RNA-Seq differential expression work flow using DESeq2

Preparing gene models from GFF files

library( "GenomicFeatures" )
#hse <- makeTranscriptDbFromGFF( "/path/to/your/genemodel_file.GTF", format="gtf" )
hse <- makeTranscriptDbFromGFF( "Homo_sapiens.GRCh37.75.subset.gtf", format="gtf" )
#Extract exons for each gene
exonsByGene <- exonsBy( hse, by="gene" )
exonsByGene

## GRangesList of length 100:
## $ENSG00000000003 
## GRanges with 13 ranges and 2 metadata columns:
##        seqnames               ranges strand   |   exon_id   exon_name
##                            |  
##    [1]        X [99883667, 99884983]      -   |      3038        
##    [2]        X [99885756, 99885863]      -   |      3039        
##    [3]        X [99887482, 99887565]      -   |      3040        
##    [4]        X [99887538, 99887565]      -   |      3041        
##    [5]        X [99888402, 99888536]      -   |      3042        
##    ...      ...                  ...    ... ...       ...         ...
##    [9]        X [99890555, 99890743]      -   |      3046        
##   [10]        X [99891188, 99891686]      -   |      3047        
##   [11]        X [99891605, 99891803]      -   |      3048        
##   [12]        X [99891790, 99892101]      -   |      3049        
##   [13]        X [99894942, 99894988]      -   |      3050        
## 
## ...
## <99 more elements>
## ---
## seqlengths:
##   7 12  2  6 16  4  3  1 17  8 19  X 11  9 20
##  NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

• Note that gene models can also be prepared directly from BioMart :

library( "GenomicFeatures" )
# takes ~10 min
txdb <- makeTranscriptDbFromBiomart( biomart="ensembl",
                                    dataset="hsapiens_gene_ensembl" )
exonsByGene <- exonsBy( txdb, by="gene" )

Use saveDb() to only do this once. Use loadDb() to load the database next time.

library(TxDb.Hsapiens.UCSC.hg19.knownGene) is also an ready to go option for gene models.

• To convert from chrX to X and back:

seqlevelsStyle(gr) <- "NCBI"
seqlevelsStyle(gr) <- "UCSC"

Reads counting

The function summarizeOverlaps from the GenomicAlignments package will do this.

library( "GenomicAlignments" )
se <- summarizeOverlaps( exonsByGene, BamFileList( bamFiles ), mode="Union",
  singleEnd=FALSE, ignore.strand=TRUE, fragments=TRUE )

We use the counting mode "Union", which indicates that those reads which overlap any portion of exactly one feature are counted. As this experiment produced paired-end reads, we specify singleEnd =FALSE. As protocol was not strand-specific, we specify ignore.strand = TRUE. fragments = TRUE indicates that we also want to count reads with unmapped pairs. This last argument is only for use with paired-end experiments.

Details on how to read from the BAM files can be specified using the BamFileList function. For example, to control the memory, we could have specified that batches of 2 000 000 reads should be read at a time:

BamFileList( bamFiles, yieldSize = 2000000 )

SummarizedExperiment object : Output of counting

We investigate the resulting SummarizedExperiment class by looking at the counts in the assay slot, the phenotypic data about the samples in colData slot (in this case an empty DataFrame), and the data about the genes in the rowData slot.

Figure 1 explains the basic structure of the SummarizedExperiment class.

# SummarizedExperiment
se

## class: SummarizedExperiment 
## dim: 100 3 
## exptData(0):
## assays(1): counts
## rownames(100): ENSG00000000003 ENSG00000000005 ... ENSG00000005469 ENSG00000005471
## rowData metadata column names(0):
## colnames(3): SRR479052.bam SRR479053.bam SRR479054.bam
## colData names(0):

# Count data
head( assay(se) )

##                 SRR479052.bam SRR479053.bam SRR479054.bam
## ENSG00000000003             0             0             1
## ENSG00000000005             0             0             0
## ENSG00000000419             0             0             0
## ENSG00000000457             0             1             1
## ENSG00000000460             0             0             0
## ENSG00000000938             0             0             0

#Column sum
colSums( assay(se) )

## SRR479052.bam SRR479053.bam SRR479054.bam 
##            31            21            30

#Phenotypic data
colData(se)

## DataFrame with 3 rows and 0 columns

#Data about genes
rowData(se)

