Stochastic elimination of cancer cells

Proceedings of the Royal Society B: Biological Sciences

Volumn 270, Issue 1528, 2003, Pages 2017-2024

  Michor, Franziska ^a   Nowak, Martin A ^a   Frank, Steven A ^b   Iwasa, Yoh ^c  

^a HARVARD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c KYUSHU UNIVERSITY   (Japan)

Author keywords

Cancer; Mathematical model; Stem cells

Indexed keywords

CANCER;

ARTICLE; CALCULATION; CANCER CELL; CELL DIVISION; CELL PROLIFERATION; MATHEMATICAL MODEL; MUTATION; PRIORITY JOURNAL; STEM CELL; STOCHASTIC MODEL; TISSUE FIXATION;

EID: 0141639747     PISSN: 09628452     EISSN: 14712970     Source Type: Journal    
DOI: 10.1098/rspb.2003.2483     Document Type: Article

References (45)

1. Armitage, P. & Doll, R. 1957 The age distribution of cancer and a multistage theory of carcinogenesis. Br. J. Cancer 11, 161-169.
2. Bach, S. P., Renehan, A. G. & Potten, C. S. 2000 Stem cells: the intestinal stem cell as a paradigm. Carcinogenesis 21, 469-476.
3. Bell, G. I. 1976 Models of carcinogenesis as an escape from mitotic inhibitors. Science 192, 569-572.
4. Boveri, T. 1914 Zur Frage der Entstchung maligner Tumoren. Jena, Germany: Gustav Fischer. English translation. The origin of malignant tumors by Boveri, M. 1929. Baltimore, MA: Williams and Wilkins.
5. Brittan, M. & Wright, N. A. 2002 Gastrointestinal stem cells. J. Pathol. 197, 492-509.
6. Cairns, J. 1975 Mutation, selection and the natural history of cancer. Nature 255, 197-200.
7. Cairns, J. 1981 The origin of human cancers. Nature 289, 353-357.
8. Cairns, J. 1998 Mutation and cancer: the antecedents to our studies of adaptive mutation. Genetics 148, 1433-1440.
9. Cairns, J. 2002 Somatic stem cells and the kinetics of mutagenesis and carcinogenesis. Proc. Natl Acad. Sci. USA 99, 10 567-10 570.
10. Chaplain, M. A. J. 1995 The mathematical modelling of tumour angiogenesis and invasion. Acta Biotheoretica 43, 387-402.
11. Durrett, R. 2002 Probability models for DNA sequence evolution. New York: Springer.
12. Fisher, J. C. 1958 Multiple mutation theory of carcinogenesis. Nature 181, 651-652.
13. Frank, S. A. & Nowak, M. A. 2003 Cell biology: developmental predisposition to cancer. Nature 422, 494.
14. Frank, S. A., Iwasa, Y. & Nowak, M. A. 2003 Patterns of cell division and the risk of cancer. Genetics 163, 1527-1532.
15. Gatenby, R. A. & Gawlinski, E. T. 1996 A reaction-diffusion model of cancer invasion. Cancer Res. 56, 5745-5753.
16. Gatenby, R. A. & Maini, P. K. 2003 Cancer summed up. Nature 421, 321.
17. Hahn, W. C. & Weinberg, R. A. 2002 Rules for making human tumor cells. New Eng. J. Med. 347, 1593-1603.
18. Iizuka, M. & Ogura, Y. 1991 Convergence of one-dimensional diffusion processes to a jump process related to population genetics. J. Math. Biol. 29, 671-687.
19. Janes, S. M., Lowell, S. & Hutter, C. 2002 Epidermal stem cells. J. Pathol. 197, 479-491.
20. Kimura, M. 1968 Evolutionary rate at the molecular level. Nature 217, 624-626.
