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TECHNOLOGY AND CODE
published: 16 September 2020
doi: 10.3389/fbioe.2020.01021
Frontiers in Bioengineering and Biotechnology | www.frontiersin.org 1September 2020 | Volume 8 | Article 1021
Edited by:
Quan Zou,
University of Electronic Science and
Technology of China, China
Reviewed by:
Stephen J. Bush,
University of Oxford, United Kingdom
Xiaojian Shao,
National Research Council Canada -
Conseil national de recherches
Canada, Canada
*Correspondence:
Piotr Słowi ´
nski
p.m.slowinski@exeter.ac.uk
Specialty section:
This article was submitted to
Computational Genomics,
a section of the journal
Frontiers in Bioengineering and
Biotechnology
Received: 21 April 2020
Accepted: 04 August 2020
Published: 16 September 2020
Citation:
Słowi ´
nski P, Li M, Restrepo P,
Alomran N, Spurr LF, Miller C,
Tsaneva-Atanasova K and Horvath A
(2020) GeTallele: A Method for
Analysis of DNA and RNA Allele
Frequency Distributions.
Front. Bioeng. Biotechnol. 8:1021.
doi: 10.3389/fbioe.2020.01021
GeTallele: A Method for Analysis of
DNA and RNA Allele Frequency
Distributions
Piotr Słowi ´
nski 1
*, Muzi Li 2, Paula Restrepo 2,3 , Nawaf Alomran 2, Liam F. Spurr 2,4, 5,6 ,
Christian Miller 2, Krasimira Tsaneva-Atanasova 1,7 and Anelia Hor vath 2,8,9
1Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, Living Systems Institute,
Translational Research Exchange @ Exeter and The Engineering and Physical Sciences Research Council Centre for
Predictive Modelling in Healthcare, University of Exeter, Exeter, United Kingdom, 2McCormick Genomics and Proteomics
Center, School of Medicine and Health Sciences, The George Washington University, Washington, DC, United States,
3Department of Genetics and Genomics Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, United States,
4Cancer Program, Broad Institute of MIT and Harvard, Cambridge, MA, United States, 5Medical Oncology, Dana-Farber
Cancer Institute, Boston, MA, United States, 6Biological Sciences Division, Pritzker School of Medicine, The University of
Chicago, Chicago, IL, United States, 7Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and
Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria, 8Department of Pharmacology and Physiology,
School of Medicine and Health Sciences, The George Washington University, Washington, DC, United States, 9Department
of Biochemistry and Molecular Medicine, School of Medicine and Health Sciences, The George Washington University,
Washington, DC, United States
Variant allele frequencies (VAF) are an important measure of genetic variation that can
be estimated at single-nucleotide variant (SNV) sites. RNA and DNA VAFs are used as
indicators of a wide-range of biological traits, including tumor purity and ploidy changes,
allele-specific expression and gene-dosage transcriptional response. Here we present
a novel methodology to assess gene and chromosomal allele asymmetries and to aid
in identifying genomic alterations in RNA and DNA datasets. Our approach is based
on analysis of the VAF distributions in chromosomal segments (continuous multi-SNV
genomic regions). In each segment we estimate variant probability, a parameter of a
random process that can generate synthetic VAF samples that closely resemble the
observed data. We show that variant probability is a biologically interpretable quantitative
descriptor of the VAF distribution in chromosomal segments which is consistent with
other approaches. To this end, we apply the proposed methodology on data from 72
samples obtained from patients with breast invasive carcinoma (BRCA) from The Cancer
Genome Atlas (TCGA). We compare DNA and RNA VAF distributions from matched
RNA and whole exome sequencing (WES) datasets and find that both genomic signals
give very similar segmentation and estimated variant probability profiles. We also find a
correlation between variant probability with copy number alterations (CNA). Finally, to
demonstrate a practical application of variant probabilities, we use them to estimate
tumor purity. Tumor purity estimates based on variant probabilities demonstrate good
concordance with other approaches (Pearson’s correlation between 0.44 and 0.76). Our
Słowi ´
nski et al. GeTallele
evaluation suggests that variant probabilities can serve as a dependable descriptor of
VAF distribution, further enabling the statistical comparison of matched DNA and RNA
datasets. Finally, they provide conceptual and mechanistic insights into relations between
structure of VAF distributions and genetic events. The methodology is implemented in a
Matlab toolbox that provides a suite of functions for analysis, statistical assessment and
visualization of Genome and Transcriptome allele frequencies distributions. GeTallele is
available at: https://github.com/SlowinskiPiotr/GeTallele.
Keywords: variant allele fraction (VAF), RNA—DNA, earth mover’s distance (EMD), circos plot, farey sequence
INTRODUCTION
RNA and DNA carry and present genetic variation in related
yet distinct manners; the differences encoding information
about functional and structural traits. In diploid organisms,
an important measure of genetic variation is the variant
allele frequency (VAF), which can be measured from both
genomic (DNA) and transcriptomic (RNA) sequencing data
as the encoded and expressed allele frequencies, respectively.
Differential DNA-RNA allele frequencies are associated with a
variety of biological processes, such as genome admixture, and
allele-specific transcriptional regulation (Ha et al., 2012; Shah
et al., 2012; Han et al., 2015; Ferreira et al., 2016; Movassagh et al.,
2016).
RNA-DNA allele comparisons from sequencing have mostly
been approached at the nucleotide level, where they have
proven to be highly informative for determining the allelic
functional consequences (ENCODE Project Consortium, 2012;
Ha et al., 2012; Shah et al., 2012; Morin et al., 2013; Han et al.,
2015; Ferreira et al., 2016; Macaulay et al., 2016; Movassagh
et al., 2016; Reuter et al., 2016; Shi et al., 2016; Shlien et al.,
2016; Yang et al., 2016). Comparatively, integration of allele
signals at the molecular level, as derived from linear DNA and
RNA, is less comprehensively explored due to the challenges
presented by limited compatibility of the outputs from the two
sequencing assays.
