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Cancer as a moving target: understanding the composition and rebound growth kinetics of recurrent tumors

  1. Jasmine Foo1,*,
  2. Kevin Leder2,
  3. Shannon M. Mumenthaler3

Article first published online: 16 NOV 2012

DOI: 10.1111/eva.12019

Issue

Evolutionary Applications

Evolutionary Applications

Special Issue: Evolution and Cancer

Volume 6, Issue 1, pages 54–69, January 2013

Total views since publication: 212

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How to Cite

Foo, J., Leder, K. and Mumenthaler, S. M. (2013), Cancer as a moving target: understanding the composition and rebound growth kinetics of recurrent tumors. Evolutionary Applications, 6: 54–69. doi: 10.1111/eva.12019

Author Information

  1. 1

    School of Mathematics, University of Minnesota, Minneapolis, MN, USA

  2. 2

    Industrial and Systems Engineering, University of Minnesota, Minneapolis, MN, USA

  3. 3

    Center for Applied Molecular Medicine, University of Southern California Keck School of Medicine, Los Angeles, CA, USA

* Correspondence
Jasmine Foo, School of Mathematics, University of Minnesota, 206 Church St SE, Minneapolis, MN 55455.
Tel.: (612) 625-0131; fax: (612) 626-2017; e-mail: jyfoo@math.umn.edu