## GRangesList of length 100:
## $ENSG00000000003 
## GRanges with 13 ranges and 2 metadata columns:
##        seqnames               ranges strand   |   exon_id   exon_name
##                            |  
##    [1]        X [99883667, 99884983]      -   |      3038        
##    [2]        X [99885756, 99885863]      -   |      3039        
##    [3]        X [99887482, 99887565]      -   |      3040        
##    [4]        X [99887538, 99887565]      -   |      3041        
##    [5]        X [99888402, 99888536]      -   |      3042        
##    ...      ...                  ...    ... ...       ...         ...
##    [9]        X [99890555, 99890743]      -   |      3046        
##   [10]        X [99891188, 99891686]      -   |      3047        
##   [11]        X [99891605, 99891803]      -   |      3048        
##   [12]        X [99891790, 99892101]      -   |      3049        
##   [13]        X [99894942, 99894988]      -   |      3050        
## 
## ...
## <99 more elements>
## ---
## seqlengths:
##   7 12  2  6 16  4  3  1 17  8 19  X 11  9 20
##  NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

Note that the rowData slot is a GRangesList, which contains all the information about the exons for each gene, i.e., for each row of the count table.

The colData slot, so far empty, should contain all the meta data. We hence assign our sample table to it:

#Column data
colData(se) <- DataFrame( sampleTable )

We can extract columns from the colData using the $ operator, and we can omit the colData to avoid extra keystrokes.

colData(se)$treatment

## [1] Control Control DPN    
## Levels: Control DPN

se$treatment

## [1] Control Control DPN    
## Levels: Control DPN

We can also use the sampleName table to name the columns of our data matrix:

colnames(se) <- sampleTable$sampleName
head( assay(se) )

##                 Ctrl_24h_1 Ctrl_48h_1 DPN_24h_1
## ENSG00000000003          0          0         1
## ENSG00000000005          0          0         0
## ENSG00000000419          0          0         0
## ENSG00000000457          0          1         1
## ENSG00000000460          0          0         0
## ENSG00000000938          0          0         0

This SummarizedExperiment object se is then all we need to start our analysis.

Preparing the data object for the analysis of interest

First we subset the relevant columns from the full dataset:

dds <- ddsCollapsed[ , ddsCollapsed$time == "48h" ]

Sometimes it is necessary to drop levels of the factors, in case that all the samples for one or more levels of a factor in the design have been removed. If time were included in the design formula, the following code could be used to take care of dropped levels in this column.

dds$time <- droplevels( dds$time )

It will be convenient to make sure that Control is the first level in the treatment factor, so that the default log2 fold changes are calculated as treatment over control and not the other way around. The function relevel achieves this:

dds$treatment <- relevel( dds$treatment, "Control" )

A quick check whether we now have the right samples:

as.data.frame( colData(dds) )

##                 run experiment patient treatment time submission     study    sample       runsCollapsed
## SRS308866 SRR479053  SRX140504       1   Control  48h  SRA051611 SRP012167 SRS308866           SRR479053
## SRS308868 SRR479055  SRX140506       1       DPN  48h  SRA051611 SRP012167 SRS308868           SRR479055
## SRS308870 SRR479057  SRX140508       1       OHT  48h  SRA051611 SRP012167 SRS308870           SRR479057
## SRS308872 SRR479059  SRX140510       2   Control  48h  SRA051611 SRP012167 SRS308872           SRR479059
## SRS308874 SRR479062  SRX140512       2       DPN  48h  SRA051611 SRP012167 SRS308874           SRR479062
## SRS308876 SRR479065  SRX140514       2       OHT  48h  SRA051611 SRP012167 SRS308876           SRR479065
## SRS308878 SRR479067  SRX140516       3   Control  48h  SRA051611 SRP012167 SRS308878           SRR479067
## SRS308880 SRR479069  SRX140518       3       DPN  48h  SRA051611 SRP012167 SRS308880           SRR479069
## SRS308882 SRR479071  SRX140520       3       OHT  48h  SRA051611 SRP012167 SRS308882           SRR479071
## SRS308883 SRR479072  SRX140521       4   Control  48h  SRA051611 SRP012167 SRS308883           SRR479072
## SRS308885 SRR479074  SRX140523       4       DPN  48h  SRA051611 SRP012167 SRS308885 SRR479074,SRR479075
## SRS308887 SRR479077  SRX140525       4       OHT  48h  SRA051611 SRP012167 SRS308887 SRR479077,SRR479078

In order to speed up some annotation steps below, it makes sense to remove genes which have zero counts for all samples. This can be done by simply indexing the dds object:

dds <- dds[ rowSums( counts(dds) ) > 0 , ]

Running the pipeline

Let’s recall what design we have specified:

#design
design(dds)

## ~patient + treatment

#Run DESeq : Modeling counts with patient and treatment effects
dds <- DESeq(dds)

This function will print out a message for the various steps it performs. Briefly these are: the estimation of size factors (which control for differences in the library size of the sequencing experiments), the estimation of dispersion for each gene, and fitting a generalized linear model.

