Abstract
Individual instances of cancer are primarily a result of a combination of a small number of genetic mutations (hits). Knowing the number of such mutations is a prerequisite for identifying specific combinations of carcinogenic mutations and understanding the etiology of cancer. We present a mathematical model for estimating the number of hits based on the distribution of somatic mutations. The model is fundamentally different from previous approaches, which are based on cancer incidence by age. Our somatic mutation based model is likely to be more robust than age-based models since it does not require knowing or accounting for the highly variable mutation rate, which can vary by over three orders of magnitude. In fact, we find that the number of somatic mutations at diagnosis is weakly correlated with age at cancer diagnosis, most likely due to the extreme variability in mutation rates between individuals. Comparing the distribution of somatic mutations predicted by our model to the actual distribution from 6904 tumor samples we estimate the number of hits required for carcinogenesis for 17 cancer types. We find that different cancer types exhibit distinct somatic mutational profiles corresponding to different numbers of hits. Why might different cancer types require different numbers of hits for carcinogenesis? The answer may provide insight into the unique etiology of different cancer types.
Highlights
Cancer is known to result primarily from genetic mutations [1,2,3]
We present a mathematical model for predicting the distribution of somatic mutations as a function of the number of hits and combination, the multi-combination multi-hit model of carcinogenesis
We compare the distribution calculated by the model to the actual distribution in somatic mutations to estimate the number of hits required for carcinogenesis
Summary
Models of carcinogenesis–the multi-stage and multi-hit models–suggest that cancer results from a small number of (two–seven) mutations [4,5,6,7,8,9,10,11]. The availability of extensive genomic data [12, 13] and decades of investigation have failed to reveal, for the vast majority of cancers, the specific mutations that result in carcinogenesis. Carcinogenesis is a result of one of many possible combinations of a small number of hits. A reliable estimate for the number of such hits will help us understand how cancers originate, and to find the specific combination of mutations responsible for individual instances of cancer [14]. Estimates from current mathematical models are questionable because they are based on simple assumptions about mutation rate, which can vary by over three orders of magnitude as discussed below [4, 15,16,17,18,19]
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