Publication History

  1. Issue published online: 21 JAN 2013
  2. Article first published online: 16 NOV 2012

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Literature cited

  • Araten, D. J., D. W. Golde, R. H. Zhang, H. T. Thaler, L. Gargiulo, R. Notaro, and L. Luzzatto. 2005. A quantitative measurement of the human somatic mutation rate. Cancer Research 65:8111–8117.
  • Athreya, K.B., and P.B. Ney 2004. Branching Processes. Courier Dover Publications.
  • Coldman, A., and J. Goldie 1986. A stochastic model for the origin and treatment of tumors containing drug-resistant cells. Bulletin of Mathematical Biology 48:279–292.
  • Coldman, A., and J. Murray 2000. Optimal control for a stochastic model of cancer chemotherapy. Mathematical Biosciences 168:187–200.
  • Detterbeck, F. C., and C. J. Gibson 2008. Turning gray: the natural history of lung cancer over time. Journal of Thoracic Oncology 3:781–792.
  • Diaz Jr, L. A., R. T. Williams, J. Wu, I. Kinde, J. R. Hecht, J. Berlin, B. Allen et al. 2012. The molecular evolution of acquired resistance to targeted EGFR blockade in colorectal cancers. Nature 486:537–540.
  • Ding, L., T. J. Ley, D. E. Larson, C. A. Miller, D. C. Koboldt, J. S. Welch, J. K. Ritchey et al. 2012. Clonal evolution in relapsed acute myeloid leukaemia revealed by whole-genome sequencing. Nature 481:506–510.
  • Durrett, R., J. Foo, K. Leder, J. Mayberry, and F. Michor 2010. Evolutionary dynamics of tumor progression with random fitness values. Theoretical Population Biology 78:54–66.
  • Durrett, R., J. Foo, K. Leder, J. Mayberry, and F. Michor 2011. Intra-tumor heterogeneity in evolutioary dynamics of tumor progression. Genetics 188:461–477.
  • Elowitz, M.B., A. Levine, E. Siggia, and P. Swain 2002. Stochastic gene expression in a single cell. Science 297:1183–1186.
  • Evans, S. M., K. D. Judy, I. Dunphy, W. T. Jenkins, W. T. Hwang, P. T. Nelson, R. A. Lustig et al. 2004. Hypoxia is important in the biology and aggression of human glial brain tumors. Clinical Cancer Research 10:8177–8184.
  • Feinerman O., J. Viega, J. Dorfma, R. Germain, and G. Altan-Bonnet 2008. Variability and robustness in t cell activation from regulated heterogeneity in protein levels. Science 321:1081–1084.
  • Foo, J., and K. Leder 2012. Dynamics of cancer recurrence. Annals of Applied Probability in press.
  • Gerlinger, M., A. J. Rowan, S. Horswell, J. Larkin, D. Endesfelder, E. Gronroos, P. Martinez et al. 2012. Intratumor heterogeneity and branched evolution revealed by multiregion sequencing. New England Journal of Medicine 366:883–892.
  • Godin-Heymann, N., I. Bryant, M. N. Rivera, L. Ulkus, D. W. Bell, D. J. Riese II, J. Settleman, and D. A. Haber. 2007. Oncogenic activity of epidermal growth factor receptor kinase mutant alleles is enhanced by the T790M drug resistance mutation. Cancer Research 67:7319–7326.
  • Goldie, J. H., and A. J. Coldman 1979. A mathematical model for relating the drug sensitivity of tumours to their spontaneous mutation rate. Cancer Treatment Reports 63:1727–1733.
  • Goldie, J. H., and A. J. Coldman 1983. Quantitative model for multiple levels of drug resistance in clinical tumors. Cancer Treatment Reports 67:923–931.
  • Haeno, H., Y. Iwasa, and F. Michor 2007. The evolution of two mutations during clonal expansion. Genetics 177:2209–2221.
  • Holyoake, T., X. Jiang, C. Eaves, and A. Eaves. 1999. Isolation of a highly quiescent subpopulation of primitive leukemic cells in chronic myeloid leukemia. Blood 94:0–0.
  • Ionov, Y., M. A. Peinado, S. Malkhosyan, D. Shibata, and M. Perucho. 1993. Ubiquitous somatic mutations in simple repeated sequences reveal a new mechanism for colonic carcinogenesis. Nature 6429:558–561.
  • Iwasa, Y., F. Michor, and M. A. Nowak 2003. Evolutionary dynamics of escape from biomedical intervention. Proceedings of the Royal Society of London, Series B 270:2572–2578.
  • Jackson, T.L. , and H. M. Byrne 2000. A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. Mathematical Biosciences 164:17–38.
  • James, K., E. Eisenhauer, M. Christian, M. Terenziani, D. Vena, A. Muldal, and P. Therasse. 1999. Measuring response in solid tumors: Unidimensional versus bidimensional measurement. Journal of the National Cancer Institute 91:523–528.
  • Kaern, M., T. Elston, W. Blake, and J. Collins 2005. Stochasticity in gene expression: from theories to phenotypes. Nature Reviews Genetics 6:451–464.
  • Komarova, N.L., and D. Wodarz 2005. Drug resistance in cancer: Principles of emergence and prevention. PNAS 102:9714–9719.
  • Komarova, N., and D. Wodarz 2007. Stochastic modeling of cellular colonies with quiescence: an application to drug resistance in cancer. Theoretical Population Biology 72:523–538.
