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Dynamics of cancer progression

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?

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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.

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Acknowledgements

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

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Correspondence to Martin A. Nowak.

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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.

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

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