`library(BiocStyle)`

The concept of mutational signatures was introduced in a series of papers by Ludmil Alexandrov et al. (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013) and (Alexandrov, Nik-Zainal, Wedge, Campbell, et al. 2013). A computational framework was published (Alexandrov 2012) with the purpose to detect a limited number of mutational processes which then describe the whole set of SNVs (single nucleotide variants) in a cohort of cancer samples. The general approach (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013) is as follows:

- The SNVs are categorized by their nucleotide exchange. In total there are
\(4 \times 3 = 12\) different nucleotide exchanges, but if summing over reverse
complements only \(12 / 2 = 6\) different categories are left. For every SNV
detected, the motif context around the position of the SNV is extracted. This
may be a trinucleotide context if taking one base upstream and one base
downstream of the position of the SNV, but larger motifs may be taken as well
(e.g.Â pentamers). Taking into account the motif context increases combinatorial
complexity: in the case of the trinucleotide context, there are
\(4 \times 6 \times 4 = 96\) different variant categories. These categories are
called
**features**in the following text. The number of features will be called \(n\). - A cohort consists of different samples with the number of samples denoted by
\(m\). For each sample we can count the occurences of each feature, yielding an
\(n\)-dimensional vector (\(n\) being the number of features) per sample. For a
cohort, we thus get an \(n \times m\) -dimensional matrix, called the
**mutational catalogue**\(V\). It can be understood as a summary indicating which sample has how many variants of which category, but omitting the information of the genomic coordinates of the variants. - The mutational catalogue \(V\) is quite big and still carries a lot of
complexity. For many analyses a reduction of complexity is desirable. One way
to achieve such a complexity reduction is a matrix decomposition: we would like
to find two smaller matrices \(W\) and \(H\) which, if multiplied, would span a high
fraction of the complexity of the big matrix \(V\) (the mutational catalogue).
Remember that \(V\) is an \(n \times m\) -dimensional matrix, \(n\) being the number
of features and \(m\) being the number of samples. \(W\) in this setting is an
\(n \times l\) -dimensional matrix and \(H\) is an \(l \times m\) -dimensional
matrix. According to the nomeclature defined in (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013), the columns of
\(W\) are called the
**mutational signatures**and the columns of \(H\) are called**exposures**. \(l\) denotes the number of mutational signatures. Hence the signatures are \(n\)-dimensional vectors (with \(n\) being the number of features), while the exposures are \(l\)-dimensional vectors (\(l\) being the number of signatures). Note that as we are dealing with count data, we would like to have only positive entries in \(W\) and \(H\). A mathematical method which is able to do such a decomposition is the**NMF**(**non-negative matrix factorization**). It basically solves the problem as illustrated in the following figure (image taken from https://en.wikipedia.org/wiki/Non-negative_matrix_factorization):

Note that the NMF itself solves the above problem for a given number of signatures \(l\). In order to achieve a reduction in complexity, the number of signatures has to be smaller than the number of features ($l < $n), as indicated in the above figure. The framework of Ludmil Alexandrov et al. (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013) performs not only the NMF decomposition itself, but also identifies the appropriate number of signatures by an iterative procedure.

Another software, the Bioconductor package *SomaticSignatures* to
perform analyses of mutational signatures, is available (Gehring et al. 2015).
It allows the matrix decomposition to be performed by NMF and alternatively
by PCA (principal component analysis). Both methods have in common that they
can be used for **discovery**, i.e.Â for the **extraction of new signatures**.
However, they only work well if the analyzed data set has sufficient
statistical power, i.e.Â a sufficient number of samples and sufficient numbers
of counts per feature per sample.

The package YAPSA introduced here is complementary to these existing software packages. It is designed for a supervised analysis of mutational signatures, i.e.Â an analysis with already known signatures \(W\), and with much lower requirements on statistical power of the input data.

In a context where mutational signatures \(W\) are already known (because they were decribed and published as in (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013) or they are available in a database as under http://cancer.sanger.ac.uk/cosmic/signatures), we might want to just find the exposures \(H\) for these known signatures in the mutational catalogue \(V\) of a given cohort. Mathematically, this is a different and potentially simpler task.

