Waiting Time Models of Cancer Progression

Abstract

Cancer progression is an evolutionary process driven by mutation and selection in a population of tumor cells. In multistage models of cancer progression, each stage is associated with the occurrence of genetic alterations and their fixation in the population. The accumulation of mutations is described using conjunctive Bayesian networks, an exponential family of waiting time models in which the occurrence of mutations is constrained by a partial temporal order. Two opposing limit cases arise if mutations either follow a linear order or occur independently. Exact analytical expressions for the waiting time until a specific number of mutations have accumulated are derived in these limit cases as well as for the general conjunctive Bayesian network. In a stochastic population genetics model that accounts for mutation and selection, waves of clonal expansions sweep through the population at equidistant intervals. An approximate analytical expression for the waiting time is compared to the results obtained with conjunctive Bayesian networks.

Keywords:

• Bayesian network
• cancer
• genetic progression
• multistage theory
• Wright-Fisher process

ACKNOWLEDGMENTS

Part of this work was presented at the conference entitled “What Are the Theoretical Tools Most Useful for Understanding Biological Systems?” on November 12–15, 2007, at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France. We are grateful to Evelyn Fox Keller, Annick Lesne, and Nadine Peyriéras for the organization and to Jean-Pierre Bourguignon for hosting this conference. We thank the three anonymous reviewers for their helpful comments which have improved the manuscript.