Differential Expression

Overview

Teaching: 75 min
Exercises: 0 min

Questions

• How can we identify genes which exhibit changes in expresion between experimental conditions?

Objectives

• Understand pre-processing steps required for standarising count data.

• Use count data and the limma package to perform normalisation and identify differentially expressed genes.

• Understand need for multiple comparisons correction, and be able to apply FWER and FDR correction methods.

• Explore alternative methods (egdeR and DESeq2) for identifying differentially expressed genes.

RNA-seq: overview

Recap

• In the last section we worked through the process of quality assessment and alignment for RNA-seq data
• This typically takes place on the command line, but can also be done from within R.
• The end result was the generation of count data (counts of reads aligned to each gene, per sample) using the FeatureCounts command from Subread/Rsubread.
• Now that we’ve got count data in R, we can begin our differential expression analysis.

Data set reminder

• Data obtained from yeast RNA-seq experiment, Lee et al 2008
• Wild-type versus RNA degradation mutants
• Six samples (3 WT / 3 MT)
• NOTE: since we are dealing with an RNA degradation mutant yeast strain, we will see MAJOR transcriptomic differences between the wild-type and mutant groups (usually the differences you observe in a typical RNA-seq study wouldn’t be this extreme).

Getting organised

NOTE: skip to the next section (“Count Data”) if you are working within Jupyter on NeSI

Create an RStudio project

One of the first benefits we will take advantage of in RStudio is something called an RStudio Project. An RStudio project allows you to more easily:

• Save data, files, variables, packages, etc. related to a specific analysis project
• Restart work where you left off
• Collaborate, especially if you are using version control such as git.

To create a project:

• Open RStudio and go to the File menu, and click New Project.
• In the window that opens select Existing Project, and browse to the RNA_seq folder.
• Finally, click Create Project.

Save source from untitled to yeast_data.R and continue saving regularly as you work.

Lecture notes

In addition to the code below, we’ll also be going through some lecture notes that explain the various concepts being covered in this part of the workshop.

Lecture notes (PDF): Differential Expression

Count data

Note: I have now aligned the data for ALL CHROMOSOMES and generated counts, so we are working with data from all 7127 genes.

Let’s look at our data set and perform some basic checks before we do a differential expression analysis.

Working directory in Jupyter

Before launching your R notebook in Jupyter, navigate to ~/obss_2021/RNA_seq/ in the navigation panel. Ensure your working directory by using getwd() and if it isn’t ~/obss_2021/RNA_seq/, set it with setwd('~/obss_2021/RNA_seq').

library(dplyr)
fcData = read.table('yeast_counts_all_chr.txt', sep='\t', header=TRUE)
fcData %>% head()

    ##      Geneid Chr Start   End Strand Length ...STAR.SRR014335.Aligned.out.sam
    ## 1   YDL248W  IV  1802  2953      +   1152                                52
    ## 2 YDL247W-A  IV  3762  3836      +     75                                 0
    ## 3   YDL247W  IV  5985  7814      +   1830                                 2
    ## 4   YDL246C  IV  8683  9756      -   1074                                 0
    ## 5   YDL245C  IV 11657 13360      -   1704                                 0
    ## 6   YDL244W  IV 16204 17226      +   1023                                 6
    ##   ...STAR.SRR014336.Aligned.out.sam ...STAR.SRR014337.Aligned.out.sam
    ## 1                                46                                36
    ## 2                                 0                                 0
    ## 3                                 4                                 2
    ## 4                                 0                                 1
    ## 5                                 3                                 0
    ## 6                                 6                                 5
    ##   ...STAR.SRR014339.Aligned.out.sam ...STAR.SRR014340.Aligned.out.sam
    ## 1                                65                                70
    ## 2                                 0                                 1
    ## 3                                 6                                 8
    ## 4                                 1                                 2
    ## 5                                 5                                 7
    ## 6                                20                                30
    ##   ...STAR.SRR014341.Aligned.out.sam
    ## 1                                78
    ## 2                                 0
    ## 3                                 5
    ## 4                                 0
    ## 5                                 4
    ## 6                                19

Check dimensions:

dim(fcData)

    ## [1] 7127   12

names(fcData)

    ##  [1] "Geneid"                            "Chr"                              
    ##  [3] "Start"                             "End"                              
    ##  [5] "Strand"                            "Length"                           
    ##  [7] "...STAR.SRR014335.Aligned.out.sam" "...STAR.SRR014336.Aligned.out.sam"
    ##  [9] "...STAR.SRR014337.Aligned.out.sam" "...STAR.SRR014339.Aligned.out.sam"
    ## [11] "...STAR.SRR014340.Aligned.out.sam" "...STAR.SRR014341.Aligned.out.sam"

Rename data columns to reflect group membership

names(fcData)[7:12] = c("WT1", "WT2", "WT3", "MT1", "MT2", "MT3")
 
fcData %>% head()

    ##      Geneid Chr Start   End Strand Length WT1 WT2 WT3 MT1 MT2 MT3
    ## 1   YDL248W  IV  1802  2953      +   1152  52  46  36  65  70  78
    ## 2 YDL247W-A  IV  3762  3836      +     75   0   0   0   0   1   0
    ## 3   YDL247W  IV  5985  7814      +   1830   2   4   2   6   8   5
    ## 4   YDL246C  IV  8683  9756      -   1074   0   0   1   1   2   0
    ## 5   YDL245C  IV 11657 13360      -   1704   0   3   0   5   7   4
    ## 6   YDL244W  IV 16204 17226      +   1023   6   6   5  20  30  19

Extract count data

• Remove annotation columns
• Add row names

counts = fcData[, 7:12]
rownames(counts) = fcData$Geneid
counts %>% head()

    ##           WT1 WT2 WT3 MT1 MT2 MT3
    ## YDL248W    52  46  36  65  70  78
    ## YDL247W-A   0   0   0   0   1   0
    ## YDL247W     2   4   2   6   8   5
    ## YDL246C     0   0   1   1   2   0
    ## YDL245C     0   3   0   5   7   4
    ## YDL244W     6   6   5  20  30  19

Visualising the data

Data are highly skewed (suggests that logging might be useful):

boxplot(as.matrix(counts) ~ col(counts))

Some genes have zero counts:

colSums(counts==0)

    ## WT1 WT2 WT3 MT1 MT2 MT3 
    ## 562 563 573 437 425 435

Log transformation (add 0.5 to avoid log(0) issues):

logCounts = log2(as.matrix(counts)+ 0.5)

Now we can see the per-sample distributions more clearly:

boxplot(as.matrix(logCounts) ~ col(logCounts))

Density plots are also a good way to visualise the data:

lineColour <- c("blue", "blue", "blue", "red", "red", "red")
lineColour

    ## [1] "blue" "blue" "blue" "red"  "red"  "red"

plot(density(logCounts[,1]), ylim=c(0,0.3), col=lineColour[1])
for(i in 2:ncol(logCounts)) lines(density(logCounts[,i]), col=lineColour[i])

The boxplots and density plots show clear differences between the sample groups - are these biological, or experimental artifacts? (often we don’t know).

Remember: the wild-type and mutant yeast strains are VERY different. You wouldn’t normally see this amount of difference in the distributions between the groups.

Read counts per sample

Normalisation process (slightly different for each analysis method) takes “library size” (number of reads generated for each sample) into account.

• A good blog about normalization: Link

colSums(counts)

    ##     WT1     WT2     WT3     MT1     MT2     MT3 
    ## 4915975 4892227 4778158 4618409 4719413 4554283

Visualise via bar plot

colSums(counts) %>% barplot(., ylab="Reads mapped per sample")

Now we are ready for differential expression analysis

Detecting differential expression:

We are going to identify genes that are differential expressed using 3 different packages (time allowing) and compare the results.

But first, lets take a brief aside, and talk about the process of detecting genes that have undergone a statistically significance change in expression between the two groups.

OPEN UP THIS PDF DOCUMENT

Limma

• Limma can be used for analysis, by transforming the RNA-seq count data in an appropriate way (log-scale normality-based assumption rather than Negative Binomial for count data)
• Use data transformation and log to satisfy normality assumptions (CPM = Counts per Million).

library(limma)
library(edgeR)

dge <- DGEList(counts=counts)
dge <- calcNormFactors(dge)
logCPM <- cpm(dge, log=TRUE, prior.count=3)

options(width=100)
head(logCPM, 3)

    ##                  WT1        WT2        WT3        MT1        MT2        MT3
    ## YDL248W    3.7199528  3.5561232  3.2538405  3.6446399  3.7156488  3.9155366
    ## YDL247W-A -0.6765789 -0.6765789 -0.6765789 -0.6765789 -0.3140297 -0.6765789
    ## YDL247W    0.1484688  0.6727144  0.1645731  0.7843936  1.0395626  0.6349276

Aside: RPKM

We can use R to generate RPKM values (or FPKM if using paired-end reads):

• Need gene length information to do this
• Can get this fromgoseq package (we’ll use this later for our pathway analysis)

library(goseq)
geneLengths = getlength(rownames(counts), "sacCer2","ensGene")
rpkmData <- rpkm(dge, geneLengths)
rpkmData %>% round(., 2) %>% head()

    ##             WT1  WT2  WT3   MT1   MT2   MT3
    ## YDL248W   10.89 9.66 7.73 10.30 10.85 12.55
    ## YDL247W-A  0.00 0.00 0.00  0.00  2.35  0.00
    ## YDL247W    0.26 0.53 0.27  0.60  0.78  0.51
    ## YDL246C    0.00 0.00 0.23  0.17  0.33  0.00
    ## YDL245C    0.00 0.43 0.00  0.54  0.73  0.44
    ## YDL244W    1.41 1.42 1.21  3.57  5.24  3.44

range(rpkmData, na.rm=TRUE)

## [1]     0.00 69786.58

Compare RPKM to logCPM

par(mfrow=c(2,3))
for(i in 1:ncol(rpkmData)){
  plot(logCPM[,i], log2(rpkmData[,i]), pch='.', 
       xlab="logCPM", ylab="RPKM", main=colnames(logCPM)[i])
}

We’re NOT going to use RPKM data here. I just wanted to show you how to calculate it, and how it relates to the logCPM data

Back to the analysis… (using logCPM)

What if we just did a t-test?

## The beeswarm package is great for making jittered dot plots
library(beeswarm)

# Specify "conditions" (groups: WT and MT)
conds <- c("WT","WT","WT","MT","MT","MT")

## Perform t-test for "gene number 6" (because I like that one...)
t.test(logCPM[6,] ~ conds)

    ## 
    ##  Welch Two Sample t-test
    ## 
    ## data:  logCPM[6, ] by conds
    ## t = 7.0124, df = 2.3726, p-value = 0.01228
    ## alternative hypothesis: true difference in means is not equal to 0
    ## 95 percent confidence interval:
    ##  0.5840587 1.9006761
    ## sample estimates:
    ## mean in group MT mean in group WT 
    ##         2.244310         1.001943

beeswarm(logCPM[6,] ~ conds, pch=16, ylab="Expression (logCPM)", xlab="Group",
         main=paste0(rownames(logCPM)[6], ": MT vs WT"))

• we basically want to do this sort of analysis, for every gene
• we’ll use a slightly more sophisticated approach though

However, before we get to statistical testing, we (might) first need to do a little bit more normalisation.

Limma: voom

• The “voom” function estimates relationship between the mean and the variance of the logCPM data, normalises the data, and creates “precision weights” for each observation that are incorporated into the limma analysis.

design <- model.matrix(~conds)
design

    ##   (Intercept) condsWT
    ## 1           1       1
    ## 2           1       1
    ## 3           1       1
    ## 4           1       0
    ## 5           1       0
    ## 6           1       0
    ## attr(,"assign")
    ## [1] 0 1
    ## attr(,"contrasts")
    ## attr(,"contrasts")$conds
    ## [1] "contr.treatment"

v <- voom(dge, design, plot=TRUE)

Voom: impact on samples

Mainly affects the low-end (low abundance genes)

par(mfrow=c(2,3))
for(i in 1:ncol(logCPM)){
  plot(logCPM[,i], v$E[,i], xlab="LogCPM",
       ylab="Voom",main=colnames(logCPM)[i])
  abline(0,1)
}

Hasn’t removed the differences between the groups

boxplot(v$E ~ col(v$E))

lineColour <- ifelse(conds=="MT", "red", "blue")
lineColour

## [1] "blue" "blue" "blue" "red"  "red"  "red"

plot(density(v$E[,1]), ylim=c(0,0.3), col=lineColour[1])
for(i in 2:ncol(logCPM)) lines(density(v$E[,i]), col=lineColour[i])

We can deal with this via “quantile normalisation”. Specify

normalize="quantile"

in the voom function.

q <- voom(dge, design, plot=TRUE, normalize="quantile")

Quantile normalisation forces all of the distributions to be the same.

