Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Dynamics of cancer progression

Nature Reviews Cancer volume 4, pages 197–205 (2004)Cite this article

Key Points

  • Cancer is principally caused by mutations in cancer-susceptibility genes, which include oncogenes, tumor-suppressor genes (TSGs) and genes causing genetic instability. Cancer arises when a single cellular lineage receives multiple mutations.

  • Epithelial tissues are subdivided into compartments, and cancer initiation occurs in compartments. Within each compartment, there is a continuous turnover of cells. Each compartment is replenished by division and differentiation of a small number of stem cells. In a healthy tissue, homeostatic mechanisms maintain constant cell numbers.

  • Mathematical models describe the process of cancer initiation and progression and provide a quantitative understanding of the dynamics of tumorigenesis with respect to mutation, selection, genetic instability and tissue architecture.

  • Mutations that activate oncogenes can confer a selective advantage to the cell. We calculate the time until a cellular lineage with an activated oncogene arises and takes over a population of cells.

  • Inactivating both alleles of a TSG also leads to a selective advantage to the cell. The dynamics of TSG inactivation are described by three kinetic laws that depend on the size of the cellular population and the mutation rates. In small, intermediate and large populations, a TSG is inactivated, respectively, by two, one and zero rate-limiting hits.

  • Chromosomal instability (CIN) accelerates the rate of TSG inactivation.

  • It takes two rate-limiting hits to inactivate a TSG in a small population of cells with or without CIN. Therefore, CIN mutations can occur early in tumorigenesis.

  • Knudson's two-hit hypothesis is compatible with the idea that one mutation occurs in the first allele of the TSG and one mutation occurs in a CIN gene. The mutation inactivating the second TSG allele is not rate-limiting in a CIN cell.

  • Because of the tremendous acceleration of loss of heterozygosity in CIN cells, it is very likely that most cancers, which require inactivation of at least two TSGs in rate-limiting scenarios, are initiated by CIN mutations, even if CIN has a severe cost in terms of somatic fitness.

Abstract

Evolutionary concepts such as mutation and selection can be best described when formulated as mathematical equations. Cancer arises as a consequence of somatic evolution. Therefore, a mathematical approach can be used to understand the process of cancer initiation and progression. But what are the fundamental principles that govern the dynamics of activating oncogenes and inactivating tumour-suppressor genes in populations of reproducing cells? Also, how does a quantitative theory of somatic mutation and selection help us to evaluate the role of genetic instability?

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Oncogene dynamics.
Figure 2: Tumour-suppressor gene dynamics.
Figure 3: Emergence of chromosomal instability during inactivation of one tumour-suppressor gene.
Figure 4: Emergence of chromosomal instability during inactivation of two tumour-suppressor genes.
Figure 5: Minimum number of chromosomal-instability (CIN) genes needed to ensure that CIN arises before the inactivation of one or two tumour-suppressor genes.

References

  1. Vogelstein, B. & Kinzler, K. W. The Genetic Basis of Human Cancer (McGraw–Hill, 1998).

    Google Scholar 

  2. Kinzler, K. W. & Vogelstein, B. Gatekeepers and caretakers. Nature 386, 761–763 (1997).

    Article  CAS  PubMed  Google Scholar 

  3. Rajagopalan, H., Nowak, M. A., Vogelstein, B. & Lengauer, C. The significance of unstable chromosomes in colorectal cancer. Nature Rev. Cancer 3, 695–701 (2003).

    Article  CAS  Google Scholar 

  4. Sieber, O. M., Heinimann, K. & Tomlinson, I. P. Genomic instability — the engine of tumorigenesis? Nature Rev. Cancer 3, 701–708 (2003).

    Article  CAS  Google Scholar 

  5. Bissell, M. J. & Radisky, D. Putting tumors in context. Nature Rev. Cancer 1, 46–54 (2001).

    Article  CAS  Google Scholar 

  6. Boveri, T. Zur Frage der Entstehung maligner Tumoren (Gustav Fischer, 1914). English translation: The origin of malignant tumors by Boveri, M. (Williams and Wilkins, 1929).

    Google Scholar 

  7. Muller, H. J. Artificial transmutation of the gene. Science 46, 84–87 (1927).

    Article  Google Scholar 

  8. Knudson, A. G. Two genetic hits to cancer. Nature Rev. Cancer 1, 157–162 (2001).

    Article  CAS  Google Scholar 

  9. Knudson, A. G. Mutation and cancer: statistical study of retinoblastoma. Proc. Natl Acad. Sci. USA 68, 820–823 (1971).

    Article  PubMed  PubMed Central  Google Scholar 

  10. Moolgavkar, S. H. & Knudson, A. G. Mutation and cancer: a model for human carcinogenesis. J. Natl Cancer Inst. 66, 1037–1052 (1981).

