Michael Love [1], Simon Anders [2], Wolfgang Huber [2]
[1] Department of Biostatistics, Dana-Farber Cancer Institute and Harvard School of Public Health, Boston, US;
[2] European Molecular Biology Laboratory (EMBL), Heidelberg, Germany.
Minor modifications by Martin Morgan, 26 October 2014.
This lab will walk you through an end-to-end RNA-Seq differential expression workflow, using DESeq2 along with other Bioconductor packages. We will start from the FASTQ files, show how these were aligned to the reference genome, prepare gene expression values as a count matrix by counting the sequenced fragments, perform exploratory data analysis (EDA), perform differential gene expression analysis with DESeq2, and visually explore the results.
We note that a number of other Bioconductor packages can also be used for statistical inference of differential expression at the gene level including edgeR, BaySeq, DSS and limma.
The data used in this workflow is an RNA-Seq experiment of airway smooth muscle cells treated with dexamethasone, a synthetic glucocorticoid steroid with anti-inflammatory effects. Glucocorticoids are used, for example, in asthma patients to prevent or 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. The reference for the experiment is:
Himes BE, Jiang X, Wagner P, Hu R, Wang Q, Klanderman B, Whitaker RM, Duan Q, Lasky-Su J, Nikolos C, Jester W, Johnson M, Panettieri R Jr, Tantisira KG, Weiss ST, Lu Q. “RNA-Seq Transcriptome Profiling Identifies CRISPLD2 as a Glucocorticoid Responsive Gene that Modulates Cytokine Function in Airway Smooth Muscle Cells.” PLoS One. 2014 Jun 13;9(6):e99625. PMID: 24926665. GEO: GSE52778.
As input, the DESeq2 package expects count data as obtained, e.g., from RNA-Seq or another high-throughput sequencing experiment, in the form of a matrix of integer values. The value in the i-th row and the j-th column of the matrix tells how many reads have been mapped to gene i in sample j. Analogously, for other types of assays, the rows of the matrix might correspond e.g., to binding regions (with ChIP-Seq) or peptide sequences (with quantitative mass spectrometry).
The count values must be raw counts of sequencing reads. This is important for DESeq2's statistical model to hold, as only the actual counts allow assessing the measurement precision correctly. Hence, please do not supply other quantities, such as (rounded) normalized counts, or counts of covered base pairs – this will only lead to nonsensical results.
The computational analysis of an RNA-Seq experiment begins earlier: what we get from the sequencing machine is 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 the 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, ability to align reads over splice junctions, speed, memory footprint, and many other features.
The reads for this experiment were aligned to the Ensembl release 75 human reference genome using the STAR read aligner:
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
SAMtools was used to generate BAM files.
cat files | parallel -j 7 samtools view -bS aligned/{}.Aligned.out.sam -o aligned/{}.bam
The BAM files for a number of sequencing runs can then be used to generate count matrices, as described in the following section.
Besides the main count matrix, which we will use later, the airway package also contains a small subset of the raw data, namely eight BAM file each with a subset of the reads. 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 table.
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, which 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] "SRR1039508_subset.bam" "SRR1039509_subset.bam"
## [5] "SRR1039512_subset.bam" "SRR1039513_subset.bam"
## [7] "SRR1039516_subset.bam" "SRR1039517_subset.bam"
## [9] "SRR1039520_subset.bam" "SRR1039521_subset.bam"
## [11] "SraRunInfo_SRP033351.csv" "sample_table.csv"
Typically, we have a table with experimental metadata for our samples. 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 this file with read.csv. The parentheses around the last
line are used to print the result in addition to storing it to the
sampleTable object.
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
Once the reads have been aligned, there are a number of tools which can be used to count the number of reads which can be unambiguously assigned to genomic features for each sample. These often take as input SAM/BAM alignment files and a file specifiying the genomic features, e.g. a GFF3 or GTF file specifying the gene models.
The following tools can be used generate count matrices:
| function | package | framework | output | DESeq2 input function |
|---|---|---|---|---|
| summarizeOverlaps | GenomicAlignments | R/Bioconductor | SummarizedExperiment | DESeqDataSet |
| featureCounts | Rsubread | R/Bioconductor | matrix | DESeqDataSetFromMatrix |
| htseq-count | HTSeq | Python | files | DESeqDataSetFromHTSeq |
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"))
We indicate in Bioconductor that these files are BAM files using the BamFileList function. Here we also specify details about how the BAM files should be treated, e.g., only process 2000000 reads at a time.
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. We can check the chromosome names 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>
Next, we need to read in the gene model which will be used for counting reads. We will read the gene model from a GTF file, using makeTranscriptDbFromGFF from the GenomicFeatures package. GTF files can be downloaded from Ensembl's FTP site or other gene model repositories. A TranscriptDb object is a database which can be used to generate a variety of range-based objects, such as exons, transcripts, and genes. We will want to make a list of exons grouped by gene.
There are other options for constructing a TranscriptDB. For the known genes track from the UCSC Genome Browser, one can use the pre-built Transcript DataBase: TxDb.Hsapiens.UCSC.hg19.knownGene. The makeTranscriptDbFromBiomart function can be used to automatically pull a gene model from Biomart.
library("GenomicFeatures")
gtffile <- file.path(dir,"Homo_sapiens.GRCh37.75_subset.gtf")
(txdb <- makeTranscriptDbFromGFF(gtffile, format="gtf"))
## Warning in .deduceExonRankings(exs, format = "gtf"): Infering Exon Rankings. If this is not what
## you expected, then please be sure that you have provided a valid attribute for
## exonRankAttributeName
## Warning in matchCircularity(chroms, circ_seqs): None of the strings in your circ_seqs argument
## match your seqnames.
## Warning: 'dbBeginTransaction' is deprecated.
## Use 'dbBegin' instead.
## See help("Deprecated")
## Warning: 'dbBeginTransaction' is deprecated.
## Use 'dbBegin' instead.
## See help("Deprecated")
## Warning: 'dbBeginTransaction' is deprecated.
## Use 'dbBegin' instead.
## See help("Deprecated")
## Warning: 'dbBeginTransaction' is deprecated.
## Use 'dbBegin' instead.
## See help("Deprecated")
## Warning: 'dbBeginTransaction' is deprecated.
## Use 'dbBegin' instead.
## See help("Deprecated")
## Warning: 'dbBeginTransaction' is deprecated.
## Use 'dbBegin' instead.
## See help("Deprecated")
## TxDb object:
## | Db type: TxDb
## | Supporting package: GenomicFeatures
## | Data source: /home/ubuntu/R/x86_64-unknown-linux-gnu-library/3.1/airway/extdata/Homo_sapiens.GRCh37.75_subset.gtf
## | Organism: NA
## | miRBase build ID: NA
## | transcript_nrow: 65
## | exon_nrow: 242
## | cds_nrow: 159
## | Db created by: GenomicFeatures package from Bioconductor
## | Creation time: 2014-10-29 20:03:30 +0000 (Wed, 29 Oct 2014)
## | GenomicFeatures version at creation time: 1.18.1
## | RSQLite version at creation time: 0.11.4
## | DBSCHEMAVERSION: 1.0
The following line produces a GRangesList of all the exons grouped by gene.
(genes <- exonsBy(txdb, by="gene"))
## GRangesList object of length 20:
## $ENSG00000009724
## GRanges object with 16 ranges and 2 metadata columns:
## seqnames ranges strand | exon_id exon_name
## <Rle> <IRanges> <Rle> | <integer> <character>
## [1] 1 [11086580, 11087705] - | 89 <NA>
## [2] 1 [11090233, 11090307] - | 90 <NA>
## [3] 1 [11090805, 11090939] - | 91 <NA>
## [4] 1 [11094885, 11094963] - | 92 <NA>
## [5] 1 [11097750, 11097868] - | 93 <NA>
## ... ... ... ... ... ... ...
## [12] 1 [11106613, 11106790] - | 100 <NA>
## [13] 1 [11106948, 11107176] - | 101 <NA>
## [14] 1 [11107260, 11107280] - | 102 <NA>
## [15] 1 [11107260, 11107284] - | 103 <NA>
## [16] 1 [11107260, 11107290] - | 104 <NA>
##
## ...
## <19 more elements>
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengths
After these preparations, the actual counting is easy. The function summarizeOverlaps from the GenomicAlignments package will do this. This produces a SummarizedExperiment object, which contains a variety of information about an 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 functions from the BiocParallel package before the counting call below.
library("GenomicAlignments")
se <- summarizeOverlaps(features=genes, 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 as a hit. These modes are shown in Figure 1 of the “Counting reads with
summarizeOverlaps” vignette for the GenomicAlignments
package. Setting singleEnd to FALSE indicates that the experiment
produced paired-end reads, and we want to count a pair of reads only once
toward the read count for a gene.
