# Inferring Somatic Signatures from Single Nucleotide Variant Calls

## Table of Contents

- 1. Motivation: The Concept Behind Mutational Signatures
- 2. Methodology: From Mutations to Somatic Signatures
- 3. Workflow: Analysis with the SomaticSignatures Package
- 4. Use case: Estimating Somatic Signatures from TCGA WES Studies
- 4.1. Data: Preproccessing of the TCGA WES Studies
- 4.2. Motifs: Extracting the Sequence Context of Somatic Variants
- 4.3. Decomposition: Inferring Somatic Signatures
- 4.4. Assessment: Number of Signatures
- 4.5. Visualization: Exploration of Signatures and Samples
- 4.6. Clustering: Grouping by Motifs or Samples
- 4.7. Extension: Correction for Batch Effects and Confounding Variables
- 4.8. Extension: Normalization of Sequence Motif Frequencies
- 4.9. Extension: Motifs from Non-Reference Genomes

- 5. Alternatives: Inferring Somatic Signatures with Different Approaches
- 6. Frequently Asked Questions
- 7. References
- 8. Session Information

## 1 Motivation: The Concept Behind Mutational Signatures

Recent publications introduced the concept of identifying mutational signatures
from cancer sequencing studies and linked them to potential mutation generation
processes [11,2,3]. Conceptually, this relates somatically
occurring *single nucleotide variants* (SNVs) to the surrounding sequence which
will be referred to as *mutational* or *somatic motifs* in the following. Based
on the frequency of the motifs occurring in multiple samples, these can be
decomposed mathematically into so called *mutational signatures*. In case of
the investigation of tumors, the term *somatic signatures* will be used here to
distinguish them from germline mutations and their generating processes.

The `SomaticSignatures`

package provides an efficient and user-friendly
implementation for the extraction of somatic motifs based on a list of
somatically mutated genomic sites and the estimation of somatic signatures with
different matrix decomposition algorithms. Methodologically, this is based on
the work of Nik-Zainal and colleagues [11]. If you
use `SomaticSignatures`

in your research, please cite it as:

Gehring, Julian S., Bernd Fischer, Michael Lawrence, and Wolfgang Huber.

SomaticSignatures: Inferring Mutational Signatures from Single Nucleotide Variants.

Bioinformatics, 2015, btv408. http://dx.doi.org/10.1093/bioinformatics/btv408

## 2 Methodology: From Mutations to Somatic Signatures

The basic idea of somatic signatures is composed of two parts:

Firstly, each somatic mutation is described in relation of the sequence context
in which it occurs. As an example, consider a SNV, resulting in the alteration
from `A`

in the normal to `G`

in the tumor sample, that is embedded in the
sequence context `TAC`

. Thus, the somatic motif can be written as `TAC>TGC`

or
`T.C A>G`

. The frequency of these motifs across multiple samples is then
represented as a matrix \(M_{ij}\), where \(i\) counts over the motifs and \(j\) over
the samples.

In a second step, the matrix \(M\) is numerically decomposed into two matrices \(W\) and \(H\)

\(M_{ij} \approx \sum_{k=1}^{r} W_{ik} H_{kj}\)

for a fixed number \(r\) of signatures. While \(W\) describes the composition of each signature in term of somatic motifs, \(H\) shows the contribution of the signature to the alterations present in each sample.

## 3 Workflow: Analysis with the SomaticSignatures Package

The `SomaticSignatures`

package offers a framework for inferring signatures of
SNVs in a user-friendly and efficient manner for large-scale data sets. A tight
integration with standard data representations of the `Bioconductor`

project
[8] was a major design goal. Further, it extends
the selection of multivariate statistical methods for the matrix decomposition
and allows a simple visualization of the results.

For a typical workflow, a set of variant calls and the reference sequence are
needed. Ideally, the SNVs are represented as a `VRanges`

object with the
genomic location as well as reference and alternative allele defined. The
reference sequence can be, for example, a `FaFile`

object, representing an
indexed FASTA file, a `BSgenome`

object, or a `GmapGenome`

object.
Alternatively, we provide functions to extract the relevant information from
other sources of inputs. At the moment, this covers the *MuTect*
[4] variant caller.