Abbreviations: BRCA, breast invasive carcinoma; CDF, cumulative distribution
function; CNA, copy number alterations; CNADELETION, copy number alterations
corresponding to deletions (see section Correlation between vPR and CNA);
CNAAMPLIFICATION, copy number alterations corresponding to amplifications (see
section Correlation between vPR and CNA); CPE, consensus purity estimate;
DNA, genome; EMD, earth mover’s distance; FWER, family-wise error rate; FDR,
false discovery rate; MEA, mean absolute error; Nex, normal exome; Ntr, normal
transcriptome; rTEX,CNA,DEL, Pearson’s correlation coefficient between vPR,TEX
and CNADELETION; rTEX,CNA,AMPl, Pearson’s correlation coefficient between
vPR,TEX and CNAAMPLIFICATION; rTTR,CNA,DEL, Pearson’s correlation coefficient
between vPR,TTR and CNADELETION; rTTR,CNA,AMPL , Pearson’s correlation
coefficient between vPR,TTR and CNAAMPLIFICATION; pFDR,p-value after multiple
comparisons Benjamini and Hochberg false discovery rate correction; PDF,
probability density function; QN (e.g., Q50), N-th percentile; RNA, transcriptome;
SNV, single-nucleotide variant; TCGA, the cancer genome atlas; Tex, tumor
exome; Ttr, tumor transcriptome; VAF, variant allele frequency; VAFTEX, variant
allele frequency in tumor exome sequence; VAFTTR , variant allele frequency in
tumor transcriptome sequence; VBP, vPR based purity; vPR, variant probability;
vPR,TEX, variant probability estimated from tumor exome sequence; vPR,TTR ,
variant probability estimated from tumor transcriptome sequence; WES, whole
exome sequencing.
Herein, we introduce a novel methodology for the analysis
of DNA and RNA VAF distributions. This methodology
is motivated by the following observations that, to our
knowledge, have not been integrated into existing VAF
analysis methodologies:
1) VAF distributions can change along a chromosome and differ
between chromosomal segments (continuous multi-SNV
genomic regions);
2) VAF distribution in a chromosomal segment is
approximately symmetric;
3) VAF distribution in a chromosomal segment is a reflection
of contributions from all the genetic events in all of the cells
constituting the sequenced sample;
4) the variant and reference read counts can be modeled as
random numbers from a binomial distribution; and
5) the support of the VAF distributions is a Farey sequence.
Guided by the first three observations, our methodology is
designed to provide an aggregate description of VAF distribution
in chromosomal segments.
The fourth observation motivates the development of a
stochastic model for generating synthetic VAF samples. The
model is a binomial mixture model, meaning that each of the
mixture components is a binomial distribution parametrised by
probability of success given a number of trials. The probability
of success is equal across all binomial distributions in the
mixture, while the number of trials varies between the mixture
components. Each individual component has number of trials
that is sampled from the total read counts in the dataset. We
interpret the random numbers from this binomial mixture model
as the number of variant reads at individual SNV loci. Namely,
the common probability of success becomes variant probability,
or vPR, defined as the probability of observing a variant allele
at any site in a given chromosomal segment. We sample the
total read counts from the data to account for technical variance
arising from the sequencing process. The binomial mixture
model implies that a variant or reference read at a given site is
a result of a Bernoulli process.
Finally, the fifth observation allows for the rigorous
comparison of observed and synthetic VAF distributions,
resulting in the estimation of vPR of observed VAF distributions.
The potential benefits of the proposed approach are 2-fold:
first, by exploiting the statistical relations between SNVs in
chromosomal segment, vPR is less dependent on read depth and
hence can help to utilize sequencing signals more efficiently;
Frontiers in Bioengineering and Biotechnology | www.frontiersin.org 2September 2020 | Volume 8 | Article 1021
Słowi ´
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second, since vPR is a high-level descriptor of VAF distributions,
it allows for the direct comparison of DNA and RNA VAF
distributions without the effects of limited comparability of DNA
and RNA sequencing data.
MATERIALS AND METHODS
Data
We evaluate and demonstrate GeTallele’s functionality using
matched whole exome and RNA sequencing datasets from paired
normal and tumor tissue obtained from 72 female patients
with breast invasive carcinoma (BRCA) from TCGA. Each
dataset contains four matched sequencing sets: normal exome
(Nex), normal transcriptome (Ntr), tumor exome (Tex), and
tumor transcriptome (Ttr) (see Supplementary Table 1). The
raw sequencing data were processed as previously described
(Movassagh et al., 2016) to generate the inputs for GeTallele.
In short, all datasets were generated through paired-end
sequencing on an Illumina HiSeq platform. The human
genome reference (hg38)-aligned sequencing reads (Binary
Alignment Maps, bams) were downloaded from the Genomic
Data Commons Data Portal (https://portal.gdc.cancer.gov/) and
processed downstream through an in-house pipeline. After
variant calling (Li, 2011), the RNA-seq and whole exome
sequencing (WES) alignments, together with their respective
variant calls, were processed through the read count module
of the package RNA2DNAlign (Movassagh et al., 2016), to
produce variant and reference sequencing read counts for all the
variant positions in all four sequencing signals (normal exome,
normal transcriptome, tumor exome and tumor transcriptome).
Selected read count assessments were visually examined using the
Integrative Genomics Viewer (Thorvaldsdóttir et al., 2013).
For each sample, to select SNV positions for analysis, we start
with heterozygous SNV calls in the normal exome (Li et al.,
2009). In each of these positions, we estimate the counts of
the variant and reference reads (nVAR and nREF, respectively)
across the 4 matching datasets, and retain positions covered by
a minimum total (variant +reference) read depth for further
analyses. This threshold is flexible and is required to ensure that
only sufficiently covered positions will be analyzed; it is set to 3
in the herein presented results. For further analysis (without loss
of generality), we transform all the original VAF values to VAF
=|VAF−0.5|+0.5. We introduce this transformation due to the
symmetric nature of the VAF distributions.
