Mutation Accumulation Simulator: Armitage-Doll Multi-Hit Cancer Model

simulator advanced ~12 min
Loading simulation...
Cumulative cancer probability by age 70: ~22% with 6 required hits

With a per-division mutation rate of 10⁻⁷, DNA repair efficiency of 99.9%, 10¹³ cell divisions per year, and 6 required driver mutations, the Armitage-Doll model predicts approximately 22% cumulative cancer probability by age 70 — consistent with observed lifetime cancer rates in developed countries.

Formula

P(cancer by age t) ≈ 1 − exp(−μ^k · N · t^k / k!)
Incidence rate I(t) ∝ μ^k · N · k · t^(k−1) / k!
log(I) ≈ (k−1)·log(t) + constant
μ_effective = μ_base × (1 − repair_efficiency)

Cancer as an Evolutionary Process

Cancer is evolution in miniature. Within the body, cells compete for resources, acquire mutations that enhance their proliferative capacity, and undergo natural selection favoring unchecked growth. The Armitage-Doll multi-hit model, published in 1954, provided the first quantitative framework linking somatic mutation accumulation to the dramatic age-dependence of cancer incidence — one of the most important insights in cancer biology.

The Multi-Hit Model

The model proposes that a normal cell must acquire k specific, rate-limiting mutations to become cancerous. If each mutation occurs independently at rate μ per cell division, and the body performs N cell divisions per year, then the probability of cancer by age t follows:

P(cancer by age t) ≈ 1 − exp(−μ^k · N · t^k / k!)

The key prediction: on a log-log plot of cancer incidence versus age, the data should fall on a straight line with slope k−1. Empirical data for most adult epithelial cancers show slopes of 4-6, suggesting 5-7 rate-limiting steps — remarkably consistent with the number of driver mutations identified by modern cancer genomics.

DNA Repair: The Guardian Against Drift

The raw mutation rate per cell division is approximately 10⁻⁷ per base pair, but DNA repair mechanisms correct the vast majority of errors. The effective mutation rate is μ_eff = μ_base × (1 − repair_efficiency). With 99.9% repair efficiency, the effective rate drops a thousandfold. This is why inherited defects in DNA repair genes (BRCA1, BRCA2, mismatch repair genes in Lynch syndrome) cause such dramatic increases in cancer risk — they shift the effective mutation rate by orders of magnitude.

From Armitage-Doll to Modern Genomics

Bert Vogelstein's landmark work on colorectal cancer identified the specific sequence of mutations required: APC → KRAS → SMAD4 → TP53, each conferring a selective growth advantage. This molecular confirmation of the multi-hit model, combined with large-scale cancer genome sequencing, has validated Armitage and Doll's 1954 insight with extraordinary precision.

Tomasetti and Vogelstein (2015) extended this framework by showing that cancer risk across different tissues correlates strongly with the number of stem cell divisions — the 'bad luck' component of cancer that is a direct consequence of unavoidable replication errors, exactly as the multi-hit model predicts.

Using the Simulator

Adjust the mutation rate and DNA repair efficiency to see how they interact. Notice that the number of hits (k) controls the steepness of the age-incidence curve: k=2 gives a shallow curve (as in retinoblastoma, consistent with Knudson's two-hit hypothesis), while k=6 gives the steep power-law increase typical of adult carcinomas. The animated DNA strand below shows mutations accumulating in real time — a visual reminder that cancer is, fundamentally, a disease of accumulated DNA damage.

FAQ

What is the Armitage-Doll model?

The Armitage-Doll model (1954) proposes that cancer arises when a single cell accumulates k specific mutations ('hits'). Since each hit occurs independently at a low rate, the probability of cancer increases as a power of age: incidence ∝ t^(k-1). This explains why cancer incidence rises dramatically with age.

Why does cancer risk increase with age?

Each cell division carries a small probability of a DNA replication error. Over a lifetime of ~10¹⁶ total cell divisions, mutations accumulate. The multi-hit model shows that the probability of accumulating all k required mutations in one cell grows as age^k, producing the steep age-incidence curves observed epidemiologically.

What is the multi-hit hypothesis of cancer?

The multi-hit hypothesis states that cancer requires multiple specific genetic alterations (typically 4-7 driver mutations) in a single cell lineage. Each mutation provides a selective growth advantage, and the final combination transforms a normal cell into a cancerous one. This was first proposed by Nordling (1953) and formalized by Armitage and Doll (1954).

How does DNA repair affect cancer risk?

DNA repair mechanisms correct the vast majority (>99.9%) of replication errors before they become permanent mutations. Inherited deficiencies in DNA repair genes (e.g., BRCA1/2, mismatch repair genes) dramatically increase the effective mutation rate, explaining why carriers have 5-10x higher cancer risk.

Sources

Embed

<iframe src="https://homo-deus.com/lab/evolution/mutation-accumulation/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub