RNA seq Analysis

Packages used

Case study

Data organization

Normalization of raw counts

Unsupervised cluster analysis

Principal Component Analysis (PCA)

Differential Expression Analysis

Extraction of the results of the Differential Expression tests

Analysis of results

Visualization of the results

Packages used

library(dplyr)
library(RColorBrewer)
library(pheatmap)
library(tidyverse)
library(edgeR)
library(DESeq2)
library(ashr)
library(RColorBrewer)

If we have doubts about the steps or the operation of the tools we can use the following function to help us

vignette("DESeq2")

## starting httpd help server ... done

In general, the analysis of differential expression for RNA-seq is divided into two steps (each one that in turn includes other steps):

QA: - Count of gene-associated reads - Normalization - Unsupervised cluster analysis

Differential Expression Analysis - Modeling of raw counts for each gene - Reduced log2 fold changes - Test the differential expression

Case study

In this case we are going to work with a dataset used by the article by Gerarduzzi et al., 2017 (DOI: 10.1172/jci.insight.90299). Basically, they want to know why mice overexpressing the Smoc2 gene are more likely to develop renal fibrosis. In this case, two sample groups are being tested: - 3 Mice without fibrosis and with overexpression of Smoc2 - 4 mice with fibrosis and with overexpression of Smoc2 Essentially, one wants to know if gene expression is differential between groups.

First we need the gene-associated read counts and the associated sample metadata

# We load the raw readings
smoc2_rawcounts <- read.csv("E:/02 Estudio/00 NOTAS IMPORTANTES/R - Notas/Datasets/fibrosis_smoc2_rawcounts_unordered.csv", row.names = 1)

# We can make dataframe with the metadata used
genotype<-rep("smoc2",7)
condition<-c("fibrosis", "fibrosis", "fibrosis", "fibrosis", "normal", "normal", "normal")
row_names<-c("smoc2_fibrosis1", "smoc2_fibrosis2","smoc2_fibrosis3","smoc2_fibrosis4" , "smoc2_normal1","smoc2_normal3","smoc2_normal4")
smoc2_metadata<-data.frame(genotype,condition,row.names = row_names)
smoc2_metadata

##                 genotype condition
## smoc2_fibrosis1    smoc2  fibrosis
## smoc2_fibrosis2    smoc2  fibrosis
## smoc2_fibrosis3    smoc2  fibrosis
## smoc2_fibrosis4    smoc2  fibrosis
## smoc2_normal1      smoc2    normal
## smoc2_normal3      smoc2    normal
## smoc2_normal4      smoc2    normal

Data organization

When comparing the names of the metadata and those of the readings, they are not in the same order. DESeq2 requires both to be in the same order in order to perform analyzes

# We check if the names are in the same order
all(rownames(smoc2_metadata)==colnames(smoc2_rawcounts))

## [1] FALSE

# We reorder the column names in the dataset guided by the metadata
reorder_idx <- match(rownames(smoc2_metadata), colnames(smoc2_rawcounts))

# We replace the names of the dataset columns with those already ordered
reordered_smoc2_rawcounts <- smoc2_rawcounts[ , reorder_idx]

# We create a DESeq2 object
dds_smoc2<-DESeqDataSetFromMatrix(countData = reordered_smoc2_rawcounts, colData = smoc2_metadata, design = ~ condition)
dds_smoc2

## class: DESeqDataSet 
## dim: 47729 7 
## metadata(1): version
## assays(1): counts
## rownames(47729): ENSMUSG00000102693 ENSMUSG00000064842 ...
##   ENSMUSG00000096730 ENSMUSG00000095742
## rowData names(0):
## colnames(7): smoc2_fibrosis1 smoc2_fibrosis2 ... smoc2_normal3
##   smoc2_normal4
## colData names(2): genotype condition

Normalization of raw counts

Normalization is the process of scaling the raw count values to account for “uninteresting” factors. In this way, expression levels are more comparable between and/or within samples. The main factors to consider are the depth of the library, the length of the genes and the composition of the RNA.

