---
title: "Understanding protein groups with adjacency matrices"
output:
    BiocStyle::html_document:
        toc_float: true
vignette: >
    %\VignetteIndexEntry{Understanding protein groups with adjacency matrices}
    %\VignetteEngine{knitr::rmarkdown}
    %\VignetteEncoding{UTF-8}
    %\VignettePackage{PSMatch}
    %\VignetteDepends{mzR,BiocStyle,msdata,SummarizedExperiment,factoextra}
---

```{r style, echo = FALSE, results = 'asis', message=FALSE}
BiocStyle::markdown()
```

**Package**: `r Biocpkg("PSMatch")`<br />
**Authors**: `r packageDescription("PSMatch")[["Author"]] `<br />
**Last modified:** `r file.info("AdjacencyMatrix.Rmd")$mtime`<br />
**Compiled**: `r date()`

```{r setup, message = FALSE, echo = FALSE}
library("PSMatch")
```

# Introduction

This vignette is one among several illustrating how to use the
`PSMatch` package, focusing on the modelling peptide-protein relations
using adjacency matrices and connected componencts. For a general
overview of the package, see the `PSMatch` package manual page
(`?PSMatch`) and references therein.


# Peptide-protein relation

Let's start by loading and filter PSM data as illustrated in the
[*Working with PSM
data*](https://rformassspectrometry.github.io/PSMatch/articles/PSM.html) vignette.

```{r}
library("PSMatch")
id <- msdata::ident(full.names = TRUE, pattern = "TMT") |>
PSM() |>
filterPsmDecoy() |>
filterPsmRank()
id
```

When identification data is stored as a table, the relation between
peptides is typically encode in two columns, once containing the
peptide sequences and the second the protein identifiers these
peptides stem from. Below are the 10 first observations of our
identification data table.

```{r}
data.frame(id[1:10, c("sequence", "DatabaseAccess")])
```

This information can however also be encoded as an adjacency matrix
with peptides along the rows and proteins along the columns, and a 1
(or more generally a value > 0) indicating that a peptides belongs to
the corresponding proteins. Such a matrix is created below for our
identification data.

```{r}
adj <- makeAdjacencyMatrix(id)
dim(adj)
adj[1:5, 1:5]
```

This matrix models the relation between the `r length(unique(id$sequence))`
peptides and the `r length(unique(id$DatabaseAccess))` is our identification
data. These numbers can be verified by checking the number of unique
peptides sequences and database accession numbers.


```{r}
length(unique(id$sequence))
length(unique(id$DatabaseAccess))
```

Some values are > 1 because some peptide sequences are observed more
than oncce, for example carrying different modification or the same
one at different sites. The adjacency matrix can be made binary by
setting `madeAdjacencyMatrix(id, binary = TRUE)`.

This large matrix is too large to be explored manually and is anyway
not interesting on its own. Subsets of this matrix that define
proteins defines by a set of peptides (whether shared or unique) is
relevant. These are represented by subsets of this large matrix named
connected component. We can easily compute all these connected
components to produce the multiple smaller and relevant adjacency
matrices.

```{r}
cc <- ConnectedComponents(adj)
length(cc)
cc
```

Among the `r length(unique(id$sequence))` and the
`r length(unique(id$DatabaseAccess))` proteins, we have `r length(cc)`
connected components.

954 thereof, such as the one shown below, correspond to single
proteins identified by a single peptide:

```{r}
connectedComponents(cc, 1)
```

7 thereof represent protein groups identified by a single shared
peptide:

```{r}
connectedComponents(cc, 527)
```

501 represent single proteins identified by multiple unique peptides:

```{r}
connectedComponents(cc, 38)
```

Finally, arguable those that warrant additional exploration are those
that are composed of multiple peptides and multiple proteins. There
are 14 thereof in this identification; here's an example:

```{r}
connectedComponents(cc, 920)
```

# Visualising adjacency matrices


Let's identify the connected components that have at least 3 peptides
(i.e. rows in the adjacency matrix) and 3 proteins (i.e. columns in
the adjacency matrix).

```{r}
(i <- which(nrows(cc) > 2 & ncols(cc) > 2))
dims(cc)[i, ]
```

We will use the second adjacency matrix, with index 1082 to learn
about the `plotAdjacencyMatrix()` function and explore how to inform
our peptides filtering beyond the `filterPsm*()` functions.

```{r}
cx <- connectedComponents(cc, 1082)
cx
```

We can now visualise the the `cx` adjacency matrix with the
`plotAdjacencyMatrix()` function. The nodes of the graph represent
proteins and petides - by default, proteins are shown as blue squares
and peptides as white circles. Edge connect peptides/circles to
proteins/squares, indicating that a peptide belongs to a protein.


```{r}
plotAdjacencyMatrix(cx)
```

We can immediately observe that peptide `VVPVGLRALVWVQR` is associated
to all four proteins; it holds that protein group together, defines
that connected component formed by these four proteins. If we were to
drop that peptides, we would obtain two single proteins, `ECA3399`
(defined by `KLKPRRR`), `ECA3398` (defined by `RRKRKPDSLKK` and
`KPTARRRKRK`) and a protein group formed of `ECA3415` and `ECA3406`
(defined by three shared peptides).

