A rapid-mutation approximation for cell population dynamics

Bulletin of Mathematical Biology

Volumn 72, Issue 2, 2010, Pages 359-374

  Sachs, Rainer K ^a   Hlatky, Lynn ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b TUFTS UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Carcinogenesis; Evolutionary ecology; Fitness alterations; Proliferation; Replicator mutator equations; Somatic cell population diversity

Indexed keywords

ALGORITHM; ANEUPLOIDY; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CELL COMMUNICATION; CELL PROLIFERATION; CELL TRANSFORMATION; GENE DOSAGE; GENETICS; HORIZONTAL GENE TRANSFER; MOUSE; MUTATION; NEOPLASM; PATHOLOGY; PROBABILITY;

ALGORITHMS; ANEUPLOIDY; ANIMALS; CELL COMMUNICATION; CELL PROLIFERATION; CELL TRANSFORMATION, NEOPLASTIC; GENE DOSAGE; GENE TRANSFER, HORIZONTAL; MARKOV CHAINS; MICE; MODELS, GENETIC; MUTATION; NEOPLASMS;

EID: 77951220871     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-009-9450-6     Document Type: Article

References (38)

1. Bjerkvig, R., Tysnes, B. B., Aboody, K. S., Najbauer, J., Terzis, A. J., 2005. Opinion: the origin of the cancer stem cell: current controversies and new insights. Nat. Rev. Cancer 5, 899-904.
2. Born, M., Wolf, E., Bhatia, A. B., 1999. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press, Cambridge.
3. Chi, Y. H., Jeang, K. T., 2007. Aneuploidy and cancer. J. Cell. Biochem. 102, 531-8.
4. Chin, L., Gray, J. W., 2008. Translating insights from the cancer genome into clinical practice. Nature 452, 553-63.
5. Coller, H. A., Khrapko, K., Bodyak, N. D., Nekhaeva, E., Herrero-Jimenez, P., Thilly, W. G., 2001. High frequency of homoplasmic mitochondrial DNA mutations in human tumors can be explained without selection. Nat. Genet. 28, 147-50.
6. Duesberg, P., Li, R., Fabarius, A., Hehlmann, R., 2005. The chromosomal basis of cancer. Cell. Oncol. 27, 293-318.
7. Duesberg, P., Li, R., Sachs, R., Fabarius, A., Upender, M. B., Hehlmann, R., 2007. Cancer drug resistance: The central role of the karyotype. Drug Resist. Updat.
8. Eshleman, J. R., Casey, G., Kochera, M. E., Sedwick, W. D., Swinler, S. E., Veigl, M. L., Willson, J. K., Schwartz, S., Markowitz, S. D., 1998. Chromosome number and structure both are markedly stable in RER colorectal cancers and are not destabilized by mutation of p53. Oncogene 17, 719-25.
9. Frank, S. A., Nowak, M. A., 2004. Problems of somatic mutation and cancer. Bioessays 26, 291-9.
10. Gatenby, R. A., Vincent, T. L., 2003. An evolutionary model of carcinogenesis. Cancer Res. 63, 6212-20.
11. Griffiths, D. J., 2004. Introduction to Quantum Mechanics. Pearson/Prentice Hall, Upper Saddle River.
12. Gusev, Y., Kagansky, V., Dooley, W. C., 2001. Long-term dynamics of chromosomal instability in cancer: a transition probability model. Math. Comput. Model. 33, 1253-1273.
13. Hofbauer, J., Sigmund, K., 1998. Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge.
14. Iwasa, Y., Michor, F., Nowak, M. A., 2004. Stochastic tunnels in evolutionary dynamics. Genetics 166, 1571-9.
15. Jin, Y., Jin, C., Lv, M., Tsao, S. W., Zhu, J., Wennerberg, J., Mertens, F., Kwong, Y. L., 2005. Karyotypic evolution and tumor progression in head and neck squamous cell carcinomas. Cancer Genet. Cytogenet. 156, 1-7.