# We calculate the normalized counts and assign them to a variable
dds_smoc2 <- estimateSizeFactors(dds_smoc2)
# DESeq2 will use these size factors to normalize the raw counts. The raw counts for each sample are divided by the sample-specific size factor associated with the normalization

# We look at the size factors used for normalization
sizeFactors(dds_smoc2)

## smoc2_fibrosis1 smoc2_fibrosis2 smoc2_fibrosis3 smoc2_fibrosis4   smoc2_normal1 
##       1.4319832       1.1189642       1.2480024       1.0826799       0.7106482 
##   smoc2_normal3   smoc2_normal4 
##       0.7989734       0.8482426

# Once normalized, we can extract the counts
dds_smoc2_normalized <- counts(dds_smoc2, normalized=TRUE)

Unsupervised cluster analysis

With the counts normalized, we can now compare the counts between the different samples to see how different they are from each other. To do this, we use visualization methods for unsupervised clustering analysis, such as hierarchical clustering heat maps, or Principal Component Analysis. Through these analyzes we can obtain a general idea of our samples and identify atypical samples.

# For RNA-seq data, DESeq2 uses a variance stabilizer transform (VST). This is a logarithmic transformation that moderates the variance through the mean.
vsd_smoc2<-vst(dds_smoc2, blind = TRUE) # blind=TRUE expresses that the transformation should be blind to the sample information given in the design formula.

# We extract the vsd matrix from the vsd object
vsd_mat_smoc2 <- assay(vsd_smoc2)

# We make a correlation matrix
vsd_cor_smoc2 <- cor(vsd_mat_smoc2)
vsd_cor_smoc2

##                 smoc2_fibrosis1 smoc2_fibrosis2 smoc2_fibrosis3 smoc2_fibrosis4
## smoc2_fibrosis1       1.0000000       0.9958622       0.9949621       0.9948457
## smoc2_fibrosis2       0.9958622       1.0000000       0.9952111       0.9946819
## smoc2_fibrosis3       0.9949621       0.9952111       1.0000000       0.9951846
## smoc2_fibrosis4       0.9948457       0.9946819       0.9951846       1.0000000
## smoc2_normal1         0.9631782       0.9651063       0.9678895       0.9668704
## smoc2_normal3         0.9637385       0.9656578       0.9691965       0.9671808
## smoc2_normal4         0.9597660       0.9618977       0.9650676       0.9635529
##                 smoc2_normal1 smoc2_normal3 smoc2_normal4
## smoc2_fibrosis1     0.9631782     0.9637385     0.9597660
## smoc2_fibrosis2     0.9651063     0.9656578     0.9618977
## smoc2_fibrosis3     0.9678895     0.9691965     0.9650676
## smoc2_fibrosis4     0.9668704     0.9671808     0.9635529
## smoc2_normal1       1.0000000     0.9935479     0.9940744
## smoc2_normal3       0.9935479     1.0000000     0.9942610
## smoc2_normal4       0.9940744     0.9942610     1.0000000

# We generate a heat map using the results of the correlation
pheatmap(vsd_cor_smoc2, annotation = smoc2_metadata["condition"])

# The annotation argument selects the factors to be used as annotation bars, in this case we use the condition column of the metadata dataset

Principal Component Analysis (PCA)

PCA finds the principal components of a data set, with the first components being the ones that explain the greatest variance of the data.

# We created a PCA
plotPCA(vsd_smoc2, intgroup="condition") # Intgroup is the argument to specify which factor from the metadata to use to color the graph

Differential Expression Analysis

# Here we use the DESeq2 object created above to apply differential expression analysis
dds_smoc2 <- DESeq(dds_smoc2) # By default, this function performs the Wald test for pairwise comparisons to test for differences between two groups of samples for the condition of interest.

## using pre-existing size factors

## estimating dispersions

## gene-wise dispersion estimates

## mean-dispersion relationship

## final dispersion estimates

## fitting model and testing

Before looking at the results we need to see how well the data fit the model. To see the variation in the data, we will look at the variation in gene expression relative to the mean. The variance, being the square of the standard deviation, represents how far the expression of the individual samples is from the mean. For RNA-seq data, the variance is typically expected to increase with mean gene expression.

To see this variation we can calculate the mean and variance for each gene in the samples using the apply() function.

apply() syntax: apply(data, rows/columns, function to apply)

# We calculate the mean and variance for each gene (each row) - in this case only from the samples with fibrosis
mean_counts<- apply(reordered_smoc2_rawcounts[, 1:4], 1, mean)
variance_counts<- apply(reordered_smoc2_rawcounts[, 1:4], 1, var)

# Then we can create a data set with these variables to plot with ggplot2
df<-data.frame(mean_counts, variance_counts)

ggplot(df, aes(x=mean_counts, y=variance_counts))+
  geom_point()+
  scale_y_log10()+
  scale_x_log10()+
  xlab("Mean counts per gene")+
  ylab("Variance per gene")

## Warning: Transformation introduced infinite values in continuous y-axis

## Warning: Transformation introduced infinite values in continuous x-axis

We can also see the dispersion of the data. Dispersion is a measure of the variance for a given mean. The dispersion in this case is used to assess the variability in expression when modeling the counts. An increase in the variance causes greater dispersion, while an increase in the mean decreases the dispersion.

# We plot the dispersion
plotDispEsts(dds_smoc2)

When the dispersion does not decrease as the mean increases or remains very high, it could be due to outliers or contamination of the sample.

Extraction of the results of the Differential Expression tests

Now that we have explored the fit of the data to the model, we can extract the results of the Differential Expression tests.

We see the results for a probability that the differences are due to chance of 5% (value of alpha). You can add the contrast parameter to specify the base condition of the sample (which would be normal in this case) and the condition to compare (fibrosis), as well as the factor to compare (condition). It is advisable to do this since sometimes, by default, the base condition of the sample is not adequate to make the comparison more understandable. For example, in this case of using the function “results(dds_smoc2, alpha=0.05)” fibrosis would be the base condition, which is not ideal.

Syntax results(DESeq2 object, contrast= c(“factor to compare”, “condition to compare”, “sample base condition”), alpha=0.05)

smoc2_res<-results(dds_smoc2, contrast= c("condition", "fibrosis", "normal"), alpha=0.05)
smoc2_res

## log2 fold change (MLE): condition fibrosis vs normal 
## Wald test p-value: condition fibrosis vs normal 
## DataFrame with 47729 rows and 6 columns
##                      baseMean log2FoldChange     lfcSE      stat      pvalue
##                     <numeric>      <numeric> <numeric> <numeric>   <numeric>
## ENSMUSG00000102693   0.000000             NA        NA        NA          NA
## ENSMUSG00000064842   0.000000             NA        NA        NA          NA
## ENSMUSG00000051951  22.478090        4.49814  0.829291  5.424085 5.82520e-08
## ENSMUSG00000102851   0.000000             NA        NA        NA          NA
## ENSMUSG00000103377   0.201024       -1.59170  3.816946 -0.417009 6.76672e-01
## ...                       ...            ...       ...       ...         ...
## ENSMUSG00000094431   0.000000             NA        NA        NA          NA
## ENSMUSG00000094621   0.300363      -0.870367  3.816946 -0.228027 8.19625e-01
## ENSMUSG00000098647   0.000000             NA        NA        NA          NA
## ENSMUSG00000096730   0.000000             NA        NA        NA          NA
## ENSMUSG00000095742 682.741942       1.822385  0.222836  8.178128 2.88287e-16
##                           padj
##                      <numeric>
## ENSMUSG00000102693          NA
## ENSMUSG00000064842          NA
## ENSMUSG00000051951 2.54201e-07
## ENSMUSG00000102851          NA
## ENSMUSG00000103377          NA
## ...                        ...
## ENSMUSG00000094431          NA
## ENSMUSG00000094621          NA
## ENSMUSG00000098647          NA
## ENSMUSG00000096730          NA
## ENSMUSG00000095742 2.33876e-15

We can make an MA plot to better understand the results. This plot shows the mean of the normalized counts against the log2 fold change for all genes tested. In the graph all the genes colored in blue (in this case) present a significant differential expression

plotMA(smoc2_res, alpha=0.1)

To improve the estimated fold changes we can use the log2 fold contraction. For genes with little information available, this contraction uses information from all genes to generate lower, most likely fold change estimates.

smoc2_res<-lfcShrink(dds_smoc2, contrast = c("condition", "fibrosis", "normal"), type = "ashr", res = smoc2_res)

## using 'ashr' for LFC shrinkage. If used in published research, please cite:
##     Stephens, M. (2016) False discovery rates: a new deal. Biostatistics, 18:2.
##     https://doi.org/10.1093/biostatistics/kxw041

plotMA(smoc2_res)

Analysis of results

To get descriptions of the columns in the result table, we can use the mcols() function

mcols(smoc2_res)

## DataFrame with 5 rows and 2 columns
##                        type            description
##                 <character>            <character>
## baseMean       intermediate mean of normalized c..
## log2FoldChange      results log2 fold change (MM..
## lfcSE               results posterior SD: condit..
## pvalue              results Wald test p-value: c..
## padj                results   BH adjusted p-values

There is a 5% probability that differentially expressed genes are false positives, that is, for a sample of more than 47,000 genes there would be more than 2,000 false positives. Therefore, DESeq2 performs a multiple test correction using the Benjamini-Hochberg, or BH method to adjust the p-values for multiple tests and control for the number of false positives. To reduce the number of genes tested, DESeq2 filters out genes that were unlikely to be differentially expressed such as genes with zero counts, genes with low mean values across all samples, and genes with outliers. These genes are represented in the results tables by a NA in the adjusted p column.

head(smoc2_res, n=10)

## log2 fold change (MMSE): condition fibrosis vs normal 
## Wald test p-value: condition fibrosis vs normal 
## DataFrame with 10 rows and 5 columns
##                     baseMean log2FoldChange     lfcSE      pvalue        padj
##                    <numeric>      <numeric> <numeric>   <numeric>   <numeric>
## ENSMUSG00000102693  0.000000       0.000000  1.317260          NA          NA
## ENSMUSG00000064842  0.000000       0.000000  1.317260          NA          NA
## ENSMUSG00000051951 22.478090       3.830239  0.789376 5.82520e-08 2.54201e-07
## ENSMUSG00000102851  0.000000       0.000000  1.317260          NA          NA
## ENSMUSG00000103377  0.201024      -0.144713  1.160599 6.76672e-01          NA
## ENSMUSG00000104017  0.000000       0.000000  1.317260          NA          NA
## ENSMUSG00000103025  0.000000       0.000000  1.317260          NA          NA
## ENSMUSG00000089699  0.000000       0.000000  1.317260          NA          NA
## ENSMUSG00000103201  0.000000       0.000000  1.317260          NA          NA
## ENSMUSG00000103147  0.674871       0.170710  0.948267 6.82688e-01          NA

summary(smoc2_res)

## 
## out of 29556 with nonzero total read count
## adjusted p-value < 0.05
## LFC > 0 (up)       : 5776, 20%
## LFC < 0 (down)     : 5332, 18%
## outliers [1]       : 15, 0.051%
## low counts [2]     : 7207, 24%
## (mean count < 1)
## [1] see 'cooksCutoff' argument of ?results
## [2] see 'independentFiltering' argument of ?results

The results show more than 10,000 genes with differential expression (divided into high or low expressed).

The fold change is the difference of a subsequent measurement with respect to the original, for example, if the original measurement is 10 and the subsequent measurement is 20, the fold change is 2 (increased twice). The fold change it uses by default is 1, so log2 of the fold change is 0. The fold change can also be modified to rule out genes that are probably not differentially expressed but whose fold change is greater than one and appear as such, so they could be false positives. To do this we must run the results again.

smoc2_res<-results(dds_smoc2, contrast= c("condition", "fibrosis", "normal"), alpha=0.05, lfcThreshold = 0.32) # we will use a fold change of 1.25 (whose log2 is 0.32)
smoc2_res

## log2 fold change (MLE): condition fibrosis vs normal 
## Wald test p-value: condition fibrosis vs normal 
## DataFrame with 47729 rows and 6 columns
##                      baseMean log2FoldChange     lfcSE      stat      pvalue
##                     <numeric>      <numeric> <numeric> <numeric>   <numeric>
## ENSMUSG00000102693   0.000000             NA        NA        NA          NA
## ENSMUSG00000064842   0.000000             NA        NA        NA          NA
## ENSMUSG00000051951  22.478090        4.49814  0.829291  5.038213 4.69897e-07
## ENSMUSG00000102851   0.000000             NA        NA        NA          NA
## ENSMUSG00000103377   0.201024       -1.59170  3.816946 -0.333172 7.39005e-01
## ...                       ...            ...       ...       ...         ...
## ENSMUSG00000094431   0.000000             NA        NA        NA          NA
## ENSMUSG00000094621   0.300363      -0.870367  3.816946  -0.14419 8.85350e-01
## ENSMUSG00000098647   0.000000             NA        NA        NA          NA
## ENSMUSG00000096730   0.000000             NA        NA        NA          NA
## ENSMUSG00000095742 682.741942       1.822385  0.222836   6.74210 1.56117e-11
##                           padj
##                      <numeric>
## ENSMUSG00000102693          NA
## ENSMUSG00000064842          NA
## ENSMUSG00000051951 2.82952e-06
## ENSMUSG00000102851          NA
## ENSMUSG00000103377          NA
## ...                        ...
## ENSMUSG00000094431          NA
## ENSMUSG00000094621          NA
## ENSMUSG00000098647          NA
## ENSMUSG00000096730          NA
## ENSMUSG00000095742 1.38581e-10

smoc2_res<-lfcShrink(dds_smoc2, contrast = c("condition", "fibrosis", "normal"), type = "ashr", res = smoc2_res)

## using 'ashr' for LFC shrinkage. If used in published research, please cite:
##     Stephens, M. (2016) False discovery rates: a new deal. Biostatistics, 18:2.
##     https://doi.org/10.1093/biostatistics/kxw041

We compare the results and see that there are indeed fewer genes, indicating that around 4000 genes were discarded from the original result, since their fold change is less than 1.25.

summary(smoc2_res)

## 
## out of 29556 with nonzero total read count
## adjusted p-value < 0.05
## LFC > 0 (up)       : 3716, 13%
## LFC < 0 (down)     : 3322, 11%
## outliers [1]       : 15, 0.051%
## low counts [2]     : 7207, 24%
## (mean count < 1)
## [1] see 'cooksCutoff' argument of ?results
## [2] see 'independentFiltering' argument of ?results

# We convert the results into a dataframe and add the logical variable threshold whose value will be TRUE only in cases where the adjusted p is less than 0.05
smoc2_res_all <- data.frame(smoc2_res) %>% mutate(threshold=padj < 0.05)

Visualization of the results

Volcano Plot

To make a volcano graph we use the results stored in the smoc2_res_all dataframe. We plot the log2 of the fold change vs. the log10 of the adjusted p, and the differences between the samples with a significant differential expression with those not given by the color (threshold).

DESeq2::plotMA(smoc2_res)

ggplot(smoc2_res_all) + 
        geom_point(aes(x = log2FoldChange, y = -log10(padj), color = threshold)) + 
        xlab("log2 fold change") + 
        ylab("-log10 adjusted p-value") + 
        theme(legend.position = "none", 
              plot.title = element_text(size = rel(1.5), hjust = 0.5), 
              axis.title = element_text(size = rel(1.25)))

Heat Map

The heat map or heatmap is used to observe the differential expression of a gene. There are generally two criteria that are taken to make these graphs: logFc value (expression rate) that must be greater than 1 (although 2 is usually used) and p-value that must be less than 0.05 .

# First we make a subset of the results that contains only the significant cases taking an adjusted p less than 0.05.
smoc2_res_sig <- subset(smoc2_res_all, padj<0.05)

# We order according to the genes with the lowest p values.
smoc2_res_sig <- smoc2_res_sig %>%
  arrange(padj)

We created a subset of the normalized counts initially, but only including genes with significant expression. “smoc2_res_sig” is the dataframe that includes only the significant genes, therefore the subset created will only search for the normalized genes whose names match the significant ones, the rest will be excluded.

sig_norm_counts_smoc2 <- dds_smoc2_normalized[rownames(smoc2_res_sig),]

# We select a color palette
display.brewer.all()

heat_colors <- brewer.pal(n = 6, name = "YlOrRd")

We plot the heat map. Remember in annotation to use the select function to select both the metadata dataframe and the parameter to compare, in this case it is condition.

pheatmap(sig_norm_counts_smoc2, 
         color = heat_colors, 
         cluster_rows = T, 
         show_rownames = F,
         annotation = smoc2_metadata["condition"], 
         scale = "row")

A marked differentiation between fibrosis/normal conditions is observed. Differentially expressed genes, both up and down are inverted in each cluster. Basically, the genes that are overexpressed in the group with fibrosis are down-expressed in the group without the disease. And the same occurs for the overexpressed genes in the normal group. Therefore, it can be said that there is a significant difference in the levels of gene expression for the fibrosis disease in the tested organisms when compared with organisms that do not present the disease.

---
title: "RNA seq Analysis"
email: alejandrorex95@gmail.com
output:
  html_document:
    toc: TRUE
    toc_float: TRUE
    code_download: TRUE
    theme: united
  csl: apa.csl
---

## Packages used

```{r message=FALSE, warning=FALSE}
library(dplyr)
library(RColorBrewer)
library(pheatmap)
library(tidyverse)
library(edgeR)
library(DESeq2)
library(ashr)
library(RColorBrewer)
```

If we have doubts about the steps or the operation of the tools we can use the following function to help us

```{r, warning=FALSE}
vignette("DESeq2")
```

In general, the analysis of differential expression for RNA-seq is divided into two steps (each one that in turn includes other steps):

QA:
- Count of gene-associated reads
- Normalization
- Unsupervised cluster analysis

Differential Expression Analysis
- Modeling of raw counts for each gene
- Reduced log2 fold changes
- Test the differential expression

## Case study

In this case we are going to work with a dataset used by the article by Gerarduzzi et al., 2017 (DOI: 10.1172/jci.insight.90299). Basically, they want to know why mice overexpressing the Smoc2 gene are more likely to develop renal fibrosis. In this case, two sample groups are being tested:
- 3 Mice without fibrosis and with overexpression of Smoc2
- 4 mice with fibrosis and with overexpression of Smoc2
Essentially, one wants to know if gene expression is differential between groups.

First we need the gene-associated read counts and the associated sample metadata

```{r, warning=FALSE}
# We load the raw readings
smoc2_rawcounts <- read.csv("E:/02 Estudio/00 NOTAS IMPORTANTES/R - Notas/Datasets/fibrosis_smoc2_rawcounts_unordered.csv", row.names = 1)

# We can make dataframe with the metadata used
genotype<-rep("smoc2",7)
condition<-c("fibrosis", "fibrosis", "fibrosis", "fibrosis", "normal", "normal", "normal")
row_names<-c("smoc2_fibrosis1", "smoc2_fibrosis2","smoc2_fibrosis3","smoc2_fibrosis4" , "smoc2_normal1","smoc2_normal3","smoc2_normal4")
smoc2_metadata<-data.frame(genotype,condition,row.names = row_names)
smoc2_metadata
```

## Data organization

When comparing the names of the metadata and those of the readings, they are not in the same order. DESeq2 requires both to be in the same order in order to perform analyzes

```{r, warning=FALSE}
# We check if the names are in the same order
all(rownames(smoc2_metadata)==colnames(smoc2_rawcounts))

# We reorder the column names in the dataset guided by the metadata
reorder_idx <- match(rownames(smoc2_metadata), colnames(smoc2_rawcounts))

# We replace the names of the dataset columns with those already ordered
reordered_smoc2_rawcounts <- smoc2_rawcounts[ , reorder_idx]

# We create a DESeq2 object
dds_smoc2<-DESeqDataSetFromMatrix(countData = reordered_smoc2_rawcounts, colData = smoc2_metadata, design = ~ condition)
dds_smoc2
```

## Normalization of raw counts

Normalization is the process of scaling the raw count values to account for "uninteresting" factors. In this way, expression levels are more comparable between and/or within samples. The main factors to consider are the depth of the library, the length of the genes and the composition of the RNA.

```{r, warning=FALSE}
# We calculate the normalized counts and assign them to a variable
dds_smoc2 <- estimateSizeFactors(dds_smoc2)
# DESeq2 will use these size factors to normalize the raw counts. The raw counts for each sample are divided by the sample-specific size factor associated with the normalization

# We look at the size factors used for normalization
sizeFactors(dds_smoc2)

# Once normalized, we can extract the counts
dds_smoc2_normalized <- counts(dds_smoc2, normalized=TRUE)
```

## Unsupervised cluster analysis

With the counts normalized, we can now compare the counts between the different samples to see how different they are from each other. To do this, we use visualization methods for unsupervised clustering analysis, such as hierarchical clustering heat maps, or Principal Component Analysis. Through these analyzes we can obtain a general idea of our samples and identify atypical samples.

```{r, warning=FALSE}
# For RNA-seq data, DESeq2 uses a variance stabilizer transform (VST). This is a logarithmic transformation that moderates the variance through the mean.
vsd_smoc2<-vst(dds_smoc2, blind = TRUE) # blind=TRUE expresses that the transformation should be blind to the sample information given in the design formula.

# We extract the vsd matrix from the vsd object
vsd_mat_smoc2 <- assay(vsd_smoc2)

# We make a correlation matrix
vsd_cor_smoc2 <- cor(vsd_mat_smoc2)
vsd_cor_smoc2

# We generate a heat map using the results of the correlation
pheatmap(vsd_cor_smoc2, annotation = smoc2_metadata["condition"])

# The annotation argument selects the factors to be used as annotation bars, in this case we use the condition column of the metadata dataset

