- Open Access
MixClone: a mixture model for inferring tumor subclonal populations
© Li and Xie; licensee BioMed Central Ltd. 2015
- Published: 21 January 2015
Tumor genomes are often highly heterogeneous, consisting of genomes from multiple subclonal types. Complete characterization of all subclonal types is a fundamental need in tumor genome analysis. With the advancement of next-generation sequencing, computational methods have recently been developed to infer tumor subclonal populations directly from cancer genome sequencing data. Most of these methods are based on sequence information from somatic point mutations, However, the accuracy of these algorithms depends crucially on the quality of the somatic mutations returned by variant calling algorithms, and usually requires a deep coverage to achieve a reasonable level of accuracy.
We describe a novel probabilistic mixture model, MixClone, for inferring the cellular prevalences of subclonal populations directly from whole genome sequencing of paired normal-tumor samples. MixClone integrates sequence information of somatic copy number alterations and allele frequencies within a unified probabilistic framework. We demonstrate the utility of the method using both simulated and real cancer sequencing datasets, and show that it significantly outperforms existing methods for inferring tumor subclonal populations. The MixClone package is written in Python and is publicly available at https://github.com/uci-cbcl/MixClone.
The probabilistic mixture model proposed here provides a new framework for subclonal analysis based on cancer genome sequencing data. By applying the method to both simulated and real cancer sequencing data, we show that integrating sequence information from both somatic copy number alterations and allele frequencies can significantly improve the accuracy of inferring tumor subclonal populations.
- Cancer genomics
- Subclonal inference
- Whole genome sequencing
- Somatic copy number alteration
- Allele frequency
- Mixture model
Tumor genomes have been shown to present extensive cellular heterogeneity for decades since Nowell's original clonal theory for tumor progression . Identifying tumor subclonal populations is important for both understanding the evolution of tumor cells, and for designing more effective treatments as pre-existing mutations occurring in some subclones could lead to drug resistance . For example, a research in lymphocytic leukemia has shown links between the presences of driver mutations within subclones and adverse clinical outcomes .
With the advancement of next-generation sequencing (NGS) and launch of large-scale cancer genome sequencing projects , computational methods have recently been developed to infer tumor subclonal populations based on cancer genome sequencing data [5–9].
Most of these methods rely on sequence information from somatic point mutations, such as PyClone , EXPANDS , PhyloSub  and rec-BTP . Methods in this category leverage the cluster pattern of allele frequencies at somatic point mutations to detect distinct subclonal populations. However, as the determination of somatic point mutations is imperfect and the inclusion of false-positives is unavoidable , deep sequencing with more than 100X coverage is often required for subclonal inferences with high sensitivity and specificity [5, 7, 8].
Other approaches utilizing the read depth information from genomic segments with somatic copy number alterations (SCNAs) to infer the cellular prevalences of subclonal populations have also been developed, such as THetA . THetA explores all combinations of copy number changes across all segments to infer the most likely collection of subclonal populations . However, with the copy number information alone, THetA suffers from the "identifiability problem", where distinct combinations of tumor purity and ploidy are able to explain the read depth information from SCNAs equally well . Additionally, the running time of THetA scales exponentially with the number of genomic segments , and often takes a prohibitively long time to run under certain parameter settings.
In this article, we present a novel probabilistic mixture model, MixClone, to infer the cellular prevalences of subclonal populations. MixClone integrates both read depth information from genomic segments with SCNAs and allele frequency information from heterozygous single-nucleotide polymorphism (SNP) sites within a unified probabilistic framework. Such integrative framework has been shown to significantly improve the accuracy of tumor purity estimation in our previous work . Here, we present that MixClone achieves two major advantages compared to the existing methods that (i) it does not require deep sequencing data, (ii) it resolves the identifiability problem. To demonstrate MixClone's utility, we conducted simulation studies and showed that it outperforms existing methods. We also applied MixClone on a breast cancer sequencing dataset , and showed that it was able to discover subclonal events not reported before.
In this section, we introduce the generative mixture model of MixClone, which is an extension of our previous work on tumor purity estimation. First, we introduce the notations for input data. Then, we describe the probabilistic models for sequence information of both SCNAs and allele frequencies. Finally, we combine these two types of data into a single likelihood model, and describe an algorithm to solve the model.
The raw input data for MixClone are two aligned whole genome sequencing read sets of paired normal-tumor samples and a genome segmentation file based on the tumor sample. Following the notations from our previous work , we assume the tumor genome has been partitioned into J segments. We also assume there are I j heterozygous SNP sites within segment j in the corresponding normal genome, and use (i, j) to index SNP site i within segment j. For each SNP site (i, j) we define the A allele to be the reference allele and the B to be the alternative allele, with respect to the reference genome. We also use a superscript N to denote data from normal samples and superscript T to denote data from tumor samples. Overall, the observed data are summarized in the following notations :
= number of reads mapped to the B allele in the normal sample at site (i, j).
= reads depth of the normal sample at site (i, j).
= total number of reads mapped to segment j of the normal sample.
The notations for the observed data from tumor samples are similarly defined, e.g. denotes total number of reads mapped to segment j of the tumor sample.
Because the mappability coefficients (θ j 's) matter only in a relative sense, we take , as these segments should have the same sequence properties between the normal and tumor samples.
where denotes the number of reads mapped to segment s of the tumor sample.
