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Reconstructing subclonal composition and evolution from whole genome sequencing of tumors

Amit G. Deshwar, Shankar Vembu, Christina K. Yung, Gun Ho Jang, Lincoln Stein, Quaid Morris

arXiv:1406.7250v3q-bio.PEcs.LGstat.ML

TL;DR

Tumor subclonal reconstruction must infer complete genotypes from mutation frequencies despite low-depth WGS, CNV-related VAF distortion, and unresolved phylogenetic ambiguity. PhyloWGS jointly models SSMs and CNVs with a phylogenetic correction for overlapping loci. It reconstructs subclonal populations from WGS in settings where prior SSM-only or CNV-only approaches fail, including medium-depth and highly rearranged tumors.

  • Problem

    WGS-based subclonal reconstruction is challenged by low read depth, CNV-induced distortion of SSM VAFs, and ambiguities that existing assumptions or CNV-only methods do not fully resolve.

  • Method

    PhyloWGS uses a generative probabilistic model and Bayesian tree prior to jointly reconstruct subclonal phylogenies from SSM allelic frequencies and CNV population frequencies and copy numbers.

  • Results

    PhyloWGS reliably reconstructs subclonal populations from SSMs at 30x-50x WGS depth, solves cases that SSM-only or CNV-only methods cannot, and recovers a previously established leukemia phylogeny.

  • Takeaways & Limitations

    Integrating SSMs and CNVs with phylogenetic correction provides a more comprehensive and accurate description of subclonal genotypes than treating either data type in isolation.

  • Takeaways & Limitations

    Strong parsimony can resolve ambiguity, but its empirical validity is not established and false vestigial-cluster interpretations increase with noise or subpopulation count.

Abstract

from arXiv · show

Tumors often contain multiple subpopulations of cancerous cells defined by distinct somatic mutations. We describe a new method, PhyloWGS, that can be applied to WGS data from one or more tumor samples to reconstruct complete genotypes of these subpopulations based on variant allele frequencies (VAFs) of point mutations and population frequencies of structural variations. We introduce a principled phylogenic correction for VAFs in loci affected by copy number alterations and we show that this correction greatly improves subclonal reconstruction compared to existing methods.

1 Introduction

Tumor subclonal reconstruction seeks to infer genetically distinct cancer-cell populations and their evolutionary histories from mutation frequencies. WGS offers many mutations but introduces low-depth uncertainty, while CNVs complicate the relationship between VAF and population frequency; PhyloWGS addresses these challenges.

  • Motivation: Tumors contain genetically diverse subclonal populations that evolve through successive expansion and selection from a progenitor population.Reconstructing their histories can help identify driver mutations and provide insight into treatment response.
  • Existing problem: Subclonal reconstruction algorithms infer tumor population structure from VAFs of somatic mutations, using SSMs, CNVs, or both.SSMs include single nucleotide variants and small indels, whereas CNVs are inferred from read-coverage changes and altered average ploidy.
  • Existing problem: Low read depth in current WGS complicates estimating mutation population frequencies, although the larger number of WGS-detected mutations may compensate for reduced depth.Accurate individual SSM frequencies were previously associated mainly with much deeper targeted resequencing.
  • Existing problem: CNVs overlapping SSMs complicate reconstruction because their effects depend on the relationship between the structural variation and mutation.Existing approaches may assume that CNVs and mutations always affect the same cells or omit structural variants from the phylogeny.
  • Contribution: PhyloWGS reconstructs complete subclonal phylogenies from WGS by correcting SSM population frequencies in CNV-affected regions.It is designed to analyze at least five cancerous subpopulations using thousands of mutations and examines recovery across read depths and CNV conditions.

2 Previous work

Previous work reconstructs tumor subclones from VAF clusters and evolutionary assumptions, but ambiguity, CNV effects, and limited CNV-only applicability constrain complete phylogenetic inference. PhyloWGS combines SSMs and CNVs while avoiding strong-parsimony selection of a single tree.

