---
title: "Gene set co-regulation analysis tutorial"
output: 
    rmarkdown::html_vignette:
        toc: true
vignette: >
  %\VignetteIndexEntry{geseca-tutorial}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```


This vignette describes GESECA (gene set co-regulation analysis): a method
to identify gene sets that have high gene correlation.
We will show how GESECA can be used to find regulated pathways
in multi-conditional data, where there is no obvious contrast that 
can be used to rank genes for GSEA analysis.
As examples we will consider a time course microarray experiment 
and a spatial transcriptomics dataset.

## Overiew of GESECA method

GESECA takes as an input:

* *E* - gene expression matrix, where rows and columns correspond to genes and samples respectively.
* *P* - list of gene sets (i.e. 
[hallmark gene sets](http://www.gsea-msigdb.org/gsea/msigdb/human/collections.jsp#H)).

**Note**: genes identifier type should be the same for both elements of *P* and for row names of matrix *E*.

By default, GESECA method performs centering for rows of the matrix *E*. 
So, after that, the gene values are assumed to have zero mean.
Then for each gene set *p* in *P* let us introduce the gene set score in the following form:

```{r eval=FALSE}
score <- sum(colSums(E[p, ])**2) / length(p)
```

This score was inspired by the variance of principal components 
from the principal component analysis (PCA).
Therefore, the given score can be viewed in terms of explained variance by the gene set *p*.
Geometrically, this can be considered as an embedding of samples into 
a one-dimensional space, given by a unit vector in which nonzero 
positions correspond to genes from gene set *p*.

In the case of row-centered matrix *E* the variance of 
highly correlated genes is summed up to a higher score.
While the genes that are not correlated cancel each other and the total
gene set variance is low.
See the toy example:

![Toy example of GESECA score calculation](geseca-vignette-score-toy-example.png){width=90%}

Another major feature of the proposed score is that it does not require 
an explicit sample annotation or a contrast.
As the result, GESECA can be applied to various types of sequencing technologies: RNA-seq, single-cell sequencing, spatial RNA-seq, etc.

To assess statistical significance for a given gene set *p* we calculate 
an empirical P-value by using gene permutations.
The definition of the P-value is given by the following expression:
\[
    \mathrm{P} \left(\text{random score} \geqslant \text{score of p} \right).
\]
The estimation of the given P-value is done by sampling random gene sets 
with the same size as *p* from the row names of matrix *E*.
In practice, the theoretical P-value can be extremely small, 
so we use the adaptive multilevel Markov Chain Monte Carlo scheme,
that we used previously in `fgseaMultilevel` procedure.
For more details, see the [preprint](https://www.biorxiv.org/content/10.1101/060012v3).

## Analysis of time course data

In the first example we will consider a time course data of Th2 activation
from the dataset GSE200250.

First, let prepare the dataset. We load it from Gene Expression Omnibus,
apply log and quantile normalization and filter lowly expressed genes.

```{r message=FALSE}
library(GEOquery)
library(limma)

gse200250 <- getGEO("GSE200250", AnnotGPL = TRUE)[[1]]

es <- gse200250
es <- es[, grep("Th2_", es$title)]
es$time <- as.numeric(gsub(" hours", "", es$`time point:ch1`))
es <- es[, order(es$time)]

exprs(es) <- normalizeBetweenArrays(log2(exprs(es)), method="quantile")

es <- es[order(rowMeans(exprs(es)), decreasing=TRUE), ]
es <- es[!duplicated(fData(es)$`Gene ID`), ]
rownames(es) <- fData(es)$`Gene ID`
es <- es[!grepl("///", rownames(es)), ]
es <- es[rownames(es) != "", ]

fData(es) <- fData(es)[, c("ID", "Gene ID", "Gene symbol")]

es <- es[head(order(rowMeans(exprs(es)), decreasing=TRUE), 12000), ]
head(exprs(es))
```


Then we obtain the pathway list. Here we use Hallmarks
collection from MSigDB database.


```{r}
library(msigdbr)
pathwaysDF <- msigdbr("mouse", category="H")
pathways <- split(as.character(pathwaysDF$entrez_gene), pathwaysDF$gs_name)
```

Now we can run GESECA analysis:

```{r message=FALSE}
library(fgsea)
set.seed(1)
gesecaRes <- geseca(pathways, exprs(es), minSize = 15, maxSize = 500)
```

The resulting table contain GESECA scores and the corresponding P-values:
```{r}
head(gesecaRes, 10)
```

We can plot gene expression profile of HALLMARK_E2F_TARGETS pathway and see
that these genes are strongly activated at 24 hours time point:


```{r fig.width=7, fig.height=4}
plotCoregulationProfile(pathway=pathways[["HALLMARK_E2F_TARGETS"]], 
                        E=exprs(es), titles = es$title, conditions=es$`time point:ch1`)
```

Hypoxia genes have slightly different profile, getting activated around 48 hours:


```{r fig.width=10, fig.height=4, out.width="100%"}
plotCoregulationProfile(pathway=pathways[["HALLMARK_HYPOXIA"]], 
                        E=exprs(es), titles = es$title, conditions=es$`time point:ch1`)


```

To get an overview of the top pathway patterns we can use `plotGesecaTable`
function:

```{r fig.width=10, fig.height=6, out.width="100%"}
plotGesecaTable(gesecaRes |> head(10), pathways, E=exprs(es), titles = es$title)
```

When the expression matrix contains many samples, a PCA-reduced expression matrix
can be used instead of the full matrix to improve the performance. 
Let reduce the sample space from `r ncol(es)` to 10 dimensions, preserving as much gene variation as possible.

```{r}
E <- t(base::scale(t(exprs(es)), scale=FALSE))
pcaRev <- prcomp(E, center=FALSE)
Ered <- pcaRev$x[, 1:10]
dim(Ered)
```

Now we can run GESECA on the reduced matrix, however we need to disable automatic centering, as we already have done it before the reduction.

```{r}
set.seed(1)
gesecaResRed <- geseca(pathways, Ered, minSize = 15, maxSize = 500, center=FALSE)
head(gesecaResRed, 10)
```

The scores and P-values are similar to the ones we obtained for the full matrix.

```{r fig.width=4, fig.height=4}
library(ggplot2)
ggplot(data=merge(gesecaRes[, list(pathway, logPvalFull=-log10(pval))],
                  gesecaResRed[, list(pathway, logPvalRed=-log10(pval))])) +
    geom_point(aes(x=logPvalFull, y=logPvalRed)) +
    coord_fixed() + theme_classic()
```


## Analysis of spatial RNA-seq

As the second example we will consider a spatial transcriptomics dataset
of a mouse brain.

To load the data we will use `SeuratData` package that can be 
installed with the following command:

```{r eval=FALSE}
devtools::install_github('satijalab/seurat-data')
```

Next we install the package with the dataset:
```{r eval=FALSE}
SeuratData::InstallData("stxBrain")
```

Now we can load the data:

```{r message=FALSE, eval=FALSE}
library(Seurat)
library(SeuratData)
library(ggplot2)
library(patchwork)
brain <- LoadData("stxBrain", type = "anterior1")
```


We apply an appropriate normalization (note that we are using 10000 genes, 
which will be later used as a gene universe for the analysis):

```{r eval=FALSE}
brain <- SCTransform(brain, assay = "Spatial", verbose = FALSE, variable.features.n = 10000)
```

To speed up the analysis, instead of using the full transformed
gene expression matrix, we will consider only its first 
principal components. Note that a "reverse" PCA should be done: 
the principal components should correspond to linear combinations
of the cells, not linear combinations of the genes as in "normal" PCA.
By default `SCTransform` returns centered gene expression, so we
can run PCA directly.


```{r eval=FALSE}
brain <- RunPCA(brain, assay = "SCT", verbose = FALSE, 
                rev.pca = TRUE, reduction.name = "pca.rev", reduction.key="PCR_")
E <- brain@reductions$pca.rev@feature.loadings
```

We will use KEGG pathways as the gene set collection.

```{r eval=FALSE}
library(msigdbr)
pathwaysDF <- msigdbr("mouse", category="C2", subcategory = "CP:KEGG")
pathways <- split(pathwaysDF$gene_symbol, pathwaysDF$gs_name)
```

Now we can run the analysis (we set `center=FALSE` because we use the 
reduced matrix):

```{r message=FALSE, eval=FALSE}
set.seed(1)

gesecaRes <- geseca(pathways, E, minSize = 15, maxSize = 500, center = FALSE)
```

Finally, let us plot spatial expression of the top four pathways:

```{r fig.width=8, fig.height=8, out.width="100%", eval=FALSE}

topPathways <- gesecaRes[, pathway] |> head(4)

for (ppn in topPathways) {
    pp <- pathways[[ppn]]
    pp <- intersect(pp, rownames(E))
    
    score <- colSums(brain@assays$SCT@scale.data[pp, ])/sqrt(length(pp))
    brain@meta.data[[ppn]] <- score
}
SpatialFeaturePlot(brain, features = topPathways, )
```

![](geseca-spatial-top.png){width=100%}