## Colouring the graph nodes

To help with the interpretation of the graph and the potential
benefits of additional manual peptide filtering, it is possible to
customise the node colours. Protein and peptide node colours can be
controlled with the `protColors` and `pepColors` arguments
respectively. Let's start with the former.

### Colouring protein nodes

`protColors` can either be a numeric or a character. The default value
is 0, which produces the figure above. Any value > 0 will lead to more
proteins being highlighted using different colours. Internally, string
distances between protein names are computed and define if proteins
should be coded with the same colours (if they are separated by small
distances, i.e. they have similar names) or different colours (large
distance, dissimilar names).

By setting the argument to 1, we see that proteins starting with
`ECA33` and those starting with `ECA34` are represented with different
colours.

```{r}
plotAdjacencyMatrix(cx, 1)
```

We can further distinguish `ECA3406`, and `ECA314` and `ECA33*9` by
setting `protColors` to 2.

```{r}
plotAdjacencyMatrix(cx, 2)
```

`protColors` can also be a character of colours named by protein
names. We will illustrate this use below, as it functions the same way
as `pepColors`.

### Colouring peptide nodes

`pepColors` can either be `NULL` to represent peptides as white nodes
(as we have seen in all examples above). Alternatively, it can be set
to a character of colours names after the peptides sequences. Let's
use the search engine score (here `MS.GF.RawScore`) to annotate the
peptide nodes.

We can extract this metric from the PSM object we started with and
create a colour palette representing the range of scores.

The named vector of scores:

```{r}
score <- id$MS.GF.RawScore
names(score) <- id$sequence
head(score)
```

The matching named vector of colours:

```{r}
cls <- as.character(cut(score, 12,
                        labels = colorRampPalette(c("white", "red"))(12)))
names(cls) <- id$sequence
head(cls)
```

Below, we see that all these peptides have relatively low scores
(light red), and that two of the three of the `ECA34*` proteins have
the highest scores.

```{r}
plotAdjacencyMatrix(cx, pepColors = cls)
```

# Using quantitative data

To conclude this vignette, we show how this same data modelling and
exploration cam be initiated from a quantitative dataset. We will use
part of the CPTAC data that is available in the `msdata` package.

Once we have the path to the tsv data, we identify the columns that
contain quantitation values (i.e. those starting with `Intensity.`)
and them create a `SummarizedExperiment` using the
[readSummarizedExperiment()](https://rformassspectrometry.github.io/QFeatures/reference/readQFeatures.html)
function from the `r Biocpkg("QFeatures")` package.

```{r, message = FALSE}
basename(f <- msdata::quant(full.names = TRUE))
(i <- grep("Intensity\\.", names(read.delim(f))))
library(QFeatures)
se <- readSummarizedExperiment(f, ecol = i, sep = "\t")
```

Below, we create a vector of protein groups (not leading razor protein
names) and name it using the peptide sequences.

```{r}
prots <- rowData(se)$Proteins
names(prots) <- rowData(se)$Sequence
head(prots)
```

Below, the `makeAdjacencyMatrix()` will split the protein groups into
individual proteins using a `;` (used by default, so not required
here) to construct the adjacency matrix, which itself can be used to
compute the connected components.

```{r}
adj <- makeAdjacencyMatrix(prots, split = ";")
dim(adj)
adj[1:3, 1:3]
cc <- ConnectedComponents(adj)
cc
```

# Prioritising connected components


The `prioritiseConnectedComponents()` function can be used to help
prioritise the most interesting connected components to
investigate. The function computes a set of metrics describing the
components composed of as least several peptides and proteins (150 in
the example above) and ranks them from the most to the least
interesting.

```{r}
head(cctab <- prioritiseConnectedComponents(cc))
```

The prioritisation table can then be further summarised using a
principal component to identify outliers (for example component 1200
below) or groups of *similar* components to explore.

```{r, message = FALSE}
library(factoextra)
fviz_pca(prcomp(cctab, scale = TRUE, center = TRUE))
```



# Session information

```{r si}
sessionInfo()
```