  • Tumor evolution: Tumor evolution produces nested subpopulations that inherit parental mutations while acquiring additional mutation sets.VAFs summarize these mutation patterns, and subclonal reconstruction aims to recover the corresponding lineages and phylogeny.
  • SSM-based approaches: VAF-clustering methods infer mutation sets from mixture models, but overlapping clusters create uncertainty about their number and SSM assignments.Correct cluster recovery is necessary but does not by itself determine complete subpopulation genotypes.
  • SSM-based approaches: The infinite sites assumption states that each SSM occurs once, enabling phylogenetic constraints that can recover genotypes from one or a few tumor samples.Without this assumption, methods require at least as many samples as subpopulations in the noiseless case and more under measurement noise.
  • SSM-based approaches: Strong parsimony resolves some ambiguity by favoring vestigial VAF clusters, but its empirical validity is unestablished and noise can produce false branching inferences.The risk increases with measurement noise or the number of tumor subpopulations.
  • CNV-based approaches: CNV-based methods can estimate average copy-number changes at lower read depths, but must infer multiple latent quantities from one non-normal average and often rely on parsimony.Existing approaches are practically limited to small numbers of cancerous subpopulations and cannot handle substantial rearrangements.
  • Combining SSMs and CNVs: CNVs alter SSM VAFs according to their phylogenetic relationship, so ignoring CNVs can make one lineage appear to be two separate lineages.Accounting for CNVs can reveal that a second VAF peak reflects amplification of a region shared by SSMs.
  • PhyloWGS: PhyloWGS integrates SSMs and CNVs, performs concurrent clustering and phylogenetic reconstruction, and reports posterior samples rather than imposing strong parsimony.This design supports reconstruction when VAF clusters overlap in only a subset of samples.

3 Results

PhyloWGS combines CNV and SSM information by representing CNVs as pseudo-SSMs and modeling their interaction with mutations. Its transformation accounts for CNV copy number, population frequency, and possible phylogenetic relationships between CNVs and SSMs.

  • Method overview: PhyloWGS converts CNVs into pseudo-SSMs and performs reconstruction jointly on SSMs and pseudo-SSMs.This integration enables an illustrative tumor reconstruction that cannot be solved correctly using CNV or SSM data alone.
  • CNV representation: For each CNV, PhyloWGS creates a pseudo-SSM using the CNV population frequency and simulated allele counts derived from total read depth.The pseudo-SSM is added to the dataset with rounded expected variant-read counts.
  • CNV representation: SSMs within a CNV-affected region are associated with that CNV’s pseudo-SSM to transform inferred population frequencies into expected VAFs.The model uses this association to account for the CNV’s effect on overlapping mutations.
  • CNV correction: The general PhyloWGS transformation allows multiple CNVs to affect an SSM locus.The simplified description considers one CNV, while the full method handles multiple overlapping CNVs.
  • CNV correction: Expected SSM allele frequency is computed from CNV population frequency, maternal and paternal copy-number components, and SSM population frequency.The maternal and paternal labels distinguish the two copies without assigning actual parental chromosome origins.
  • Phylogenetic relationships: An SSM and overlapping CNV may be ordered with the SSM before the CNV, after the CNV, or on a separate phylogenetic branch.PhyloWGS accounts for these three possible relationships when modeling their interaction.

Case 1 (SSM →CNV)

The expected VAF depends on the phylogenetic relationship between an SSM and CNV, with copy-number decomposition and phasing affecting only Case 1. Under some conditions, these rules allow single-sample data to identify branching phylogenies.

  • Case 1 (SSM →CNV): In Case 1, CNV-bearing cells contain C_m copies of the SSM, while SSM-bearing cells without the CNV contain one mutated copy.
  • Case 1 (SSM →CNV): The expected allele frequency is the average number of SSM-mutated copies per cell divided by the average total copies per cell.With no copy-number change, the numerator is φ_s; with C_m = 0, it is φ_s − φ_c.
  • Case 1 (SSM →CNV): The SSM–CNV relationship changes observed VAFs, and PhyloWGS illustrates these changes across phylogenetic configurations.
  • Case 1 (SSM →CNV): Copy-number decomposition and SSM phasing affect expected VAF only in Case 1; PhyloWGS considers both phasing possibilities when computing likelihood.If copy-number callers do not provide maternal and paternal decomposition, PhyloWGS should use loci where C ∈ {0, 1, 2}.
  • Case 1 (SSM →CNV): Under some conditions, single-sample data can unambiguously identify a branching phylogeny.For the example x_ssm = 0.1, φ_c = 0.4, C_m = 10, and C_p = 1, Case 1 is ruled out because its inferred φ_s is negative.

3.2 The combination of CNVs with SSMs is required for accurate subclonal reconstruction

An example tumor contains normal cells, an SSM-defined population, and a descendant population carrying additional SSMs and a homozygous deletion. PhyloWGS recovered the known structure, whereas methods ignoring or incompletely modeling CNVs misassigned mutations or missed populations.

