Abstract
Tissues of multicellular organisms consist of stem cells and differentiated cells. Stem cells divide to produce new stem cells or differentiated cells. Differentiated cells divide to produce new differentiated cells. We show that such a tissue design can reduce the rate of fixation of mutations that increase the net proliferation rate of cells. It has, however, no consequence for the rate of fixation of neutral mutations. We calculate the optimum relative abundance of stem cells that minimizes the rate of generating cancer cells. There is a critical fraction of stem cell divisions that is required for a stochastic elimination ('wash out') of cancer cells.
Full Text
The Full Text of this article is available as a PDF (562.2 KB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- ARMITAGE P., DOLL R. A two-stage theory of carcinogenesis in relation to the age distribution of human cancer. Br J Cancer. 1957 Jun;11(2):161–169. doi: 10.1038/bjc.1957.22. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Bach S. P., Renehan A. G., Potten C. S. Stem cells: the intestinal stem cell as a paradigm. Carcinogenesis. 2000 Mar;21(3):469–476. doi: 10.1093/carcin/21.3.469. [DOI] [PubMed] [Google Scholar]
- Bell G. I. Models of carcinogenesis as an escape from mitotic inhibitors. Science. 1976 May 7;192(4239):569–572. doi: 10.1126/science.130679. [DOI] [PubMed] [Google Scholar]
- Brittan Mairi, Wright Nicholas A. Gastrointestinal stem cells. J Pathol. 2002 Jul;197(4):492–509. doi: 10.1002/path.1155. [DOI] [PubMed] [Google Scholar]
- Cairns J. Mutation and cancer: the antecedents to our studies of adaptive mutation. Genetics. 1998 Apr;148(4):1433–1440. doi: 10.1093/genetics/148.4.1433. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Cairns J. Mutation selection and the natural history of cancer. Nature. 1975 May 15;255(5505):197–200. doi: 10.1038/255197a0. [DOI] [PubMed] [Google Scholar]
- Cairns J. The origin of human cancers. Nature. 1981 Jan 29;289(5796):353–357. doi: 10.1038/289353a0. [DOI] [PubMed] [Google Scholar]
- Chaplain M. A. The mathematical modelling of tumour angiogenesis and invasion. Acta Biotheor. 1995 Dec;43(4):387–402. doi: 10.1007/BF00713561. [DOI] [PubMed] [Google Scholar]
- FISHER J. C. Multiple-mutation theory of carcinogenesis. Nature. 1958 Mar 1;181(4609):651–652. doi: 10.1038/181651b0. [DOI] [PubMed] [Google Scholar]
- Frank Steven A., Iwasa Yoh, Nowak Martin A. Patterns of cell division and the risk of cancer. Genetics. 2003 Apr;163(4):1527–1532. doi: 10.1093/genetics/163.4.1527. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Frank Steven A., Nowak Martin A. Cell biology: Developmental predisposition to cancer. Nature. 2003 Apr 3;422(6931):494–494. doi: 10.1038/422494a. [DOI] [PubMed] [Google Scholar]
- Gatenby R. A., Gawlinski E. T. A reaction-diffusion model of cancer invasion. Cancer Res. 1996 Dec 15;56(24):5745–5753. [PubMed] [Google Scholar]
- Gatenby Robert A., Maini Philip K. Mathematical oncology: cancer summed up. Nature. 2003 Jan 23;421(6921):321–321. doi: 10.1038/421321a. [DOI] [PubMed] [Google Scholar]
- Hahn William C., Weinberg Robert A. Rules for making human tumor cells. N Engl J Med. 2002 Nov 14;347(20):1593–1603. doi: 10.1056/NEJMra021902. [DOI] [PubMed] [Google Scholar]
- Iizuka M., Ogura Y. Convergence of one-dimensional diffusion processes to a jump process related to population genetics. J Math Biol. 1991;29(7):671–687. doi: 10.1007/BF00163918. [DOI] [PubMed] [Google Scholar]
