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 Sjöblom 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 can be understood as the result of multiple sequential mutations, each of which has a relatively small but positive effect on net cell growth. Cancer is a disease of multicellular organisms that is characterized by a breakdown of cooperation between individual cells. The progression of cancer proceeds from a single genetically altered cell to billions of invasive cells through a series of clonal expansions. During tumorigenesis the cancer cells undergo replication and mutation, thereby increasing the size and invasiveness of the tumor. Recent sequencing projects of cancer cells suggest that mutations in up to 20 different genes might be responsible for driving an individual tumor's development. This insight contrasts with most mathematical models of cancer progression, which assume that the cancer phenotype is driven by mutations in only a few genes. We present a new mathematical model in which tumorigenesis is driven by mutations in many genes, most of which confer only a small selective advantage. Specifically, the progression of a benign tumor of the colon (adenoma) to a malignant tumor (carcinoma) is described by a Wright-Fisher process with growing population size. We explore the basic parameters of the model that are consistent with observed data. We also derive an analytical formula for the expected waiting time for the progression from benign to maligant tumor in terms of the population size, the mutation rate, the selective advantage, and the number of susceptible genes.