A DESeqDataSet is returned which contains all the fitted information within it, and the following section describes how to extract out results tables of interest from this object.

Inspecting the results table

Calling results without any arguments will extract the estimated log2 fold changes and p values for the last variable in the design formula. If there are more than 2 levels for this variable – as is the case in this analysis – results will extract the results table for a comparison of the last level over the first level. The following section describes how to extract other comparisons.

res <- results( dds )
res

## log2 fold change (MAP): treatment OHT vs Control 
## Wald test p-value: treatment OHT vs Control 
## DataFrame with 32082 rows and 6 columns
##                  baseMean log2FoldChange     lfcSE      stat    pvalue      padj
##                           
## ENSG00000000003  613.8196      -0.044799   0.08787  -0.50983  0.610173    0.9837
## ENSG00000000005    0.5502      -0.568326   1.08754  -0.52258  0.601268        NA
## ENSG00000000419  304.0482       0.116118   0.09623   1.20668  0.227555        NA
## ENSG00000000457  183.5157       0.007441   0.12314   0.06042  0.951819        NA
## ENSG00000000460  207.4336       0.470836   0.14493   3.24867  0.001159        NA
## ...                   ...            ...       ...       ...       ...       ...
## ENSG00000271699   0.17125       -1.09753    0.9097  -1.20646   0.22764        NA
## ENSG00000271704   0.10233       -0.01414    0.7157  -0.01975   0.98424        NA
## ENSG00000271707   9.21112       -0.84445    0.4832  -1.74774   0.08051        NA
## ENSG00000271709   0.08257       -0.01108    0.6782  -0.01633   0.98697        NA
## ENSG00000271711   0.74835       -0.95188    1.0655  -0.89335   0.37167        NA

As res is a DataFrame object, it carries metadata with information on the meaning of the columns:

mcols(res, use.names=TRUE)

## DataFrame with 6 rows and 2 columns
##                        type                                      description
##                                                       
## baseMean       intermediate                      the base mean over all rows
## log2FoldChange      results log2 fold change (MAP): treatment OHT vs Control
## lfcSE               results         standard error: treatment OHT vs Control
## stat                results         Wald statistic: treatment OHT vs Control
## pvalue              results      Wald test p-value: treatment OHT vs Control
## padj                results                             BH adjusted p-values

The first column, baseMean, is a just the average of the normalized count values, dividing by size factors, taken over all samples. The remaining four columns refer to a specific contrast, namely the comparison of the levels DPN versus Control of the factor variable treatment.

See the help page for results (by typing ?results) for information on how to obtain other contrasts.

The column log2FoldChange is the effect size estimate. It tells us how much the gene’s expression seems to have changed due to treatment with DPN in comparison to control. This value is reported on a logarithmic scale to base 2: for example, a log2 fold change of 1.5 means that the gene’s expression is increased by a multiplicative factor of 2^1.5 ≈ 2.82.

Of course, this estimate has an uncertainty associated with it, which is available in the column lfcSE, the standard error estimate for the log2 fold change estimate. The column p value indicates wether the observed difference between treatment and control is significantly different.

We note that a subset of the p values in res are NA (“notavailable”). This is DESeq’s way of reporting that all counts for this gene were zero, and hence not test was applied. In addition, p values can be assigned NA if the gene was excluded from analysis because it contained an extreme count outlier. For more information, see the outlier detection section of the advanced vignette.

We can examine the counts and normalized counts for the gene with the smallest p value:

# SmallestPvalue
idx <- which.min(res$pvalue)
counts(dds)[idx, ]

## SRS308866 SRS308868 SRS308870 SRS308872 SRS308874 SRS308876 SRS308878 SRS308880 SRS308882 SRS308883 SRS308885 SRS308887 
##        95        62        30        24        13        21       276       357       112       388       404       296

#Normalization
counts(dds, normalized=TRUE)[ idx, ]

## SRS308866 SRS308868 SRS308870 SRS308872 SRS308874 SRS308876 SRS308878 SRS308880 SRS308882 SRS308883 SRS308885 SRS308887 
##     86.81     61.43     37.42     35.25     15.96     25.85    314.96    201.94    136.92    461.46    269.09    172.00

Other comparisons

The results for a comparison of any two levels of a variable can be extracted using the contrast argument to results. The user should specify three values: The name of the variable, the name of the level in the numerator, and the name of the level in the denominator.

