Quantifying Clonal and Subclonal Passenger Mutations in Cancer Evolution

Abstract

The vast majority of mutations in the exome of cancer cells are passengers, which do not affect the reproductive rate of the cell. Passengers can provide important information about the evolutionary history of an individual cancer, and serve as a molecular clock. Passengers can also become targets for immunotherapy or confer resistance to treatment. We study the stochastic expansion of a population of cancer cells describing the growth of primary tumors or metastatic lesions. We first analyze the process by looking forward in time and calculate the fixation probabilities and frequencies of successive passenger mutations ordered by their time of appearance. We compute the likelihood of specific evolutionary trees, thereby informing the phylogenetic reconstruction of cancer evolution in individual patients. Next, we derive results looking backward in time: for a given subclonal mutation we estimate the number of cancer cells that were present at the time when that mutation arose. We derive exact formulas for the expected numbers of subclonal mutations of any frequency. Fitting this formula to cancer sequencing data leads to an estimate for the ratio of birth and death rates of cancer cells during the early stages of clonal expansion.

Author Summary

Cancer is the consequence of an evolutionary process, which lasts several decades, is impossible to observe during most of its time, and only becomes apparent in late stages. We use mathematical modeling to shed light on the evolutionary dynamics of cancer by studying the accumulation of passenger mutations. We show that the frequencies obtained by passenger mutations depend strongly on the ratio of death and birth rates of cancer cells. We use genetic data of colorectal cancer to estimate this important quantity in vivo. We estimate the size of the cancer cell population that was present when a specific mutation first emerged. Our theory informs the analysis of cancer sequencing data and the phylogenetic reconstruction of cancer evolution.