Modeling Clonal Evolution with Branching Processes

Abstract

Clonal evolution in tumorigenesis assumes a tumor arises from a single ancestor cell followed by a sequence of mutations that increase fitness in clones. Waves of clonal expansions take place with each new mutation contributing to the selection of the cell. Not all mutations affect a clone's growth dynamics, and some have a neutral effect on cell growth. We create a branching process model of clonal evolution that distinguishes between selective (driver) and neutral (passenger) mutations. In this model, cells grow according to distributions unique to their set of mutations, and further mutations can arise as stochastic events during replication. The models are introduced as infinite-allele multitype branching processes, and we prove asymptotic results about the number and distribution of neutral alleles. The model can be used to determine the growth rate of a tumor and the clonal subpopulations within, and we discuss how this model may be used for estimation of growth parameters in clones. Using variant frequency data from a tumor at a single time point, estimation methods can then be used to rebuild the evolutionary history of a tumor. We discuss how the rate of growth of the number of neutral alleles can be used as a molecular clock to help us in this task.