- Janes Sam M., Lowell Sally, Hutter Caroline. Epidermal stem cells. J Pathol. 2002 Jul;197(4):479–491. doi: 10.1002/path.1156. [DOI] [PubMed] [Google Scholar]
- Kimura M. Evolutionary rate at the molecular level. Nature. 1968 Feb 17;217(5129):624–626. doi: 10.1038/217624a0. [DOI] [PubMed] [Google Scholar]
- Kimura M., Ohta T. The Average Number of Generations until Fixation of a Mutant Gene in a Finite Population. Genetics. 1969 Mar;61(3):763–771. doi: 10.1093/genetics/61.3.763. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Kinzler K. W., Vogelstein B. Cancer-susceptibility genes. Gatekeepers and caretakers. Nature. 1997 Apr 24;386(6627):761–763. doi: 10.1038/386761a0. [DOI] [PubMed] [Google Scholar]
- Knudson A. G., Jr Mutation and cancer: statistical study of retinoblastoma. Proc Natl Acad Sci U S A. 1971 Apr;68(4):820–823. doi: 10.1073/pnas.68.4.820. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Knudson A. G. Two genetic hits (more or less) to cancer. Nat Rev Cancer. 2001 Nov;1(2):157–162. doi: 10.1038/35101031. [DOI] [PubMed] [Google Scholar]
- Komarova Natalia L., Lengauer Christoph, Vogelstein Bert, Nowak Martin A. Dynamics of genetic instability in sporadic and familial colorectal cancer. Cancer Biol Ther. 2002 Nov-Dec;1(6):685–692. doi: 10.4161/cbt.321. [DOI] [PubMed] [Google Scholar]
- Lengauer C., Kinzler K. W., Vogelstein B. Genetic instabilities in human cancers. Nature. 1998 Dec 17;396(6712):643–649. doi: 10.1038/25292. [DOI] [PubMed] [Google Scholar]
- Levine A. J. The tumor suppressor genes. Annu Rev Biochem. 1993;62:623–651. doi: 10.1146/annurev.bi.62.070193.003203. [DOI] [PubMed] [Google Scholar]
- Little M. P., Wright E. G. A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math Biosci. 2003 Jun;183(2):111–134. doi: 10.1016/s0025-5564(03)00040-3. [DOI] [PubMed] [Google Scholar]
- Michor Franziska, Iwasa Yoh, Komarova Natalia L., Nowak Martin A. Local regulation of homeostasis favors chromosomal instability. Curr Biol. 2003 Apr 1;13(7):581–584. doi: 10.1016/s0960-9822(03)00172-6. [DOI] [PubMed] [Google Scholar]
- Mintz B. Clonal basis of mammalian differentiation. Symp Soc Exp Biol. 1971;25:345–370. [PubMed] [Google Scholar]
- Mintz B. Malignancy vs. normal differentiation of stem cells as analyzed in genetically mosaic animals. Adv Pathobiol. 1977;(6):153–157. [PubMed] [Google Scholar]
- Moolgavkar S. H., Knudson A. G., Jr Mutation and cancer: a model for human carcinogenesis. J Natl Cancer Inst. 1981 Jun;66(6):1037–1052. doi: 10.1093/jnci/66.6.1037. [DOI] [PubMed] [Google Scholar]
- Muller H. J. ARTIFICIAL TRANSMUTATION OF THE GENE. Science. 1927 Jul 22;66(1699):84–87. doi: 10.1126/science.66.1699.84. [DOI] [PubMed] [Google Scholar]
- Reya T., Morrison S. J., Clarke M. F., Weissman I. L. Stem cells, cancer, and cancer stem cells. Nature. 2001 Nov 1;414(6859):105–111. doi: 10.1038/35102167. [DOI] [PubMed] [Google Scholar]
- Sherratt J. A., Nowak M. A. Oncogenes, anti-oncogenes and the immune response to cancer: a mathematical model. Proc Biol Sci. 1992 Jun 22;248(1323):261–271. doi: 10.1098/rspb.1992.0071. [DOI] [PubMed] [Google Scholar]
- Turksen K., Troy T. C. Epidermal cell lineage. Biochem Cell Biol. 1998;76(6):889–898. doi: 10.1139/bcb-76-6-889. [DOI] [PubMed] [Google Scholar]
- Winton D. J., Ponder B. A. Stem-cell organization in mouse small intestine. Proc Biol Sci. 1990 Jul 23;241(1300):13–18. doi: 10.1098/rspb.1990.0059. [DOI] [PubMed] [Google Scholar]