In addition, we required each tumor sample to have at least
three of the following five purity estimates—Estimate, Absolute,
LUMP, IHC, and the consensus purity estimate (CPE) (Katkovnik
et al., 2002; Pagès et al., 2010; Carter et al., 2012; Yoshihara et al.,
2013; Zheng et al., 2014; Aran et al., 2015). On the same datasets,
we applied THetA (Oesper et al., 2013, 2014)—a popular tool for
assessing CNA and admixture from sequencing data—was also
applied to the datasets.
Statistics
To test statistical significance, GeTallele uses parametric and
non-parametric methods and statistical tests (Hollander et al.,
2013; Corder and Foreman, 2014). Namely, to compare
distributions of the variant allele frequencies (VAF) we use the
Kolmogorov–Smirnov test (examples of VAF distributions are
depicted in Figures 2,3). To study concurrence of windows,
we use permutation/bootstrap tests. To test relations between
vPR and copy number alterations (CNA), we use Pearson’s
correlation coefficient.
To account for multiple comparisons, we set the probability
for rejecting the null hypothesis at p<1e−5, which corresponds
to Bonferroni (Dunn, 1961) family-wise error rate (FWER)
correction against 100,000 comparisons. We use a fixed value,
rather than other approaches, to ensure better consistency and
reproducibility of the results. Alternatively, we apply Benjamini
and Hochberg (Benjamini and Hochberg, 1995) false discovery
rate (FDR) correction with a probability of accepting false
positive results pFDR <0.05. We specify the method used in the
text when reporting the results.
DESCRIPTION OF THE NOVEL
METHODOLOGY
The overall workflow of the proposed methodology as
implemented in the GeTallele is shown in Figure 1. As
input, GeTallele requires the absolute number of sequencing
reads bearing the variant and reference nucleotide in each
single-nucleotide variant (SNV) position. For each available
dataset (4 in the presented analysis) GeTallele estimates
VAF based on the variant and reference reads (nVAR and
nREF, respectively) covering the positions of interest: VAF
=nVAR/(nVAR +nREF). An example of genome-wide VAF
values estimated from tumor exome Tex dataset, and their
corresponding histogram is shown in Figure 2.
Data Segmentation
To analyse variant allele frequencies (VAF) at genome-wide level,
GeTallele first divides the VAF sequence into a set of non-
overlapping segments along the chromosomes. To partition the
data into segments, GeTallele uses a parametric global method,
which detects the breakpoints in a signal using its mean, as
implemented in the Matlab function findchangepts (Lavielle,
2005; Killick et al., 2012) In each segment, the VAFs of the
chosen signal must have a different mean than that of the adjacent
segment. In the Matlab implementation, sensitivity of breakpoint
detection can be controlled using parameter MinThreshold; with
a default setting of 0.2. Segments containing fewer than 10 data
points were merged with the preceding segment. For analysis of
matched signals, segmentation is based on one signal, and then
applied to the others. In the presented analysis, segmentation
is based mainly on Tex dataset, for comparison we also use
Ttr dataset (dataset used for segmentation is specified in the
description of the results presented in Section Results).
Estimation of Variant Probability vPR
Variant probability is a biologically interpretable quantitative
descriptor of the VAF distribution. It is the common probability
of observing a variant allele at any site in a given chromosomal
segment. The vPR is a measure describing the genomic event
that, through the sequencing process, was transformed into
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AB
CE
DF
FIGURE 1 | GeTallele and visualization of VAF data. (A) Toolbox description. (B) Visualization of the whole dataset on the level of genome using Circos plot (blue,
normal exome; cyan, normal transcriptome; orange, tumor exome; yellow, tumor transcriptome). (C) CNA values for chromosome 1. (D–F) Visualization of the VAF
values with fitted variant probability (vPR–see section Estimation of Variant Probability vPR and Figure 3). VAFTEX and VAFTTR values at the level of: chromosome
(chromosome 1) (D), custom genome region (E), and gene (F).(D) Shows that there are two chromosomal segments with different VAF distributions, likely
representing a region of copy-neutral loss of heterozygosity. (C) Shows that large scale change in the CNA is concurrent with the change in the VAF distributions. In
panel titles: Tex, vPR estimate for VAF distributions of tumor exome (orange); Ttr, vPR estimate for VAF distributions of tumor transcriptome (yellow).
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A B
FIGURE 2 | Sample and distribution of variant allele frequencies (VAF) values. (A) All the VAF values of a tumor exome sequencing signal (chromosomes 1–22) from
one of the datasets. (B) Histogram of the VAF values from (A). Centers of bins of the histogram are located at elements of a Farey sequence.
an observed distribution of VAFs. For example, in VAFDNA
from a diploid genome, we assume variant probability vPR
=0.5 (meaning that both alleles are equally probable)
corresponds to a true allelic ratio of 1:1 for heterozygous
sites. The value might differ from 0.5 due to reference
mapping biases (Degner et al., 2009). For heterozygous
sites in the DNA from a diploid monoclonal samples, the
corresponding tumor VAFDNA is expected to have the following
interpretations: vPR =1 or vPR =0 corresponding to a
monoallelic status resulting from a deletion, and vPR =0.8
(or 0.2), 0.75 (or 0.25), 0.67 (or 0.33) corresponding to allele-
specific tetra-, tri-, and duplication of the variant-bearing
allele, respectively.
The vPR of the VAFRNA is interpreted as follows. In
positions corresponding to heterozygote sites in DNA, alleles
not preferentially targeted by regulatory traits are expected
to have expression rates with variant probability vPR =0.5,
which (by default) scale with the DNA allele distribution.
Differences between VAFDNA and VAFRNA values are observed
in special cases of transcriptional regulation where one
of the alleles is preferentially transcribed over the other.