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 FALSE.
The fragments argument can be used when singleEnd=FALSE
to specify if unpaired reads should be counted (yes if fragments=TRUE).
Here we show the component parts of a SummarizedExperiment object,
and also its subclasses, such as the DESeqDataSet which is
explained in the next section. The assay(s) (red block) contains
the matrix (or matrices) of summarized values, the rowData (blue
block) contains information about the genomic ranges, and the
colData (purple block) contains information about the samples or
experiments. 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.
This example code above actually only counts a small subset of reads
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 rowData slot.
se
## class: SummarizedExperiment
## dim: 20 8
## exptData(0):
## assays(1): counts
## rownames(20): ENSG00000009724 ENSG00000116649 ... ENSG00000271794 ENSG00000271895
## rowData metadata column names(0):
## colnames(8): SRR1039508_subset.bam SRR1039509_subset.bam ... SRR1039520_subset.bam
## SRR1039521_subset.bam
## colData names(0):
head(assay(se))
## SRR1039508_subset.bam SRR1039509_subset.bam SRR1039512_subset.bam
## ENSG00000009724 38 28 66
## ENSG00000116649 1004 1255 1122
## ENSG00000120942 218 256 233
## ENSG00000120948 2751 2080 3353
## ENSG00000171819 4 50 19
## ENSG00000171824 869 1075 1115
## SRR1039513_subset.bam SRR1039516_subset.bam SRR1039517_subset.bam
## ENSG00000009724 24 42 41
## ENSG00000116649 1313 1100 1879
## ENSG00000120942 252 269 465
## ENSG00000120948 1614 3519 3716
## ENSG00000171819 543 1 10
## ENSG00000171824 1051 944 1405
## SRR1039520_subset.bam SRR1039521_subset.bam
## ENSG00000009724 47 36
## ENSG00000116649 745 1536
## ENSG00000120942 207 400
## ENSG00000120948 2220 1990
## ENSG00000171819 14 1067
## ENSG00000171824 748 1590
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
colData(se)
## DataFrame with 8 rows and 0 columns
rowData(se)
## GRangesList object of length 20:
## $ENSG00000009724
## GRanges object with 16 ranges and 2 metadata columns:
## seqnames ranges strand | exon_id exon_name
## <Rle> <IRanges> <Rle> | <integer> <character>
## [1] 1 [11086580, 11087705] - | 89 <NA>
## [2] 1 [11090233, 11090307] - | 90 <NA>
## [3] 1 [11090805, 11090939] - | 91 <NA>
## [4] 1 [11094885, 11094963] - | 92 <NA>
## [5] 1 [11097750, 11097868] - | 93 <NA>
## ... ... ... ... ... ... ...
## [12] 1 [11106613, 11106790] - | 100 <NA>
## [13] 1 [11106948, 11107176] - | 101 <NA>
## [14] 1 [11107260, 11107280] - | 102 <NA>
## [15] 1 [11107260, 11107284] - | 103 <NA>
## [16] 1 [11107260, 11107290] - | 104 <NA>
##
## ...
## <19 more elements>
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengths
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 matrix. It also contains metadata about the construction
of the gene model in the metadata slot.
str(metadata(rowData(se)))
## List of 1
## $ genomeInfo:List of 13
## ..$ Db type : chr "TxDb"
## ..$ Supporting package : chr "GenomicFeatures"
## ..$ Data source : chr "/home/ubuntu/R/x86_64-unknown-linux-gnu-library/3.1/airway/extdata/Homo_sapiens.GRCh37.75_subset.gtf"
## ..$ Organism : chr NA
## ..$ miRBase build ID : chr NA
## ..$ transcript_nrow : chr "65"
## ..$ exon_nrow : chr "242"
## ..$ cds_nrow : chr "159"
## ..$ Db created by : chr "GenomicFeatures package from Bioconductor"
## ..$ Creation time : chr "2014-10-29 20:03:30 +0000 (Wed, 29 Oct 2014)"
## ..$ GenomicFeatures version at creation time: chr "1.18.1"
## ..$ RSQLite version at creation time : chr "0.11.4"
## ..$ DBSCHEMAVERSION : chr "1.0"
The colData slot, so far empty, should contain all the metadata.