Here we extract results for the log2 of the fold change of DPN/Control:

#Save result table
resOHT <- res
#Other comparisons
res <- results( dds, contrast = c("treatment", "DPN", "Control") )
res

## log2 fold change (MAP): treatment DPN vs Control 
## Wald test p-value: treatment DPN vs Control 
## DataFrame with 32082 rows and 6 columns
##                  baseMean log2FoldChange     lfcSE      stat    pvalue      padj
##                           
## ENSG00000000003  613.8196       -0.01722   0.08665  -0.19868   0.84252    0.9775
## ENSG00000000005    0.5502       -0.10344   1.09363  -0.09458   0.92465        NA
## ENSG00000000419  304.0482       -0.01695   0.09517  -0.17807   0.85867    0.9811
## ENSG00000000457  183.5157       -0.09654   0.12138  -0.79533   0.42642    0.8945
## ENSG00000000460  207.4336        0.35004   0.14375   2.43497   0.01489    0.2762
## ...                   ...            ...       ...       ...       ...       ...
## ENSG00000271699   0.17125        -1.1391    0.9251   -1.2313    0.2182        NA
## ENSG00000271704   0.10233         0.5925    0.7547    0.7851    0.4324        NA
## ENSG00000271707   9.21112        -0.5099    0.4579   -1.1136    0.2655        NA
## ENSG00000271709   0.08257         0.5156    0.7112    0.7250    0.4685        NA
## ENSG00000271711   0.74835        -0.6649    1.0511   -0.6326    0.5270        NA

Adding gene names

Our result table only uses Ensembl gene IDs, but gene names may be more informative. Bioconductor’s annotation packages help with mapping various ID schemes to each other.

We load the annotation package org.Hs.eg.db:

library( "org.Hs.eg.db" )

This is the organism annotation package (“org”“) for Homo sapiens (”Hs“”), organized as an AnnotationDbi package (“db”“), using Entrez Gene IDs (”eg“) as primary key.

To get a list of all available key types, use

columns(org.Hs.eg.db)

##  [1] "ENTREZID"     "PFAM"         "IPI"          "PROSITE"      "ACCNUM"       "ALIAS"        "CHR"         
##  [8] "CHRLOC"       "CHRLOCEND"    "ENZYME"       "MAP"          "PATH"         "PMID"         "REFSEQ"      
## [15] "SYMBOL"       "UNIGENE"      "ENSEMBL"      "ENSEMBLPROT"  "ENSEMBLTRANS" "GENENAME"     "UNIPROT"     
## [22] "GO"           "EVIDENCE"     "ONTOLOGY"     "GOALL"        "EVIDENCEALL"  "ONTOLOGYALL"  "OMIM"        
## [29] "UCSCKG"

Converting IDs with the native functions from the AnnotationDbi package is currently a bit cumbersome, so we provide the following convenience function (without explaining how exactly it works):

#ids = list of IDS
#fromKey = key type; toKey = key type we want to convert to
#db = the AnnotationDb object to use.
#ifMultiple = the argument specifies what to do if one source ID maps to several target IDs:
  #should the function return an NA or simply the first of the multiple IDs?
convertIDs <- function( ids, fromKey, toKey, db, ifMultiple=c( "putNA", "useFirst" ) ) {
   stopifnot( inherits( db, "AnnotationDb" ) )
   ifMultiple <- match.arg( ifMultiple )
   suppressWarnings( selRes <- AnnotationDbi::select( 
      db, keys=ids, keytype=fromKey, columns=c(fromKey,toKey) ) )
   if( ifMultiple == "putNA" ) {
      duplicatedIds <- selRes[ duplicated( selRes[,1] ), 1 ]   
      selRes <- selRes[ ! selRes[,1] %in% duplicatedIds, ] }
   return( selRes[ match( ids, selRes[,1] ), 2 ] )
}

To convert the Ensembl IDs in the rownames of res to gene symbols and add them as a new column, we use:

res$hgnc_symbol <- convertIDs( row.names(res), "ENSEMBL", "SYMBOL", org.Hs.eg.db )
res$entrezid <- convertIDs( row.names(res), "ENSEMBL", "ENTREZID", org.Hs.eg.db )
head(res, 4)

## log2 fold change (MAP): treatment DPN vs Control 
## Wald test p-value: treatment DPN vs Control 
## DataFrame with 4 rows and 8 columns
##                  baseMean log2FoldChange     lfcSE      stat    pvalue      padj hgnc_symbol    entrezid
##                             
## ENSG00000000003  613.8196       -0.01722   0.08665  -0.19868    0.8425    0.9775      TSPAN6        7105
## ENSG00000000005    0.5502       -0.10344   1.09363  -0.09458    0.9246        NA        TNMD       64102
## ENSG00000000419  304.0482       -0.01695   0.09517  -0.17807    0.8587    0.9811        DPM1        8813
## ENSG00000000457  183.5157       -0.09654   0.12138  -0.79533    0.4264    0.8945       SCYL3       57147

This conversion can be done from Ensembl BioMart web site.

Multiple testing

DESeq2 uses the so-called Benjamini-Hochberg (BH) adjustment for multiple testing problem; in brief, this method calculates for each gene an adjusted p value which answers the following question: if one called significant all genes with a p value less than or equal to this gene’s p value threshold, what would be the fraction of false positives (the false discovery rate, FDR) among them (in the sense of the calculation outlined above)? These values, called the BH-adjusted p values, are given in the column padj of the results object.

Hence, if we consider a fraction of 10% false positives acceptable, we can consider all genes with an adjusted p value below 10%=0.1 as significant. How many such genes are there?

sum( res$padj < 0.1, na.rm=TRUE )

## [1] 249

We subset the results table to these genes and then sort it by the log2 fold change estimate to get the significant genes with the strongest down-regulation:

resSig <- subset(res, res$padj < 0.1 )
head( resSig[ order( resSig$log2FoldChange ), ], 4)

## log2 fold change (MAP): treatment DPN vs Control 
## Wald test p-value: treatment DPN vs Control 
## DataFrame with 4 rows and 8 columns
##                  baseMean log2FoldChange     lfcSE      stat    pvalue      padj hgnc_symbol    entrezid
##                             
## ENSG00000163631     233.3        -0.9307    0.2842    -3.275 1.058e-03   0.05817         ALB         213
## ENSG00000119946     151.6        -0.6903    0.1566    -4.408 1.041e-05   0.00246       CNNM1       26507
## ENSG00000041982    1377.0        -0.6859    0.1845    -3.717 2.018e-04   0.02045         TNC        3371
## ENSG00000155111     530.9        -0.6756    0.2109    -3.203 1.359e-03   0.06850       CDK19       23097

and with the strongest upregulation :

head( resSig[ order( -resSig$log2FoldChange ), ], 4)

## log2 fold change (MAP): treatment DPN vs Control 
## Wald test p-value: treatment DPN vs Control 
## DataFrame with 4 rows and 8 columns
##                  baseMean log2FoldChange     lfcSE      stat    pvalue      padj hgnc_symbol    entrezid
##                             
## ENSG00000092621     558.5         0.9002    0.1258     7.158 8.191e-13 2.628e-09       PHGDH       26227
## ENSG00000101255     255.1         0.8860    0.1694     5.229 1.706e-07 2.346e-04       TRIB3       57761
## ENSG00000103257     168.5         0.8259    0.1644     5.024 5.064e-07 3.249e-04      SLC7A5        8140
## ENSG00000156414     142.8         0.7582    0.1661     4.564 5.025e-06 1.547e-03       TDRD9      122402

Diagnostic plot

plotMA( res, ylim = c(-3, 3) )

This plot demonstrates that only genes with a large average normalized count contain sufficient information to yield a significant call.

plotDispEsts( dds, ylim = c(1e-6, 1e1) )

hist( res$pvalue, breaks=20, col="grey" )

Independent filtering

The MA plot highlights an important property of RNA-Seq data. For weakly expressed genes, we have no chance of seeing differential expression, because the low read counts suffer from so high Poisson noise that any biological effect is drowned in the uncertainties from the read counting. We can also show this by examining the ratio of small p values (say, less than, 0.01) for genes binned by mean normalized count:

# create bins using the quantile function
qs <- c( 0, quantile( res$baseMean[res$baseMean > 0], 0:7/7 ) )
# "cut" the genes into the bins
bins <- cut( res$baseMean, qs )
# rename the levels of the bins using the middle point
levels(bins) <- paste0("~",round(.5*qs[-1] + .5*qs[-length(qs)]))
# calculate the ratio of p values less than .01 for each bin
ratios <- tapply( res$pvalue, bins, function(p) mean( p < .01, na.rm=TRUE ) )
# plot these ratios
barplot(ratios, xlab="mean normalized count", ylab="ratio of small p values")

At first sight, there may seem to be little benefit in filtering out these genes. After all, the test found them to be non-significant anyway. However, these genes have an influence on the multiple testing adjustment, whose performance improves if such genes are removed. By removing the weakly-expressed genes from the input to the FDR procedure, we can find more genes to be significant among those which we keep, and so improved the power of our test. This approach is known as independent filtering.

The DESeq software automatically performs independent filtering which maximizes the number of genes which will have adjusted p value less than a critical value (by default, alpha is set to 0.1). This automatic independent filtering is performed by, and can be controlled by, the results function. We can observe how the number of rejections changes for various cutoffs based on mean normalized count. The following optimal threshold and table of possible values is stored as an attribute of the results object.

attr(res,"filterThreshold")

##   70% 
## 126.9

plot(attr(res,"filterNumRej"),type="b",
     xlab="quantiles of 'baseMean'",
     ylab="number of rejections")

The term independent highlights an important caveat. Such filtering is permissible only if the filter criterion is independent of the actual test statistic. Otherwise, the filtering would invalidate the test and consequently the assumptions of the BH procedure. This is why we filtered on the average over all samples: this filter is blind to the assignment of samples to the treatment and control group and hence independent.

