Efficiency of carcinogenesis with and without a mutator mutation

Carcinogenesis involves the acquisition of multiple genetic changes altering various cellular phenotypes. These changes occur within the fixed time period of a human lifespan, and mechanisms that accelerate this process are more likely to result in clinical cancers. Mutator mutations decrease genome stability and, hence, accelerate the accumulation of random mutations, including those in oncogenes and tumor suppressor genes. However, if the mutator mutation is not in itself oncogenic, acquiring that mutation would add an extra, potentially time-consuming step in carcinogenesis. We present a deterministic mathematical model that allows quantitative prediction of the efficiency of carcinogenesis with and without a mutator mutation occurring at any time point in the process. By focusing on the ratio of probabilities of pathways with and without mutator mutations within cell lineages, we can define the frequency or importance of mutator mutations in populations independently of absolute rates and circumvent the question of whether mutator mutations are "necessary" for cancers to evolve within a human lifetime. We analyze key parameters that predict the relative contribution of mutator mutants in carcinogenesis. Mechanisms of carcinogenesis involving mutator mutations are more likely if they occur early. Involvement of mutator mutations in carcinogenesis is favored by an increased initial mutation rate, by greater fold-increase in mutation rate due to the mutator mutation, by increased required steps in carcinogenesis, and by increased number of cell generations to the development of cancer.