional information

Associate Editor Scott L. Diamond oversaw the review of this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chakrabarti, A., Verbridge, S., Stroock, A.D. et al. Multiscale Models of Breast Cancer Progression. Ann Biomed Eng 40, 2488–2500 (2012). https://doi.org/10.1007/s10439-012-0655-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-012-0655-8

Keywords

Navigation