  • Leder, K., J. Foo, B. Skaggs, M. Gorre, C. L. Sawyers, and F. Michor. 2011. Diversity in pre-existing resistance to BCR-ABL inhibitors in chronic myeloid leukemia. PLoS ONE 6(11): e27682. in press.
  • Merlo, L., J. Pepper, B. Reid, and C. Maley 2006. Cancer as an evolutionary and ecological process. Nature Reviews Cancer 6:924–935.
  • Mery, C. M., A. N. Pappas, B. M. Burt, R. Bueno, P. A. Linden, D. J. Sugarbaker, and M. T. Jaklitsch. 2005. Diameter of non-small cell lung cancer correlates with long- term survival: implications for t stage. Chest 128:3255–3260.
  • Michor, F., M.A. Nowak, and Y. Iwasa 2006. Evolution of resistance to cancer therapy. Current Pharmaceutical Design 12:261–271.
  • Ohashi, K., L. V. Sequist, M. E. Arcila, T. Moran, J. Chmielecki, Y.L. Lin, Y. Pan et al. 2012. Lung cancers with acquired resistance to EGFR inhibitors occasionally harbor BRAF gene mutations but lack mutations in KRAS, NRAS, or MEK1. PNAS 109:E2127E2133.
  • Pao, W., V. Miller, M. Zakowski, J. Doherty et al. 2004. EGF receptor gene mutations are common in lung cancers from never smokers and are associated with sensitivity of tumors to gefitinib and erlotinib. Proceedings of the National Academy of Sciences of the United States of America 101:13306–13311.
  • Port, J. L., M. S. Kent, R. J. Korst, D. Libby, M. Pasmantier, and N. K. Altorki. 2003. Tumor size predicts survival within stage IA non-small cell lung cancer. Chest 124: 1828–1833.
  • Quaranta, V., D. R. Tyson, S. P. Garbett, B. Weidow, M. P. Harris, and W. Georgescu. 2009. Trait variability of cancer cells quantified by high-content automated microscopy of single cells. Methods in Enzymology 467: 23–57.
  • Reya, T., S. Morrison, M. Clarke, and I. Weissman 2001. Stem cells, cancer and cancer stem cells. Nature 414:105–111.
  • Sagitov, S., and M. C. Serra 2012. Multitype Bienayme–Galton–Watson processes escaping extinction. Advances in Applied Probability 41:225–246.
  • Sarry, J. E., K. Murphy, R. Perry, P. V. Sanchez, A. Secreto, C. Keefer, C. R. Swider et al. 2011. Human acute myelogenous leukemia stem cells are rare and heterogeneous when assayed in NOD/SCID/IL2Rc-deficient mice. The Journal of Clinical Investigation 121:384–395.
  • Sekeres, M., M. Kalacyio, and B. Bolwell 2007. Clinical Malignant Hematology. McGraw-Hill Professional, New York.
  • Seshadri, R., R. J. Kutlaca, K. Trainor, C. Matthews, and A.A. Morley 1987. Mutation rate of normal and malignant human lymphocytes. Cancer Research 47: 407.
  • Sierra, J., V. Cepero, and S. Giordano 2010. Molecular mechanisms of acquired resistance to tyrosine kinase targeted therapy. Molecular Cancer 9:75.
  • Silva, A., and R. Gatenby 2010. A theoretical quantitative model for evolution of cancer chemotherapy resistance. Biology Direct 5:25.
  • Skaggs, B. J., M. E. Gorre, A. Ryvkin, M. R. Burgess, Y. Xie, Y. Han, E. Komisopoulou et al. 2006. Phosphorylation of the ATP-binding loop directs oncogenicity of drug-resistant BCR-ABL mutants. Proceedings of the National Academy of Sciences of the United States of America 103:19466–19471.
  • Son, S., A. Tzur, Y. Weng, P. Jorgensen, J. Kim, M. W. Kirschner, and S. R. Manalis. 2012. Direct observation of mammalian cell growth and size regulation. Nature Methods 0:0–0.
  • van de Stolpe, A., K. Pantel, S. Sleijfer, L. W. Terstappen, and J. M. den Toonder. 2011. Circulating tumor cell isolation and diagnostics: toward routine clinical use. Cancer Research 71:5955–5960.
  • Talmadge, J. 2007. Clonal selection of metastasis within the life history of a tumor. Cancer Research 67:11471–11475.
  • Taniguchi, K., J. Uchida, K. Nishino, T. Kumagai, T. Okuyama, J. Okami, M. Higashiyama et al. 2011. Quantitative detection of EGFR mutations in circulating tumor dna derived from lung adenocarcinomas. Clinical Cancer Research 17:1–8.
  • Turke, A. B., K. Zejnullahu, Y. L. Wu, Y. Song, D. Dias-Santagata, E. Lifshits, L. Toschi et al. 2010. Preexistence and clonal selection of MET amplification in EGFR mutant nsclc. Cancer Cell 17:77–88.
  • Wang, Y., C. Sung, C. Dartois, R. Ramchandan, B. P. Booth, E. Rock, and T. Gobburu. 2009. Elucidation of relationship between tumor size and survival in non-small-cell lung cancer patients can aid early decision making in clinical drug development. Clinical Pharmacology and Therapeutics 86:167–174.
  • Xu, L., E. Kikuchi, C. Xu, H. Ebi, D. Ercan, K. A. Cheng, R. Padera et al. 2012. Combined EGFR/MET or EGFR/HSP90 inhibition is effective in the treatment of lung cancers codriven by mutant EGFR containing T790M and MET. Cancer Research 72:3302–3311.
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