The **YAPSA**-package (Yet Another Package for Signature Analysis) presented
here provides the function `LCD`

(**l**inear **c**ombination **d**ecomposition)
to perform this task. The advantage of this method is that there are **no
constraints on the cohort size**, so `LCD`

can be run for as little as one
sample and thus be used e.g.Â for signature analysis in personalized oncology.
In contrast to NMF, `LCD`

is very fast and requires very little computational
resources. YAPSA has some other unique functionalities, which are briefly
mentioned below and described in detail in separate vignettes.

In the following, we will denote the columns of \(V\) by \(V_{(\cdot j)}\), which
corresponds to the mutational catalogue of sample \(j\). Analogously we denote
the columns of \(H\) by \(H_{(\cdot j)}\), which is the exposure vector of sample
\(j\). Then `LCD`

is designed to solve the optimization problem:

- \[ \begin{aligned} \min_{H_{(\cdot j)} \in \mathbb{R}^l}||W \cdot H_{(\cdot j)} - V_{(\cdot j)}|| \quad \forall j \in \{1...m\} \\ \textrm{under the constraint of non-negativity:} \quad H_{(ij)} >= 0 \quad \forall i \in \{1...l\} \quad \forall j \in \{1...m\} \end{aligned} \]

Remember that \(j\) is the index over samples, \(m\) is the number of samples,
\(i\) is the index over signatures and \(l\) is the number of signatures. `LCD`

uses a non-negative least squares (NNLS) algorithm (from the R package

*nnls* ) to solve this optimization problem. Note that the
optimization procedure is carried out for every \(V_{(\cdot j)}\), i.e.Â for every
column of \(V\) separately. Of course \(W\) is constant, i.e.Â the same for every
\(V_{(\cdot j)}\).

This procedure is highly sensitive: as soon as a signature has a contribution
or an exposure in at least one sample of a cohort, it will be reported (within
the floating point precision of the operating system). This might blur the
picture and counteracts the initial purpose of complexity reduction. Therefore
there is a function `LCD_complex_cutoff`

. This function takes as a second
argument a cutoff (a value between zero and one). In the analysis, it will keep
only those signatures which have a cumulative (over the cohort) normalized
exposure greater than this cutoff. In fact it runs the LCD-procedure twice:
once to find initial exposures, summing over the cohort and excluding the ones
with too low a contribution as described just above, and a second time doing
the analysis only with the signatures left over. Beside the exposures \(H\)
corresponding to this reduced set of signatures, the function
`LCD_complex_cutoff`

also returns the reduced set of signatures itself.

Another R package for the supervised analysis of mutational signatures is
available: *deconstructSigs* (Rosenthal et al. 2016). One difference
between `LCD_complex_cutoff`

as described here in `YAPSA`

and the corresponding
function `whichSignatures`

in *deconstructSigs* is that
`LCD_complex_cutoff`

accepts different cutoffs and signature-specific cutoffs
(accounting for potentially different detectability of different signatures),
whereas in `whichSignatures`

in *deconstructSigs* a general fixed
cutoff is set to be 0.06. In the following, we briefly mention other features
of the software package YAPSA and refer to the corresponding vignettes for
detailed descriptions.

One special characteristic of YAPSA is that it provides the opportunity to perform analyses of mutational signtures with signature-specific cutoffs. Different signatures have different detectability. Those with high detectability will occur as false positive calls more often. In order to account for the different detectability, we introduced the concept of signature-specific cutoffs: a signature which leads to many false positive calls has to cross a higher threshold than a signature which rarely leads to false positive calls. While this vignette introduces how to work with signature-specific cutoffs in general, optimal signature-specific cutoffs are presented in 2. Signature-specific cutoffs.

In order to evaluate the confidence of computed exposures to mutational signatures, YAPSA provides 95% confidence intervals (CIs). The computation relies on the concept of profile likelihood (Raue et al. 2009). Details can be found in 3. Confidence Intervals.

For some questions it is useful to assign the SNVs detected in the samples of a
cohort to categories. We call an analysis of mutational signatures which takes
into account these strata a *stratified* analysis, which has the potential to
reveal enrichment and depletion patterns. Of note, this is different from
performing completely separate and independent NNLS analyses of mutational
signatures on the different strata. Instead, the results of the unstratified
analysis are used as input for a constrained analysis for the strata. Details
can be found in
4. Stratified Analysis of Mutational Signatures

Recently a new and extended set of mutational signatures was published by the Pan Cancer Analysis of Whole Genomes (PCAWG) consortium (Alexandrov et al. 2020). In addition to an extended set of SNV mutational signatures, that analysis for the first time had sufficient statistical power to also extract 17 Indel signatures, based on a classification of Indels into 83 categories or features. YAPSA also offers functionality to perform supervised analyses of mutational signatures on these Indel signatures, details can be found in 5. Indel signature analysis

We will now apply some functions of the YAPSA package to Whole Genome Sequencing datasets published in Alexandrov et al. (2013). First we have to load this data and get an overview (first subsection). Then we will load data on published signatures (second subsection). Only in the third subsection we will actually start using the YAPSA functions.

```
library(YAPSA)
library(knitr)
opts_chunk$set(echo=TRUE)
opts_chunk$set(fig.show='asis')
```

In the following, we will load and get an overview of the data used in the analysis by Alexandrov et al. (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013)

`data("lymphoma_Nature2013_raw")`

This creates a dataframe with 128639 rows. It is equivalent to executing the R code

```
lymphoma_Nature2013_ftp_path <- paste0(
"ftp://ftp.sanger.ac.uk/pub/cancer/AlexandrovEtAl/",
"somatic_mutation_data/Lymphoma B-cell/",
"Lymphoma B-cell_clean_somatic_mutations_",
"for_signature_analysis.txt")
lymphoma_Nature2013_raw_df <- read.csv(file=lymphoma_Nature2013_ftp_path,
header=FALSE,sep="\t")
```

The format is inspired by the vcf format with one line per called variant. Note that the files provided at that URL have no header information, therefore we have to add some. We will also slightly adapt the data structure:

```
names(lymphoma_Nature2013_raw_df) <- c("PID","TYPE","CHROM","START",
"STOP","REF","ALT","FLAG")
lymphoma_Nature2013_df <- subset(lymphoma_Nature2013_raw_df,TYPE=="subs",
select=c(CHROM,START,REF,ALT,PID))
names(lymphoma_Nature2013_df)[2] <- "POS"
kable(head(lymphoma_Nature2013_df),
caption = "First rows of the file containing the SNV variant calls.")
```

CHROM | POS | REF | ALT | PID |
---|---|---|---|---|

1 | 183502381 | G | A | 07-35482 |

18 | 60985506 | T | A | 07-35482 |

18 | 60985748 | G | T | 07-35482 |

18 | 60985799 | T | C | 07-35482 |

2 | 242077457 | A | G | 07-35482 |

6 | 13470412 | C | T | 07-35482 |

Here, we have selected only the variants characterized as `subs`

(those are the
SNVs we are interested in for the mutational signatures
analysis, small indels are filtered out by this step), so we are left with
128212 variants or rows. Note that there are
48 different samples:

`unique(lymphoma_Nature2013_df$PID)`

```
## [1] 07-35482 1060 1061 1065 1093
## [6] 1096 1102 4101316 4105105 4108101
## [11] 4112512 4116738 4119027 4121361 4125240
## [16] 4133511 4135350 4142267 4158726 4159170
## [21] 4163639 4175837 4177856 4182393 4189200
## [26] 4189998 4190495 4193278 4194218 4194891
## [31] 515 DLBCL-PatientA DLBCL-PatientB DLBCL-PatientC DLBCL-PatientD
## [36] DLBCL-PatientE DLBCL-PatientF DLBCL-PatientG DLBCL-PatientH DLBCL-PatientI
## [41] DLBCL-PatientJ DLBCL-PatientK DLBCL-PatientL DLBCL-PatientM EB2
## [46] FL009 FL-PatientA G1
## 48 Levels: 07-35482 1060 1061 1065 1093 1096 1102 4101316 4105105 ... G1
```

For convenience later on, we annotate subgroup information to every variant (indirectly through the sample it occurs in). For reasons of simplicity, we also restrict the analysis to the Whole Genome Sequencing (WGS) datasets:

```
lymphoma_Nature2013_df$SUBGROUP <- "unknown"
DLBCL_ind <- grep("^DLBCL.*",lymphoma_Nature2013_df$PID)
lymphoma_Nature2013_df$SUBGROUP[DLBCL_ind] <- "DLBCL_other"
MMML_ind <- grep("^41[0-9]+$",lymphoma_Nature2013_df$PID)
lymphoma_Nature2013_df <- lymphoma_Nature2013_df[MMML_ind,]
data(lymphoma_PID)
for(my_PID in rownames(lymphoma_PID_df)) {
PID_ind <- which(as.character(lymphoma_Nature2013_df$PID)==my_PID)
lymphoma_Nature2013_df$SUBGROUP[PID_ind] <-
lymphoma_PID_df$subgroup[which(rownames(lymphoma_PID_df)==my_PID)]
}
lymphoma_Nature2013_df$SUBGROUP <- factor(lymphoma_Nature2013_df$SUBGROUP)
unique(lymphoma_Nature2013_df$SUBGROUP)
```

```
## [1] WGS_D WGS_F WGS_B WGS_I
## Levels: WGS_B WGS_D WGS_F WGS_I
```

Rainfall plots provide a quick overview of the mutational load of a sample. To this end we have to compute the intermutational distances. But first we still do some reformattingâ€¦

```
lymphoma_Nature2013_df <- translate_to_hg19(lymphoma_Nature2013_df,"CHROM")
lymphoma_Nature2013_df$change <-
attribute_nucleotide_exchanges(lymphoma_Nature2013_df)
lymphoma_Nature2013_df <-
lymphoma_Nature2013_df[order(lymphoma_Nature2013_df$PID,
lymphoma_Nature2013_df$CHROM,
lymphoma_Nature2013_df$POS),]
lymphoma_Nature2013_df <- annotate_intermut_dist_cohort(lymphoma_Nature2013_df,
in_PID.field="PID")
data("exchange_colour_vector")
lymphoma_Nature2013_df$col <-
exchange_colour_vector[lymphoma_Nature2013_df$change]
```

Now we can select one sample and make the rainfall plot. The plot function used
here relies on the package *gtrellis* by Zuguang Gu
(Gu, Eils, and Schlesner 2016).

```
choice_PID <- "4121361"
PID_df <- subset(lymphoma_Nature2013_df,PID==choice_PID)
#trellis_rainfall_plot(PID_df,in_point_size=unit(0.5,"mm"))
```

This shows a rainfall plot typical for a lymphoma sample with clusters of increased mutation density e.g.Â at the immunoglobulin loci.

As stated above, one of the functions in the YAPSA package (`LCD`

) is
designed to do mutational signatures analysis with known signatures. There are
(at least) two possible sources for signature data: i) the ones published
initially by Alexandrov et al. (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013), and ii) an updated and curated
current set of mutational signatures is maintained by Ludmil Alexandrov at
http://cancer.sanger.ac.uk/cosmic/signatures. The following three subsections
describe how you can load the data from these resources. Alternatively, you can
bypass the three following subsections because the signature datasets are also
included in this package:

`data(sigs)`

We first load the (older) set of signatures as published in Alexandrov et al. (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013):

```
Alex_signatures_path <- paste0("ftp://ftp.sanger.ac.uk/pub/cancer/",
"AlexandrovEtAl/signatures.txt")
AlexInitialArtif_sig_df <- read.csv(Alex_signatures_path,header=TRUE,sep="\t")
kable(AlexInitialArtif_sig_df[c(1:9),c(1:4)])
```

Substitution.Type | Trinucleotide | Somatic.Mutation.Type | Signature.1A |
---|---|---|---|