In the absence of allele-preferential transcription, VAFDNA,
and VAFRNA are anticipated to have similar vPR across
both diploid (normal) and copy number altered genomic
regions. Consequently, VAFDNA, and VAFRNA are expected
to synchronously switch between allelic patterns along the
chromosomes, with the switches indicating breakpoints of DNA
deletions or amplifications.
Since we observed that DNA and RNA signals have different
distributions of total reads and also that the distributions
of total reads vary between participants, the synthetic VAF
distributions are generated individually for each sequencing
signal and each participant.
To estimate vPR in the signals, GeTallele first generates
synthetic VAF distributions and then uses the earth mover’s
distance (EMD) (Kantorovich and Rubinstein, 1958; Levina and
Bickel, 2001) to fit them to the data. To generate a synthetic
VAF distribution with a given variant probability, vPR, GeTallele,
bootstraps 10,000 values of the total reads (sum of the variant and
reference reads; nVAR +nREF) from the analyzed signal in the
dataset. It then uses binomial pseudorandom number generator
to get number of successes for given number of total reads
and a given value of vPR (implemented in the Matlab function
binornd). The vPR is the common value of the probability of
success and generated number of successes is interpreted as an
nVAR. Since the vPR of the synthetic sample can take any value,
it can correspond to a single genomic event as well as any
combination of genomic events in any mixture of normal and
tumor populations (See section vPR Values in Mixtures of Normal
and Tumour Populations).
The analysis presented in the paper uses 51 synthetic VAF
distributions with vPR values that vary from 0.5 to 1 with
step (increment of) 0.01. The synthetic VAF distributions are
parametrized using only vPR ≥0.5, however, to generate them
we use vPR and its symmetric counterpart 1-vPR. The process of
generating synthetic VAF distributions along with examples of
synthetic and real VAF distributions with different values of vPR
are illustrated in Figure 3.
To estimate vPR, we compute the Earth mover’s distance
between the distribution of VAF values in the considered window
and the 51 synthetic VAF distributions (i.e., observed vs. synthetic
VAF). The estimate is given by the vPR of the synthetic VAF
distribution that is closest to the VAF distribution in the segment.
Earth mover’s distance (EMD) is a metric for quantifying
differences between probability distributions (Kantorovich and
Rubinstein, 1958; Levina and Bickel, 2001) and in the case of
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AB
C
D
E
F
FIGURE 3 | Synthetic and observed VAF distributions. (A) Description of the model used to generate synthetic VAF distributions, Bin(n,p) stands for binomial
distribution with parameters n (number of trials) and p (probability of success). (B–F) Synthetic VAF distributions for different values of vPR.(B,F) Show additionally
distributions of VAFTEX for the two windows shown in Figure 1D.
univariate distributions it can be computed as:
EMD (PDF1, PDF2)=ZZ
|CDF1(z)CDF2(z)|dz.
Here, PDF1and PDF2are two probability density functions,
and CDF1and CDF2are their respective cumulative distribution
functions. Z is the support of the PDFs (i.e., set of all the possible
values of the random variables described by them). Because VAFs
are defined as simple fractions with values between 0 and 1,
their support is given by a Farey sequence (Hardy and Wright,
2008) of order n; n is the highest denominator in the sequence.
For example, Farey sequence of order 2 is 0, 1/2, 1, and Farey
sequence of order 3 is 0, 1/3, 1/2, 2/3, 1. We use a Farey sequence
of order 1,000 as the support Z for estimating the vPR.
Examples of VAF distributions with fitted synthetic VAF
distributions are shown in Figures 3A,D. The dependence of
the confidence intervals of the estimation on the number of
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FIGURE 4 | Confidence intervals for artificial samples with different numbers of VAFs. Each confidence interval is based on estimation of vPR in 1,000 randomly
generated samples with a fixed vPR (True value). Light gray bar is 95% confidence interval (950 samples lay within this interval), dark gray bar is 50% confidence
interval (500 samples lay within this interval), red dot is median value.
VAF values in a segment is illustrated in Figure 4, which clearly
demonstrates that the accuracy of the estimate is positively
correlated with the number of VAFs in the chosen segment.
vPR Values in Mixtures of Normal and
Tumor Populations
Since the vPR can take any value between 0.5 and 1 it
can correspond to a single genomic event as well as any
combination of genomic events in any mixture of normal and
tumor populations. A mixture vPR value that corresponds to
a combination of genomic events can be computed using the
following expression:
vPR =Ppl=N
pl=1PeVAR={events}eVAR ·pPL
Ppl=N
pl=1PeVAR={events}eVAR ·pPL +Ppl=N
pl=1PeREF={events}eREF ·pPL
Where eVAR and eREF are the multiplicities of variant and
reference alleles and pPL is a proportion of one of the populations.
For heterozygote sites eVAR =1 and eREF =1, for deletions eVAR
=0 or eREF =0, for du-, tri- and tetraplications eVAR or eREF can
be equal to 2, 3 or 4, respectively. The sum of proportions pPL
over the populations is equal 1. For example, for a mixture of 1
normal (N, pN=0.44) and 2 tumor populations (T1, pT1 =0.39
and T2, pT2 =0.17), T1 with deletion and T2 with deletion the
mixture vPR value can be computed as follows:
vPR =pN·B+pT1 ·B+pT2 ·B
pN·(A+B)+pT1 ·(0+B)+pT2 ·(0+B)
=0.44 ·1+0.39 ·1+0.17 ·1
0.44 ·(1+1)+0.39 ·(1+0)+0.17 ·(1+0)=0.694.