Exporting results

You can easily save the results table in a CSV file, which you can then load with a spreadsheet program such as Excel:

res[1:2,]
write.csv( as.data.frame(res), file="results.csv" )

Gene-set enrichment analysis

Do the genes with a strong up- or down-regulation have something in common? We perform next a gene-set enrichment analysis (GSEA) to examine this question.

We here present a relatively simplistic approach, to demonstrate the basic ideas, but note that a more careful treatment will be needed for more definitive results.

We use the gene sets in the Reactome database:

#source("http://bioconductor.org/biocLite.R")
#biocLite("reactome.db")
library( "reactome.db" )

This database works with Entrez IDs, so we will need the entrezid column that we added earlier to the res object.

First, we subset the results table, res, to only those genes for which the Reactome database has data (i.e, whose Entrez ID we find in the respective key column of reactome.db and for which the DESeq2 test gave an adjusted p value that was not NA.

res2 <- res[ res$entrezid %in% keys( reactome.db, "ENTREZID" ) & !is.na( res$padj ) , ]
head(res2)

## log2 fold change (MAP): treatment DPN vs Control 
## Wald test p-value: treatment DPN vs Control 
## DataFrame with 6 rows and 8 columns
##                  baseMean log2FoldChange     lfcSE      stat    pvalue      padj hgnc_symbol    entrezid
##                             
## ENSG00000000419     304.0      -0.016946   0.09517  -0.17807    0.8587    0.9811        DPM1        8813
## ENSG00000001084     312.0       0.039811   0.10228   0.38923    0.6971    0.9540        GCLC        2729
## ENSG00000001167     398.8      -0.056003   0.09711  -0.57669    0.5641    0.9357        NFYA        4800
## ENSG00000001630     463.5       0.070002   0.09676   0.72348    0.4694    0.9123     CYP51A1        1595
## ENSG00000002822     169.5      -0.001926   0.13784  -0.01397    0.9889    0.9982      MAD1L1        8379
## ENSG00000003056     995.8       0.007716   0.06785   0.11373    0.9095    0.9859        M6PR        4074

Using select, a function from AnnotationDbi for querying database objects, we get a table with the mapping from Entrez IDs to Reactome Path IDs :

reactomeTable <- AnnotationDbi::select( reactome.db, 
   keys=as.character(res2$entrezid), keytype="ENTREZID", 
   columns=c("ENTREZID","REACTOMEID") )
head(reactomeTable)

##   ENTREZID REACTOMEID
## 1     8813     162699
## 2     8813     163125
## 3     8813     392499
## 4     8813     446193
## 5     8813     446203
## 6     8813     446219

The next code chunk transforms this table into an incidence matrix. This is a Boolean matrix with one row for each Reactome Path and one column for each unique gene in res2, which tells us which genes are members of which Reactome Paths.

#problem with this code is that res2$entrez are not unique
#ft2mat <- function(x, y) {
  # ux = unique(x)
  # uy = unique(y)
  # im = matrix(FALSE, nrow=length(ux), ncol=length(uy), dimnames=list(ux, uy))
  # im[ cbind(x, y) ] = TRUE
  # return(im)
 #}
#incm <- with(reactomeTable, ft2mat(REACTOMEID, ENTREZID))

incm <- do.call( rbind, with(reactomeTable, tapply( 
  ENTREZID, factor(REACTOMEID), function(x) res2$entrezid %in% x ) ))
colnames(incm) <- res2$entrez
str(incm)

##  logi [1:1458, 1:3400] FALSE FALSE FALSE FALSE FALSE FALSE ...
##  - attr(*, "dimnames")=List of 2
##   ..$ : chr [1:1458] "1059683" "109581" "109582" "109606" ...
##   ..$ : chr [1:3400] "8813" "2729" "4800" "1595" ...