• it is a strong assumption, and can have a major impact on the analysis
• potentially removing biological differences between groups.

par(mfrow=c(2,3))
for(i in 1:ncol(logCPM)){
  plot(logCPM[,i], q$E[,i], xlab="LogCPM",
       ylab="Voom (+quantile norm)",main=colnames(logCPM)[i])
  abline(0,1)
}

boxplot(q$E ~ col(q$E))

lineColour <- ifelse(conds=="MT", "red", "blue")
lineColour

## [1] "blue" "blue" "blue" "red"  "red"  "red"

plot(density(q$E[,1]), ylim=c(0,0.3), col=lineColour[1])
for(i in 2:ncol(logCPM)) lines(density(q$E[,i]), col=lineColour[i])

Note: we’re NOT going to use the quantile normalised data here, but I wanted to show you how that method works.

Statistical testing: fitting a linear model

The next step is to fit a linear model to the transformed count data.

The lmFit() command does this for each gene (all at once).

fit <- lmFit(v, design)

The eBayes() function then performs Emprical Bays shrinkage estimation to adjust the variability estimates for each gene, and produce the moderated t-statistics.

fit <- eBayes(fit)

We then summarize this information using the topTable() function, which list the genes in order of the strength of statistical support for differential expression (i.e., genes with lowest p-values are at the top of the list):

tt <- topTable(fit, coef=ncol(design), n=nrow(counts))
head(tt)

##            logFC  AveExpr        t      P.Value    adj.P.Val        B
## YAL038W 2.313985 10.80214 319.5950 3.725452e-13 8.850433e-10 21.08951
## YOR161C 2.568389 10.80811 321.9628 3.574510e-13 8.850433e-10 21.08187
## YML128C 1.640664 11.40819 286.6167 6.857932e-13 9.775297e-10 20.84520
## YMR105C 2.772539  9.65092 331.8249 3.018547e-13 8.850433e-10 20.16815
## YHL021C 2.034496 10.17510 269.4034 9.702963e-13 1.152550e-09 20.07857
## YDR516C 2.085424 10.05426 260.8061 1.163655e-12 1.184767e-09 19.87217

Significant genes

Adjusted p-values less than 0.05:

sum(tt$adj.P.Val < 0.05)

## [1] 5140

Adjusted p-values less than 0.01:

sum(tt$adj.P.Val <= 0.01)

## [1] 4566

By default, limma uses FDR adjustment (but lets check):

sum(p.adjust(tt$P.Value, method="fdr") <= 0.01)

## [1] 4566

Volcano plots are a popular method for summarising the limma output:

volcanoplot(fit, coef=2)
abline(h=-log10(0.05))

Significantly DE genes:

sigGenes = which(tt$adj.P.Val <= 0.05)
length(sigGenes)

## [1] 5140

volcanoplot(fit, coef=2)
points(tt$logFC[sigGenes], -log10(tt$P.Value[sigGenes]), col='red', pch=16, cex=0.5)

Significantly DE genes above fold-change threshold:

sigGenes = which(tt$adj.P.Val <= 0.05 & (abs(tt$logFC) > log2(2)))
length(sigGenes)

## [1] 1891

volcanoplot(fit, coef=2)
points(tt$logFC[sigGenes], -log10(tt$P.Value[sigGenes]), col='red', pch=16, cex=0.5)

Get the rows of top table with significant adjusted p-values - we’ll save these for later to compare with the other methods.

limmaPadj <- tt[tt$adj.P.Val <= 0.01, ]

DESeq2

• The DESeq2 package uses the Negative Binomial distribution to model the count data from each sample.
• A statistical test based on the Negative Binomial distribution (via a generalized linear model, GLM) can be used to assess differential expression for each gene.
• Use of the Negative Binomial distribution attempts to accurately capture the variation that is observed for count data.