    Article  CAS  PubMed  Google Scholar 

  11. Cairns, J. Mutation selection and the natural history of cancer. Nature 255, 197–200 (1975).

    Article  CAS  PubMed  Google Scholar 

  12. Cairns, J. Somatic stem cells and the kinetics of mutagenesis and carcinogenesis. Proc. Natl Acad. Sci. USA 99, 10567–10570 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Frank, S. A., Iwasa, Y. & Nowak, M. A. Patterns of cell division and the risk of cancer. Genetics 163, 1527–1532 (2003).

    PubMed  PubMed Central  Google Scholar 

  14. Frank, S. A. & Nowak, M. A. Cell biology: developmental predisposition to cancer. Nature 422, 494 (2003).

    Article  CAS  PubMed  Google Scholar 

  15. Gatenby, R. A & Maini, P. K. Mathematical oncology: cancer summed up. Nature 421, 321 (2003).

    Article  CAS  PubMed  Google Scholar 

  16. Nordling, C. O. A new theory on cancer-inducing mechanism. Br. J. Cancer 7, 68–72 (1953).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Armitage, P. & Doll, R. The age distribution of cancer and a multi-stage theory of carcinogenesis. Br. J. Cancer 8, 1–12 (1954).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Armitage, P. & Doll, R. A two-stage theory of carcinogenesis in relation to the age distribution of human cancer. Br. J. Cancer 11, 161–169 (1957).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Fisher, J. C. Multiple-mutation theory of carcinogenesis. Nature 181, 651–652 (1959).

    Article  Google Scholar 

  20. Nunney, L. Lineage selection and the evolution of multistage carcinogenesis. Proc. Roy. Soc. Lond. B Biol. Sci. 266, 493–498 (1999).

    Article  CAS  Google Scholar 

  21. Tomlinson, I., Sasieni, P. & Bodmer, W. How many mutations in a cancer? Am. J. Pathol. 160, 755–758 (2002).

    Article  PubMed  PubMed Central  Google Scholar 

  22. Moolgavkar, S. H. & Knudson, A. G. Mutation and cancer: a model for human carcinogenesis. J. Natl Cancer Inst. 66, 1037–1052 (1981).

    Article  CAS  PubMed  Google Scholar 

  23. Luebeck, E. G. & Moolgavkar, S. H. Multistage carcinogenesis and the incidence of colorectal cancer. Proc. Natl Acad. Sci. USA 99, 15095–15100 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Grist, S. A., McCarron, M., Kutlaca, A., Turner, D. R. & Morley, A. A. In vivo human somatic mutation: frequency and spectrum with age. Mutat. Res. 266, 189–196 (1992).

    Article  CAS  PubMed  Google Scholar 

  25. Gatenby, R. A. & Vincent, T. L. An evolutionary model of carcinogenesis. Cancer Res. 63, 6212–6220 (2003).

    CAS  PubMed  Google Scholar 

  26. Goldie, J. H. & Coldman, A. J. A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate. Cancer Treat. Rep. 63, 1727–1733 (1979).

    CAS  PubMed  Google Scholar 

  27. Goldie, J. H & Coldman, A. J. Quantitative model for multiple levels of drug resistance in clinical tumors. Cancer Treat. Rep. 67, 923–931 (1983).

    CAS  PubMed  Google Scholar 

  28. Anderson, A. R. & Chaplain, M. A. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60, 857–899 (1998).

    Article  CAS  PubMed  Google Scholar 

  29. Owen, M. R. & Sherratt, J. A. Mathematical modeling of macrophage dynamics in tumors. Math. Models Methods Appl. Biol. Chem. 377, 675–684 (1999).

    Google Scholar 

  30. Chang, S., Khoo, C. & DePinho, R. A. Modeling chromosomal instability and epithelial carcinogenesis in the telomerase-deficient mouse. Semin. Cancer Biol. 11, 227–239 (2001).

    Article  CAS  PubMed  Google Scholar 

  31. Chang, S., Khoo, C., Naylor, M. L., Maser, R. S. & DePinho, R. A. Telomere-based crisis: functional differences between telomerase activation and ALT in tumor progression. Genes Dev. 17, 88–100 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. Maser, R. S. & DePinho, R. A. Connecting chromosomes, crisis, and cancer. Science 297, 565–569 (2002).

    Article  CAS  PubMed  Google Scholar 

  33. Taddei, F. et al. Role of mutator alleles in adaptive evolution. Nature 387, 700–702 (1997).

    Article  CAS  PubMed  Google Scholar 

  34. Otsuka, K. et al. Analysis of the human APC mutation spectrum in a saccharomyces cerevisiae strain with a mismatch repair defect. Int. J. Cancer 103, 624–630 (2003).

