Modeling DNA Methylation in a Population of Cancer Cells

Little is known about how human cancers grow because direct observations are impractical. Cancers are clonal populations and the billions of cancer cells present in a visible tumor are progeny of a single transformed cell. Therefore, human cancers can be represented by somatic cell ancestral trees that start from a single transformed cell and end with billions of present day cancer cells. We use a genealogical approach to infer tumor growth from somatic trees, employing haplotype DNA methylation pattern variation, or differences between specific CpG sites or "tags," in the cancer genome. DNA methylation is an epigenetic mark that is copied, with error, during genome replication. At our tags, neutral copy errors in DNA methylation appear to occur at random, and much more frequently than sequence copy errors. To reconstruct a cancer tree, we sample and compare human colorectal genomes within small geographic regions (a cancer fragment), between fragments on the same side of the tumor, and between fragments from opposite tumor halves. The combined information on both physical distance and epigenetic distance informs our model for tumor ancestry. We use approximate Bayesian computation, a simulation-based method, to model tumor growth under a variety of evolutionary scenarios, estimating parameters that fit observed DNA methylation patterns. We conclude that methylation patterns sampled from human cancers are consistent with replication errors and certain simple cancer growth models. The inferred cancer trees are consistent with Gompertzian growth, a well-known cancer growth pattern.