```

## Principal Component Analysis (PCA)

PCA finds the principal components of a data set, with the first components being the ones that explain the greatest variance of the data.

```{r, warning=FALSE}
# We created a PCA
plotPCA(vsd_smoc2, intgroup="condition") # Intgroup is the argument to specify which factor from the metadata to use to color the graph

```

## Differential Expression Analysis

```{r, warning=FALSE}
# Here we use the DESeq2 object created above to apply differential expression analysis
dds_smoc2 <- DESeq(dds_smoc2) # By default, this function performs the Wald test for pairwise comparisons to test for differences between two groups of samples for the condition of interest.

```

Before looking at the results we need to see how well the data fit the model. To see the variation in the data, we will look at the variation in gene expression relative to the mean. The variance, being the square of the standard deviation, represents how far the expression of the individual samples is from the mean.
For RNA-seq data, the variance is typically expected to increase with mean gene expression.

To see this variation we can calculate the mean and variance for each gene in the samples using the apply() function.

apply() syntax:
apply(data, rows/columns, function to apply)

```{r}
# We calculate the mean and variance for each gene (each row) - in this case only from the samples with fibrosis
mean_counts<- apply(reordered_smoc2_rawcounts[, 1:4], 1, mean)
variance_counts<- apply(reordered_smoc2_rawcounts[, 1:4], 1, var)

# Then we can create a data set with these variables to plot with ggplot2
df<-data.frame(mean_counts, variance_counts)

ggplot(df, aes(x=mean_counts, y=variance_counts))+
  geom_point()+
  scale_y_log10()+
  scale_x_log10()+
  xlab("Mean counts per gene")+
  ylab("Variance per gene")

```

We can also see the dispersion of the data. Dispersion is a measure of the variance for a given mean. The dispersion in this case is used to assess the variability in expression when modeling the counts. An increase in the variance causes greater dispersion, while an increase in the mean decreases the dispersion.

```{r}
# We plot the dispersion
plotDispEsts(dds_smoc2)
```

When the dispersion does not decrease as the mean increases or remains very high, it could be due to outliers or contamination of the sample.

## Extraction of the results of the Differential Expression tests

Now that we have explored the fit of the data to the model, we can extract the results of the Differential Expression tests.

We see the results for a probability that the differences are due to chance of 5% (value of alpha). You can add the contrast parameter to specify the base condition of the sample (which would be normal in this case) and the condition to compare (fibrosis), as well as the factor to compare (condition). It is advisable to do this since sometimes, by default, the base condition of the sample is not adequate to make the comparison more understandable. For example, in this case of using the function "results(dds_smoc2, alpha=0.05)" fibrosis would be the base condition, which is not ideal.

Syntax
results(DESeq2 object, contrast= c("factor to compare", "condition to compare", "sample base condition"), alpha=0.05)

```{r, warning=FALSE}
smoc2_res<-results(dds_smoc2, contrast= c("condition", "fibrosis", "normal"), alpha=0.05)
smoc2_res
```

We can make an MA plot to better understand the results. This plot shows the mean of the normalized counts against the log2 fold change for all genes tested.
In the graph all the genes colored in blue (in this case) present a significant differential expression

```{r}
plotMA(smoc2_res, alpha=0.1)
```

To improve the estimated fold changes we can use the log2 fold contraction. For genes with little information available, this contraction uses information from all genes to generate lower, most likely fold change estimates.

```{r}
smoc2_res<-lfcShrink(dds_smoc2, contrast = c("condition", "fibrosis", "normal"), type = "ashr", res = smoc2_res)
plotMA(smoc2_res)
```


## Analysis of results
To get descriptions of the columns in the result table, we can use the mcols() function

```{r, warning=FALSE}
mcols(smoc2_res)
```
There is a 5% probability that differentially expressed genes are false positives, that is, for a sample of more than 47,000 genes there would be more than 2,000 false positives. Therefore, DESeq2 performs a multiple test correction using the Benjamini-Hochberg, or BH method to adjust the p-values for multiple tests and control for the number of false positives. To reduce the number of genes tested, DESeq2 filters out genes that were unlikely to be differentially expressed such as genes with zero counts, genes with low mean values across all samples, and genes with outliers. These genes are represented in the results tables by a NA in the adjusted p column.

```{r}
head(smoc2_res, n=10)

summary(smoc2_res)
```

The results show more than 10,000 genes with differential expression (divided into high or low expressed).

