Genetic progression and the waiting time to cancer

Abstract

Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of cancer is complex and that individual cancers may evolve through mutations in as many as 20 different cancer-associated genes. We use data published by Sjoblom et al. (2006) to develop a new mathematical model for the somatic evolution of colorectal cancers. We employ the Wright-Fisher process for exploring the basic parameters of this evolutionary process and derive an analytical approximation for the expected waiting time to the cancer phenotype. Our results highlight the relative importance of selection over both the size of the cell population at risk and the mutation rate. The model predicts that the observed genetic diversity of cancer genomes can arise under a normal mutation rate if the average selective advantage per mutation is on the order of 1%. Increased mutation rates due to genetic instability would allow even smaller selective advantages during tumorigenesis. The complexity of cancer progression thus can be understood as the result of multiple sequential mutations, each of which has a relatively small but positive effect on net cell growth.

Details available as supplementary material at http://www.people.fas.harvard.edu/~antal/publications.html

References in corpus (3)

• The traveling wave approach to asexual evolution: Muller's ratchet and speed of adaptation
• A waiting time problem arising from the study of multi-stage carcinogenesis
• A non-linear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt

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