Details on curating the baseline segments are given in Supplementary, Additional file 1.
Modeling allele frequencies
in which, ε ≪ 1 is a small random deviation accounting for general sequencing errors. We choose E = 0.01, which is equivalent to a Phred quality of 20 .
Combining SCNAs and allele frequencies
Now, we combine sequence information from both SCNAs and heterozygous SNP sites. For all the heterozygous SNP sites within the same segment, their genotypes should be consistent with the underlying allelic configuration of the segment. We model this consistency through a predefined conditional probability . If the genotype g is inconsistent with the allelic configuration h, e.g. AA is inconsistent with PM, we assign a small probability σ as Q gh , otherwise we assign equal probabilities to genotypes that are consistent with the allelic configuration.
which is the cumulative log-likelihood increase from K = 1 to K = i as a percentage regarding to the total increase Δ. If δ i ≥ 0.9 and δi−1 < 0.9, MixClone selects K = i as the number of subclonal populations.
In practice, we suggest users use this criterion as a heuristic guide when analyzing real data, and determine the number of subclonal populations in conjunction with regard to other external information.
MixClone software package
In this section, we evaluate the performance of MixClone on both simulated and real datasets and compare its performance with two published algorithms: (i) PyClone, a method based on somatic point mutations, and (ii) THetA, a method based on somatic copy number alterations.
Results from simulated data
To generate simulation data, we simulated ten sets of NGS reads from chromosome 1 of artificial paired normal-tumor samples, each with 60X coverage. Heterozygous SNP sites from dbSNP  were inserted to the reference human genome to create the artificial normal genome. Both heterozygous SNP sites and somatic point mutations from  were inserted to the reference human genome to create artificial tumor genomes. Five of the artificial tumor genomes contain two subclonal populations and the other five contain three subclonal populations. Each artificial tumor genome was randomly assigned with segmentations, allelic configurations and subclonal cellular prevalences. We used segmentations based on both ground truth and BIC-seq  as the input for MixClone. We used ground truth somatic point mutation sites and copy numbers as the input for PyClone and THetA. Details on how reads were simulated and preprocessed are given in Supplementary, Additional file 1.
Results from breast cancer sequencing data
Figure 3b shows the five log-likelihoods of MB-116 under different numbers of sub-clonal populations. The magenta, red and yellow curves represent the log-likelihoods corresponding to number 1, 3, and 5, respectively. Because the distance between the magenta and red curves (the cumulative log-likelihood increase from 1 to 3) is greater than 0.9 of the distance between the magenta and yellow curves (the total log-likelihood increase from 1 to 5), MixClone selected K = 3 as the number of subclonal populations for MB-116.
Besides MB-116, MixClone also detected significant subclonal events in MB-45 and MB-123. Results of MB-45 and MB-123 are given in Supplementary, Additional file 1.
In this article, we demonstrated MixClone's utility using whole genome sequencing data. However, most of the existing cancer genome sequencing data are from exome sequencing. An important future direction is to extend the current methodology to handle the exome sequencing data. Yet, extending MixClone to whole exome sequencing data is not trivial, as reads coverage on targeted exonic regions are no longer randomly distributed due to probe's variable efficiency . Instead of Poisson distribution, using Gaussian distribution to model reads depth ratios between tumor and normal samples might be more appropriate to account for such additional variances, which has been demonstrated in whole exome sequencing based copy number analysis .
Another important future direction to extend MixClone is to implement joint analysis based on multiple samples, which is supported by PyClone and PhyloSub [5, 7]. Multiple samples have been obtained for a single heterogeneous tumor tissue both temporally and spatially, and joint analysis based on these samples may reveal additional patterns of the history of tumor progression .
Currently, MixClone runs the subclonal analysis five times with different number of subclonal populations in range of 1 to 5 by default. In reality, larger numbers of subclonal populations may coexist within one tumor sample, but in this case some of the populations are very likely to share similar cellular prevalences. Since Mix-Clone defines different subclonal populations based on distinct cellular prevalences, those populations with similar cellular prevalences may not be differentiated by MixClone. To achieve finer resolution of subclonal populations, subclonal lineages information would be necessary to further differentiate each population in addition to cellular prevalences. And phylogenetic methods may be possible solutions to explicitly incorporate subclonal lineages information .
In summary, we have developed a new method for inferring tumor subclonal populations by integrating sequence information gathered from SCNAs and heterozygous SNP sites. We showed that our method outperforms existing ones on simulation data, and applying it to a real breast cancer dataset is able to reveal new subclonal events not discovered before. Compared with existing methods, our method requires no additional deep sequencing of somatic point mutation sites.
The work was partly supported by National Institute of Health grant R01HG006870. The authors would also like to acknowledge dbGaP repository for providing the cancer sequencing datasets. The accession numbers for the breast cancer and prostate cancer datasets are phs000369.v1.p1 and phs000447.v1.p1, respectively.
This article has been published as part of BMC Genomics Volume 16 Supplement 2, 2015: Selected articles from the Thirteenth Asia Pacific Bioinformatics Conference (APBC 2015): Genomics. The full contents of the supplement are available online at http://0-www.biomedcentral.com.brum.beds.ac.uk/bmcgenomics/supplements/16/S2
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