By comparing the vPR values estimated from data with possible
mixture vPR values we propose to estimate sample purity and
its clonal composition. To this end, we first generate a full set
of proportions of all the population in the mixture with step
(increment of) 0.01 and compute all the possible vPR values
that each of the mixtures could produce. For step 0.01: two
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populations (1 tumor) give 99 proportions, three populations
(2 tumors) give 4,851 proportions, four populations (3 tumors)
give 156,849 proportions. The matrices with mixture vPR values
for each proportion, vary from 2 ×2, for two populations
with deletions, to 35 ×35 for four populations with all events
up to tetra-plications. Then, we run an exhaustive approximate
search over all the matrices with mixture vPR values over all the
proportions. The search is approximate because the estimated
vPR values have limited accuracy and because we consider only
discrete values of proportions. In the analysis we define a match
between estimated and mixture vPR values if they differ by <
0.009 (we chose a value that is smaller than the smallest difference
between possible vPR estimates). The search returns a large
number of admissible mixtures that could produce the estimated
vPR values. This process is illustrated in Figure 5.
To visualize the admissible mixtures, we use ternary plots,
which allow us to illustrate composition of three components in
two dimensions. The composition, represented by ratios of the
three components, which sum to a constant, is depicted as point
inside or on the edge of an equilateral triangle. If the point is on
the edges, the composition has only two components. To help
interpretation of the ternary plots, we also plot the grid lines that
are parallel to the sides of the triangle. These gridlines indicate
the directions of constant ratios of the components. Along such
direction the ratio of one of the components is fixed and only
the other two ratios vary. Examples of visualization of admissible
mixtures on ternary plots are shown in Figures 5,6.
To facilitate analysis of the admissible mixtures returned
by the search procedure we introduce mixture complexity.
Mixture complexity is a measure that increases with number
of populations as well as with variety of genetic events. From
the simplest mixture of 1 normal and 1 tumor population in
which only deletions are possible to a model with 1 normal
and multiple tumor populations where each can have deletions,
and any level of multiplications. In practice, we set the limit at
3 tumor populations and tetra-plications. Mixture complexity
helps to group and visualize admissible mixtures. Mixtures with
higher complexity allow more possible vPR values, meaning that
it is easier to find the match with the estimated vPR values but
that the number of admissible mixtures increases (see Figure 6).
We, further, observe that proportion of normal population, pN,
increases with a number of clonal tumor populations included
in the model mixture and that, generally, pNstays constant with
increasing variety of genetic events, for a fixed number of clonal
tumor populations. We note that this is just one of many possible
ways of deciding which solution should be chosen.
RESULTS
To evaluate the proposed methodology, we apply it on matched
normal and tumor exome and transcriptome sequencing data of
72 breast carcinoma (BRCA) datasets with pre-assessed copy-
number and genome admixture estimates acquired through
TCGA (see Materials and Methods). We first compare DNA
and RNA VAF distributions from matched sequencing datasets
and find that both genomic signals give very similar results in
terms of segmentation and estimated variant probability values.
We further assess the correlations between vPR values and copy
number alterations (CNA) values and find that they are in
agreement with each other. Finally, we use the vPR values to
estimate tumor purity. The purity estimates based on vPR values
show good concordance with alternative approaches.
Segmentation Results
Segmentation of the data, based on the tumor exome signal,
resulted in 2,697 chromosomal segments across the 72 datasets.
We excluded from further analysis 294 chromosomal segments
where either tumor exome or transcriptome had vPR >=
0.58 but their VAF distribution could not be differentiated
from the model VAF distributions with vPR =0.5 (p>
1e−5, Kolmogorov Smirnov test, equivalent to Bonferroni
FWER correction for 100,000 comparisons). The 294 excluded
chromosomal segments, corresponding to 4% of the total length
of the data in base pairs and 4% of all the available data
points. This implies these short segments containing few VAF
values. In the remaining 2,403 chromosomal segments, we
systematically examined the similarity between corresponding
VAFTEX (tumor exome), VAFTTR (tumor transcriptome), and
CNA. We obtained several distinct patterns of coordinated RNA-
DNA allelic behavior as well as correlations with CNA data.
In 60% of all analyzed chromosomal segments the
distributions of VAFTEX and VAFTTR were statistically
concordant (P>1e−5, Kolmogorov Smirnov test), and in
40% they were statistically discordant (P<1e−5, Kolmogorov
Smirnov test). In two chromosomal segments, VAFTEX and
VAFTTR, had the same vPR, while having statistically different
VAF distributions (P <1e−5, Kolmogorov Smirnov test).
We consider such chromosomal segments as concordant.
The vPR robustly characterizes VAF sample while the
Kolmogorov-Smirnov test is very sensitive for differences
between distributions that might be caused by to technical
variance. In the vast majority of the discordant chromosomal
segments vPR of the VAFTTR, vPR,T TR, was higher than vPR of the
VAFTEX, vPR,TEX , (only in 21 out of 959 discordant chromosomal
segments vPR,TTR was lower than vPR,TEX).
Concurrence of Segmentation Based on
DNA and RNA
We next analyzed the concurrence between chromosomal
segments resulting from independent segmentations of the
tumor exome (VAFTEX) and transcriptome (VAFTTR) datasets
(2,697 and 3,605 chromosomal segments, respectively, across
all the samples). We first assessed chromosome-wise alignment
of the start and end points of the chromosomal segments.
In 45% of the chromosomes both VAFTEX and VAFTTR
signals produce a single segment that contains the whole
chromosome. In 33% of chromosomes both signals produced
multiple chromosomal segments. These chromosomal segments
are well aligned, with 90% of the breakpoints differing <7%
of data points in the chromosome, e.g., they are <70 points
apart if the chromosome contains 1,000 data points; Q50 =
0.02%, Q75 =2% of data points in the chromosome. The
probability of observing such an alignment by chance is smaller
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FIGURE 5 | Mixtures admissible by the vPR values estimated from data. To uncover mixtures that could produce the three estimated vPR values we perform an
exhaustive approximate search of all the possible vPR values produced by any mixture of the populations with a given set of genetic events. In each case we generate
a full set of proportions with a given step (e.g., 0.01) and compute all the possible vPR values that such a mixture could produce. In the illustrated cases: 2 populations
(1 tumor) could produce the estimated vPR values through a deletion (estimated vPR =0.62 and vPR =0.63) and via deletion of one allele and duplication of another
(estimated vPR =0.69); 3 populations (2 tumors) could produce the estimated vPR values through a deletion in one of the tumor populations (estimated vPR =0.62
and vPR =0.63) and via deletion in both of the tumor populations (estimated vPR =0.69). The 2 populations case admits a single mixture and the 3 populations allow
9 mixtures with similar compositions. The admissible mixtures are depicted on the ternary plots, red circle indicates solution corresponding to the presented matrix.
