A mutational model of carcinogenesis.

A model of carcinogenesis based on spontaneous somatic mutation in expanding cell clones is presented and compared with previous mathematical treatments of this concept. The model shows that if cancer is purely a consequence of gene mutation then four independent mutations are required. To explain the marked increase in the incidence of cancer with age it is necessary to postulate that stem cells with a subset of the four key mutations show some loss of growth suppression and expand relative to unaffected stem cells. The model also predicts that for carcinogens acting during extrauterine life the incidence of cancer will be proportional to the dose of carcinogen raised to a power between one and two, even though the carcinogen increases the chance of all four mutations. This power relationship accords with data on human cancer and experimentally induced tumours in animals, but is hitherto unexplained.