    Article  CAS  PubMed  Google Scholar 

  35. Strauss, B. S. Hypermutability in carcinogenesis. Genetics 148, 1619–1626 (1998).

    CAS  PubMed  PubMed Central  Google Scholar 

  36. Mintz, B. Clonal basis of mammalian differentiation. Symp. Soc. Exp. Biol. 25, 345–370 (1971).

    CAS  PubMed  Google Scholar 

  37. Michor, F., Nowak, M. A., Frank, S. A. & Iwasa, Y. Stochastic elimination of cancer cells. Proc. Roy. Soc. Lond. B Biol. Sci. 270, 2017–2024 (2003).

    Article  Google Scholar 

  38. Moran, P. The Statistical Processes of Evolutionary Theory (Clarendon Press, 1962).

    Google Scholar 

  39. Komarova, N. L., Sengupta, A. & Nowak, M. A. Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability. Jour. Theor Biol. 223, 433–450 (2003).

    Article  CAS  Google Scholar 

  40. Kimura, M. The role of compensatory neutral mutations in molecular evolution. J. Genet. 64, 7–19 (1985).

    Article  CAS  Google Scholar 

  41. Michor, F., Iwasa, Y., Komarova, N. L. & Nowak, M. A. Local regulation of homeostasis favors chromosomal instability. Curr. Biol. 13, 581–584 (2003).

    Article  CAS  PubMed  Google Scholar 

  42. Michor, F., Frank, S. A., May, R. M., Iwasa, Y. & Nowak, M. A. Somatic selection for and against cancer. J. Theor. Biol. 225, 337–382 (2003).

    Article  Google Scholar 

  43. Nowak, M. A., Michor, F. & Iwasa, Y. The linear process of somatic evolution. Proc. Natl Acad. Sci. USA 100, 14966–14969 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Michor, F., Iwasa, Y., Rajagopalan, H., Lengauer, C. & Nowak, M. A. Linear model of colon cancer initiation. Cell Cycle (in the press).

  45. Kunkel, T. A. & Bebenek, K. DNA replication fidelity. Annu. Rev. Biochem. 69, 497–529 (2000).

    Article  CAS  PubMed  Google Scholar 

  46. Bach, S. P., Renehan, A. G. & Potten, C. S. Stem cells: the intestinal stem cell as a paradigm. Carcinogenesis 21, 469–476 (2000).

    Article  CAS  PubMed  Google Scholar 

  47. Yatabe, Y., Tavare, S. & Shibata, D. Investigating stem cells in human colon by using methylation patterns. Proc. Natl Acad. Sci. USA 98, 10839–10844 (2001).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Weinberg, R. A. Tumor suppressor genes. Science 254, 1138–1146 (1991).

    Article  CAS  PubMed  Google Scholar 

  49. Levine, A. J. The tumor suppressor genes. Annu. Rev. Biochem. 62, 623–651 (1993).

    Article  CAS  PubMed  Google Scholar 

  50. Friend, S. H. et al. A human DNA segment with properties of the gene that predisposes to retinoblastoma and osteosarcoma. Nature 323, 643–646 (1986).

    Article  CAS  PubMed  Google Scholar 

  51. Iwasa, Y., Michor, F. & Nowak, M. A. Stochastic tunnels in evolutionary dynamics. Genetics, (in the press).

  52. Nowak, M. A. et al. The role of chromosomal instability in tumor initiation. Proc. Natl Acad. Sci. USA 99, 16226–16231 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Lengauer, C., Kinzler, K. W. & Vogelstein, B. Genetic instabilities in human cancers. Nature 396, 623–649 (1998).

    Article  Google Scholar 

  54. Nasmyth, K. Segregating sister genomes: the molecular biology of chromosome separation. Science 297, 559–565 (2002).

    Article  CAS  PubMed  Google Scholar 

  55. Kolodner, R. D., Putnam, C. D. & Myung, K. Maintenance of genome stability in Saccharomyces cerevisiae. Science 297, 552–557 (2002).

    Article  CAS  PubMed  Google Scholar 

  56. Shonn, M. A., McCarroll, R. & Murray, A. W. Requirement of the spindle checkpoint for proper chromosome segregation in budding yeast meiosis. Science 289, 300–303 (2000).

