RNA-Seq workflow: gene-level exploratory analysis and differential expression

Experimental data

The data used in this workflow is stored in the airway package that summarizes an RNA-seq experiment wherein airway smooth muscle cells were treated with dexamethasone, a synthetic glucocorticoid steroid with anti-inflammatory effects¹. Glucocorticoids are used, for example, by people with asthma to reduce inflammation of the airways. In the experiment, four primary human airway smooth muscle cell lines were treated with 1 micromolar dexamethasone for 18 hours. For each of the four cell lines, we have a treated and an untreated sample. For more description of the experiment see the PubMed entry 24926665 and for raw data see the GEO entry GSE52778.

Aligning reads to a reference genome

The computational analysis of an RNA-seq experiment begins earlier: we first obtain a set of FASTQ files that contain the nucleotide sequence of each read and a quality score at each position. These reads must first be aligned to a reference genome or transcriptome. It is important to know if the sequencing experiment was single-end or paired-end, as the alignment software will require the user to specify both FASTQ files for a paired-end experiment. The output of this alignment step is commonly stored in a file format called SAM/BAM.

A number of software programs exist to align reads to a reference genome, and the development is too rapid for this document to provide an up-to-date list. We recommend consulting benchmarking papers that discuss the advantages and disadvantages of each software, which include accuracy, sensitivity in aligning reads over splice junctions, speed, memory footprint, usability, and many other features.

The reads for this experiment were aligned to the Ensembl release 75⁸ human reference genome using the STAR read aligner⁹. In this example, we have a file in the current directory called files with each line containing an identifier for each experiment, and we have all the FASTQ files in a subdirectory fastq. If you have downloaded the FASTQ files from the Sequence Read Archive, the identifiers would be SRA run IDs, e.g. SRR1039520. You should have two files for a paired-end experiment for each ID, fastq/SRR1039520_1.fastq1 and fastq/SRR1039520_2.fastq, which give the first and second read for the paired-end fragments. If you have performed a single-end experiment, you would only have one file per ID. We have also created a subdirectory, aligned, where STAR will output its alignment files.

for f in 'cat files'; do STAR --genomeDir ../STAR/ENSEMBL.homo_sapiens.release-75 \
--readFilesIn fastq/$f\_1.fastq fastq/$f\_2.fastq \
--runThreadN 12 --outFileNamePrefix aligned/$f.; done

SAMtools¹⁰ was used to generate BAM files. The –@ flag can be used to allocate additional threads.

for f in 'cat files'; do samtools view -bS aligned/$f.Aligned.out.sam \
-o aligned/$f.bam; done

The BAM files for a number of sequencing runs can then be used to generate count matrices, as described in the following section.

Locating alignment files

Besides the count matrix that we will use later, the airway package also contains eight files with a small subset of the total number of reads in the experiment. The reads were selected which aligned to a small region of chromosome 1. We chose a subset of reads because the full alignment files are large (a few gigabytes each), and because it takes between 10–30 minutes to count the fragments for each sample. We will use these files to demonstrate how a count matrix can be constructed from BAM files. Afterwards, we will load the full count matrix corresponding to all samples and all data, which is already provided in the same package, and will continue the analysis with that full matrix.

We load the data package with the example data:

library("airway")

The R function system.file can be used to find out where on your computer the files from a package have been installed. Here we ask for the full path to the extdata directory, where R packages store external data, that is part of the airway package.

dir <- system.file("extdata", package="airway", mustWork=TRUE)

In this directory, we find the eight BAM files (and some other files):

list.files(dir)

##  [1] "GSE52778_series_matrix.txt"	"Homo_sapiens.GRCh37.75_subset.gtf"
##  [3] "sample_table.csv"		"SraRunInfo_SRP033351.csv"
##  [5] "SRR1039508_subset.bam"		"SRR1039508_subset.bam.bai"
##  [7] "SRR1039509_subset.bam"		"SRR1039512_subset.bam"
##  [9] "SRR1039513_subset.bam"		"SRR1039516_subset.bam"
## [11] "SRR1039517_subset.bam"		"SRR1039520_subset.bam"
## [13] "SRR1039521_subset.bam"

Typically, we have a table with detailed information for each of our samples that links samples to the associated FASTQ and BAM files. For your own project, you might create such a comma-separated value (CSV) file using a text editor or spreadsheet software such as Excel.

We load such a CSV file with read.csv:

csvfile <- file.path(dir,"sample_table.csv")
(sampleTable <- read.csv(csvfile,row.names=1))

##	      SampleName    cell   dex albut        Run avgLength Experiment    Sample    BioSample
## SRR1039508 GSM1275862  N61311 untrt untrt SRR1039508       126  SRX384345 SRS508568 SAMN02422669
## SRR1039509 GSM1275863  N61311   trt untrt SRR1039509       126  SRX384346 SRS508567 SAMN02422675
## SRR1039512 GSM1275866 N052611 untrt untrt SRR1039512       126  SRX384349 SRS508571 SAMN02422678
## SRR1039513 GSM1275867 N052611   trt untrt SRR1039513        87  SRX384350 SRS508572 SAMN02422670
## SRR1039516 GSM1275870 N080611 untrt untrt SRR1039516       120  SRX384353 SRS508575 SAMN02422682
## SRR1039517 GSM1275871 N080611   trt untrt SRR1039517       126  SRX384354 SRS508576 SAMN02422673
## SRR1039520 GSM1275874 N061011 untrt untrt SRR1039520       101  SRX384357 SRS508579 SAMN02422683
## SRR1039521 GSM1275875 N061011   trt untrt SRR1039521        98  SRX384358 SRS508580 SAMN02422677

Note: here and elsewhere in the workflow, the parentheses () around the entire code of the last line above is an R trick to print the output of the function in addition to saving it to sampleTable. This is equivalent to assigning and then showing the object in two steps:

sampleTable <- read.csv(csvfile,row.names=1)
sampleTable

Once the reads have been aligned, there are a number of tools that can be used to count the number of reads/fragments that can be uniquely assigned to genomic features for each sample. These often take as input SAM/BAM alignment files and a file specifying the genomic features, e.g. a GFF3 or GTF file specifying the gene models.

The following tools can be used generate count matrices: summarizeOverlaps¹¹, featureCounts¹², or htseq-count¹³ (Table 1).

We now proceed using the summarizeOverlaps method of counting. Using the Run column in the sample table, we construct the full paths to the files we want to perform the counting operation on:

filenames <- file.path(dir, paste0(sampleTable$Run, "_subset.bam"))
file.exists(filenames)

## [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE

We indicate in Bioconductor that these files are BAM files using the BamFileList function from the Rsamtools package that provides an R interface to BAM files. Here we also specify details about how the BAM files should be treated, e.g., only process 2 million reads at a time. See ?BamFileList for more information.

library("Rsamtools")
bamfiles <- BamFileList(filenames, yieldSize=2000000)

Note: make sure that the chromosome names of the genomic features in the annotation you use are consistent with the chromosome names of the reference used for read alignment. Otherwise, the scripts might fail to count any reads to features due to the mismatching names. For example, a common mistake is when the alignment files contain chromosome names in the style of 1 and the gene annotation in the style of chr1, or the other way around. See the seqlevelsStyle function in the GenomeInfoDb package for solutions. We can check the chromosome names (here called “seqnames”) in the alignment files like so:

seqinfo(bamfiles[1])

## Seqinfo object with 84 sequences from an unspecified genome:
##   seqnames   seqlengths isCircular genome
##   1		 249250621       <NA>   <NA>
##   10          135534747       <NA>   <NA>
##   11          135006516       <NA>   <NA>
##   12          133851895       <NA>   <NA>
##   13          115169878       <NA>   <NA>
##   ...	       ...        ...    ...
##   GL000210.1      27682       <NA>   <NA>
##   GL000231.1      27386       <NA>   <NA>
##   GL000229.1      19913       <NA>   <NA>
##   GL000226.1      15008       <NA>   <NA>
##   GL000207.1       4262       <NA>   <NA>

Defining gene models

Next, we need to read in the gene model that will be used for counting reads/fragments. We will read the gene model from an Ensembl GTF file⁸, using makeTxDbFromGFF from the GenomicFeatures package. GTF files can be downloaded from Ensembl’s FTP site or other gene model repositories. A TxDb object is a database that can be used to generate a variety of range-based objects, such as exons, transcripts, and genes. We want to make a list of exons grouped by gene for counting read/fragments.

There are other options for constructing a TxDb. For the known genes track from the UCSC Genome Browser¹⁴, one can use the pre-built Transcript DataBase: TxDb.Hsapiens.UCSC.hg19.knownGene. If the annotation file is accessible from AnnotationHub (as is the case for the Ensembl genes), a pre-scanned GTF file can be imported using makeTxDbFromGRanges. Finally, the makeTxDbFromBiomart function can be used to automatically pull a gene model from Biomart using biomaRt¹⁵.

Here we will demonstrate loading from a GTF file:

library("GenomicFeatures")

We indicate that none of our sequences (chromosomes) are circular using a 0-length character vector.

gtffile <- file.path(dir,"Homo_sapiens.GRCh37.75_subset.gtf")
(txdb <- makeTxDbFromGFF(gtffile, format="gtf", circ_seqs=character()))

## TxDb object:
## # Db type: TxDb
## # Supporting package: GenomicFeatures
## # Data source: /Users/michael/Library/R/3.2/library/airway/extdata/Homo_sapiens.GRCh37.75_subset.gtf
## # Organism: NA
## # miRBase build ID: NA
## # Genome: NA
## # transcript_nrow: 65
## # exon_nrow: 279
## # cds_nrow: 158
## # Db created by: GenomicFeatures package from Bioconductor
## # Creation time: 2015-09-09 14:48:56 -0400 (Wed, 09 Sep 2015)
## # GenomicFeatures version at creation time: 1.20.3
## # RSQLite version at creation time: 1.0.0
## # DBSCHEMAVERSION: 1.1

The following line produces a GRangesList of all the exons grouped by gene¹¹. Each element of the list is a GRanges object of the exons for a gene.

(ebg <- exonsBy(txdb, by="gene"))

## GRangesList object of length 20:
## $ENSG00000009724
## GRanges object with 18 ranges and 2 metadata columns:
##	  seqnames		 ranges strand	 |   exon_id	   exon_name
##	     <Rle>	      <IRanges>	 <Rle>	 | <integer>	 <character>
##    [1]	 1 [11086580, 11087705]	     -	 |	  98 ENSE00000818830
##    [2]	 1 [11090233, 11090307]	     -	 |	  99 ENSE00000472123
##    [3]	 1 [11090805, 11090939]	     -	 |	 100 ENSE00000743084
##    [4]	 1 [11094885, 11094963]	     -	 |	 101 ENSE00000743085
##    [5]	 1 [11097750, 11097868]	     -	 |	 103 ENSE00003520086
##    ...      ...		    ...	   ... ...	 ...		 ...
##   [14]	 1 [11106948, 11107176]	     -	 |	 111 ENSE00003467404
##   [15]	 1 [11106948, 11107176]	     -	 |	 112 ENSE00003489217
##   [16]	 1 [11107260, 11107280]	     -	 |	 113 ENSE00001833377
##   [17]	 1 [11107260, 11107284]	     -	 |	 114 ENSE00001472289
##   [18]	 1 [11107260, 11107290]	     -	 |	 115 ENSE00001881401
##								
## ...
## <19 more elements>
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengths

Read counting step

After these preparations, the actual counting is easy. The function summarizeOverlaps from the GenomicAlignments package will do this. This produces a SummarizedExperiment object that contains a variety of information about the experiment, and will be described in more detail below.

Note: If it is desired to perform counting using multiple cores, one can use the register and MulticoreParam or SnowParam functions from the BiocParallel package before the counting call below. Expect that the summarizeOverlaps call will take at least 30 minutes per file for a human RNA-seq file with 30 million aligned reads. By sending the files to separate cores, one can speed up the entire counting process.

library("GenomicAlignments")
library("BiocParallel")

Here we specify to use one core, not multiple cores. We could have also skipped this line and the counting step would run in serial.

register(SerialParam())

The following call creates the SummarizedExperiment object with counts:

se <- summarizeOverlaps(features=ebg, reads=bamfiles,
			  mode="Union",
			  singleEnd=FALSE,
			  ignore.strand=TRUE,
			  fragments=TRUE )

We specify a number of arguments besides the features and the reads. The mode argument describes what kind of read overlaps will be counted. These modes are shown in Figure 1 of the Counting reads with summarizeOverlaps vignette for the GenomicAlignments package. Note that fragments will be counted only once to each gene, even if they overlap multiple exons of a gene which may themselves be overlapping. Setting singleEnd to FALSE indicates that the experiment produced paired-end reads, and we want to count a pair of reads (a fragment) only once toward the count for a gene.

Figure 1. The component parts of a SummarizedExperiment object.

The assay (pink block) contains the matrix of counts, the rowRanges (blue block) contains information about the genomic ranges and the colData (green block) contains information about the samples. The highlighted line in each block represents the first row (note that the first row of colData lines up with the first column of the assay).

In order to produce correct counts, it is important to know if the RNA-seq experiment was strand-specific or not. This experiment was not strand-specific so we set ignore.strand to TRUE. The fragments argument can be used when singleEnd=FALSE to specify if unpaired reads should be counted (yes if fragments=TRUE).

SummarizedExperiment

The SummarizedExperiment container is diagrammed in Figure 1 and discussed in the latest Bioconductor paper¹⁶. In our case we have created a single matrix named “counts” that contains the fragment counts for each gene and sample, which is stored in assay. It is also possible to store multiple matrices, accessed with assays. The rowRanges for our object is the GRangesList we used for counting (one GRanges of exons for each row of the count matrix). The component parts of the SummarizedExperiment are accessed with an R function of the same name: assay (or assays), rowRanges and colData.

This example code above actually only counted a small subset of fragments from the original experiment. Nevertheless, we can still investigate the resulting SummarizedExperiment 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 rowRanges slot.

se

## class: SummarizedExperiment
## dim: 20 8
## exptData(0):
## assays(1): counts
## rownames(20): ENSG00000009724 ENSG00000116649 ... ENSG00000271794 ENSG00000271895
## rowRanges metadata column names(0):
## colnames(8): SRR1039508_subset.bam SRR1039509_subset.bam ... SRR1039520_subset.bam SRR1039521_subset.bam
## colData names(0):

dim(se)

## [1] 20 8

assayNames(se)

## [1] "counts"

head(assay(se), 3)

##		   SRR1039508_subset.bam	SRR1039509_subset.bam	SRR1039512_subset.bam
## ENSG00000009724		      38		           28		           66
## ENSG00000116649		    1004		         1255		         1122
## ENSG00000120942		     218		          256		          233
##		   SRR1039513_subset.bam	SRR1039516_subset.bam	SRR1039517_subset.bam
## ENSG00000009724		      24		           42		           41
## ENSG00000116649		    1313		         1100		         1879
## ENSG00000120942		     252		          269		          465
##		   SRR1039520_subset.bam	SRR1039521_subset.bam	
## ENSG00000009724		      47		           36	
## ENSG00000116649		     745		         1536	
## ENSG00000120942		     207		          400

colSums(assay(se))

## SRR1039508_subset.bam SRR1039509_subset.bam SRR1039512_subset.bam SRR1039513_subset.bam
##		    6478		  6501		        7699		      6801
## SRR1039516_subset.bam SRR1039517_subset.bam SRR1039520_subset.bam SRR1039521_subset.bam
##		    8009		 10849		        5254		      9168

The rowRanges, when printed, only shows the first GRanges, and tells us there are 19 more elements:

rowRanges(se)

## GRangesList object of length 20:
## $ENSG00000009724
## GRanges object with 18 ranges and 2 metadata columns:
##	  seqnames		 ranges strand	 |   exon_id	   exon_name
##	     <Rle>	      <IRanges>	 <Rle>	 | <integer>	 <character>
##    [1]	 1 [11086580, 11087705]	     -	 |	  98 ENSE00000818830
##    [2]	 1 [11090233, 11090307]	     -	 |	  99 ENSE00000472123
##    [3]	 1 [11090805, 11090939]	     -	 |	 100 ENSE00000743084
##    [4]	 1 [11094885, 11094963]	     -	 |	 101 ENSE00000743085
##    [5]	 1 [11097750, 11097868]	     -	 |	 103 ENSE00003520086
##    ...      ...		    ...	   ... ...	 ...		 ...
##   [14]	 1 [11106948, 11107176]	     -	 |	 111 ENSE00003467404
##   [15]	 1 [11106948, 11107176]	     -	 |	 112 ENSE00003489217
##   [16]	 1 [11107260, 11107280]	     -	 |	 113 ENSE00001833377
##   [17]	 1 [11107260, 11107284]	     -	 |	 114 ENSE00001472289
##   [18]	 1 [11107260, 11107290]	     -	 |	 115 ENSE00001881401
##								
## ...
## <19 more elements>
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengths

The rowRanges also contains metadata about the construction of the gene model in the metadata slot. Here we use a helpful R function, str, to display the metadata compactly:

str(metadata(rowRanges(se)))

## List of 1
##  $ genomeInfo:List of 14
##   ..$ Db type				 : chr "TxDb"
##   ..$ Supporting package		  	 : chr "GenomicFeatures"
##   ..$ Data source				 : chr "/Users/michael/Library/R/3.2/library/airway/extd
##   ..$ Organism				 : chr NA
##   ..$ miRBase build ID		 	 : chr NA
##   ..$ Genome					 : chr NA
##   ..$ transcript_nrow		 	 : chr "65"
##   ..$ exon_nrow				 : chr "279"
##   ..$ cds_nrow				 : chr "158"
##   ..$ Db created by			 	 : chr "GenomicFeatures package from Bioconductor"
##   ..$ Creation time				 : chr "2015-09-09 14:48:56 -0400 (Wed, 09 Sep 2015)"
##   ..$ GenomicFeatures version at creation time: chr "1.20.3"
##   ..$ RSQLite version at creation time	 : chr "1.0.0"
##   ..$ DBSCHEMAVERSION	    		 : chr "1.1"

The colData:

colData(se)

## DataFrame with 8 rows and 0 columns

The colData slot, so far empty, should contain all the metadata. Because we used a column of sampleTable to produce the bamfiles vector, we know the columns of se are in the same order as the rows of sampleTable. We can assign the sampleTable as the colData of the summarized experiment, by converting it into a DataFrame and using the assignment function:

(colData(se) <- DataFrame(sampleTable))

## DataFrame with 8 rows and 9 columns
##	      SampleName     cell      dex    albut	   Run avgLength  Experiment	Sample
##	        <factor> <factor> <factor> <factor>   <factor> <integer>    <factor>  <factor>
## SRR1039508 GSM1275862   N61311    untrt    untrt SRR1039508	     126   SRX384345 SRS508568
## SRR1039509 GSM1275863   N61311      trt    untrt SRR1039509	     126   SRX384346 SRS508567
## SRR1039512 GSM1275866  N052611    untrt    untrt SRR1039512	     126   SRX384349 SRS508571
## SRR1039513 GSM1275867  N052611      trt    untrt SRR1039513	      87   SRX384350 SRS508572
## SRR1039516 GSM1275870  N080611    untrt    untrt SRR1039516	     120   SRX384353 SRS508575
## SRR1039517 GSM1275871  N080611      trt    untrt SRR1039517	     126   SRX384354 SRS508576
## SRR1039520 GSM1275874  N061011    untrt    untrt SRR1039520	     101   SRX384357 SRS508579
## SRR1039521 GSM1275875  N061011      trt    untrt SRR1039521	      98   SRX384358 SRS508580
##		 BioSample	
##		  <factor>
## SRR1039508 SAMN02422669	
## SRR1039509 SAMN02422675	
## SRR1039512 SAMN02422678	
## SRR1039513 SAMN02422670	
## SRR1039516 SAMN02422682	
## SRR1039517 SAMN02422673	
## SRR1039520 SAMN02422683	
## SRR1039521 SAMN02422677

Branching point

At this point, we have counted the fragments which overlap the genes in the gene model we specified. This is a branching point where we could use a variety of Bioconductor packages for exploration and differential expression of the count data, including edgeR³, limma with the voom method⁴, DSS⁵, EBSeq⁶ and BaySeq⁷. We will continue, using DESeq2². The SummarizedExperiment object is all we need to start our analysis. In the following section we will show how to use it to create the data object used by DESeq2.

Starting from count matrices

In this section, we will show how to build an DESeqDataSet supposing we only have a count matrix and a table of sample information.

Note: if you have prepared a SummarizedExperiment you should skip this section. While the previous section would be used to construct a DESeqDataSet from a SummarizedExperiment, here we first extract the individual object (count matrix and sample info) from the SummarizedExperiment in order to build it back up into a new object – only for demonstration purposes. In practice, the count matrix would either be read in from a file or perhaps generated by an R function like featureCounts from the Rsubread package¹².

The information in a SummarizedExperiment object can be accessed with accessor functions. For example, to see the actual data, i.e., here, the fragment counts, we use the assay function. (The head function restricts the output to the first few lines.)

countdata <- assay(se)
head(countdata, 3)

##		  SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520
## ENSG00000000003	 679	    448	       873        408       1138       1047	   770
## ENSG00000000005	   0	      0	   	 0	    0	       0	  0	     0
## ENSG00000000419	 467	    515	       621        365        587        799	   417
##		  SRR1039521	
## ENSG00000000003	 572	
## ENSG00000000005	   0	
## ENSG00000000419	 508

In this count matrix, each row represents an Ensembl gene, each column a sequenced RNA library, and the values give the raw numbers of fragments that were uniquely assigned to the respective gene in each library. We also have information on each of the samples (the columns of the count matrix). If you’ve counted reads with some other software, it is very important to check that the columns of the count matrix correspond to the rows of the sample information table.

coldata <- colData(se)

We now have all the ingredients to prepare our data object in a form that is suitable for analysis, namely:

To now construct the DESeqDataSet object from the matrix of counts and the sample information table, we use:

(ddsMat <- DESeqDataSetFromMatrix(countData = countdata,
                                      colData = coldata,
                                      design = ~ cell + dex))

## class: DESeqDataSet
## dim: 64102 8
## exptData(0):
## assays(1): counts
## rownames(64102): ENSG00000000003 ENSG00000000005 ... LRG_98 LRG_99
## rowRanges metadata column names(0):
## colnames(8): SRR1039508 SRR1039509 ... SRR1039520 SRR1039521
## colData names(9): SampleName cell ... Sample BioSample

We will continue with the object generated from the SummarizedExperiment section.

Pre-filtering the dataset

Our count matrix with our DESeqDataSet contains many rows with only zeros, and additionally many rows with only a few fragments total. In order to reduce the size of the object, and to increase the speed of our functions, we can remove the rows that have no or nearly no information about the amount of gene expression. Here we remove rows of the DESeqDataSet that have no counts, or only a single count across all samples:

nrow(dds)

## [1] 64102

dds <- dds[ rowSums(counts(dds)) > 1, ]
nrow(dds)

## [1] 29391

The rlog transformation

Many common statistical methods for exploratory analysis of multidimensional data, for example clustering and principal components analysis (PCA), work best for data that generally has the same range of variance at different ranges of the mean values. When the expected amount of variance is approximately the same across different mean values, the data is said to be homoskedastic. For RNA-seq raw counts, however, the variance grows with the mean. For example, if one performs PCA directly on a matrix of size-factor-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 the very lowest counts will tend to dominate the results because, due to the strong Poisson noise inherent to small count values, and the fact that the logarithm amplifies differences for the smallest values, these low count genes will show the strongest relative differences between samples.

As a solution, DESeq2 offers transformations for count data that stabilize the variance across the mean. One such transformation is the regularized-logarithm transformation or rlog². For genes with high counts, the rlog transformation will give similar result to the ordinary log2 transformation of normalized counts. For genes with lower counts, however, the values are shrunken towards the genes’ averages across all samples. Using an empirical Bayesian prior on inter-sample differences in the form of a ridge penalty, the rlog-transformed data then becomes approximately homoskedastic, and can be used directly for computing distances between samples and making PCA plots. Another transformation, the variance stabilizing transformation¹⁷, is discussed alongside the rlog in the DESeq2 vignette.

Note: 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 later in this workflow, 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 that contains the rlog-transformed values in its assay slot.

rld <- rlog(dds, blind=FALSE)
head(assay(rld), 3)

##		   SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520
## ENSG00000000003   9.385536   9.051592   9.517044   9.284930   9.839980   9.530510   9.663767
## ENSG00000000419   8.868967   9.138776   9.036191   9.075538   8.971927   9.132297   8.860846
## ENSG00000000457   7.962223   7.881317   7.823335   7.921887   7.750083   7.886432   7.957928
##		   SRR1039521	
## ENSG00000000003   9.277281	
## ENSG00000000419   9.061085	
## ENSG00000000457   7.912412

We specify blind=FALSE, which means that differences between cell lines and treatment should not add to the variance-mean profile of the experiment. However, the experimental design is not used directly in the transformation, only in estimating the global amount of variability in the counts. For a fully unsupervised transformation, one can set blind=TRUE (which is the default).

Note: for large datasets (hundreds of samples), the variance stabilizing transformation will be faster to compute.

To show the effect of the transformation, in Figure 2 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. For the log2 approach, we need to first estimate size factors to account for sequencing depth, and then specify normalized=TRUE. Sequencing depth correction is done automatically for the rlog method (and for varianceStabilizingTransformation).

Figure 2. Scatterplot of transformed counts from two samples.

Shown are scatterplots using the log2 transform of normalized counts (left side) and using the rlog (right side).

par( mfrow = c( 1, 2 ) )
dds <- estimateSizeFactors(dds)
plot(log2(counts(dds, normalized=TRUE)[,1:2] + 1),
     pch=16, cex=0.3)
plot(assay(rld)[,1:2],
     pch=16, cex=0.3)

We can see how genes with low counts (bottom left-hand corner) seem to be excessively variable on the ordinary logarithmic scale, while the rlog transform compresses differences for the low count genes for which the data provide little information about differential expression.

Sample distances

A useful first step in an RNA-seq analysis is often to assess overall similarity between samples: Which samples are similar to each other, which are different? Does this fit to the expectation from the experiment’s design?

We use the R function dist to calculate the Euclidean distance between samples. To ensure we have a roughly equal contribution from all genes, we use it on the rlog-transformed data. We need to transpose the matrix of values using t, because the dist function expects the different samples to be rows of its argument, and different dimensions (here, genes) to be columns.

sampleDists <- dist( t( assay(rld) ) )
sampleDists

##	      SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520
## SRR1039509   46.25524						
## SRR1039512   39.94490   55.67572					
## SRR1039513   63.36642   45.19462   49.30007				
## SRR1039516   45.28129   59.89304   44.32383   64.54450			
## SRR1039517   65.34730   52.25475   60.05523   50.64861   48.05714		
## SRR1039520   40.20215   58.19904   37.35413   59.19401   47.15396   64.44641	
## SRR1039521   64.09339   45.70177   58.59277   37.10803   66.36711   53.09669   50.72310

We visualize the distances in a heatmap in Figure 3, using the function pheatmap from the pheatmap package.

Figure 3. Heatmap of sample-to-sample distances using the rlog-transformed values.

library("pheatmap")
library("RColorBrewer")

In order to plot the sample distance matrix with the rows/columns arranged by the distances in our distance matrix, we manually provide sampleDists to the clustering_distance argument of the pheatmap function. Otherwise the pheatmap function would assume that the matrix contains the data values themselves, and would calculate distances between the rows/columns of the distance matrix, which is not desired. We also manually specify a blue color palette using the colorRampPalette function from the RColorBrewer package.

sampleDistMatrix <- as.matrix( sampleDists )
rownames(sampleDistMatrix) <- paste( rld$dex, rld$cell, sep="-" )
colnames(sampleDistMatrix) <- NULL
colors <- colorRampPalette( rev(brewer.pal(9, "Blues")) )(255)
pheatmap(sampleDistMatrix,
	  clustering_distance_rows=sampleDists,
	  clustering_distance_cols=sampleDists,
	  col=colors)

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 option for calculating sample distances is to use the Poisson Distance¹⁸, implemented in the PoiClaClu package. This measure of dissimilarity between counts also takes the inherent variance structure of counts into consideration when calculating the distances between samples. The PoissonDistance function takes the original count matrix (not normalized) with samples as rows instead of columns, so we need to transpose the counts in dds.

library("PoiClaClu")
poisd <- PoissonDistance(t(counts(dds)))

We plot the Poisson Distance heatmap in Figure 4.

Figure 4. Heatmap of sample-to-sample distances using the Poisson Distance.

samplePoisDistMatrix <- as.matrix( poisd$dd )
rownames(samplePoisDistMatrix) <- paste( rld$dex, rld$cell, sep="-" )
colnames(samplePoisDistMatrix) <- NULL
pheatmap(samplePoisDistMatrix,
	  clustering_distance_rows=poisd$dd,
	  clustering_distance_cols=poisd$dd,
	  col=colors)

PCA plot

Another way to visualize sample-to-sample distances is a principal components analysis (PCA). In this ordination method, the data points (here, the samples) are projected onto the 2D plane such that they spread out in the two directions that explain most of the differences (Figure 5). The x-axis is the direction that separates the data points the most. The values of the samples in this direction are written PC1. The y-axis is a direction (it must be orthogonal to the first direction) that separates the data the second most. The values of the samples in this direction are written PC2. The percent of the total variance that is contained in the direction is printed in the axis label. Note that these percentages do not add to 100%, because there are more dimensions that contain the remaining variance (although each of these remaining dimensions will explain less than the two that we see).

Figure 5. PCA plot using the rlog-transformed values.

Each unique combination of treatment and cell line is given its own color.

plotPCA(rld,  intgroup = c("dex", "cell"))

Here, we have used the function plotPCA that comes with DESeq2. The two terms specified by intgroup are the interesting groups for labeling the samples; they tell the function to use them to choose colors. We can also build the PCA plot from scratch using the ggplot2 package¹⁹. This is done by asking the plotPCA function to return the data used for plotting rather than building the plot. See the ggplot2 documentation for more details on using ggplot.

(data <- plotPCA(rld, intgroup = c( "dex", "cell"), returnData=TRUE))

##		    PC1	       PC2	     group   dex    cell       name
## SRR1039508 -17.88882	 -4.157888  untrt : N61311 untrt  N61311 SRR1039508
## SRR1039509	8.43675  -1.650879    trt : N61311   trt  N61311 SRR1039509
## SRR1039512 -10.27798	 -5.066577 untrt : N052611 untrt N052611 SRR1039512
## SRR1039513  17.64271	 -3.910902   trt : N052611   trt N052611 SRR1039513
## SRR1039516 -14.74069	 15.990031 untrt : N080611 untrt N080611 SRR1039516
## SRR1039517  10.95638	 20.806181   trt : N080611   trt N080611 SRR1039517
## SRR1039520 -12.12010 -11.962545 untrt : N061011 untrt N061011 SRR1039520
## SRR1039521  17.99175 -10.047421   trt : N061011   trt N061011 SRR1039521

percentVar <- round(100 * attr(data, "percentVar"))

We can then use this data to build up a second plot in Figure 6, specifying that the color of the points should reflect dexamethasone treatment and the shape should reflect the cell line.

Figure 6. PCA plot using the rlog-transformed values with custom ggplot2 code.

Here we specify cell line (plotting symbol) and dexamethasone treatment (color).

library("ggplot2")

ggplot(data, aes(PC1, PC2, color=dex, shape=cell)) +   geom_point(size=3) +
   xlab(paste0("PC1: ",percentVar[1],"% variance")) +
   ylab(paste0("PC2: ",percentVar[2],"% variance"))

From the PCA plot, we see that the differences between cells (the different plotting shapes) are considerable, though not stronger than the differences due to treatment with dexamethasone (red vs blue color). This shows why it will be important to account for this in differential testing by using a paired design (“paired”, because each dex treated sample is paired with one untreated sample from the same cell line). We are already set up for this design by assigning the formula ~ cell + dex earlier.

MDS plot

Another plot, very similar to the PCA plot, can be made using the multidimensional scaling (MDS) function in base R. This is useful when we don’t have a matrix of data, but only a matrix of distances. Here we compute the MDS for the distances calculated from the rlog transformed counts and plot these (Figure 7):

Figure 7. MDS plots.

Shown are the plots based on the rlog-transformed values (left) and the Poisson Distance (right).

mdsData <- data.frame(cmdscale(sampleDistMatrix))
mds <- cbind(mdsData, as.data.frame(colData(rld)))
ggplot(mds, aes(X1,X2,color=dex,shape=cell)) + geom_point(size=3)

Creating the same plot for the PoissonDistance (also Figure 7):

mdsPoisData <- data.frame(cmdscale(samplePoisDistMatrix))
mdsPois <- cbind(mdsPoisData, as.data.frame(colData(dds)))
ggplot(mdsPois, aes(X1,X2,color=dex,shape=cell)) + geom_point(size=3)

Running the differential expression pipeline

As we have already specified an experimental design when we created the DESeqDataSet, we can run the differential expression pipeline on the raw counts with a single call to the function DESeq:

dds <- DESeq(dds)

This function will print out a message for the various steps it performs. These are described in more detail in the manual page for DESeq, which can be accessed by typing ?DESeq. Briefly these are: the estimation of size factors (controlling for differences in the sequencing depth of the samples), the estimation of dispersion values for each gene, and fitting a generalized linear model.

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

Building 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, results will extract the results table for a comparison of the last level over the first level. This comparison is printed at the top of the output: dex trt vs untrt.

(res <- results(dds))

## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 29391 rows and 6 columns
##		      baseMean log2FoldChange	   lfcSE       stat	pvalue	       padj
##		     <numeric>	    <numeric>  <numeric>  <numeric>   <numeric>   <numeric>
## ENSG00000000003 708.6021697	  -0.37423028 0.09872592 -3.7905980 0.000150285 0.001224146
## ENSG00000000419 520.2979006	   0.20214241 0.10929202  1.8495625 0.064376631 0.189223539
## ENSG00000000457 237.1630368	   0.03624420 0.13682871  0.2648874 0.791096181 0.907794192
## ENSG00000000460  57.9326331	  -0.08520813 0.24645454 -0.3457357 0.729541350 0.875201476
## ENSG00000000938   0.3180984	  -0.11522629 0.14589383 -0.7897955 0.429647219		 NA
## ...			   ...		  ...	     ...	...	    ...		...
## ENSG00000273485   1.2864477	   0.03490688  0.2986168  0.1168952   0.9069431		 NA
## ENSG00000273486  15.4525365	  -0.09662406  0.3385222 -0.2854290   0.7753155   0.8990371
## ENSG00000273487   8.1632350	   0.56255493  0.3731295  1.5076666   0.1316399   0.3177048
## ENSG00000273488   8.5844790	   0.10794134  0.3680474  0.2932811   0.7693073   0.8960855
## ENSG00000273489   0.2758994	   0.11249632  0.1420250  0.7920882   0.4283092		 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
##		      <character>			        <character>
## baseMean          intermediate mean of normalized counts for all samples
## log2FoldChange         results  log2 fold change (MAP): dex trt vs untrt
## lfcSE		  results          standard error: dex trt vs untrt
## stat			  results          Wald statistic: dex trt vs untrt
## pvalue		  results       Wald test p-value: dex trt vs untrt
## 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 in the DESeqDataSet. The remaining four columns refer to a specific contrast, namely the comparison of the trt level over the untrt level for the factor variable dex. We will find out below 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 dexamethasone in comparison to untreated samples. 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. We can also express the uncertainty of a particular effect size estimate as the result of a statistical test. The purpose of a test for differential expression is to test whether the data provides sufficient evidence to conclude that this value is really different from zero. DESeq2 performs for each gene a hypothesis test to see whether evidence is sufficient to decide against the null hypothesis that there is zero effect of the treatment on the gene and that the observed difference between treatment and control was merely caused by experimental variability (i.e., the type of variability that you can expect between different samples in the same treatment group). As usual in statistics, the result of this test is reported as a p value, and it is found in the column pvalue. Remember that a p value indicates the probability that a fold change as strong as the observed one, or even stronger, would be seen under the situation described by the null hypothesis.

We can also summarize the results with the following line of code, which reports some additional information, that will be covered in later sections.

summary(res)

##
## out of 29391 with nonzero total read count
## adjusted p-value < 0.1
## LFC > 0 (up)     : 2647, 9%
## LFC < 0 (down)   : 2250, 7.7%
## outliers [1]     : 0, 0%
## low counts [2]   : 11756, 40%
## (mean count < 5.2)
## [1] see 'cooksCutoff' argument of ?results
## [2] see 'independentFiltering' argument of ?results

Note that there are many genes with differential expression due to dexamethasone treatment at the FDR level of 10%. This makes sense, as the smooth muscle cells of the airway are known to react to glucocorticoid steroids. However, there are two ways to be more strict about which set of genes are considered significant:

If we lower the false discovery rate threshold, we should also tell this value to results(), so that the function will use an alternative threshold for the optimal independent filtering step:

res.05 <- results(dds, alpha=.05)
table(res.05$padj < .05)

##
## FALSE  TRUE
## 12095  4070

If we want to raise the log2 fold change threshold, so that we test for genes that show more substantial changes due to treatment, we simply supply a value on the log2 scale. For example, by specifying lfcThreshold=1, we test for genes that show significant effects of treatment on gene counts more than doubling or less than halving, because 2¹ = 2.

resLFC1 <- results(dds, lfcThreshold=1)
table(resLFC1$padj < 0.1)

##
## FALSE  TRUE
## 14492   204

Sometimes a subset of the p values in res will be NA (“not available”). This is DESeq’s way of reporting that all counts for this gene were zero, and hence no 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 DESeq2 vignette.

If you use the results from an R analysis package in published research, you can find the proper citation for the software by typing citation("pkgName"), where you would substitute the name of the package for pkgName. Citing methods papers helps to support and reward the individuals who put time into open source software for genomic data analysis.

Other comparisons

In general, 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 for the numerator, and the name of the level for the denominator. Here we extract results for the log2 of the fold change of one cell line over another:

results(dds, contrast=c("cell", "N061011", "N61311"))

## log2 fold change (MAP): cell N061011 vs N61311
## Wald test p-value: cell N061011 vs N61311
## DataFrame with 29391 rows and 6 columns
##		      baseMean log2FoldChange	   lfcSE         stat	 pvalue	     padj
##		     <numeric>	    <numeric>  <numeric>    <numeric> <numeric> <numeric>
## ENSG00000000003 708.6021697	   0.29054171 0.13600021   2.13633281 0.0326523 0.1981039
## ENSG00000000419 520.2979006	  -0.05069310 0.14916364  -0.33984894 0.7339703 0.9238903
## ENSG00000000457 237.1630368	   0.01474318 0.18161982   0.08117606 0.9353019 0.9862379
## ENSG00000000460  57.9326331	   0.20241839 0.28064506   0.72126120 0.4707488 0.8108444
## ENSG00000000938   0.3180984	   0.00000000 0.07169692   0.00000000 1.0000000	       NA
## ...			   ...		  ...	     ...	...	    ...	      ...
## ENSG00000273485   1.2864477	 -0.180248108 0.16456445 -1.095304052 0.2733835	       NA
## ENSG00000273486  15.4525365   -0.029979349 0.30827915 -0.097247409 0.9225299	       NA
## ENSG00000273487   8.1632350	 -0.001914497 0.28117903 -0.006808819 0.9945674	       NA
## ENSG00000273488   8.5844790	  0.380608540 0.29209485  1.303030638 0.1925643	       NA
## ENSG00000273489   0.2758994	  0.000000000 0.06955643  0.000000000 1.0000000	       NA

If results for an interaction term are desired, the name argument of results should be used. Please see the help for the results function for more details.

Multiple testing

In high-throughput biology, we are careful to not use the p values directly as evidence against the null, but to correct for multiple testing. What would happen if we were to simply threshold the p values at a low value, say 0.05? There are 5722 genes with a p value below 0.05 among the 29391 genes, for which the test succeeded in reporting a p value:

sum(res$pvalue < 0.05, na.rm=TRUE)

## [1] 5722

sum(!is.na(res$pvalue))

## [1] 29391

Now, assume for a moment that the null hypothesis is true for all genes, i.e., no gene is affected by the treatment with dexamethasone. Then, by the definition of the p value, we expect up to 5% of the genes to have a p value below 0.05. This amounts to 1470 genes. If we just considered the list of genes with a p value below 0.05 as differentially expressed, this list should therefore be expected to contain up to 1470/5722 = 26% false positives.

DESeq2 uses the Benjamini-Hochberg (BH) adjustment²⁰ as implemented in the base R p.adjust function; in brief, this method calculates for each gene an adjusted p value that answers the following question: if one called significant all genes with an adjusted p value less than or equal to this gene’s adjusted 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 res object.

The FDR is a useful statistic for many high-throughput experiments, as we are often interested in reporting or focusing on a set of interesting genes, and we would like to put an upper bound on the percent of false positives in this set.

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] 4897

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, padj < 0.1)
head(resSig[ order(resSig$log2FoldChange), ])

## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 6 rows and 6 columns
##		    baseMean log2FoldChange	lfcSE       stat       pvalue	      padj
##		   <numeric>	  <numeric> <numeric>  <numeric>    <numeric>    <numeric>
## ENSG00000162692 508.17023	  -3.452454 0.1763751 -19.574503 2.551125e-85 3.460700e-82
## ENSG00000146006  46.80760	  -2.856273 0.3366877  -8.483451 2.186122e-17 1.073879e-15
## ENSG00000105989 333.21469	  -2.850960 0.1754638 -16.248133 2.302720e-59 1.194366e-56
## ENSG00000214814 243.27698	  -2.759539 0.2224907 -12.402938 2.519140e-35 4.113429e-33
## ENSG00000267339  26.23357	  -2.743928 0.3511985  -7.813041 5.582443e-15 2.182846e-13
## ENSG00000013293 244.49733	  -2.646116 0.1981216 -13.356020 1.092517e-40 2.240295e-38

... and with the strongest up-regulation:

head(resSig[ order(resSig$log2FoldChange, decreasing=TRUE), ])

## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 6 rows and 6 columns
##		    baseMean log2FoldChange	lfcSE       stat        pvalue	       padj
##		   <numeric>	  <numeric> <numeric>  <numeric>     <numeric>     <numeric>
## ENSG00000179593  67.24305	   4.880507 0.3308119   14.75312  2.937594e-49  9.418996e-47
## ENSG00000109906 385.07103	   4.860877 0.3321627   14.63403  1.704000e-48  5.181040e-46
## ENSG00000152583 997.43977	   4.315374 0.1723805   25.03400 2.608143e-138 4.599460e-134
## ENSG00000250978  56.31819	   4.090157 0.3288246   12.43872  1.610666e-35  2.679631e-33
## ENSG00000163884 561.10717	   4.078073 0.2103212   19.38974  9.421379e-84  1.038413e-80
## ENSG00000168309 159.52692	   3.991146 0.2547755   15.66534  2.610147e-55  1.180255e-52

Gene clustering

In the sample distance heatmap made previously, 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 a signal, one usually would only cluster a subset of the most highly variable genes. Here, for demonstration, let us select the 20 genes with the highest variance across samples. We will work with the rlog transformed counts:

library("genefilter")
topVarGenes <- head(order(rowVars(assay(rld)),decreasing=TRUE),20)

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 each genes’ values across samples, and plot a heatmap (Figure 13). We provide a data.frame that instructs the pheatmap function how to label the columns.

Figure 13. Heatmap of relative rlog-transformed values across samples.

Treatment status and cell line information are shown with colored bars at the top of the heatmap. Note that a set of genes at the top of the heatmap are separating the N061011 cell line from the others. In the center of the heatmap, we see a set of genes for which the dexamethasone treated samples have higher gene expression.

mat <- assay(rld)[ topVarGenes, ]
mat <- mat - rowMeans(mat)
df <- as.data.frame(colData(rld)[,c("cell","dex")])
pheatmap(mat, annotation_col=df)

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 such high Poisson noise that any biological effect is drowned in the uncertainties from the sampling at a low rate. We can also show this by examining the ratio of small p values (say, less than, 0.05) for genes binned by mean normalized count. We will use the results table subjected to the threshold to show what this looks like in a case when there are few tests with small p value.

In the following code chunk, we create bins using the quantile function, bin the genes by base mean using cut, rename the levels of the bins using the middle point, calculate the ratio of p values less than 0.05 for each bin, and finally plot these ratios (Figure 14).

Figure 14. The ratio of small p values for genes binned by mean normalized count.

Here the p values are for a test of log2 fold change greater than 1 or less than -1. This plot demonstrates that genes with low mean count are underpowered, and best excluded before multiple test correction.

qs <- c(0, quantile(resLFC1$baseMean[resLFC1$baseMean > 0], 0:6/6))
bins <- cut(resLFC1$baseMean, qs) 
levels(bins) <- paste0("~",round(signif(.5*qs[-1] + .5*qs[-length(qs)],2)))
ratios <- tapply(resLFC1$pvalue, bins, function(p) mean(p < .05, na.rm=TRUE))
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 low count genes from the input to the FDR procedure, we can find more genes to be significant among those that we keep, and so improved the power of our test. This approach is known as independent filtering.

The DESeq2 software automatically performs independent filtering that maximizes the number of genes with 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.

The term independent highlights an important caveat. Such filtering is permissible only if the statistic that we filter on (here the mean of normalized counts across all samples) is independent of the actual test statistic (the p value) under the null hypothesis. Otherwise, the filtering would invalidate the test and consequently the assumptions of the BH procedure. The independent filtering software used inside DESeq2 comes from the genefilter package, that contains a reference to a paper describing the statistical foundation for independent filtering²².

Exporting results

You can easily save the results table in a CSV file, that you can then share or load with a spreadsheet program such as Excel. The call to as.data.frame is necessary to convert the DataFrame object (IRanges package) to a data.frame object that can be processed by write.csv. Here, we take just the top 100 genes for demonstration.

resOrderedDF <- as.data.frame(resOrdered)[1:100,]
write.csv(resOrderedDF, file="results.csv")

Another more sophisticated package for exporting results from various Bioconductor analysis packages is the ReportingTools package²³. ReportingTools will automatically generate dynamic HTML documents, including links to external databases using gene identifiers and boxplots summarizing the normalized counts across groups. See the ReportingTools vignettes for full details. The simplest version of creating a dynamic ReportingTools report is performed with the following code:

library("ReportingTools")
htmlRep <- HTMLReport(shortName="report", title="My report",
		        reportDirectory="./report")
publish(resOrderedDF, htmlRep)
url <- finish(htmlRep)
browseURL(url)

Plotting fold changes in genomic space

If we have used the summarizeOverlaps function to count the reads, then our DESeqDataSet object is built on top of ready-to-use Bioconductor objects specifying the genomic ranges of the genes. We can therefore easily plot our differential expression results in genomic space. While the results function by default returns a DataFrame, using the format argument, we can ask for GRanges or GRangesList output.

(resGR <- results(dds, lfcThreshold=1, format="GRanges"))

## GRanges object with 29391 ranges and 6 metadata columns:
##		     seqnames		      ranges strand   |		 baseMean      log2FoldChange
##		        <Rle>		   <IRanges>  <Rle>   |		<numeric>	    <numeric>
##   ENSG00000000003	    X [ 99883667,  99894988]	  -   |  708.602169691234  -0.374230275713608
##   ENSG00000000419	   20 [ 49551404,  49575092]	  -   |  520.297900552084   0.202142414893829
##   ENSG00000000457	    1 [169818772, 169863408]	  -   |  237.163036796015  0.0362442044069634
##   ENSG00000000460	    1 [169631245, 169823221]	  +   |  57.9326331250967 -0.0852081341501509
##   ENSG00000000938	    1 [ 27938575,  27961788]	  -   | 0.318098378392895  -0.115226286496983
##   		 ...	  ...			 ...	... ...	     	      ...		  ...
##   ENSG00000273485	   10 [105209953, 105210609]	  +   |	 1.28644765243289  0.0349068755370733
##   ENSG00000273486	    3 [136556180, 136557863]	  -   |	 15.4525365439045 -0.0966240584195589
##   ENSG00000273487	    1 [ 92654794,  92656264]	  +   |	  8.1632349843654   0.562554926745931
##   ENSG00000273488	    3 [100080031, 100080481]	  +   |	 8.58447903624707   0.107941339873098
##   ENSG00000273489	    7 [131178723, 131182453]	  -   | 0.275899382507797   0.112496317318932
##				 lfcSE	    stat    pvalue      padj

##			     <numeric> <numeric> <numeric> <numeric>
##   ENSG00000000003 0.098725921418789	       0	 1	   1
##   ENSG00000000419 0.109292016112333	       0	 1	   1
##   ENSG00000000457 0.136828705643854	       0	 1	   1
##   ENSG00000000460 0.246454541134745	       0	 1	   1
##   ENSG00000000938 0.145893828687766	       0	 1	<NA>
##  		 ...		   ...	     ...       ...	 ...
##   ENSG00000273485 0.298616754374375	       0	 1	<NA>
##   ENSG00000273486 0.338522172238827	       0	 1	<NA>
##   ENSG00000273487 0.373129529007307	       0	 1	<NA>
##   ENSG00000273488 0.368047431494871	       0	 1	<NA>
##   ENSG00000273489 0.142024983011115	       0	 1	<NA>
##   -------				
##   seqinfo: 722 sequences (1 circular) from an unspecified genome

We need to add the symbol again for labeling the genes on the plot:

resGR$symbol <- mapIds(org.Hs.eg.db, names(resGR), "SYMBOL", "ENSEMBL")

We will use the Gviz package for plotting the GRanges and associated metadata: the log fold changes due to dexamethasone treatment.

library("Gviz")

The following code chunk specifies a window of 1 million base pairs upstream and downstream from the gene with the smallest p value. We create a subset of our full results, for genes within the window We add the gene symbol as a name, if the symbol exists or is not duplicated in our subset.

window <- resGR[topGene] + 1e6
strand(window) <- "*"
resGRsub <- resGR[resGR %over% window]
naOrDup <- is.na(resGRsub$symbol) | duplicated(resGRsub$symbol)
resGRsub$group <- ifelse(naOrDup, names(resGRsub), resGRsub$symbol)

We create a vector specifying if the genes in this subset had a low false discovery rate.

sig <- factor(ifelse(resGRsub$padj < .1 & !is.na(resGRsub$padj),"sig","notsig"))

We can then plot the results using Gviz functions (Figure 15). We create an axis track specifying our location in the genome, a track that will show the genes and their names, colored by significance, and a data track that will draw vertical bars showing the moderated log fold change produced by DESeq2, which we know are only large when the effect is well supported by the information in the counts.

Figure 15. Plotting log2 fold changes in a genomic region surrounding the gene with smallest adjusted p value.

Genes highlighted in pink have adjusted p value less than 0.1.

options(ucscChromosomeNames=FALSE)
g <- GenomeAxisTrack()
a <- AnnotationTrack(resGRsub, name="gene ranges", feature=sig)
d <- DataTrack(resGRsub, data="log2FoldChange", baseline=0, type="h", name="log2 fold change", strand="+")
plotTracks(list(g,d,a), groupAnnotation="group", notsig="grey", sig="hotpink")

Removing hidden batch effects

Suppose we did not know that there were different cell lines involved in the experiment, only that there was treatment with dexamethasone. The cell line effect on the counts then would represent some hidden and unwanted variation that might be affecting many or all of the genes in the dataset. We can use statistical methods designed for RNA-seq from the sva package²⁴ to detect such groupings of the samples, and then we can add these to the DESeqDataSet design, in order to account for them. The SVA package uses the term surrogate variables for the estimated variables that we want to account for in our analysis. Another package for detecting hidden batches is the RUVSeq package²⁵, with the acronym “Remove Unwanted Variation”.

library("sva")

Below we obtain a matrix of normalized counts for which the average count across samples is larger than 1. As we described above, we are trying to recover any hidden batch effects, supposing that we do not know the cell line information. So we use a full model matrix with the dex variable, and a reduced, or null, model matrix with only an intercept term. Finally we specify that we want to estimate 2 surrogate variables. For more information read the manual page for the svaseq function by typing ?svaseq.

dat <- counts(dds, normalized=TRUE)
idx <- rowMeans(dat) > 1
dat <- dat[idx,]
mod <- model.matrix(~ dex, colData(dds))
mod0 <- model.matrix(~ 1, colData(dds))
svseq <- svaseq(dat, mod, mod0, n.sv=2)

## Number of significant surrogate variables is:  2
## Iteration (out of 5 ):1  2  3  4  5

svseq$sv

##	      [,1]	  [,2]
## [1,]  0.2481108 -0.52600157
## [2,]  0.2629867 -0.58115433
## [3,]  0.1502704  0.27428267
## [4,]  0.2023800  0.38419545
## [5,] -0.6086586 -0.07854931
## [6,] -0.6101210 -0.02923693
## [7,]  0.1788509  0.25708985
## [8,]  0.1761807  0.29937417

Because we actually do know the cell lines, we can see how well the SVA method did at recovering these variables (Figure 16).

Figure 16. Surrogate variables 1 and 2 plotted over cell line.

Here, we know the hidden source of variation (cell line), and therefore can see how the SVA procedure is able to identify sources of variation which are correlated with cell line.

par(mfrow=c(2,1),mar=c(3,5,3,1))
stripchart(svseq$sv[,1] ~ dds$cell,vertical=TRUE,main="SV1")
abline(h=0)
stripchart(svseq$sv[,2] ~ dds$cell,vertical=TRUE,main="SV2")
abline(h=0)

Finally, in order to use SVA to remove any effect on the counts from our surrogate variables, we simply add these two surrogate variables as columns to the DESeqDataSet and then add them to the design:

ddssva <- dds
ddssva$SV1 <- svseq$sv[,1]
ddssva$SV2 <- svseq$sv[,2]
design(ddssva) <- ~ SV1 + SV2 + dex

We could then produce results controlling for surrogate variables by running DESeq with the new design:

ddssva <- DESeq(ddssva)