The copy-number tree mixture deconvolution problem and applications to multi-sample bulk sequencing tumor data

Cancer is an evolutionary process driven by somatic mutation. This process can be represented as a phylogenetic tree. Constructing such a phylogenetic tree from genome sequencing data is a challenging task due to the mutational complexity of cancer and the fact that nearly all cancer sequencing is of bulk tissue, measuring a super-position of somatic mutations present in different cells. We study the problem of reconstructing tumor phylogenies from copy number aberrations (CNAs) measured in bulk-sequencing data. We introduce the Copy-Number Tree Mixture Deconvolution (CNTMD) problem, which aims to find the phylogenetic tree with the fewest number of CNAs that explain the copy number data from multiple samples of a tumor. CNTMD generalizes two approaches that have been researched intensively in recent years: deconvolution/factorization algorithms that aim to infer the number and proportions of clones in a mixed tumor sample; and phylogenetic models of copy number evolution that model the dependencies between copy number events that affect the same genomic loci. We design an algorithm for solving the CNTMD problem and apply the algorithm to both simulated and real data. On simulated data, we find that our algorithm outperforms existing approaches that perform either deconvolution or phylogenetic tree construction under the assumption of a single tumor clone per sample. On real data, we analyze multiple samples from a prostate cancer patient, identifying clones within these samples and a phylogenetic tree that relates these clones and their differing proportions across samples. This phylogenetic tree provides a higher-resolution view of copy number evolution of this cancer than published analyses.