16. Kijima, M., 1997. Markov Processes for Stochastic Modeling. Cambridge University Press, Cambridge.
17. Komarova, N. L., 2005. Mathematical modeling of tumorigenesis: mission possible. Curr. Opin. Oncol. 17, 39-43.
18. Li, L., McCormack, A. A., Nicholson, J. M., Fabarius, A., Hehlmann, R., Sachs, R. K., Duesberg, P. H., 2009. Cancer-causing karyotypes: chromosomal equilibria between destabilizing aneuploidy and stabilizing selection for oncogenic function. Cancer Genet. Cytogenet. 188, 1-25.
19. Little, M. P., Vineis, P., Li, G., 2008. A stochastic carcinogenesis model incorporating multiple types of genomic instability fitted to colon cancer data. J. Theor. Biol. 254, 229-38.
20. Macville, M., Schrock, E., Padilla-Nash, H., Keck, C., Ghadimi, B. M., Zimonjic, D., Popescu, N., Ried, T., 1999. Comprehensive and definitive molecular cytogenetic characterization of HeLa cells by spectral karyotyping. Cancer Res. 59, 141-50.
21. Marx, C., Posch, H. A., Thirring, W., 2007. Emergence of order in selection-mutation dynamics. Phys. Rev. E 75, 061109.
22. Merlo, L. M., Pepper, J. W., Reid, B. J., Maley, C. C., 2006. Cancer as an evolutionary and ecological process. Nat. Rev. Cancer 6, 924-35.
23. Michor, F., Frank, S. A., May, R. M., Iwasa, Y., Nowak, M. A., 2003. Somatic selection for and against cancer. J. Theor. Biol. 225, 377-82.
24. Michor, F., Hughes, T. P., Iwasa, Y., Branford, S., Shah, N. P., Sawyers, C. L., Nowak, M. A., 2005. Dynamics of chronic myeloid leukaemia. Nature 435, 1267-70.
25. Minc, H., 1988. Nonnegative Matrices. Wiley, New York.
26. Mitelman, F., Johansson, B., Mertens, F., 2007. The impact of translocations and gene fusions on cancer causation. Nat. Rev. Cancer 7, 233-45.
27. Moolgavkar, S. H., Luebeck, E. G., 2003. Multistage carcinogenesis and the incidence of human cancer. Genes Chromosomes Cancer 38, 302-6.
28. Nagy, J. D., 2004. Competition and natural selection in a mathematical model of cancer. Bull. Math. Biol. 66, 663-87.
29. Nowell, P. C., 1976. The clonal evolution of tumor cell populations. Science 194, 23-8.
30. Page, K. M., Nowak, M. A., 2002. Unifying evolutionary dynamics. J. Theor. Biol. 219, 93-8.
31. Roschke, A. V., Stover, K., Tonon, G., Schaffer, A. A., Kirsch, I. R., 2002. Stable karyotypes in epithelial cancer cell lines despite high rates of ongoing structural and numerical chromosomal instability. Neoplasia 4, 19-31.
32. Sachs, R. K., Chan, M., Hlatky, L., Hahnfeldt, P., 2005. Modeling intercellular interactions during carcinogenesis. Radiat. Res. 164, 324-31.
33. Sachs, R. K., Shuryak, I., Brenner, D., Fakir, H., Hlatky, L., Hahnfeldt, P., 2007. Second cancers after fractionated radiotherapy: Stochastic population dynamics effects. J. Theor. Biol. 249, 518-531.
34. Tan, W., 2002. Stochastic Models with Applications to Genetics, Cancers, AIDS, and Other Biomedical Systems. World Scientific, Singapore.
35. Thompson, S. L., Compton, D. A., 2008. Examining the link between chromosomal instability and aneuploidy in human cells. J. Cell. Biol. 180, 665-72.
36. Vucic, E. A., Brown, C. J., Lam, W. L., 2008. Epigenetics of cancer progression. Pharmacogenomics 9, 215-34.
37. Weinberg, R. A., 2007. The Biology of Cancer. Garland Science, New York. Chaps. 13 and 15.
38. Yuen, K. W., Desai, A., 2008. The wages of CIN. J. Cell. Biol. 180, 661-3.