  • 3.2 The combination of CNVs with SSMs is required for accurate subclonal reconstruction: The simulated tumor comprises 25% normal cells, 25% cells with SSM1–4, and 50% descendant cells carrying SSM1–8 plus homozygous deletion CNV1.
  • 3.2 The combination of CNVs with SSMs is required for accurate subclonal reconstruction: PhyloWGS correctly reconstructed the example’s evolutionary history and subpopulation structure.The example used simulated variant and reference allele counts at 60× read depth.
  • 3.2 The combination of CNVs with SSMs is required for accurate subclonal reconstruction: Ignoring CNVs caused PhyloSub to assign SSM4 to population C, although SSM4’s expected VAF was altered by the deletion.
  • 3.2 The combination of CNVs with SSMs is required for accurate subclonal reconstruction: CNV-only data cannot recover population B, so full and accurate reconstruction requires integrating SSM and CNV data.PyClone produced different clusterings depending on whether CNV alterations were supplied and could not directly represent a homozygous deletion.

3.3 Applying PhyloWGS to simulated data

Simulations evaluated PhyloWGS runtime, recovery of the true number of subpopulations, and SSM-to-population clustering accuracy across read depths and tumor complexities.

  • Simulation design: Simulations varied population counts from 3 to 6, read depths from 20x to 300x, and 5 to 1000 SSMs per population.Each parameter combination was evaluated using simulated read counts with known subclonal structure.
  • Runtime: Inference completed in less than three hours on a single core for datasets containing up to 1000 SSMs.Timing used 2500 MCMC iterations and 5000 inner Metropolis-Hastings iterations for simulations with five subpopulations.
  • Population-count recovery: Higher read depth and fewer subpopulations improved accuracy when estimating the number of subpopulations.The estimate was obtained from the highest-complete-data-likelihood sampled tree after removing subpopulations with zero assigned SSMs.
  • Population-count recovery: For three or four subpopulations, 20x–30x read depth was sufficient in simulations, whereas six-subpopulation tumors required 200x–300x to resolve.Accuracy also followed a U-shaped relationship with the number of SSMs per population in ambiguous phylogeny simulations.
  • Clustering accuracy: AUPRC increased with read depth and decreased population count, but showed no clear relationship with the number of SSMs.The evaluation compared true and inferred co-clustering matrices and illustrated AUPRC values from 0.65 to 0.98.

3.4 Simulations with CNV changes

CNV simulations tested PhyloWGS on tumors combining ordinary mutations with subclonal amplifications or deletions, while benchmark analyses examined reconstruction after structural-variation filtering.

  • CNV simulations: Complex simulations included 20% normal tissue, a 40% CNV-free population with 500 mutations, and a descendant with 200 mutations plus a CNV affecting 50% of the genome.The CNV was simulated as either an amplification or a deletion across read depths from 20x to 300x.
  • TCGA benchmark: TCGA benchmark samples contained a normal population, the HCC 1143 cancer cell line, and spiked-in subclonal descendants sequenced at 30x coverage.BIC-seq was used to identify possible structural-variation locations after changing its bandwidth parameter to reduce noisy segmentation.
  • Accuracy evaluation: Reconstruction accuracy was evaluated with AUPR across read depths for subclonal additions and deletions, including comparisons between PhyloWGS and PyClone.The figure-based evaluation varied the number of populations and SSMs per cancerous population in simulated data.
  • TCGA benchmark: THetA produced nearly identical composition inferences despite subclonal proportions ranging from 40% to 10%, so its copy-number calls were not used.SSMs in regions flagged by BIC-seq were removed, leaving 62 of the original 4,344 SSMs.
  • TCGA benchmark: After structural-variation filtering, PhyloWGS identified the correct number of populations and captured changing sample composition across the three benchmark samples.The inferred SSM content of each cluster was identical across three separate runs.

3.6 Chronic Lymphocytic Leukemia

The CLL077 analysis compared a PhyloWGS phylogeny from WGS allele frequencies with an expert phylogeny derived from targeted deep sequencing across five tumor samples.

  • CLL077 analysis: CLL077 provided five tumor samples collected over the course of treatment for comparison with an expert-generated phylogeny.PhyloWGS used allele frequencies of the same SSMs identified by WGS.
  • Phylogeny comparison: The reported difference from the expert tree was a single SSM assigned to a child of the subpopulation where it appears in the expert phylogeny.This was the specific exception noted in the comparison.

3.7 Breast Tumor

The breast-tumor analysis applied PhyloWGS to high-coverage WGS data restricted to genomic regions with concordant copy-number calls and compared its inferred phylogeny with expert-generated results.