The fold change is the difference of a subsequent measurement with respect to the original, for example, if the original measurement is 10 and the subsequent measurement is 20, the fold change is 2 (increased twice). The fold change it uses by default is 1, so log2 of the fold change is 0. The fold change can also be modified to rule out genes that are probably not differentially expressed but whose fold change is greater than one and appear as such, so they could be false positives. To do this we must run the results again.

```{r}
smoc2_res<-results(dds_smoc2, contrast= c("condition", "fibrosis", "normal"), alpha=0.05, lfcThreshold = 0.32) # we will use a fold change of 1.25 (whose log2 is 0.32)
smoc2_res

smoc2_res<-lfcShrink(dds_smoc2, contrast = c("condition", "fibrosis", "normal"), type = "ashr", res = smoc2_res)
```

We compare the results and see that there are indeed fewer genes, indicating that around 4000 genes were discarded from the original result, since their fold change is less than 1.25.

```{r}
summary(smoc2_res)

# We convert the results into a dataframe and add the logical variable threshold whose value will be TRUE only in cases where the adjusted p is less than 0.05
smoc2_res_all <- data.frame(smoc2_res) %>% mutate(threshold=padj < 0.05)
```



## Visualization of the results

#### Volcano Plot

To make a volcano graph we use the results stored in the smoc2_res_all dataframe. We plot the log2 of the fold change vs. the log10 of the adjusted p, and the differences between the samples with a significant differential expression with those not given by the color (threshold).

```{r, warning=FALSE}
DESeq2::plotMA(smoc2_res)

ggplot(smoc2_res_all) + 
        geom_point(aes(x = log2FoldChange, y = -log10(padj), color = threshold)) + 
        xlab("log2 fold change") + 
        ylab("-log10 adjusted p-value") + 
        theme(legend.position = "none", 
              plot.title = element_text(size = rel(1.5), hjust = 0.5), 
              axis.title = element_text(size = rel(1.25)))
```

#### Heat Map

The heat map or heatmap is used to observe the differential expression of a gene. There are generally two criteria that are taken to make these graphs: logFc value (expression rate) that must be greater than 1 (although 2 is usually used) and p-value that must be less than 0.05 .

```{r}

# First we make a subset of the results that contains only the significant cases taking an adjusted p less than 0.05.
smoc2_res_sig <- subset(smoc2_res_all, padj<0.05)

# We order according to the genes with the lowest p values.
smoc2_res_sig <- smoc2_res_sig %>%
  arrange(padj)
```

We created a subset of the normalized counts initially, but only including genes with significant expression. "smoc2_res_sig" is the dataframe that includes only the significant genes, therefore the subset created will only search for the normalized genes whose names match the significant ones, the rest will be excluded.

```{r}
sig_norm_counts_smoc2 <- dds_smoc2_normalized[rownames(smoc2_res_sig),]

# We select a color palette
display.brewer.all()
heat_colors <- brewer.pal(n = 6, name = "YlOrRd")
```

We plot the heat map. Remember in annotation to use the select function to select both the metadata dataframe and the parameter to compare, in this case it is condition.

```{r}
pheatmap(sig_norm_counts_smoc2, 
         color = heat_colors, 
         cluster_rows = T, 
         show_rownames = F,
         annotation = smoc2_metadata["condition"], 
         scale = "row")
```

A marked differentiation between fibrosis/normal conditions is observed. Differentially expressed genes, both up and down are inverted in each cluster. Basically, the genes that are overexpressed in the group with fibrosis are down-expressed in the group without the disease. And the same occurs for the overexpressed genes in the normal group. Therefore, it can be said that there is a significant difference in the levels of gene expression for the fibrosis disease in the tested organisms when compared with organisms that do not present the disease.