Free Access
Issue |
Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012
Cancer modeling
|
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Page(s) | 136 - 165 | |
DOI | https://doi.org/10.1051/mmnp/20127107 | |
Published online | 25 January 2012 |
- S. Ahmed, J.F. Passos, M.J. Birket, T. Beckmann, S. Brings, H. Peters, M.A. Birch-Machin, T. von Zglinicki, G. Saretzki. Telomerase Does Not Counteract Telomere Shortening But Protects Mitochondrial Function Under Oxidative Stress. Journal of Cell Science, 121 (2008), No. 7, 1046–1053. [CrossRef] [PubMed] [Google Scholar]
- O. Arino, M. Kimmel, G.F. Webb. Mathematical Modeling of the Loss of Telomere Sequences. J. theor. Biol., 177 (1995), No. 1, 45–57. [Google Scholar]
- O. Arino, E. Sánchez, G.F. Webb. Polynomial Growth Dynamics of Telomere Loss in a Heterogeneous Cell Population. Dynamic Control Discrete Impulsive System, 3 (1997), No. 3, 263–282. [Google Scholar]
- P. Armitage, R. Doll. The age distribution of cancer and a multi-stage theory of carcinogenosis. IJE, 33 (2004), No. 6, 1174–1179. [Google Scholar]
- S. Bagheri, M. Nosrati, S. Li, S. Fong, S. Torabian, J. Rangel, D.H. Moore, S. Federman, R.R. LaPosa, F.L. Baehner, R.W. Sagebiel, J.E. Cleaver, C. Haqq, R.J. Debs, E.H. Blackburn, M. Kashani-Sabet. Genes and pathways downstream of telomerase in melanoma metastasis. PNAS, 103 (2006), No. 30, 11306–11311. [CrossRef] [Google Scholar]
- H.T. Banks, K.L. Sutton, W.C. Thompson, G. Bocharov, D. Roose, T. Schenkel, A. Meyerhans. Estimation of Cell Proliferation Dynamics Using CFSE Data. Bulletin of Mathematical Biology, 73 (2011), 1, 116–150. [Google Scholar]
- S. Bernard, L. Pujo-Menjouet, M.C. Mackey. Analysis of Cell Kinetics Using a Cell Division Marker : Mathematical Modeling of Experimental Data. Biophysical Journal, 84 (2003), No. 5, 3414–3424. [Google Scholar]
- D.S. Bernstein. Matrix Mathematics, Second Edition., Princeton University Press, 2009. [Google Scholar]
- D. Bonnet, J.E. Dick. Human Acute Myeloid Leukemia is Organized as a Hierarchy That Originates From a Primitive Hematopoetic Cell. Nature Medicine, 3 (1997), No. 7, 730–737. [CrossRef] [PubMed] [Google Scholar]
- A. Brú, S. Albertos, J.L. Subiza, J.L. García-Asenjo, I. Brú. The Universal Dynamics of Tumor Growth. Biophysical Journal, 85 (2003), No. 5, 2948–2961. [Google Scholar]
- E.D. Cohen, Y. Tian, E.E. Morrisey. Wnt signaling : an essential regulator of cardiovascular differentiation, morphogenesis and progenitor self-renewal. Development, 135 (2008), No. 5, 789–798. [CrossRef] [PubMed] [Google Scholar]
- A.T. Collins, P.A. Berry, C. Hyde, M.J. Stower, N.J. Maitland. Prospective Identification of Tumorigenic Prostate Cancer Stem Cells. Cancer Res., 65 (2005), No. 23, 10946–10951. [CrossRef] [PubMed] [Google Scholar]
- P. Dalerba, S.J. Dylla, I.-K. Park, R. Liu, X. Wang, R.W. Cho, T. Hoey, A. Gurney, E.H. Huang, D.M. Simeone, A.A. Shelton, G. Parmiani, C. Castelli, M.F. Clarke. Phenotypic characterization of human colorectal cancer stem cells. PNAS, 104 (2007), No. 24, 10158–10163. [Google Scholar]
- L.G. de Pillis, A.E. Radunskaya, C.L. Wiseman. A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth. Cancer Res., 65 (2005), No. 17, 7950–7958. [PubMed] [Google Scholar]
- B.M. Deasy, R.J. Jankowski, T.R. Payne, B. Cao, J.P. Goff, J.S. Greenberger, J. Huard. Modeling Stem Cell Population Growth : Incorporating Terms for Proliferative Heterogeneity. Stem Cells, 21 (2003), No. 5, 536 – 545. [CrossRef] [PubMed] [Google Scholar]
- J.E. Dick. Breast cancer stem cells revealed. PNAS, 100 (2003), No. 7, 3547–3549. [CrossRef] [Google Scholar]
- D. Dingli, F. Michor. Successful Therapy Must Eradicate Cancer Stem Cells. Stem Cells, 24 (2006), No. 12, 2603–2610. [CrossRef] [PubMed] [Google Scholar]
- J. Dyson, E. Sánchez, R. Villella-Bressan, G.F. Webb. Stabilization of telomeres in nonlinear models of proliferating cell lines. Journal of Theoretical Biology, 244 (2007), No. 3, 400–408. [Google Scholar]
- J. Dyson, R. Villella-Bressan, G.F. Webb. Asymptotic Behaviour Of Solutions To Abstract Logistic Equations. Mathematical Biosciences, 206 (2007), No. 2, 216–232. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- H. Enderling, D. Park, L. Hlatky, P. Hahnfeldt. The Importance of Spatial Distribution of Stemness and Proliferation State in Determining Tumor Radioresponse. Math. Model. Nat. Phenom., 4 (2009), No. 3, 117–133. [CrossRef] [EDP Sciences] [Google Scholar]
- A. Eramo, F. Lotti, G. Sette, E. Pilozzi, M. Biffoni, A. Di Virgilio, C. Conticello, L. Ruco, C. Peschle, R. De Maria. Identification and expansion of the tumorigenic lung cancer stem cell population. Cell Death and Differentiation, 15 (2008), No. 3, 504–514. [CrossRef] [PubMed] [Google Scholar]
- E.R. Fearon, B. Vogelstein. A Genetic Model for Colorectal Tumorigenesis. Cell, 61 (1990), 759–767. [CrossRef] [PubMed] [Google Scholar]
- R.W. Frenck, Jr., E.H Blackburn, K.M. Shannon. The rate of telomere sequence loss in human leukocytes varies with age. PNAS, 95 (1998), No. 10, 5607-5610. [CrossRef] [Google Scholar]
- S.N. Gentry, R. Ashkenazi, T.L. Jackson. A Maturity Structured Mathematical Model of Mutation Acquisition in the Absence of Homeostatic Regulation. Math. Model. Nat. Phenom., 4 (2009), 403–422. [CrossRef] [EDP Sciences] [Google Scholar]
- D. Hanahan, R.A. Weinberg. The Hallmarks of Cancer : The Next Generation. Cell., 144 (2011), No. 5, 646–674. [CrossRef] [Google Scholar]
- K.E. Huffman, S.D. Levene, V.M. Tesmer, J.W. Shay, W.E. Wright. Telomere Shortening Is Proportional to the Size of the G-rich Telomeric 3’-Overhang. The Journal of Biological Chemistry, 275 (2000), No. 26, 19719–19722. [CrossRef] [PubMed] [Google Scholar]
- A. G. Knudson, Two genetic hits (more or less) to cancer. Nat. Rev. Cancer., 1 (2001), 157–162. [CrossRef] [PubMed] [Google Scholar]
- S.H. Lang, F.M. Frame, A.T. Collins. Prostate cancer stem cells. Journal of Pathology, 217 (2009), No. 9, 299–306. [CrossRef] [PubMed] [Google Scholar]
- M.Z. Levy, R.C. Allsopp, A.B. Futcher, C.W. Greider, C.B. Harley. Telomere End-replication Problem and Cell Aging. J. Mol. Biol., 225 (1992), No. 4, 951–960. [CrossRef] [PubMed] [Google Scholar]
- H. Lodish, J. Flygare, S. Chou. From stem cell to erythroblast : Regulation of red cell production at multiple levels by multiple hormones. IUBMB Life, 62 (2010), No. 7, 492–496. [CrossRef] [PubMed] [Google Scholar]
- A. Marciniak-Czochra. Mathematical models of stem cells renewal and differentiation. Oberwolfach Reports, 2 (2009), 3414–3424. [Google Scholar]
- S.J. Morrison, N. Uchida, I.L. Weissman. The biology of hematopoietic stem cells. Annu. Rev. Cell Dev. Biol., 11 (1995), 35–71. [Google Scholar]