21. Kimura, M. & Ohta, K. 1968 The average number of generations until fixation of a mutant gene in a finite population. Genetics 61, 763-771.
22. Kinzler, K. W. & Vogelstein, B. 1997 Gatekeepers and caretakers. Nature 386, 761-763.
23. Kinzler, K. W. & Vogelstein, B. 1998 The genetic basis of human cancer. Toronto, CA: McGraw-Hill.
24. Knudson, A. G. 1971 Mutation and cancer: statistical study of retinoblastoma. Proc. Natl Acad. Sci. USA 68, 820-823.
25. Knudson, A. G. 2001 Two genetic hits to cancer. Nature Rev. Cancer 1, 157-162.
26. Komarova, N. L., Lengauer, C., Vogelstein, B. & Nowak, M. A. 2003 Dynamics of genetic instability in sporadic and familial colorectal cancer. Cancer Biol. Therapy 1, 685-692.
27. Lengauer, C., Kinzler, K. W. & Vogelstein, B. 1998 Genetic instabilities in human cancers. Nature 396, 643-649.
28. Levine, A. J. 1993 The tumor suppressor genes. A. Rev. Biochem. 62, 623-651.
29. Little, M. P. & Wright, E. G. 2003 Stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math. Biosci. 183, 111-134.
30. Luebeck, E. G. & Moolgavkar, S. H. 2002 Multistage carcinogenesis and the incidence of colorectal cancer. Proc. Natl Acad. Sci. USA 99, 15 095-15 100.
31. Marshak, D. R., Gardner, R. L. & Gottleib, D. 2001 Stem cell biology. New York: Cold Spring Harbor Laboratory Press.
32. Michor, F., Iwasa, Y., Komarova, N. L. & Nowak, M. A. 2003 Local regulation of homeostasis favors chromosomal instability. Curr. Biol. 13, 581-584.
33. Mintz, B. 1971 Clonal basis of mammalian differentiation. Symp. Soc. Exp. Biol. 25, 345-370.
34. Mintz, B. 1977 Malignancy versus normal differentiation of stem cells as analyzed in genetically mosaic animals. Adv. Pathobiol. 6, 153-157.
35. Mitelman, F., Johansson, B. & Mertens, F. 1994 Catalog of chromosome aberrations in cancer, vol. 2. New York: Wiley-Liss.
36. Moolgavkar, S. H. & Knudson, A. G. 1981 Mutation and cancer: a model for human carcinogenesis. J. Natl Cancer Inst. 66, 1037-1052.
37. Moran, P. 1962 The statistical processes of evolutionary theory. Oxford: Clarendon.
38. Muller, H. J. 1927 Artificial transmutation of the gene. Science 46, 84-87.
39. Nowak, M. A., Komarova, N. L., Sengupta, A., Jallepalli, P. V., Shih, I.-M., Vogelstein, B. & Lengauer, C. 2002 The role of chromosomal instability in tumor initiation. Proc. Natl Acad. Sci. USA 99, 16 226-16 231.
40. Sherratt, J. A. & Nowak, M. A. 1992 Oncogenes, anti-oncogenes and the immune response to cancer: a mathematical model. Proc. R. Soc. Lond. B 248, 261-271.
41. Tannishtha, R., Morrison, S. J., Clarke, M. F. & Weissman, I. L. 2001 Stem cells, cancer, and cancer stem cells. Nature 414, 105.
42. Tomlinson, I. P. M., Novelli, M. R. & Bodmer, W. F. 1996 The mutation rate and cancer. Proc. Natl Acad. Sci. USA 93, 14 800-14 803.
43. Turksen, K. & Troy, T. C. 1998 Epidermal cell lineage. Biochem. Cell Biol. 76, 889-898.
44. Wheldon, T. E. 1988 Mathematical models in cancer research. Bristol, UK: IOP Publishing Ltd.
45. Winton, D. J. & Ponder, B. A. 1990 Stem-cell organization in mouse small intestine. Proc. R. Soc. Lond. B 241, 13-18.