We exclude mixture vPR values that result from deletion of both the variant and reference alleles (empty fields in the matrices).
than p=1e−5 (100,000 bootstrap samples with breakpoints
assigned randomly in all the individual chromosomes where
both signals produced multiple chromosomal segments). In 22%
of the chromosomes, segments based on VAFTEX and VAFTTR
signals were positionally discordant—one signal produced a
single segment containing whole chromosome while the other
produced multiple chromosomal segments.
To compare the vPR values in the 55% of chromosomes
where at least one signal produced more than one chromosomal
segment, we computed chromosome-wise mean absolute error
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A
B
FIGURE 6 | Admissible mixtures for increasing mixture complexity. (A) Shows admissible mixtures for 3 different mixtures with increasing complexity. The simplest
mixture (mixture with the lowest number of components and the simplest set of genetic events) is show within the gray frame. On each ternary plot, the admissible
mixtures are indicated by gray dots. The green axis indicates proportion of the normal population (N), the yellow axis indicates proportion of the 1st tumor population
(T1), the blue axis shows proportion of the 2nd tumor population (T2), or sum of the 2nd and 3rd tumor populations (T2 +T3). (B) Schematic representation of
increasing complexity of the mixture models. From a mixture of 1 normal and 1 tumor population in which only deletion is possible to a model with 1 normal and 3
tumor populations and each can have deletions, du-, tri-, and tetraplications.
(MAE) between the vPR in two sets of chromosomal segments.
To account for different start and end points of the segments
we interpolated the vPR values (nearest neighbor interpolation)
at each data point in the chromosome. We separately compared
the vPR,TEX and vPR,TTR values. Assessment of alignment using
MAE showed strong concordance: vPR,TEX agreed perfectly in
11% of the chromosomes and had the percentiles of MAE equal
to Q50 =0.012, Q75 =0.022 and Q97.5 =0.047, while vPR,TTR
agreed perfectly in 8% but had slightly higher percentiles of
MAE Q50 =0.019, Q75 =0.034 and Q97.5 =0.07. vPR,TEX
and vPR,TTR values had MAE =0 simultaneously in 4% of the
chromosomes. Probability of observing such values of MAE by
chance is smaller than p=1e−3 (1,000 random assignments of
vPR,TEX and vPR,TTR values to windows in the 873 chromosomes
where at least one signal had more than one chromosomal
segment). It is noteworthy that MAE Q97.5 <0.07 is comparable
with the confidence interval of single vPR estimate based on
50 VAF values. In other words, both signals in a sample (Tex
and Ttr) give very similar results in terms of segmentation and
estimated values of the vPR. Albeit, segmentation of VAFTTR
generates a higher number of chromosomal segments. The
higher number of VAFTTR chromosomal segments indicates
that transcriptional regulation occurs at a smaller scale than
alterations in DNA. Figure 7 shows examples of concurrence
between chromosomal segments based on VAFTEX and VAFTTR
signals in a positionally concordant chromosome (both signals
produced multiple segments).
Correlation Between vPR and CNA
Finally, we assess the correlations between vPR and CNA in
the individual samples. We separately computed correlations for
deletions and amplifications. In order to separate deletions and
amplifications, for each data set we found CNAMIN, value of the
CNA in the range −0.3 to 0.3 that had the smallest corresponding
vPR,TEX. To account for observed variability of the CNA values
near the CNAMIN, we set the threshold for amplifications to
CNAAMPLIFICATION =CNAMIN-0.05, and for deletions we set
it to CNADELETION =CNAMIN +0.05 (each data set had a
different threshold).
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A
B
C
D
FIGURE 7 | Illustration of concurrence between chromosomal segment resulting from independent segmentations of the dataset based on the VAFTEX and VAFTTR
signals. (A) Yellow dots, VAFTTR; gray circles, vPR,TTR interpolated at all data points in segments based on VAFTEX; yellow crosses, vPR,TTR interpolated at all data points
in segments based on VAFTTR.(B) Bar plot of the absolute difference between the vPR values in the two kinds of chromosomal segments. (C) orange dots, VAFTEX;
gray crosses, vPR,TEX interpolated at all data points in segments based on VAFTEX; orange dots vPR,TEX interpolated at all data points in segments based on VAFTTR.
(D) Bar plot of the absolute difference between the vPR values in the two kinds of chromosomal segments.
For VAFTEX, we observed significant correlations with
negative trend between vPR,TEX and CNA ≤CNADELETION in
57 datasets and with a positive trend between vPR,TEX and CNA
≥CNAAMPLIFICATION in 39 datasets (pFDR <0.05, Pearson’s
correlation with Benjamini Hochberg multiple comparison
correction for 72 samples). For VAFTTR, we observed significant
correlations with a negative trend between vPR,TTR and CNA ≤
CNADELETION in 62 datasets and with positive trend between
vPR,TTR and CNA ≥CNAAMPLIFICATION in 33 datasets (pFDR <
0.05, Pearson correlation with Benjamini Hochberg correction).
These correlations indicate that the segmentation and the
estimated vPR values are concordant with CNA calls. However,
the vPR values (estimated at the level of chromosomal segments)
do not differentiate between positive and negative values of
the CNA, meaning it is not possible to use vPR alone to call
amplifications and deletions.