We hence assign our sample table to it:
(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
At this point, we have counted the reads 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 counts, including edgeR, BaySeq, DSS and limma. We will continue, using DESeq2. 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.
Bioconductor software packages often define and use a custom class for
their data object, which makes sure that all the needed data slots are
consistently provided and fulfill the requirements. In addition,
Bioconductor has general data classes (such as the
SummarizedExperiment) that can be used to move data between
packages. In DESeq2, the custom class is called
DESeqDataSet. It is built on top of the SummarizedExperiment class
(in technical term, it is a subclass), and it is easy
to convert SummarizedExperiment instances into DESeqDataSet and vice versa.
One of the main differences is that the assay slot is instead
accessed using the count accessor, and the class enforces that the
values in this matrix are non-negative integers.
A second difference is that the DESeqDataSet has an associated
design formula. The experimental design is specified at the
beginning of the analysis, as it will inform many of the DESeq2
functions how to treat the samples in the analysis (one exception is
the size factor estimation, i.e., the adjustment for differing library
sizes, which does not depend on the design formula). The design
formula tells which variables in the column metadata table (colData)
specify the experimental design and how these factors should be used
in the analysis.
The simplest design formula for differential expression would be
~ condition, where condition is a column in colData(dds) which
specifies which of two (or more groups) the samples belong to. For
the airway experiment, we will specify ~ cell + dex, which
means that we want to test for the effect of dexamethasone (the last
factor), controlling for the effect of different cell line (the first
factor).
You can use R's formula notation to express any experimental design
that can be described within an ANOVA-like framework. Note that
DESeq2 uses the same formula notation as, for instance, the lm
function of base R. If the question of interest is whether a fold
change due to treatment is different across groups, interaction terms
can be included using models such as
~ group + treatment + group:treatment. See the manual page for
?results for examples of extracting contrasts from more complex
designs such as these.
In the following sections, we will demonstrate the construction of the DESeqDataSet from two starting points:
For a full example of using the HTSeq Python package for read counting, please see the pasilla vignette. For an example of generating the DESeqDataSet from files produced by htseq-count, please see the DESeq2 vignette.
We now use R's data command to load a prepared
SummarizedExperiment that was generated from the publicly available
sequencing data files associated with the Himes et al. paper,
described above. The steps we used to produce this object were
equivalent to those you worked through in the previous sections,
except that we used all the reads and all the genes. For more details
on the exact steps used to create this object type
browseVignettes("airway") into your R session.
data("airway")
se <- airway
We can quickly check the millions of fragments which uniquely aligned to the genes (the second argument of round tells how many decimal points to keep).
round( colSums(assay(se)) / 1e6, 1 )
## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520 SRR1039521
## 20.6 18.8 25.3 15.2 24.4 30.8 19.1 21.2
Supposing we have constructed a SummarizedExperiment using
one of the methods described in the previous section, we now need to
make sure that the object contains all the necessary information about
the samples, i.e., a table with metadata on the count matrix's columns
stored in the colData slot:
colData(se)
## 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
Here we see that this object already contains an informative
colData slot – because we have already prepared it for you, as
described in the airway vignette.
However, when you work with your own data, you will have to add the
pertinent sample / phenotypic information for the experiment at this stage.
We highly recommend keeping this information in a comma-separated
value (CSV) or tab-separated value (TSV) file, which can be exported
from an Excel spreadsheet, and the assign this to the colData slot,
making sure that the rows correspond to the columns of the
SummarizedExperiment. We made sure of this correspondence by
specifying the BAM files using a column of the sample table.
Once we have our fully annotated SummarizedExperiment object, we can construct a DESeqDataSet object from it, which will then form the starting point of the actual DESeq2 package, described in the following sections. We add an appropriate design for the analysis.
library("DESeq2")
dds <- DESeqDataSet(se, design = ~ cell + dex)
Note that there are two alternative functions, DESeqDataSetFromMatrix and DESeqDataSetFromHTSeq, which allow you to get started in case you have your data not in the form of a SummarizedExperiment object, but either as a simple matrix of count values or as output files from the htseq-count script from the HTSeq Python package.
Below we demonstrate using DESeqDataSetFromMatrix.
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 contruct 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 package.
The information in a SummarizedExperiment object can be accessed with accessor functions. For example, to see the actual data, i.e., here, the read counts, we use the assay function. (The head function restricts the output to the first few lines.)
countdata <- assay(se)
head(countdata)
## 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
## ENSG00000000457 260 211 263 164 245 331 233
## ENSG00000000460 60 55 40 35 78 63 76
## ENSG00000000938 0 0 2 0 1 0 0
## SRR1039521
## ENSG00000000003 572
## ENSG00000000005 0
## ENSG00000000419 508
## ENSG00000000457 229
## ENSG00000000460 60
## ENSG00000000938 0
In this count matrix, each row represents an Ensembl gene, each column a sequenced RNA library, and the values give the raw numbers of sequencing reads that were mapped to the respective gene in each library. We also have metadata on each of the samples (the columns of the count matrix). If you've counted reads with some other software, you need to check at this step that the columns of the count matrix correspond to the rows of the column metadata.
coldata <- colData(se)
We now have all the ingredients to prepare our data object in a form that is suitable for analysis, namely:
countMatrix: a table with the read countscoldata: a table with metadata on the count matrix's columnsTo now construct the data object from the matrix of counts and the metadata 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
## rowData 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.
Many common statistical methods for exploratory analysis of multidimensional data, especially methods for clustering and ordination (e.g., principal-component analysis and the like), work best for (at least approximately) homoskedastic data; this means that the variance of an observed quantity (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 (principal components analysis) 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 on inter-sample differences in the form of
a ridge penalty, this is done such that the rlog-transformed data
are approximately homoskedastic. See the help for ?rlog for more
information and options. Another transformation, the variance
stabilizing transformation, 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 which contains the rlog-transformed values in its assay slot:
rld <- rlog(dds)
head(assay(rld))
## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520
## ENSG00000000003 9.399151 9.142478 9.501695 9.320796 9.757212 9.512183 9.617378
## ENSG00000000005 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## ENSG00000000419 8.901283 9.113976 9.032567 9.063925 8.981930 9.108531 8.894830
## ENSG00000000457 7.949897 7.882371 7.834273 7.916459 7.773819 7.886645 7.946411
## ENSG00000000460 5.849521 5.882363 5.486937 5.770334 5.940407 5.663847 6.107733
## ENSG00000000938 -1.638084 -1.637483 -1.558248 -1.636072 -1.597606 -1.639362 -1.637608
## SRR1039521
## ENSG00000000003 9.315309
## ENSG00000000005 0.000000
## ENSG00000000419 9.052303
## ENSG00000000457 7.908338
## ENSG00000000460 5.907824
## ENSG00000000938 -1.637724
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. For the log2 method, we need estimate size factors to account for sequencing depth (this is done automatically for the rlog method).
par( mfrow = c( 1, 2 ) )
dds <- estimateSizeFactors(dds)
plot( log2( 1 + counts(dds, normalized=TRUE)[ , 1:2] ),
col=rgb(0,0,0,.2), pch=16, cex=0.3 )
plot( assay(rld)[ , 1:2],
col=rgb(0,0,0,.2), pch=16, cex=0.3 )
Note that, in order to make it easier to see where several points are
plotted on top of each other, we set the plotting color to a
semi-transparent black and changed the points to solid circles
(pch=16) with reduced size (cex=0.3).
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.
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 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) ) )
sampleDists
## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520
## SRR1039509 40.89060
## SRR1039512 37.35231 50.07638
## SRR1039513 55.74569 41.49280 43.61052
## SRR1039516 41.98797 53.58929 40.99513 57.10447
## SRR1039517 57.69438 47.59326 53.52310 46.13742 42.10583
## SRR1039520 37.06633 51.80994 34.86653 52.54968 43.21786 57.13688
## SRR1039521 56.04254 41.46514 51.90045 34.82975 58.40428 47.90244 44.78171
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.
library("gplots")
library("RColorBrewer")
We have to provide a hierarchical clustering hc to the heatmap.2
function based on the sample distances, or else the heatmap.2
function would calculate a clustering based on the distances between
the rows/columns of the distance matrix.
sampleDistMatrix <- as.matrix( sampleDists )
rownames(sampleDistMatrix) <- paste( rld$dex, rld$cell, sep="-" )
colors <- colorRampPalette( rev(brewer.pal(9, "Blues")) )(255)
hc <- hclust(sampleDists)
heatmap.2( sampleDistMatrix, Rowv=as.dendrogram(hc),
symm=TRUE, trace="none", col=colors,
margins=c(2,10), labCol=FALSE )
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
Distance, implemented in the CRAN package
PoiClaClu. Similar to the transformations offered in
DESeq2, this measure of dissimilarity also takes the 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 tranpose the counts in dds.
library("PoiClaClu")
poisd <- PoissonDistance(t(counts(dds)))
We can plot the heatmap as before:
samplePoisDistMatrix <- as.matrix( poisd$dd )
rownames(samplePoisDistMatrix) <- paste( dds$dex, dds$cell, sep="-" )
colors <- colorRampPalette( rev(brewer.pal(9, "Blues")) )(255)
hc <- hclust(poisd$dd)
heatmap.2( samplePoisDistMatrix, Rowv=as.dendrogram(hc),
symm=TRUE, trace="none", col=colors,
margins=c(2,10), labCol=FALSE )
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 in the two directions which explain most of the differences in the data. The x-axis is the direction (or principal component) which separates the data points the most. The amount of the total variance which is contained in the direction is printed in the axis label.
plotPCA(rld, intgroup = c("dex", "cell"))
Here, we have used the function plotPCA which comes with DESeq2.
The two terms specified by intgroup are the interesting groups for
labelling the samples; they tell the function to use them to choose
colors. We can also build the PCA plot from scratch using
ggplot2. 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 names
## SRR1039508 -14.331359 -4.208796 untrt : N61311 untrt N61311 SRR1039508
## SRR1039509 6.754169 -2.245244 trt : N61311 trt N61311 SRR1039509
## SRR1039512 -8.130393 -3.952904 untrt : N052611 untrt N052611 SRR1039512
## SRR1039513 14.505648 -2.941862 trt : N052611 trt N052611 SRR1039513
## SRR1039516 -11.891410 13.735002 untrt : N080611 untrt N080611 SRR1039516
## SRR1039517 8.373975 17.823844 trt : N080611 trt N080611 SRR1039517
## SRR1039520 -9.965898 -10.014674 untrt : N061011 untrt N061011 SRR1039520
## SRR1039521 14.685269 -8.195366 trt : N061011 trt N061011 SRR1039521
percentVar <- round(100 * attr(data, "percentVar"))
We can then use this data to build up the plot, specifying that the color of the points should reflect dexamethasone treatment and the shape should reflect the cell line.
library("ggplot2")
qplot(PC1, PC2, color=dex, shape=cell, data=data) +
xlab(paste0("PC1: ",percentVar[1],"% variance")) +
ylab(paste0("PC2: ",percentVar[2],"% variance"))
From both visualizations, we see that the differences between cells are
considerable, though not stronger than the differences due to
treatment with dexamethasone. 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 by using the design formula ~ cell + dex when setting up the
data object in the beginning.
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 the original data, but only a matrix of distances. Here we have the MDS plot for the distances calculated from the rlog transformed counts:
mds <- data.frame(cmdscale(sampleDistMatrix))
mds <- cbind(mds, colData(rld))
qplot(X1,X2,color=dex,shape=cell,data=mds)
And here from the PoissonDistance:
mds <- data.frame(cmdscale(samplePoisDistMatrix))
mds <- cbind(mds, colData(dds))
qplot(X1,X2,color=dex,shape=cell,data=mds)
It will be convenient to make sure that untrt is the first level in
the dex factor, so that the default log2 fold changes are calculated
as treated over untreated (by default R will chose the first
alphabetical level, remember: computers don't know what to do unless
you tell them). The function relevel achieves this:
dds$dex <- relevel(dds$dex, "untrt")
In addition, if you have at any point subset the columns of the DESeqDataSet you should similarly call droplevels on the factors if the subsetting has resulted in some levels having 0 samples.
Finally, we are ready to run the differential expression pipeline. With the data object prepared, the DESeq2 analysis can now be run 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 (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.
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.
(res <- results(dds))
## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 64102 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000000003 708.60217 -0.37424998 0.09873107 -3.7906000 0.0001502838 0.001217611
## ENSG00000000005 0.00000 NA NA NA NA NA
## ENSG00000000419 520.29790 0.20215551 0.10929899 1.8495642 0.0643763851 0.188306353
## ENSG00000000457 237.16304 0.03624826 0.13684258 0.2648902 0.7910940556 0.907203245
## ENSG00000000460 57.93263 -0.08523371 0.24654402 -0.3457140 0.7295576905 0.874422374
## ... ... ... ... ... ... ...
## LRG_94 0 NA NA NA NA NA
## LRG_96 0 NA NA NA NA NA
## LRG_97 0 NA NA NA NA NA
## LRG_98 0 NA NA NA NA NA
## LRG_99 0 NA NA NA NA 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. 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. 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 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 \(2^{1.5} \approx 2.82\).
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 no 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 just as well 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, which will be covered in later sections.
summary(res)
##
## out of 33469 with nonzero total read count
## adjusted p-value < 0.1
## LFC > 0 (up) : 2646, 7.9%
## LFC < 0 (down) : 2251, 6.7%
## outliers [1] : 0, 0%
## low counts [2] : 15928, 48%
## (mean count < 5.3)
## [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:
padj in
the results table)lfcThreshold
argument of results. See the DESeq2 vignette for a demonstration
of the use of this argument.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 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 vignette.
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 in the numerator, and the name of the
level in 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 64102 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000000003 708.60217 0.29055775 0.1360076 2.13633388 0.03265221 0.1961655
## ENSG00000000005 0.00000 NA NA NA NA NA
## ENSG00000000419 520.29790 -0.05069642 0.1491735 -0.33984871 0.73397047 0.9220321
## ENSG00000000457 237.16304 0.01474463 0.1816382 0.08117584 0.93530211 0.9862824
## ENSG00000000460 57.93263 0.20247610 0.2807312 0.72124547 0.47075850 0.8068941
## ... ... ... ... ... ... ...
## LRG_94 0 NA NA NA NA NA
## LRG_96 0 NA NA NA NA NA
## LRG_97 0 NA NA NA NA NA
## LRG_98 0 NA NA NA NA NA
## LRG_99 0 NA NA NA NA 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.
Novices in high-throughput biology often assume that thresholding these p values at a low value, say 0.05, as is often done in other settings, would be appropriate – but it is not. We briefly explain why:
There are 5722 genes with a p value below 0.05 among the 33469 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] 33469
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 p value, we expect up to 5% of the genes to have a p value below 0.05. This amounts to 1673 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 1673 / 5722 = 29% false positives.
DESeq2 uses the Benjamini-Hochberg (BH) adjustment as described in
the base R p.adjust function; 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 res
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$padj < 0.1, na.rm=TRUE)
## [1] 4897
We subset the results table to these genes and then sort it by the log2 fold change estimate to get the significant genes with the strongest down-regulation.
resSig <- subset(res, padj < 0.1)
head(resSig[ order( resSig$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 -3.453076 0.1764098 -19.574173 2.567708e-85 3.464629e-82
## ENSG00000146006 46.80760 -2.858867 0.3369900 -8.483538 2.184477e-17 1.067351e-15
## ENSG00000105989 333.21469 -2.851447 0.1754994 -16.247620 2.322038e-59 1.197967e-56
## ENSG00000214814 243.27698 -2.760339 0.2225604 -12.402652 2.528167e-35 4.106165e-33
## ENSG00000267339 26.23357 -2.746830 0.3515707 -7.813022 5.583283e-15 2.171538e-13
## ENSG00000013293 244.49733 -2.646722 0.1981697 -13.355834 1.095240e-40 2.233907e-38
…and with the strongest upregulation. The order function gives
the indices in increasing order, so a simple way to ask for decreasing
order is to add a - sign. Alternatively, you can use the argument
decreasing=TRUE.
head(resSig[ order( -resSig$log2FoldChange ), ])
## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 6 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000179593 67.24305 4.884730 0.3312025 14.74847 3.147214e-49 1.003732e-46
## ENSG00000109906 385.07103 4.865889 0.3324560 14.63619 1.650703e-48 4.992238e-46
## ENSG00000152583 997.43977 4.316100 0.1724127 25.03354 2.637881e-138 4.627108e-134
## ENSG00000250978 56.31819 4.093661 0.3291519 12.43699 1.645805e-35 2.723496e-33
## ENSG00000163884 561.10717 4.079128 0.2103817 19.38917 9.525995e-84 1.044347e-80
## ENSG00000168309 159.52692 3.992788 0.2549099 15.66353 2.685734e-55 1.207961e-52
A quick way to visualize the counts for a particular gene is to use the plotCounts function, which takes as arguments the DESeqDataSet, a gene name, and the group over which to plot the counts.