Generally, the individual steps of the analysis can be summarized as:

- The somatic motifs for each variant are retrieved from the reference sequence
with the
`mutationContext`

function and converted to a matrix representation with the`motifMatrix`

function. - Somatic signatures are estimated with a method of choice (the package
provides with
`nmfDecomposition`

and`pcaDecomposition`

two approaches for the NMF and PCA). - The somatic signatures and their representation in the samples are assessed with a set of accessor and plotting functions.

To decompose \(M\), the `SomaticSignatures`

package implements two methods:

- Non-negative matrix factorization (NMF)
- The NMF decomposes \(M\) with the constraint of positive components in \(W\) and \(H\) [7]. The method was used [11] for the identification of mutational signatures, and can be computationally expensive for large data sets.
- Principal component analysis (PCA)
- The PCA employs the eigenvalue decomposition and is therefore suitable for large data sets [13]. While this is related to the NMF, no constraint on the sign of the elements of \(W\) and \(H\) exists.

Other methods can be supplied through the `decomposition`

argument of the
`identifySignatures`

function.

## 4 Use case: Estimating Somatic Signatures from TCGA WES Studies

In the following, the concept of somatic signatures and the steps for inferring
these from an actual biological data set are shown. For the example, somatic
variant calls from whole exome sequencing (WES) studies from The Cancer Genome
Atlas (TCGA) project will be used, which are part of the
`SomaticCancerAlterations`

package.

library(SomaticSignatures)

library(SomaticCancerAlterations) library(BSgenome.Hsapiens.1000genomes.hs37d5)

### 4.1 Data: Preproccessing of the TCGA WES Studies

The `SomaticCancerAlterations`

package provides the somatic SNV calls for eight
WES studies, each investigating a different cancer type. The metadata
summarizes the biological and experimental settings of each study.

sca_metadata = scaMetadata() sca_metadata

Cancer_Type Center NCBI_Build Sequence_Source gbm_tcga GBM broad.mit.edu 37 WXS hnsc_tcga HNSC broad.mit.edu 37 Capture kirc_tcga KIRC broad.mit.edu 37 Capture luad_tcga LUAD broad.mit.edu 37 WXS lusc_tcga LUSC broad.mit.edu 37 WXS ov_tcga OV broad.mit.edu 37 WXS skcm_tcga SKCM broad.mit.edu 37 Capture thca_tcga THCA broad.mit.edu 37 WXS Sequencing_Phase Sequencer Number_Samples gbm_tcga Phase_I Illumina GAIIx 291 hnsc_tcga Phase_I Illumina GAIIx 319 kirc_tcga Phase_I Illumina GAIIx 297 luad_tcga Phase_I Illumina GAIIx 538 lusc_tcga Phase_I Illumina GAIIx 178 ov_tcga Phase_I Illumina GAIIx 142 skcm_tcga Phase_I Illumina GAIIx 266 thca_tcga Phase_I Illumina GAIIx 406 Number_Patients Cancer_Name gbm_tcga 291 Glioblastoma multiforme hnsc_tcga 319 Head and Neck squamous cell carcinoma kirc_tcga 293 Kidney Chromophobe luad_tcga 519 Lung adenocarcinoma lusc_tcga 178 Lung squamous cell carcinoma ov_tcga 142 Ovarian serous cystadenocarcinoma skcm_tcga 264 Skin Cutaneous Melanoma thca_tcga 403 Thyroid carcinoma

The starting point of the analysis is a `VRanges`

object which describes the
somatic variants in terms of their genomic locations as well as reference and
alternative alleles. For more details about this class and how to construct it,
please see the documentation of the `VariantAnnotation`

package
[12]. In this example, all mutational calls
of a study will be pooled together, in order to find signatures related to a
specific cancer type.

sca_data = unlist(scaLoadDatasets()) sca_data$study = factor(gsub("(.*)_(.*)", "\\1", toupper(names(sca_data)))) sca_data = unname(subset(sca_data, Variant_Type %in% "SNP")) sca_data = keepSeqlevels(sca_data, hsAutosomes(), pruning.mode = "coarse") sca_vr = VRanges( seqnames = seqnames(sca_data), ranges = ranges(sca_data), ref = sca_data$Reference_Allele, alt = sca_data$Tumor_Seq_Allele2, sampleNames = sca_data$Patient_ID, seqinfo = seqinfo(sca_data), study = sca_data$study) sca_vr

VRanges object with 594607 ranges and 1 metadata column: seqnames ranges strand ref alt <Rle> <IRanges> <Rle> <character> <characterOrRle> [1] 1 887446 * G A [2] 1 909247 * C T [3] 1 978952 * C T [4] 1 981607 * G A [5] 1 985841 * C T ... ... ... ... ... ... [594603] 22 50961303 * G T [594604] 22 50967746 * C A [594605] 22 50967746 * C A [594606] 22 51044090 * C T [594607] 22 51044095 * G A totalDepth refDepth altDepth sampleNames <integerOrRle> <integerOrRle> <integerOrRle> <factorOrRle> [1] <NA> <NA> <NA> TCGA-06-5858 [2] <NA> <NA> <NA> TCGA-32-1977 [3] <NA> <NA> <NA> TCGA-06-0237 [4] <NA> <NA> <NA> TCGA-06-0875 [5] <NA> <NA> <NA> TCGA-06-6693 ... ... ... ... ... [594603] <NA> <NA> <NA> TCGA-BJ-A0Z0 [594604] <NA> <NA> <NA> TCGA-BJ-A2NA [594605] <NA> <NA> <NA> TCGA-BJ-A2NA [594606] <NA> <NA> <NA> TCGA-EM-A3FK [594607] <NA> <NA> <NA> TCGA-EL-A3T0 softFilterMatrix | study <matrix> | <factor> [1] | GBM [2] | GBM [3] | GBM [4] | GBM [5] | GBM ... ... . ... [594603] | THCA [594604] | THCA [594605] | THCA [594606] | THCA [594607] | THCA ------- seqinfo: 22 sequences from an unspecified genome hardFilters: NULL

To get a first impression of the data, we count the number of somatic variants per study.

sort(table(sca_vr$study), decreasing = TRUE)

LUAD SKCM HNSC LUSC KIRC GBM THCA OV 208724 200589 67125 61485 24158 19938 6716 5872

### 4.2 Motifs: Extracting the Sequence Context of Somatic Variants

In a first step, the sequence motif for each variant is extracted based on the
genomic sequence. Here, the `BSgenomes`

object of the human hg19 reference is
used for all samples. However, personalized genomes or other sources for
sequences, for example an indexed FASTA file, can be used naturally.
Additionally, we transform all motifs to have a pyrimidine base (`C`

or `T`

) as
a reference base [2]. The resulting `VRanges`

object
then contains the new columns `context`

and `alteration`

which specify the
sequence content and the base substitution.

sca_motifs = mutationContext(sca_vr, BSgenome.Hsapiens.1000genomes.hs37d5) head(sca_motifs)

VRanges object with 6 ranges and 3 metadata columns: seqnames ranges strand ref alt <Rle> <IRanges> <Rle> <character> <characterOrRle> [1] 1 887446 * G A [2] 1 909247 * C T [3] 1 978952 * C T [4] 1 981607 * G A [5] 1 985841 * C T [6] 1 1120451 * C T totalDepth refDepth altDepth sampleNames <integerOrRle> <integerOrRle> <integerOrRle> <factorOrRle> [1] <NA> <NA> <NA> TCGA-06-5858 [2] <NA> <NA> <NA> TCGA-32-1977 [3] <NA> <NA> <NA> TCGA-06-0237 [4] <NA> <NA> <NA> TCGA-06-0875 [5] <NA> <NA> <NA> TCGA-06-6693 [6] <NA> <NA> <NA> TCGA-26-1439 softFilterMatrix | study alteration context <matrix> | <factor> <DNAStringSet> <DNAStringSet> [1] | GBM CT G.G [2] | GBM CT A.G [3] | GBM CT G.G [4] | GBM CT G.C [5] | GBM CT A.G [6] | GBM CT C.G ------- seqinfo: 22 sequences from an unspecified genome hardFilters: NULL

To continue with the estimation of the somatic signatures, the matrix \(M\) of the
form {motifs × studies} is constructed. The `normalize`

argument specifies
that frequencies rather than the actual counts are returned.

sca_mm = motifMatrix(sca_motifs, group = "study", normalize = TRUE) head(round(sca_mm, 4))

GBM HNSC KIRC LUAD LUSC OV SKCM THCA CA A.A 0.0083 0.0098 0.0126 0.0200 0.0165 0.0126 0.0014 0.0077 CA A.C 0.0093 0.0082 0.0121 0.0217 0.0156 0.0192 0.0009 0.0068 CA A.G 0.0026 0.0061 0.0046 0.0144 0.0121 0.0060 0.0004 0.0048 CA A.T 0.0057 0.0051 0.0070 0.0134 0.0100 0.0092 0.0007 0.0067 CA C.A 0.0075 0.0143 0.0215 0.0414 0.0390 0.0128 0.0060 0.0112 CA C.C 0.0075 0.0111 0.0138 0.0415 0.0275 0.0143 0.0018 0.0063

The observed occurrence of the motifs, also termed *somatic spectrum*, can be
visualized across studies, which gives a first impression of the data. The
distribution of the motifs clearly varies between the studies.

plotMutationSpectrum(sca_motifs, "study")

### 4.3 Decomposition: Inferring Somatic Signatures

The somatic signatures can be estimated with each of the statistical methods
implemented in the package. Here, we will use the `NMF`

and `PCA`

, and compare
the results. Prior to the estimation, the number \(r\) of signatures to obtain
has to be fixed; in this example, the data will be decomposed into 5 signatures.

n_sigs = 5 sigs_nmf = identifySignatures(sca_mm, n_sigs, nmfDecomposition) sigs_pca = identifySignatures(sca_mm, n_sigs, pcaDecomposition)

```
sigs_nmf
```

MutationalSignatures: Samples (8): GBM, HNSC, ..., SKCM, THCA Signatures (5): S1, S2, S3, S4, S5 Motifs (96): CA A.A, CA A.C, ..., TG T.G, TG T.T

```
sigs_pca
```

MutationalSignatures: Samples (8): GBM, HNSC, ..., SKCM, THCA Signatures (5): S1, S2, S3, S4, S5 Motifs (96): CA A.A, CA A.C, ..., TG T.G, TG T.T

The individual matrices can be further inspected through the accessors
`signatures`

, `samples`

, `observed`

and `fitted`

.

### 4.4 Assessment: Number of Signatures

Up to now, we have performed the decomposition based on a known number \(r\) of signatures. In many settings, prior biological knowledge or complementing experiments may allow to determine \(r\) independently. If this is not the case, we can try to infer suitable values for \(r\) from the data.

Using the `assessNumberSignatures`

function, we can compute the residuals sum of
squares (RSS) and the explained variance between the observed \(M\) and fitted
\(WH\) mutational spectrum for different numbers of signatures. These measures
are generally applicable to all kinds of decomposition methods, and can aid in
choosing a likely number of signatures. The usage and arguments are analogous
to the `identifySignatures`

function.

n_sigs = 2:8 gof_nmf = assessNumberSignatures(sca_mm, n_sigs, nReplicates = 5) gof_pca = assessNumberSignatures(sca_mm, n_sigs, pcaDecomposition)

The obtained statistics can further be visualized with the
`plotNumberSignatures`

. For each tested number of signatures, black crosses
indicate the results of individual runs, while the red dot represents the
average over all respective runs. Please note that having multiple runs is only
relevant for randomly seeded decomposition methods, as the NMF in our example.

plotNumberSignatures(gof_nmf)

Warning: `fun.y` is deprecated. Use `fun` instead.

plotNumberSignatures(gof_pca)

Warning: `fun.y` is deprecated. Use `fun` instead.

\(r\) can then be chosen such that increasing the number of signatures does not yield a significantly better approximation of the data, i.e. that the RSS and the explained variance do not change sufficiently for more complex models. The first inflection point of the RSS curve has also been proposed as a measure for the number of features in this context [9]. Judging from both statistics for our dataset, a total of 5 signatures seems to explain the characteristics of the observed mutational spectrum well. In practice, a combination of a statistical assessment paired with biological knowledge about the nature of the data will allow for the most reliable interpretation of the results.

### 4.5 Visualization: Exploration of Signatures and Samples

To explore the results for the TCGA data set, we will use the plotting
functions. All figures are generated with the `ggplot2`

package, and thus,
their properties and appearances can directly be modified, even at a later
stage.

library(ggplot2)

Focusing on the results of the NMF first, the five somatic signatures (named S1 to S5) can be visualized either as a heatmap or as a barchart.

plotSignatureMap(sigs_nmf) + ggtitle("Somatic Signatures: NMF - Heatmap")

plotSignatures(sigs_nmf) + ggtitle("Somatic Signatures: NMF - Barchart")