    Article  CAS  PubMed  Google Scholar 

  57. Rajagopalan, H. et al. Inactivation of hCDC4 can cause chromosomal instability. Nature (in the press).

  58. Loeb, L. A. Mutator phenotype may be required for multistage carcinogenesis. Cancer Res. 51, 3075–3079 (1991).

    CAS  PubMed  Google Scholar 

  59. Sieber, O. M. et al. Analysis of chromosomal instability in human colorectal adenomas with two mutational hits at APC. Proc. Natl Acad. Sci. USA 99, 16910–16915 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Tomlinson, I. P., Novelli, M. R. & Bodmer, W. F. The mutation rate and cancer. Proc. Natl Acad. Sci. USA 93, 14800–14803 (1996).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Little, M. P. & Wright, E. G. A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math. Biosciences 183, 111–134 (2003).

    Article  CAS  Google Scholar 

  62. Wodarz, D. & Krakauer, D. C. Genetic instability and the evolution of angiogenic tumor cell lines. Oncol. Rep. 8, 1195–1201 (2001).

    CAS  PubMed  Google Scholar 

  63. Plotkin, J. B. & Nowak, M. A. The different effects of apoptosis and DNA repair on tumorigenesis. J. Theor. Biol. 214, 452–467 (2002).

    Article  Google Scholar 

  64. Komarova, N. L., Lengauer, C., Vogelstein, B. & Nowak, M. A. Dynamics of genetic instability in sporadic and familial colorectal cancer. Cancer Biol. Ther. 1, 685–692 (2002).

    Article  CAS  PubMed  Google Scholar 

  65. Bardelli, A. et al. Carcinogen-specific induction of genetic instability. Proc. Natl Acad. Sci. USA 98, 5770–5775 (2001).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Nowak, M. A. & Sigmund, K. Evolutionary dynamic of biological games. Science 303, 793–799 (2004).

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

We thank C. Lengauer for discussion. Support from J. Epstein is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, 02138, MA, USA

    Franziska Michor & Martin A. Nowak

  2. Department of Biology, Kyushu University, Fukuoka, 812-8581, Japan

    Yoh Iwasa

Authors
  1. Franziska Michor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yoh Iwasa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin A. Nowak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin A. Nowak.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Related links

Related links

DATABASES

LocusLink

CDC4

RB

OMIM

ataxia telangiectasia

Bloom syndrome

familial adenomatous polyposis

Werner syndrome

Glossary

SELECTION

The process of survival of the fittest by which organisms that adapt to their environment survive and those that do not adapt disappear.

FIXATION

A state in which every individual in a population is identical with respect to a particular mutation.

RANDOM DRIFT

Changes in the genetic composition of a population due to probabilistic events.

MORAN PROCESS

Stochastic process that is used to describe the dynamics within a population with strictly constant population size.

STEM CELL

A precursor cell that can self renew and undergo clonal, multilineage differentiation.

MITOTIC RECOMBINATION

The exchange — reciprocal or nonreciprocal — of genetic material between one DNA molecule and a homologous region of DNA that occurs during mitotic cell divisions.

NON-DISJUNCTION

An error in cell division in which the chromosomes fail to disjoin, so that both pass to the same daughter cell.

LOSS OF HETEROZYGOSITY

At a particular locus that is heterozygous for a mutant allele and a normal allele, a deletion or other mutational event within the normal allele renders the cell either hemizygous (one mutant allele and one deleted allele) or homozygous for the mutant allele.

MISMATCH REPAIR

A DNA-repair mechanism that corrects nucleotide sequence errors made during DNA replication by excising the defective sequence and replacing it with the correct sequence.

MICROSATELLITE INSTABILITY

Genetic instability because of mismatch-repair deficiency involving subtle sequence changes that alter one or a few base pairs.

BUB1 AND MAD2

Their gene products act cooperatively to prevent unequal sister chromatid separation by inhibiting the anaphase-promoting complex.

BRCA2

Its gene product is implicated in DNA repair and recombination, and checkpoint control of the cell cycle. In mice, its loss might result in chromosomal instability.

DOMINANT-NEGATIVE MUTATION

A mutation whose gene product adversely affects the wild-type gene product within the same cell, often by dimerizing with it.

BLM AND WRN

Their gene products participate in DNA-repair pathways, particularly those that repair double-strand DNA breaks, and their loss results in genetic instability.

NUCLEOTIDE-EXCISION REPAIR

A DNA-repair mechanism that excises and replaces damaged DNA bases.

ATM

Its gene product functions in X-ray-induced DNA-repair mechanisms.

APC

A tumour-suppressor that is thought to initiate colorectal tumorigenesis. Mutation of APC leads to increased β-catenin-mediated transcription of growth-promoting genes.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Michor, F., Iwasa, Y. & Nowak, M. Dynamics of cancer progression. Nat Rev Cancer 4, 197–205 (2004). https://doi.org/10.1038/nrc1295

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/nrc1295

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing