Geodesic
A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies
G. Kapitanov1
1 Vanderbilt University Department of Mathematics 1326 Stevenson Center, Nashville, TN 37240, USA
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 1, pp. 136-165

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There is evidence that cancer develops when cells acquire a sequence of mutations that alter normal cell characteristics. This sequence determines a hierarchy among the cells, based on how many more mutations they need to accumulate in order to become cancerous. When cells divide, they exhibit telomere loss and differentiate, which defines another cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model, which combines the mutation-accumulation hierarchy with the differentiation hierarchy of the cells, allowing us to take a step further in examining cancer development and growth. The results of the model support the hypothesis of the cancer stem cell’s role in cancer pathogenesis: a very small fraction of the cancer cell population is responsible for the cancer growth and development. Also, according to the model, the nature of mutation accumulation is sufficient to explain the faster growth of the cancer cell population. However, numerical results show that in order for a cancer to develop within a reasonable time frame, cancer cells need to exhibit a higher proliferation rate than normal cells.
DOI : 10.1051/mmnp/20127107

G. Kapitanov 1

1 Vanderbilt University Department of Mathematics 1326 Stevenson Center, Nashville, TN 37240, USA 
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G. Kapitanov. A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 1, pp. 136-165. doi: 10.1051/mmnp/20127107

[1] S. Ahmed, J.F. Passos, M.J. Birket, T. Beckmann, S. Brings, H. Peters, M.A. Birch-Machin, T. Von Zglinicki, G. Saretzki Journal of Cell Science 2008 1046 1053

[2] O. Arino, M. Kimmel, G.F. Webb J. theor. Biol. 1995 45 57

[3] O. Arino, E. Sánchez, G.F. Webb Dynamic Control Discrete Impulsive System 1997 263 282

[4] P. Armitage, R. Doll IJE 2004 1174 1179

[5] 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 PNAS 2006 11306 11311

[6] H.T. Banks, K.L. Sutton, W.C. Thompson, G. Bocharov, D. Roose, T. Schenkel, A. Meyerhans Bulletin of Mathematical Biology 2011 116 150

[7] S. Bernard, L. Pujo-Menjouet, M.C. Mackey Biophysical Journal 2003 3414 3424

[8] D.S. Bernstein. Matrix Mathematics, Second Edition., Princeton University Press, 2009.

[9] D. Bonnet, J.E. Dick Nature Medicine 1997 730 737

[10] A. Brú, S. Albertos, J.L. Subiza, J.L. García-Asenjo, I. Brú Biophysical Journal 2003 2948 2961

[11] E.D. Cohen, Y. Tian, E.E. Morrisey Development 2008 789 798

[12] A.T. Collins, P.A. Berry, C. Hyde, M.J. Stower, N.J. Maitland Cancer Res. 2005 10946 10951

[13] 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 PNAS 2007 10158 10163

[14] L.G. De Pillis, A.E. Radunskaya, C.L. Wiseman Cancer Res. 2005 7950 7958

[15] B.M. Deasy, R.J. Jankowski, T.R. Payne, B. Cao, J.P. Goff, J.S. Greenberger, J. Huard Stem Cells 2003 536

[16] J.E. Dick PNAS 2003 3547 3549

[17] D. Dingli, F. Michor Stem Cells 2006 2603 2610

[18] J. Dyson, E. Sánchez, R. Villella-Bressan, G.F. Webb Journal of Theoretical Biology 2007 400 408

[19] J. Dyson, R. Villella-Bressan, G.F. Webb Mathematical Biosciences 2007 216 232

[20] H. Enderling, D. Park, L. Hlatky, P. Hahnfeldt Math. Model. Nat. Phenom. 2009 117 133

[21] A. Eramo, F. Lotti, G. Sette, E. Pilozzi, M. Biffoni, A. Di Virgilio, C. Conticello, L. Ruco, C. Peschle, R. De Maria Cell Death and Differentiation 2008 504 514

[22] E.R. Fearon, B. Vogelstein Cell 1990 759 767

[23] R.W. Frenck, E.H Blackburn, K.M. Shannon PNAS 1998 5607 5610

[24] S.N. Gentry, R. Ashkenazi, T.L. Jackson Math. Model. Nat. Phenom. 2009 403 422

[25] D. Hanahan, R.A. Weinberg Cell. 2011 646 674

[26] K.E. Huffman, S.D. Levene, V.M. Tesmer, J.W. Shay, W.E. Wright The Journal of Biological Chemistry 2000 19719 19722

[27] A. G. Knudson Nat. Rev. Cancer. 2001 157 162

[28] S.H. Lang, F.M. Frame, A.T. Collins Journal of Pathology 2009 299 306

[29] M.Z. Levy, R.C. Allsopp, A.B. Futcher, C.W. Greider, C.B. Harley J. Mol. Biol. 1992 951 960

[30] H. Lodish, J. Flygare, S. Chou IUBMB Life 2010 492 496

[31] A. Marciniak-Czochra Oberwolfach Reports 2009 3414 3424

[32] S.J. Morrison, N. Uchida, I.L. Weissman Annu. Rev. Cell Dev. Biol. 1995 35 71

[33] P. Olofsson. Modeling of the Process of Telomere Shortening : an Overview.

[34] L. Perko. Differential Equations and Dynamical Systems, 3rd edition. Springer, New York, NY, 2001.

[35] F. Roegiers, Y.N. Jan Current Opinion in Cell Biology 2004 195 205

[36] G.R. Simon, H. Wagner Chest 2003 259 271

[37] S.K. Singh, I.D. Clarke, M. Terasaki, V.E. Bonn, C. Hawkins, J. Squire, P.B. Dirks Cancer Res. 2003 5821 5828

[38] P. Skehan, S.J. Friedman Cell Tissue Kinet. 1984 335 343

[39] G.I. Solyanik, N.M. Berezetskaya, R.I. Bulkiewicz, G.I. Kulik Cell Prolif 1995 263 278

[40] G.J. Spangrude, S. Heimfeld, I.L. Weissman Science 1988 58 62

[41] J.F. Speer, V.E. Petrosky, M.W. Retsky, R.H. Wardwell" Cancer Res. 1984 4124 4130

[42] K. Sprouffske, J.W. Pepper, C.C. Maley Cancer Prev. Res. 2011 1135 1144

[43] 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 PNAS 2002 12606 12611

[44] M.R. Stratton, P.J. Campbell, P.A. Futreal Nature 2009 156 182

[45] L.G. Van Der Flier, H. Clevers Annu. Rev. Physiol. 2009 241 260

[46] T. Von Zglinicki Trends in Biochemical Scoences 2002 339 344

[47] G.F. Webb Comp and Maths. with Appls. 1986 527 539

[48] G.D. Weinstein, J.L. Mccullough, P. Ross The Journal of Investigative Dermatology 1984 623 628

[49] G.D. Wilson, N.J. Mcnally, S. Dische, M.I. Saunders, C. Des Rochers, A.A. Lewis, M.H. Bennett Br. J. Cancer 1988 423 431

[50] Q.-L. Ying, J. Wray, J. Nichols, L. Batlle-Morera, B. Doble, J. Woodgett, P. Cohen, A. Smith Nature 2008 519 523

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