Figure 8 shows four typical patterns of correlation between
the CNA and vPR values observed in the data. In Figure 8A,
all the values of CNA are close to CNAMIN. In Figure 8B, the
relationship between CNA and vPR is noisy, only correlations
between vPR,TTR and CNA ≤CNADELETION are statistically
significant (rTEX,CNA,DEL = −0.29, pFDR =0.063; rTEX,CNA,DEL
= −0.38, pFDR =0.012; rTEX,CNA,AMPL =0.14, pFDR =0.58;
rTEX,CNA,AMPL =0.19, pFDR =0.47; Pearson’s correlation with
Benjamini Hochberg multiple comparison correction for 72
samples). In Figure 8C all the correlations are statistically
significant, vPR,TTR values (circles) follow closely the vPR,TEX
(squares) indicating that in most of the windows distributions
of the VAFTEX and VAFTTR are concordant (rTEX,CNA,D =
−0.91, pFDR <1e−10; rTEX,CNA,DEL = −0.96, pFDR <1e−10;
rTEX,CNA,AMPL =0.92, pFDR <1e−10; rTEX,CNA,AMPL =0.95,
pFDR <1e−10). In Figure 8D correlations between vPR,TEX,
vPR,TTR and CNA ≤CNADare statistically significant, but there
is a large difference (with median of 0.18) between vPR,TEX
and vPR,TTR values, indicating that in most of the windows the
distributions of the VAFTEX and VAFTTR in this dataset are
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A B
CD
FIGURE 8 | Illustration of the correlations between vPR and CNA. Orange squares vPR,TEX, yellow circles vPR,TTR . Lines, least-squares fitted trends for significant
correlations (orange correlation with vPR,TEX, yellow correlation with vPR,TTR). Black, vPR for CNAMIN ±0.05. Correlations for all the datasets are shown in
Supplementary Figure 1.(A) All the values of CNA are close to CNAMIN =0. (B) Relationship between CNA and vPR is noisy, only some correlations are statistically
significant. (C) All the correlations are statistically significant, vPR,TTR values (circles) follow closely the vPR,TEX (squares) indicating concordance of the VAFTEX and
VAFTTR distributions. (D) Only correlations for CNA ≤CNADare statistically significant.
discordant (rTEX,CNA,DEL = −0.44, pFDR =0.047; rTEX,CNA,DEL
= −0.64, pFDR =0.0017; rTEX,CNA,AMPL =0.44 pFDR =0.16;
rTEX,CNA,AMPL =0.28, pFDR =0.41). In many of the datasets we
observe that the vPR,TTR values are higher than the corresponding
vPR,TEX values (median vPR,TTR-vPR,TEX =0.03), likely indicative
of preferential transcription of some alleles in the chromosomal
segment. Correlations between vPR and CNA in all datasets are
shown in the Supplementary Figure 1.
vPR Based Purity Estimation
To demonstrate a practical application of the vPR values we use
them to estimate tumor purity of the samples. To this end we
compared the vPR based purity (VBP) estimates with ESTIMATE,
ABSOLUTE, LUMP, IHC, and the Consensus Purity Estimation
(CPE) (Katkovnik et al., 2002; Pagès et al., 2010; Carter et al.,
2012; Yoshihara et al., 2013; Zheng et al., 2014; Aran et al., 2015).
To obtain the VBP estimate we used vPR,TEX values. We,
first, selected the vPR,TEX values that: 1. are estimated with high
confidence, i.e., are based on at least 50 VAF values; 2. are most
likely heterozygous in normal exome, i.e., have a corresponding
vPR value in normal exome vPR,NEX <0.58; 3. most likely have
vPR,TEX >0.5, i.e., their p-value for comparison with vPR,TEX =
0.5 is very small p<1e−5 (Kolmogorov-Smirnov test).
Next, we used the selected vPR,TEX values to find all admissible
mixtures (with 1–3 tumor populations and allowing for all events,
from deletions to tetraplications). To estimate the VBP, out of
all the admissible mixtures we chose these with lowest mixture
complexity and among these mixtures we take one with the
highest pN(proportion of the normal population). The VBP,
percentage of tumor populations in the sample, is then given as
1-pN. Such approach provides rather conservative estimates of
VBP (the smallest 1-pN). However, GetAllele can be extended to
offer alternative methods of employing the admissible mixtures
to estimate VBP. Development, analysis and comparison of
alternative VBP estimation methods is beyond scope of the
current paper.
Figure 9A shows violin plots of all considered 1-pNvalues
and (x) indicates the smallest value taken as a VBP estimate.
In two of the datasets we could not estimate the purity due to
lack of suitable vPR,TEX values. The VBP estimates shows the
best agreement with ABSOLUTE method (y =0.86 x +0.02,
r=0.76, p<3.4e−14, Pearson’s correlation, Figure 9B2). We
suppose that this is because the ABSOLUTE method is based on
copy number distributions, and our analysis (Section Correlation
Between vPR and CNA) revealed high correlations between the
CNAs and vPR values. Similar, to the ABSOLUTE method, VBP
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A
B1
B4 B5
B2 B3
C
FIGURE 9 | Illustration of purity estimation based on model mixtures and vPR,TEX . Comparison of the Estimate (EST), Absolute (ABS), LUMP, IHC, and the consensus
purity estimate (CPE) methods with vPR based purity (VBP). (A) Violin plots show distributions of purity based on all the admissible proportions of the normal
population (x) indicates the lowest value selected as the most conservative estimate; colors corresponding to the different methods are indicated in (B1–5).(B1–5)
Correlation of the VBP with individual methods; colored line indicates best fit linear trend. (C) Matrix showing significant p<0.05 Pearson’s correlation coefficients
between all tested methods.
estimates are generally lower than the other purity estimates
(ESTIMATE, LUMP, IHC, CPE); see Figures 9B1–5.