We remove all rows corresponding to Reactome Paths with less than 20 or more than 80 assigned genes.

within <- function(x, lower, upper) (x>=lower & x<=upper)
incm <- incm[ within(rowSums(incm), lower=20, upper=80), ]

To test whether the genes in a Reactome Path behave in a special way in our experiment, we calculate a number of statistics, including a t-statistic to see whether the average of the genes’ log2 fold change values in the gene set is different from zero. To facilitate the computations, we define a little helper function:

testCategory <- function( reactomeID ) {
  isMember <- incm[ reactomeID, ]
  data.frame( 
     reactomeID  = reactomeID,
     numGenes    = sum( isMember ),
     avgLFC      = mean( res2$log2FoldChange[isMember] ),
     sdLFC       = sd( res2$log2FoldChange[isMember] ),
     zValue      = mean( res2$log2FoldChange[isMember] ) /sd( res2$log2FoldChange[isMember] ),
     strength    = sum( res2$log2FoldChange[isMember] ) / sqrt(sum(isMember)),
     pvalue      = t.test( res2$log2FoldChange[ isMember ] )$p.value,
     reactomeName = reactomePATHID2NAME[[reactomeID]],
     stringsAsFactors = FALSE ) }

The function can be called with a Reactome Path ID:

testCategory("109606")

##   reactomeID numGenes   avgLFC   sdLFC  zValue strength pvalue                                  reactomeName
## 1     109606       31 -0.02215 0.07769 -0.2852  -0.1234 0.1228 Homo sapiens: Intrinsic Pathway for Apoptosis

As you can see the function not only performs the t test and returns the p value but also lists other useful information such as the number of genes in the category, the average log fold change, a “strength”" measure (see below) and the name with which Reactome describes the Path.

We call the function for all Paths in our incidence matrix and collect the results in a data frame:

reactomeResult <- do.call( rbind, lapply( rownames(incm), testCategory ) )

As we performed many tests, we should again use a multiple testing adjustment.

reactomeResult$padjust <- p.adjust( reactomeResult$pvalue, "BH" )

This is a list of Reactome Paths which are significantly differentially expressed in our comparison of DPN treatment with control, sorted according to sign and strength of the signal:

reactomeResultSignif <- reactomeResult[ reactomeResult$padjust < 0.05, ]
head( reactomeResultSignif[ order(-reactomeResultSignif$strength), ] )

##     reactomeID numGenes   avgLFC   sdLFC  zValue strength    pvalue
## 174     191273       21  0.10808 0.09894  1.0923   0.4953 6.786e-05
## 308     381070       41  0.07055 0.13898  0.5076   0.4517 2.341e-03
## 60     1638091       30  0.06877 0.10742  0.6402   0.3767 1.499e-03
## 150    1799339       75  0.04083 0.07791  0.5240   0.3536 2.153e-05
## 405      72689       64  0.02905 0.07284  0.3989   0.2324 2.213e-03
## 23     1169091       53 -0.02579 0.06195 -0.4162  -0.1877 3.804e-03
##                                                                  reactomeName  padjust
## 174                                    Homo sapiens: Cholesterol biosynthesis 0.007838
## 308                              Homo sapiens: IRE1alpha activates chaperones 0.041597
## 60                  Homo sapiens: Heparan sulfate/heparin (HS-GAG) metabolism 0.032968
## 150 Homo sapiens: SRP-dependent cotranslational protein targeting to membrane 0.003316
## 405                    Homo sapiens: Formation of a pool of free 40S subunits 0.041130
## 23                           Homo sapiens: Activation of NF-kappaB in B cells 0.048870

The rlog transform

Many common statistical methods for exploratory analysis of multidimensional data, especially methods for clustering (e.g., principal-component analysis and the like), work best for (at least approximately) homoskedastic data; this means that the variance of an observable quantity (i.e., here, the expression strength of a gene) does not depend on the mean. In RNA-Seq data, however, variance grows with the mean. For example, if one performs PCA directly on a matrix of normalized read counts, the result typically depends only on the few most strongly expressed genes because they show the largest absolute differences between samples. A simple and often used strategy to avoid this is to take the logarithm of the normalized count values plus a small pseudocount; however, now the genes with low counts tend to dominate the results because, due to the strong Poisson noise inherent to small count values, they show the strongest relative differences between samples.

As a solution, DESeq2 offers the regularized-logarithm transformation, or rlog for short. For genes with high counts, the rlog transformation differs not much from an ordinary log2 transformation. For genes with lower counts, however, the values are shrunken towards the genes’ averages across all samples. Using an empirical Bayesian prior in the form of a ridge penalty, this is done such that the rlog-transformed data are approximately homoskedastic.

Note that the rlog transformation is provided for applications other than differential testing. For differential testing we recommend the DESeq function applied to raw counts, as described earlier in this vignette, which also takes into account the dependence of the variance of counts on the mean value during the dispersion estimation step.

The function rlog returns a SummarizedExperiment object which contains the rlog-transformed values in its assay slot:

rld <- rlog( dds )
assay(rld)[ 1:3, 1:3]

##                 SRS308866 SRS308868 SRS308870
## ENSG00000000003    9.7614    9.7285    9.8653
## ENSG00000000005   -0.9813   -0.7408   -0.9447
## ENSG00000000419    8.0647    8.0770    8.1186

To show the effect of the transformation, we plot the first sample against the second, first simply using the log2 function (after adding 1, to avoid taking the log of zero), and then using the rlog-transformed values.

plot( log2( 1+counts(dds, normalized=TRUE)[, 1:2] ), col="#00000020", pch=20, cex=0.3 )
plot( assay(rld)[, 1:2], col="#00000020", pch=20, cex=0.3 )

In Figure , we can see how genes with low counts seem to be excessively variable on the ordinary logarithmic scale, while the rlog transform compresses differences for genes for which the data cannot provide good information anyway.