More information about DESeq2: article by Love et al, 2014

Set up “DESeq object” for analysis:

library(DESeq2)
dds <- DESeqDataSetFromMatrix(countData = as.matrix(counts), 
                              colData = data.frame(conds=factor(conds)), 
                              design = formula(~conds))

Can access the count data in teh dds object via the counts() function:

counts(dds) %>% head()

##           WT1 WT2 WT3 MT1 MT2 MT3
## YDL248W    52  46  36  65  70  78
## YDL247W-A   0   0   0   0   1   0
## YDL247W     2   4   2   6   8   5
## YDL246C     0   0   1   1   2   0
## YDL245C     0   3   0   5   7   4
## YDL244W     6   6   5  20  30  19

Fit DESeq model to identify DE transcripts

dds <- DESeq(dds)

Take a look at the results table

res <- DESeq2::results(dds)
knitr::kable(res[1:6,])

Summary of differential gene expression

summary(res) 

## 
## out of 6830 with nonzero total read count
## adjusted p-value < 0.1
## LFC > 0 (up)       : 2520, 37%
## LFC < 0 (down)     : 2521, 37%
## outliers [1]       : 0, 0%
## low counts [2]     : 0, 0%
## (mean count < 0)
## [1] see 'cooksCutoff' argument of ?results
## [2] see 'independentFiltering' argument of ?results

Note: p-value adjustment

• The “padj” column of the DESeq2 results (res) contains adjusted p-values (FDR).
• Can use the p.adjust function to manually adjust the DESeq2 p-values if needed (e.g., to use Holm correction)

# Remove rows with NAs
res = na.omit(res)

# Get the rows of "res" with significant adjusted p-values
resPadj<-res[res$padj <= 0.05 , ]

# Get dimensions
dim(resPadj)

## [1] 4811    6

Number of adjusted p-values less than 0.05

sum(res$padj <= 0.05)

## [1] 4811

Check that this is the same using p.adjust with FDR correction

sum(p.adjust(res$pvalue, method="fdr") <= 0.05)

## [1] 4811

Number of Holm adjusted p-values less than 0.05

sum(p.adjust(res$pvalue, method="holm") <= 0.01)

## [1] 3429

Sort summary list by p-value and save the table as a CSV file that can be read in Excel (or any other spreadhseet program).

res <- res[order(res$padj),]

write.csv(as.data.frame(res),file='deseq2.csv')

edgeR

• The edgeR package also uses the negative binomial distribution to model the RNA-seq count data.
• Takes an empirical Bayes approach to the statistical analysis, in a similar way to how the limma package handles RNA-seq data.

Identify DEGs with edgeR’s “Exact” Method

Load edgeR package

library(edgeR)

Construct DGEList object

y <- DGEList(counts=counts, group=conds)

Calculate library size (counts per sample)

y <- calcNormFactors(y)

Estimate common dispersion (overall variability)

y <- estimateCommonDisp(y)

Estimate tagwise dispersion (per gene variability)

y <- estimateTagwiseDisp(y)

edgeR analysis and output

Compute exact test for the negative binomial distribution.

et <- exactTest(y) 

knitr::kable(topTags(et, n=4)$table)

Adjusted p-values

edge <- as.data.frame(topTags(et, n=nrow(counts))) 
sum(edge$FDR <= 0.05)

## [1] 5242

sum(p.adjust(edge$PValue, method="fdr") <= 0.05)

## [1] 5242

Get the rows of “edge” with significant adjusted p-values

edgePadj <- edge[edge$FDR <= 0.05, ]

DESeq2 vs edgeR

Generate Venn diagram to compare DESeq2 and edgeR results.

There is fairly good overlap:

library(gplots)
setlist <- list(edgeRexact=rownames(edgePadj), DESeq2=rownames(resPadj))
venn(setlist)

Limma vs edgeR vs DESeq2

Again, fairly good overlap across the three methods we’ve looked at:

setlist <- list(edgeRexact=rownames(edgePadj), 
                DESeq2=rownames(resPadj),
                LimmaVoom=rownames(limmaPadj))
venn(setlist)

Summary

• Once we’ve generated count data, there are a number of ways to perform a differential expression analysis.
  • DESeq2 and edgeR model the count data, and assume a Negative Binomial distribution
  • Limma transforms (and logs) the data and assumes normality
• Here we’ve seen that these three approaches give quite similar results.
• The next step in a “standard” RNA-seq workflow is to perform “pathway analysis”.

Save limma topTable results for next session…

save(list='tt', file='topTable.RData')

Key Points

• Statistical analysis is required to identify genes exhibiting altered expression between experimental conditions.

• The limma processing pipeline is a fairly standard (and robust) way to do this.

• DESeq2 and edgeR offer alternative methods for identifying differetially expressed genes.