C>A | ACA | A[C>A]A | 0.0112 |

C>A | ACC | A[C>A]C | 0.0092 |

C>A | ACG | A[C>A]G | 0.0015 |

C>A | ACT | A[C>A]T | 0.0063 |

C>A | CCA | C[C>A]A | 0.0067 |

C>A | CCC | C[C>A]C | 0.0074 |

C>A | CCG | C[C>A]G | 0.0009 |

C>A | CCT | C[C>A]T | 0.0073 |

C>A | GCA | G[C>A]A | 0.0083 |

We will now reformat the dataframe:

```
Alex_rownames <- paste(AlexInitialArtif_sig_df[,1],
AlexInitialArtif_sig_df[,2],sep=" ")
select_ind <- grep("Signature",names(AlexInitialArtif_sig_df))
AlexInitialArtif_sig_df <- AlexInitialArtif_sig_df[,select_ind]
number_of_Alex_sigs <- dim(AlexInitialArtif_sig_df)[2]
names(AlexInitialArtif_sig_df) <- gsub("Signature\\.","A",
names(AlexInitialArtif_sig_df))
rownames(AlexInitialArtif_sig_df) <- Alex_rownames
kable(AlexInitialArtif_sig_df[c(1:9),c(1:6)],
caption="Exemplary data from the initial Alexandrov signatures.")
```

A1A | A1B | A2 | A3 | A4 | A5 | |
---|---|---|---|---|---|---|

C>A ACA | 0.0112 | 0.0104 | 0.0105 | 0.0240 | 0.0365 | 0.0149 |

C>A ACC | 0.0092 | 0.0093 | 0.0061 | 0.0197 | 0.0309 | 0.0089 |

C>A ACG | 0.0015 | 0.0016 | 0.0013 | 0.0019 | 0.0183 | 0.0022 |

C>A ACT | 0.0063 | 0.0067 | 0.0037 | 0.0172 | 0.0243 | 0.0092 |

C>A CCA | 0.0067 | 0.0090 | 0.0061 | 0.0194 | 0.0461 | 0.0097 |

C>A CCC | 0.0074 | 0.0047 | 0.0012 | 0.0161 | 0.0614 | 0.0050 |

C>A CCG | 0.0009 | 0.0013 | 0.0006 | 0.0018 | 0.0088 | 0.0028 |

C>A CCT | 0.0073 | 0.0098 | 0.0011 | 0.0157 | 0.0432 | 0.0111 |

C>A GCA | 0.0083 | 0.0169 | 0.0093 | 0.0107 | 0.0376 | 0.0119 |

This results in a dataframe for signatures, containing 27 signatures as column vectors. It is worth noting that in the initial publication, only a subset of these 27 signatures were validated by an orthogonal sequencing technology. So we can filter down:

```
AlexInitialValid_sig_df <- AlexInitialArtif_sig_df[,grep("^A[0-9]+",
names(AlexInitialArtif_sig_df))]
number_of_Alex_validated_sigs <- dim(AlexInitialValid_sig_df)[2]
```

We are left with 22 signatures.

An updated and curated set of mutational signatures is maintained by Ludmil Alexandrov at http://cancer.sanger.ac.uk/cosmic/signatures. We will use this set for the following analysis:

```
Alex_COSMIC_signatures_path <-
paste0("http://cancer.sanger.ac.uk/cancergenome/",
"assets/signatures_probabilities.txt")
AlexCosmicValid_sig_df <- read.csv(Alex_COSMIC_signatures_path,
header=TRUE,sep="\t")
Alex_COSMIC_rownames <- paste(AlexCosmicValid_sig_df[,1],
AlexCosmicValid_sig_df[,2],sep=" ")
COSMIC_select_ind <- grep("Signature",names(AlexCosmicValid_sig_df))
AlexCosmicValid_sig_df <- AlexCosmicValid_sig_df[,COSMIC_select_ind]
number_of_Alex_COSMIC_sigs <- dim(AlexCosmicValid_sig_df)[2]
names(AlexCosmicValid_sig_df) <- gsub("Signature\\.","AC",
names(AlexCosmicValid_sig_df))
rownames(AlexCosmicValid_sig_df) <- Alex_COSMIC_rownames
kable(AlexCosmicValid_sig_df[c(1:9),c(1:6)],
caption="Exemplary data from the updated Alexandrov signatures.")
```

AC1 | AC2 | AC3 | AC4 | AC5 | AC6 | |
---|---|---|---|---|---|---|

C>A ACA | 0.0110983 | 0.0006827 | 0.0221723 | 0.0365 | 0.0149415 | 0.0017 |

C>A ACC | 0.0091493 | 0.0006191 | 0.0178717 | 0.0309 | 0.0089609 | 0.0028 |

C>A ACG | 0.0014901 | 0.0000993 | 0.0021383 | 0.0183 | 0.0022078 | 0.0005 |

C>A ACT | 0.0062339 | 0.0003239 | 0.0162651 | 0.0243 | 0.0092069 | 0.0019 |

C>G ACA | 0.0018011 | 0.0002635 | 0.0240026 | 0.0097 | 0.0116710 | 0.0013 |

C>G ACC | 0.0025809 | 0.0002699 | 0.0121603 | 0.0054 | 0.0072921 | 0.0012 |

C>G ACG | 0.0005925 | 0.0002192 | 0.0052754 | 0.0031 | 0.0023038 | 0.0000 |

C>G ACT | 0.0029640 | 0.0006110 | 0.0232777 | 0.0054 | 0.0116962 | 0.0018 |

C>T ACA | 0.0295145 | 0.0074416 | 0.0178722 | 0.0120 | 0.0218392 | 0.0312 |

This results in a dataframe containing 30 signatures as column vectors. For reasons of convenience and comparability with the initial signatures, we reorder the features. To this end, we adhere to the convention chosen in the initial publication by Alexandrov et al. (Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013) for the initial signatures.

```
COSMIC_order_ind <- match(Alex_rownames,Alex_COSMIC_rownames)
AlexCosmicValid_sig_df <- AlexCosmicValid_sig_df[COSMIC_order_ind,]
kable(AlexCosmicValid_sig_df[c(1:9),c(1:6)],
caption=paste0("Exemplary data from the updated Alexandrov ",
"signatures, rows reordered."))
```

AC1 | AC2 | AC3 | AC4 | AC5 | AC6 | |
---|---|---|---|---|---|---|

C>A ACA | 0.0110983 | 0.0006827 | 0.0221723 | 0.0365 | 0.0149415 | 0.0017 |

C>A ACC | 0.0091493 | 0.0006191 | 0.0178717 | 0.0309 | 0.0089609 | 0.0028 |

C>A ACG | 0.0014901 | 0.0000993 | 0.0021383 | 0.0183 | 0.0022078 | 0.0005 |

C>A ACT | 0.0062339 | 0.0003239 | 0.0162651 | 0.0243 | 0.0092069 | 0.0019 |

C>A CCA | 0.0065959 | 0.0006774 | 0.0187817 | 0.0461 | 0.0096749 | 0.0101 |

C>A CCC | 0.0073424 | 0.0002137 | 0.0157605 | 0.0614 | 0.0049523 | 0.0241 |

C>A CCG | 0.0008928 | 0.0000068 | 0.0019634 | 0.0088 | 0.0028006 | 0.0091 |

C>A CCT | 0.0071866 | 0.0004163 | 0.0147229 | 0.0432 | 0.0110135 | 0.0571 |

C>A GCA | 0.0082326 | 0.0003520 | 0.0096965 | 0.0376 | 0.0118922 | 0.0024 |

Note that the order of the features, i.e.Â nucleotide exchanges in their trinucleotide content, is changed from the fifth line on as indicated by the row names.

For every set of signatures, the functions in the YAPSA package require an
additional dataframe containing meta information about the signatures. In that
dataframe you can specify the order in which the signatures are going to be
plotted and the colours asserted to the different signatures. In the following
subsection we will set up such a dataframe. However, the respective dataframes
are also stored in the package. If loaded by `data(sigs)`

the following
code block can be bypassed.

```
signature_colour_vector <- c("darkgreen","green","pink","goldenrod",
"lightblue","blue","orangered","yellow",
"orange","brown","purple","red",
"darkblue","magenta","maroon","yellowgreen",
"violet","lightgreen","sienna4","deeppink",
"darkorchid","seagreen","grey10","grey30",
"grey50","grey70","grey90")
bio_process_vector <- c("spontaneous deamination","spontaneous deamination",
"APOBEC","BRCA1_2","Smoking","unknown",
"defect DNA MMR","UV light exposure","unknown",
"IG hypermutation","POL E mutations","temozolomide",
"unknown","APOBEC","unknown","unknown","unknown",
"unknown","unknown","unknown","unknown","unknown",
"nonvalidated","nonvalidated","nonvalidated",
"nonvalidated","nonvalidated")
AlexInitialArtif_sigInd_df <- data.frame(sig=colnames(AlexInitialArtif_sig_df))
AlexInitialArtif_sigInd_df$index <- seq_len(dim(AlexInitialArtif_sigInd_df)[1])
AlexInitialArtif_sigInd_df$colour <- signature_colour_vector
AlexInitialArtif_sigInd_df$process <- bio_process_vector
COSMIC_signature_colour_vector <- c("green","pink","goldenrod",
"lightblue","blue","orangered","yellow",
"orange","brown","purple","red",
"darkblue","magenta","maroon",
"yellowgreen","violet","lightgreen",
"sienna4","deeppink","darkorchid",
"seagreen","grey","darkgrey",
"black","yellow4","coral2","chocolate2",
"navyblue","plum","springgreen")
COSMIC_bio_process_vector <- c("spontaneous deamination","APOBEC",
"defect DNA DSB repair hom. recomb.",
"tobacco mutatgens, benzo(a)pyrene",
"unknown",
"defect DNA MMR, found in MSI tumors",
"UV light exposure","unknown","POL eta and SHM",
"altered POL E",
"alkylating agents, temozolomide",
"unknown","APOBEC","unknown",
"defect DNA MMR","unknown","unknown",
"unknown","unknown",
"associated w. small indels at repeats",
"unknown","aristocholic acid","unknown",
"aflatoxin","unknown","defect DNA MMR",
"unknown","unknown","tobacco chewing","unknown")
AlexCosmicValid_sigInd_df <- data.frame(sig=colnames(AlexCosmicValid_sig_df))
AlexCosmicValid_sigInd_df$index <- seq_len(dim(AlexCosmicValid_sigInd_df)[1])
AlexCosmicValid_sigInd_df$colour <- COSMIC_signature_colour_vector
AlexCosmicValid_sigInd_df$process <- COSMIC_bio_process_vector
```

YAPSA can also perform analyses based on other sets of mutational signatures. Details can be found in additional vignettes on signature-specific cutoffs and Indel signatures.

Now we can start using the functions from the YAPSA package. We will start with
a mutational signatures analysis using known signatures (the ones we loaded in
the above paragraph). For this, we will use the functions `LCD`

and
`LCD_complex_cutoff`

.

This section uses functions which are to a large extent wrappers for functions in the package SomaticSignatures by Julian Gehring (Gehring et al. 2015).

`library(BSgenome.Hsapiens.UCSC.hg19)`

```
word_length <- 3
lymphomaNature2013_mutCat_list <-
create_mutation_catalogue_from_df(
lymphoma_Nature2013_df,
this_seqnames.field = "CHROM", this_start.field = "POS",
this_end.field = "POS", this_PID.field = "PID",
this_subgroup.field = "SUBGROUP",
this_refGenome = BSgenome.Hsapiens.UCSC.hg19,
this_wordLength = word_length)
```

The function `create_mutation_catalogue_from_df`

returns a list object with
several entries. We will use the one called `matrix`

.

`names(lymphomaNature2013_mutCat_list)`

`## [1] "matrix" "frame"`

```
lymphomaNature2013_mutCat_df <- as.data.frame(
lymphomaNature2013_mutCat_list$matrix)
kable(lymphomaNature2013_mutCat_df[c(1:9),c(5:10)])
```

4116738 | 4119027 | 4121361 | 4125240 | 4133511 | 4135350 | |
---|---|---|---|---|---|---|

C>A ACA | 127 | 31 | 72 | 34 | 49 | 75 |

C>A ACC | 104 | 36 | 39 | 19 | 36 | 80 |

C>A ACG | 13 | 2 | 2 | 1 | 6 | 8 |

C>A ACT | 102 | 33 | 48 | 22 | 47 | 56 |

C>A CCA | 139 | 43 | 47 | 29 | 51 | 70 |

C>A CCC | 66 | 34 | 35 | 7 | 25 | 42 |

C>A CCG | 9 | 7 | 6 | 3 | 7 | 11 |

C>A CCT | 167 | 47 | 50 | 32 | 58 | 84 |

C>A GCA | 90 | 47 | 66 | 29 | 45 | 66 |

The `LCD`

function performs the decomposition of a mutational catalogue into a
priori known signatures and the respective exposures to these signatures as
described in the second section of this vignette. We use the signatures from
(Alexandrov, Nik-Zainal, Wedge, Aparicio, et al. 2013) from the COSMIC website
(https://cancer.sanger.ac.uk/cosmic/signatures_v2).

```
current_sig_df <- AlexCosmicValid_sig_df
current_sigInd_df <- AlexCosmicValid_sigInd_df
lymphomaNature2013_COSMICExposures_df <-
LCD(lymphomaNature2013_mutCat_df,current_sig_df)
```

Some adaptation (extracting and reformatting the information which sample belongs to which subgroup):

```
COSMIC_subgroups_df <-
make_subgroups_df(lymphoma_Nature2013_df,
lymphomaNature2013_COSMICExposures_df)
```

The resulting signature exposures can be plotted using custom plotting functions. First as absolute exposures:

```
exposures_barplot(
in_exposures_df = lymphomaNature2013_COSMICExposures_df,
in_subgroups_df = COSMIC_subgroups_df)
```

`## Warning: `offset` is deprecated, use `location` instead.`

Here, as no colour information was given to the plotting function
`exposures_barplot`

, the identified signatures are coloured in a rainbow
palette. If you want to assign colours to the signatures, this is possible via
a data structure of type `sigInd_df`

.

```
exposures_barplot(
in_exposures_df = lymphomaNature2013_COSMICExposures_df,
in_signatures_ind_df = current_sigInd_df,
in_subgroups_df = COSMIC_subgroups_df)
```

`## Warning: `offset` is deprecated, use `location` instead.`

This figure has a colour coding which suits our needs, but there is one slight inconsistency: colour codes are assigned to all 30 provided signatures, even though some of them might not have any contributions in this cohort:

`rowSums(lymphomaNature2013_COSMICExposures_df)`

```
## AC1 AC2 AC3 AC4 AC5 AC6
## 7600.27742 6876.08962 7532.33628 0.00000 11400.47725 165.58975
## AC7 AC8 AC9 AC10 AC11 AC12
## 1360.82451 10792.42576 40780.45251 750.23999 2330.47206 1416.84002
## AC13 AC14 AC15 AC16 AC17 AC18
## 1278.21673 972.57536 1277.88738 1616.08615 10715.25907 1345.94448
## AC19 AC20 AC21 AC22 AC23 AC24
## 1269.86003 231.99919 909.70554 48.66650 61.22061 0.00000
## AC25 AC26 AC27 AC28 AC29 AC30
## 639.25443 258.02212 382.52388 4768.13630 76.81403 4745.16264
```

This can be overcome by using `LCD_complex_cutoff`

. It requires an additional
parameter: `in_cutoff_vector`

; this is already the more general framework which
will be explained in more detail in the following section.

```
zero_cutoff_vector <- rep(0,dim(current_sig_df)[2])
CosmicValid_cutoffZero_LCDlist <- LCD_complex_cutoff(
in_mutation_catalogue_df = lymphomaNature2013_mutCat_df,
in_signatures_df = current_sig_df,
in_cutoff_vector = zero_cutoff_vector,
in_sig_ind_df = current_sigInd_df)
```

We can re-create the subgroup information (even though this is identical to the already determined one):

```
COSMIC_subgroups_df <-
make_subgroups_df(lymphoma_Nature2013_df,
CosmicValid_cutoffZero_LCDlist$exposures)
```

And if we plot this, we obtain:

```
exposures_barplot(
in_exposures_df = CosmicValid_cutoffZero_LCDlist$exposures,
in_signatures_ind_df = CosmicValid_cutoffZero_LCDlist$out_sig_ind_df,
in_subgroups_df = COSMIC_subgroups_df)
```

`## Warning: `offset` is deprecated, use `location` instead.`