Inferring the Mutational History of a Tumor Using Multi-state Perfect Phylogeny Mixtures

Abstract

Phylogenetic techniques are increasingly applied to infer the somatic mutational history of a tumor from DNA sequencing data. However, standard phylogenetic tree reconstruction techniques do not account for the fact that bulk sequencing data measures mutations in a population of cells. We formulate and solve the multi-state perfect phylogeny mixture deconvolution problem of reconstructing a phylogenetic tree given mixtures of its leaves, under the multi-state perfect phylogeny, or infinite alleles model. Our somatic phylogeny reconstruction using combinatorial enumeration (SPRUCE) algorithm uses this model to construct phylogenetic trees jointly from single-nucleotide variants (SNVs) and copy-number aberrations (CNAs). We show that SPRUCE addresses complexities in simultaneous analysis of SNVs and CNAs. In particular, there are often many possible phylogenetic trees consistent with the data, but the ambiguity decreases considerably with an increasing number of samples. These findings have implications for tumor sequencing strategies, suggest caution in drawing strong conclusions based on a single tree reconstruction, and explain difficulties faced by applying existing phylogenetic techniques to tumor sequencing data.

Assessing intratumor heterogeneity and tracking longitudinal and spatial clonal evolutionary history by next-generation sequencing

“…Because knowing integer-valued copy number is akin to knowing its MCF, in essence, in essence, PhyloWGS requires a two-step procedure where the underlying clones are first identified with their absolute copy numbers estimated using CNA data only, and this information is then used to compute the MCF of SNAs. SPRUCE (27) is another recent method that analyzes both SNAs with CNAs and characterizes the tumor phylogeny as a restricted class of spanning trees. Like PhyloWGS, SPRUCE takes processed CNA calls, for example, from THetA, and assumes known MCF for CNA events.…”

“…For example, it is possible to assert that under the infinite-sites assumption, mutations with lower CCFs cannot be ancestral to mutations with higher CCFs. To deal with copy number changes, El-Kebir et al (27) proposed instead an infinite-alleles assumption, or the multistate perfect phylogeny, where a mutation may change state more than once on the tree due to gain or loss of copy number, but changes to the same state at most once. Furthermore, Deshwar et al (20) introduces the "weak parsimony" assumption, which posits that mutations with similar CCFs across all samples lie on the same branch segment in the phylogeny.…”

“…Furthermore, Deshwar et al (20) introduces the "weak parsimony" assumption, which posits that mutations with similar CCFs across all samples lie on the same branch segment in the phylogeny. Canopy relies on both the infinite-sites assumption and the weak parsimony assumption, but takes a different approach from El-Kebir et al (27) in modeling CNAs: Canopy extends the infinite-sites assumption to CNAs by assuming that copy number events with the same breakpoints and the same copy number across all samples must be the result of a single CNA event that occurs exactly once in the tumor's evolution. CNAs that overlap but have different breakpoints or different copy number states are treated as separate events.…”

“…One practical drawback of Clomial (25) is that it takes only SNA input and assumes that all mutational loci are heterozygous from copy numberneutral regions. SCHISM (24), BitPhylogeny (26), PhyloWGS (20), and SPRUCE (27) adjust for CNAs in their model in different ways, but these methods still require limiting assumptions and do not make full use of the data, as we discuss in detail a bit later.…”

The Copy-Number Tree Mixture Deconvolution Problem and Applications to Multi-sample Bulk Sequencing Tumor Data

“…While intra-tumor heterogeneity complicates the identification of mutations in bulk-sequencing data from a tumor sample containing millions of cells, it also provides a signal for inferring the tumor composition-the number and proportion of clones within a sample-as well as the ancestral history of somatic mutations during cancer development [12]. Thus, a number of methods have been developed to infer phylogenetic trees from DNA sequencing data from one or more samples of a tumor [5,8,[12][13][14]17,19,20,28].…”