  • Data and filtering: PD4120a was analyzed at 288x coverage using 26,029 SSMs from genomic regions where THetA and the original analysis agreed on copy-number status.The retained regions included chromosomes 3, 4q, 5, 10, 13, 16q, 17, 19, and 20.
  • Data and filtering: Among the analyzed SSMs, 4,739 occurred in regions with clonal copy-number changes and 2,171 in regions with subclonal copy-number changes.These counts describe the copy-number contexts included in the restricted analysis.
  • Method comparison: The study ran PhyloWGS and PyClone on the filtered PD4120a data for comparison with the expert-generated phylogeny.The provided passage states the analysis setup but does not report the comparison outcome.
  • Phylogeny comparison: The figure presents expert-generated and PhyloWGS-inferred phylogenies, with labeled mutation sets identifying genes assigned to inferred lineages.Gene labels include BCL2L13, NAMPTL, GPR158, SAMHD1, SLC12A1, DAZAP1, EXOC6B, GHDC, OCA2, PLA2G16, LRRC16A, KLHDC2, COL24A1, and NOD1.

4 Discussion

PhyloWGS integrates SSMs and CNVs into tumor phylogenies while correcting SSM frequencies according to their phylogenetic relationships with CNVs. Results show accurate reconstruction in settings where previous approaches fail, although preprocessing and copy-number decomposition impose scope constraints.

  • Integrating SSMs and CNVs allows CNVs overlapping SSM loci to constrain tumor-tree structure beyond SSM frequencies alone.The effect of a CNV on an SSM’s allele frequency depends on their phylogenetic relationship.
  • PhyloWGS’s phylogenetic correction recovered breast-tumor subpopulations better than methods that do not apply the correction.
  • Highly rearranged cancer populations were reconstructed from SSM frequencies in normal-copy-number regions, whereas a state-of-the-art CNV-based method failed on the same data.
  • PhyloWGS requires CNV-based preprocessing and, for amplifications with Ci > 2, decomposition into maternal and paternal copy counts.Without that decomposition, it can be restricted to copy-number losses where only one breakdown is possible.
  • PhyloWGS can detect additional SSM-defined populations that CNV preprocessing misses, despite current CNV methods often detecting at most two cancerous populations.
  • An alternative strategy uses regions unaffected by CNVs, which can yield reasonably accurate reconstructions even in highly rearranged genomes.The approach was demonstrated using limited SSMs from normal-copy-number regions in a TCGA benchmark.

5 Conclusions

PhyloWGS reconstructs tumor phylogenies and subclonal populations from SSM and CNV data using a probabilistic tree model. Across simulated and real WGS datasets, it reconstructs populations at medium depth, handles cases unresolved by single-data-type methods, and achieves state-of-the-art breast-tumor performance.

  • PhyloWGS groups SSMs and CNVs into subpopulations and estimates their population frequencies and phylogenetic relationships.
  • A generative probabilistic allele-frequency model with a nonparametric Bayesian tree prior accounts for CNV effects on overlapping SSM VAFs.PhyloWGS runs more than 50 times faster than PhyloSub, enabling analysis of thousands of WGS-detected SSMs.
  • PhyloWGS reliably reconstructs subclonal populations from SSMs alone at medium-depth WGS of 30x-50x.
  • PhyloWGS solves simulated cases that SSM-only or CNV-only methods cannot solve alone and reconstructs highly rearranged samples where a CNV-based method fails.
  • In a chronic lymphocytic leukemia time series, PhyloWGS recovered the tumor phylogeny previously obtained from deep targeted resequencing.

6 Methods

PhyloWGS models SSM and CNV evidence jointly to infer subclonal frequencies and tree structure. Its likelihood accounts for read counts, copy-number effects, sequencing error, and phylogenetic constraints under the infinite-sites assumption.

  • 6.1 PhyloSub model: SSM evidence is represented by reference and variant read counts ai and bi, with total depth di = ai+bi and error-adjusted allele probabilities.
  • 6.1 PhyloSub model: A Dirichlet-process prior groups mutations sharing population frequencies without requiring the number of mutation groups to be chosen in advance.
  • 6.1 PhyloSub model: A tree-structured stick-breaking prior models clonal evolution as a rooted tree, with parameters controlling tree height and width.
  • 6.1 PhyloSub model: Auxiliary variables ηv enforce that each non-leaf node’s SSM frequency is at least the sum of its children’s frequencies.MCMC and Metropolis-Hastings sampling infer tree structure, auxiliary variables, and SSM population frequencies.
  • 6.2 Integrating CNVs and SSMs: CNVs enter the model as pseudo-SSMs when they lack overlapping SSMs, using read counts whose allele frequency approximates φj/2.
  • 6.2.2 If CNVs overlap with SSMs: When CNVs overlap SSMs, the relevant CNV for each population is the first affecting event encountered while ascending the evolutionary tree.
  • 6.2.2 If CNVs overlap with SSMs: The method can average maternal- and paternal-placement likelihoods when phasing an SSM to a chromosome copy is unavailable.Without maternal/paternal copy-number decomposition, analysis can be restricted to CNVs with Cj < 2.
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