A regression based approach to phylogenetic reconstruction from multi-sample bulk DNA sequencing of tumors

Motivation: DNA sequencing of multiple bulk samples from a tumor provides the opportunity to investigate tumor heterogeneity and reconstruct a phylogeny of a patient’s cancer. However, since bulk DNA sequencing of tumor tissue measures thousands of cells from a heterogeneous mixture of distinct sub-populations, accurate reconstruction of the tumor phylogeny requires simultaneous deconvolution of cancer clones and inference of ancestral relationships, leading to a challenging computational problem. Many existing methods for phylogenetic reconstruction from bulk sequencing data do not scale to large datasets, such as recent datasets containing upwards of ninety samples with dozens of distinct sub-populations. Results: We develop an approach to reconstruct phylogenetic trees from multi-sample bulk DNA sequencing data by separating the reconstruction problem into two parts: a structured regression problem for a fixed tree T, and an optimization over tree space. We derive an algorithm for the regression sub-problem by exploiting the unique, combinatorial structure of the matrices appearing within the problem. This algorithm has both asymptotic and empirical improvements over linear programming (LP) approaches to the problem. Using our algorithm for this regression sub-problem, we develop fastBE, a simple method for phylogenetic inference from multi-sample bulk DNA sequencing data. We demonstrate on simulated data with hundreds of samples and upwards of a thousand distinct sub-populations that fastBE outperforms existing approaches in terms of reconstruction accuracy, sample efficiency, and runtime. Owing to its scalability, fastBE enables both phylogenetic reconstruction directly from indvidual mutations without requiring the clustering of mutations into clones, as well as a new phylogeny constrained mutation clustering algorithm. On real data from fourteen B-progenitor acute lymphoblastic leukemia patients, fastBE infers mutation phylogenies with fewer violations of a widely used evolutionary constraint and better agreement to the observed mutational frequencies. Using our phylogeny constrained mutation clustering algorithm, we also find mutation clusters with lower distortion compared to state-of-the-art approaches. Finally, we show that on two patient-derived colorectal cancer models, fastBE infers mutation phylogenies with less violation of a widely used evolutionary constraint compared to existing methods. Author summary: DNA sequencing of a bulk tumor sample measures the genomes of the heterogeneous mixture of cells that comprise a tumor. Reconstructing the evolutionary history of a cancer from such admixed measurements is challenging, as standard phylogenetic techniques assume that genomes of individual cells are measured. Multiple specialized techniques aim to simultaneously infer the unmeasured genomes and construct the evolutionary history of these genomes, but many of these methods do not scale to large numbers of genomes in the mixture. We introduce a new tool, fast Bulk Evolution (fastBE), which accurately reconstructs the evolutionary history of tumors containing hundreds-thousands of genomes from bulk DNA sequencing data. Key to the success of fastBE are new algorithmic insights which make this task tractable. fastBE is a useful tool to analyze large multi-region tumor sequencing datasets.