The approach presented in this section differs from other
methods for inferring genomic mixture composition in that
it is based on chromosomal segments with at least 50 VAF
values which can extend over millions of base pairs. In
contrast, PyClone (Roth et al., 2014) is based on sets of
carefully selected individual deeply sequenced VAF values,
while SciClone (Miller et al., 2014) and TPES (Locallo et al.,
2019) are based on analysis of selected VAF values aggregated
from the genome-wide sequences (multiple chromosomes). By
using chromosomal segments, vPR allows for a more granular
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description of the VAF distributions than aggregating genome-
wide VAF values. At the same time, basing purity estimation on
vPR values allows for the use of SNVs with a low sequencing
depth (3 in the presented analysis). Rigorous comparison
of the performance of the different methods is beyond the
scope of this demonstration of potential practical applications
of vPR.
DISCUSSION
We present a novel methodology to assess allele asymmetries
in RNA and DNA datasets using VAF. Simultaneous analysis of
RNA and DNA VAF is becoming more feasible with the growing
accessibility of paired RNA and DNA sequencing datasets
from the same individual (ENCODE Project Consortium, 2012;
Macaulay et al., 2016; Reuter et al., 2016). Our approach
addresses the compatibility between RNA and DNA VAF
estimations and the high VAF variability by introducing
variant probability, vPR, a high-level descriptor of VAF
distributions in chromosomal segments (continuous multi-SNV
genomic regions).
vPR is a parameter of a stochastic model of VAF distributions
that allows for the generation of synthetic VAF samples
that closely resembles the observed data. The simplicity and
transparency of vPR is one of the biggest advantages of the
presented methodology over other existing methods.
Using variant probability, we analyzed relationships between
DNA and RNA VAF estimations and biological processes.
We observed that, in chromosomes affected by deletions and
amplifications, VAFRNA and VAFDNA showed highly concordant
breakpoint calls. This indicates that VAFRNA alone can serve
as preliminary indicator for break points of DNA deletions
or amplifications if they fall within the regions covered by
sequencing, and potential could facilitate the estimation of CNAs
from RNA-sequencing data. Furthermore, a large proportion of
vPR estimates based on VAFRNA samples are higher than vPR
estimates based on VAFDNA indicating preferential transcription
of some alleles in a number of chromosomal segments. Finally,
we showcased that matched vPR,NEX and vPR,TEX values can be
used to model the proportions of normal and tumor populations,
thereby providing an estimate of the tumor purity. The purity
estimates based on variant probabilities show good concordance
with other approaches (Pearson’s correlation between 0.44 and
0.76; as illustrated in Figure 9). Additionally, once the mixture
composition is estimated, vPR values allow for the interrogation
of genetic events in each population at a specific chromosomal
segment (as illustrated in Figure 5).
Since VAF estimations can be affected by allele mapping
bias (Degner et al., 2009) which can lead to overestimation of
the reference allele count (Brandt et al., 2015), we suggest that
GetAllele input is generated from SNV-aware alignments, which
perform better in VAF-based downstream analyses (Spurr et al.,
2020). We note that SNV-aware alignments are now facilitated by
recent methodological advances, including the implementation
of the WASP method (Van De Geijn et al., 2015) in the STAR
aligner (Dobin et al., 2013).
Based on our results, variant probabilities can serve as a
dependable descriptor of VAF distribution and can be used
to assess allele asymmetries or to aid in making matched
calls of genomic events in sequencing RNA and DNA datasets
without limitations caused by their different molecular nature.
Finally, vPR provides conceptual and mechanistic insights
into relationships between VAF distributions and underlying
genetic events.
Methods for estimating and analyzing vPR values are
implemented in a GeTallele toolbox. GeTallele allows to analyse
and visualize patterns observed in the VAF distributions at
a desired resolution, such as the chromosome, gene or other
custom genomic level.
DATA AVAILABILITY STATEMENT
The data analyzed in this study is subject to the following
licenses/restrictions: The datasets used and/or analyzed during
the current study are available from the corresponding author on
reasonable request. Requests to access these datasets should be
directed to p.m.slowinski@exeter.ac.uk.
AUTHOR CONTRIBUTIONS
PS, ML, PR, NA, LS, CM, KT-A, and AH conception and design
of the work. ML data acquisition. PS data analysis. PS, ML, PR,
LS, KT-A, and AH interpretation of data. PS creation of new
software used in the work. PS, ML, PR, LS, KT-A, and AH
have drafted the work or substantively revised it. All authors
approved the submitted version. All authors agreed both to be
personally accountable for the author’s own contributions and
to ensure that questions related to the accuracy or integrity of
any part of the work, even ones in which the author was not
personally involved, are appropriately investigated, resolved, and
the resolution documented in the literature.
FUNDING
This work was supported by McCormick Genomic and
Proteomic Center (MGPC), The George Washington University;
[MGPC_PG2018 to AH]. Work of PS was generously supported
by the Wellcome Trust Institutional Strategic Support Award
[204909/Z/16/Z]. KT-A gratefully acknowledges the financial
support of the EPSRC via grant EP/N014391/1.
ACKNOWLEDGMENTS
This manuscript has been released as a pre-print at bioRxiv
https://www.biorxiv.org/content/10.1101/491209v3, (Słowi´
nski
et al., 2020).
SUPPLEMENTARY MATERIAL
The Supplementary Material for this article can be found
online at: https://www.frontiersin.org/articles/10.3389/fbioe.
2020.01021/full#supplementary-material
Frontiers in Bioengineering and Biotechnology | www.frontiersin.org 14 September 2020 | Volume 8 | Article 1021
Słowi ´
nski et al. GeTallele
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Conflict of Interest: The authors declare that the research was conducted in the
absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
Copyright © 2020 Słowi´
nski, Li, Restrepo, Alomran, Spurr, Miller, Tsaneva-
Atanasova and Horvath. This is an open-access article distributed under the terms
of the Creative Commons Attribution License (CC BY). The use, distribution
or reproduction in other forums is permitted, provided the original author(s)
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