- P. Olofsson. Modeling of the Process of Telomere Shortening : an Overview. [Google Scholar]
- L. Perko. Differential Equations and Dynamical Systems, 3rd edition. Springer, New York, NY, 2001. [Google Scholar]
- F. Roegiers, Y.N. Jan. Asymmetric cell division. Current Opinion in Cell Biology, 16 (2004), No. 2, 195-205. [CrossRef] [PubMed] [Google Scholar]
- G.R. Simon, H. Wagner. Small Cell Lung Cancer*. Chest, 123 (2003), No. 1, 259–271. [CrossRef] [Google Scholar]
- S.K. Singh, I.D. Clarke, M. Terasaki, V.E. Bonn, C. Hawkins, J. Squire, P.B. Dirks. Identification of a Cancer Stem Cell in Human Brain Tumors. Cancer Res., 63 (2003), No. 18, 5821–5828. [PubMed] [Google Scholar]
- P. Skehan, S.J. Friedman. Non-exponential growth by mammalian cells in culture. Cell Tissue Kinet., 17 (1984), No. 4, 335–343. [PubMed] [Google Scholar]
- G.I. Solyanik, N.M. Berezetskaya, R.I. Bulkiewicz, G.I. Kulik. Different growth patterns of a cancer cell population as a function of its starting growth characteristics : analysis by mathematical modelling. Cell Prolif, 28 (1995), No. 5, 263–278. [CrossRef] [PubMed] [Google Scholar]
- G.J. Spangrude, S. Heimfeld, I.L. Weissman. Purification and characterization of mouse hematopoietic stem cells. Science, 244 (1988), No. 4861, 58–62. [CrossRef] [PubMed] [Google Scholar]
- J.F. Speer, V.E. Petrosky, M.W. Retsky, R.H. Wardwell", A Stochastic Numerical Model of Breast Cancer Growth That Simulates Clinical Data. Cancer Res., 44 (1984), No. 9, 4124–4130. [PubMed] [Google Scholar]
- K. Sprouffske, J.W. Pepper, C.C. Maley. Accurate Reconstruction of the Temporal Order of Mutations in Neoplastic Progression. Cancer Prev. Res., 4 (2011), No. 7, 1135–1144. [Google Scholar]
- S.A. Stewart, W.C. Hahn, B.F. O’Connor, E.N. Banner, A.S. Lundberg, P. Modha, H. Mizuno, M.W. Brooks, M. Fleming, D.B. Zimonjic, N.C. Popescu, R.A. Weinberg. Telomerase contributes to tumorigenesis by a telomere length-independent mechanism. PNAS, 99 (2002), No. 20, 12606–12611. [CrossRef] [Google Scholar]
- M.R. Stratton, P.J. Campbell, P.A. Futreal. The Cancer Genome. Nature, 458 (2009), No. 7239, 156–182. [CrossRef] [PubMed] [Google Scholar]
- L.G. van der Flier, H. Clevers. Stem Cells, Self-Renewal, and Differentiation in the Intestinal Epithelium. Annu. Rev. Physiol., 71 (2009), No. 1, 241–260. [CrossRef] [PubMed] [Google Scholar]
- T. von Zglinicki. Oxidative Stress Shortens Telomeres. Trends in Biochemical Scoences, 27 (2002), No. 7, 339–344. [CrossRef] [Google Scholar]
- G.F. Webb. Logistic Models Of Structured Population Growth. Comp and Maths. with Appls., 12 (1986), No. 4-5A, 527–539. [CrossRef] [Google Scholar]
- G.D. Weinstein, J.L. McCullough, P. Ross. Cell Proliferation in Normal Epidermis. The Journal of Investigative Dermatology, 82 (1984), No. 6, 623–628. [CrossRef] [PubMed] [Google Scholar]
- G.D. Wilson, N.J. McNally, S. Dische, M.I. Saunders, C. Des Rochers, A.A. Lewis, M.H. Bennett. Measurement of cell kinetics in human tumours in vivo using bromodeoxyuridine incorporation and flow cytometry. Br. J. Cancer, 58 (1988), No. 4, 423–431. [CrossRef] [PubMed] [Google Scholar]
- Q.-L. Ying, J. Wray, J. Nichols, L. Batlle-Morera, B. Doble, J. Woodgett, P. Cohen, A. Smith. The ground state of embryonic stem cell self-renewal. Nature, 453 (2008), No. 7194, 519–523. [CrossRef] [PubMed] [Google Scholar]
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