Sample distances

A useful first step in an RNA-Seq analysis is often to assess overall similarity between samples.

We use the R function dist to calculate the Euclidean distance between samples. To avoid that the distance measure is dominated by a few highly variable genes, and have a roughly equal contribution from all genes, we use it on the rlog-transformed data:

sampleDists <- dist( t( assay(rld) ) )
as.matrix( sampleDists )[ 1:3, 1:3 ]

##           SRS308866 SRS308868 SRS308870
## SRS308866      0.00     32.87     31.21
## SRS308868     32.87      0.00     33.73
## SRS308870     31.21     33.73      0.00

Note the use of the function t to transpose the data matrix. We need this because dist calculates distances between data rows and our samples constitute the columns.

We visualize the distances in a heatmap, using the function heatmap.2 from the gplots package.

sampleDistMatrix <- as.matrix( sampleDists )
rownames(sampleDistMatrix) <- paste( rld$treatment, 
   rld$patient, sep="-" )
colnames(sampleDistMatrix) <- NULL   
library( "gplots" )
library( "RColorBrewer" )
colours = colorRampPalette( rev(brewer.pal(9, "Blues")) )(255)
heatmap.2( sampleDistMatrix, trace="none", col=colours)

Note that we have changed the row names of the distance matrix to contain treatment type and patient number instead of sample ID, so that we have all this information in view when looking at the heatmap. 

Another way to visualize sample-to-sample distances is a principal-components analysis (PCA). In this ordination method, the data points (i.e., here, the samples) are projected onto the 2D plane such that they spread out optimally.

colours <- c(rgb(1:3/4,0,0),rgb(0,1:3/4,0),rgb(0,0,1:3/4),rgb(1:3/4,0,1:3/4))
plotPCA( rld, intgroup = c("patient","treatment"), col=colours )

Here, we have used the function plotPCA which comes with DESeq2. The two terms specified as intgroup are column names from our sample data; they tell the function to use them to choose colours.

From both visualizations, we see that the differences between patients is much larger than the difference between treatment and control samples of the same patient. This shows why it was important to account for this paired design (``paired’’, because each treated sample is paired with one control sample from the same patient).

We did so by using the design formula ~ patient + treatment when setting up the data object in the beginning. Had we used an un-paired analysis, by specifying only , we would not have found many hits, because then, the patient-to-patient differences would have drowned out any treatment effects.

Gene clustering

In the above heatmap, the dendrogram at the side shows us a hierarchical clustering of the samples. Such a clustering can also be performed for the genes.

Since the clustering is only relevant for genes that actually carry signal, one usually carries it out only for a subset of most highly variable genes. Here, for demonstration, let us select the 35 genes with the highest variance across samples:

library( "genefilter" )
topVarGenes <- head( order( rowVars( assay(rld) ), decreasing=TRUE ), 35 )

The heatmap becomes more interesting if we do not look at absolute expression strength but rather at the amount by which each gene deviates in a specific sample from the gene’s average across all samples. Hence, we center and scale each genes’ values across samples, and plot a heatmap.

heatmap.2( assay(rld)[ topVarGenes, ], scale="row", 
     trace="none", dendrogram="column", 
     col = colorRampPalette( rev(brewer.pal(9, "RdBu")) )(255),
     ColSideColors = c( Control="gray", DPN="darkgreen", OHT="orange" )[
        colData(rld)$treatment ] )

We can now see on the heatmap, blocks of genes which covary across patients. Often, such a heatmap is insightful, even though here, seeing these variations across patients is of limited value because we are rather interested in the effects between the treatments from each patient. 

Going further

Analyze more datasets: use the function defined in the following code chunk to download a processed count matrix from the ReCount website.

The following function takes a name of the dataset from the ReCount website, e.g. “hammer”, and returns a SummarizedExperiment object.

recount2SE <- function(name) {
  filename <- paste0(name,"_eset.RData")
  if (!file.exists(filename)) download.file(paste0(
    "http://bowtie-bio.sourceforge.net/recount/ExpressionSets/",
    filename),filename)
  load(filename)
  e <- get(paste0(name,".eset"))
  se <- SummarizedExperiment(SimpleList(counts=exprs(e)),
                             colData=DataFrame(pData(e)))
  se                   
}