topGene <- rownames(res)[which.min(res$padj)]
plotCounts(dds, gene=topGene, intgroup=c("dex"))
We can also make more customizable plots using the ggplot function from the ggplot2 package:
data <- plotCounts(dds, gene=topGene, intgroup=c("dex","cell"), returnData=TRUE)
ggplot(data, aes(x=dex, y=count, color=cell)) +
scale_y_log10() +
geom_point(position=position_jitter(width=.1,height=0))
Here we use a more structural arrangement instead of random jitter, and color by the treatment.
ggplot(data, aes(x=dex, y=count, fill=dex)) +
scale_y_log10() +
geom_dotplot(binaxis="y", stackdir="center")
Note that the DESeq test actually takes into account the cell line effect, so a more detailed plot would also show the cell lines.
ggplot(data, aes(x=dex, y=count, color=cell, group=cell)) +
scale_y_log10() +
geom_point() + geom_line()
An “MA-plot” provides a useful overview for an experiment with a two-group comparison. The log2 fold change for a particular comparison is plotted on the y-axis and the average of the counts normalized by size factor is shown on the x-axis (“M” for minus, because a log ratio is equal to log minus log, and “A” for average).
plotMA(res, ylim=c(-5,5))
Each gene is represented with a dot. Genes with an adjusted \(p\) value below a threshold (here 0.1, the default) are shown in red. The DESeq2 package incorporates a prior on log2 fold changes, resulting in moderated log2 fold changes from genes with low counts and highly variable counts, as can be seen by the narrowing of spread of points on the left side of the plot. This plot demonstrates that only genes with a large average normalized count contain sufficient information to yield a significant call.
We can label individual points on the MA plot as well. Here we use the
with R function to plot a circle and text for a selected row of the
results object. Within the with function, only the baseMean and
log2FoldChange values for the selected rows of res are used.
plotMA(res, ylim=c(-5,5))
with(res[topGene, ], {
points(baseMean, log2FoldChange, col="dodgerblue", cex=2, lwd=2)
text(baseMean, log2FoldChange, topGene, pos=2, col="dodgerblue")
})
Whether a gene is called significant depends not only on its LFC but also on its within-group variability, which DESeq2 quantifies as the dispersion. For strongly expressed genes, the dispersion can be understood as a squared coefficient of variation: a dispersion value of 0.01 means that the gene's expression tends to differ by typically \(\sqrt{0.01} = 10\%\) between samples of the same treatment group. For weak genes, the Poisson noise is an additional source of noise.
The function plotDispEsts visualizes DESeq2's dispersion estimates:
plotDispEsts(dds)
The black points are the dispersion estimates for each gene as obtained by considering the information from each gene separately. Unless one has many samples, these values fluctuate strongly around their true values. Therefore, we fit the red trend line, which shows the dispersions' dependence on the mean, and then shrink each gene's estimate towards the red line to obtain the final estimates (blue points) that are then used in the hypothesis test. The blue circles above the main “cloud” of points are genes which have high gene-wise dispersion estimates which are labelled as dispersion outliers. These estimates are therefore not shrunk toward the fitted trend line.
Another useful diagnostic plot is the histogram of the p values.
hist(res$pvalue, breaks=20, col="grey50", border="white")
This plot becomes a bit smoother by excluding genes with very small counts:
hist(res$pvalue[res$baseMean > 1], breaks=20, col="grey50", border="white")
In the sample distance heatmap made previously, the dendrogram at the side shows us a hierarchical clustering of the samples. Such a clustering can also be performed for the genes. Since the clustering is only relevant for genes that actually carry signal, one usually carries it out only for a subset of most highly variable genes. Here, for demonstration, let us select the 35 genes with the highest variance across samples. We will work with the rlog transformed counts:
library("genefilter")
topVarGenes <- head(order(-rowVars(assay(rld))),35)
The heatmap becomes more interesting if we do not look at absolute expression strength but rather at the amount by which each gene deviates in a specific sample from the gene's average across all samples. Hence, we center each genes' values across samples, and plot a heatmap. We provide the column side colors to help identify the treated samples (in blue) from the untreated samples (in grey).
colors <- colorRampPalette( rev(brewer.pal(9, "PuOr")) )(255)
sidecols <- c("grey","dodgerblue")[ rld$dex ]
mat <- assay(rld)[ topVarGenes, ]
mat <- mat - rowMeans(mat)
colnames(mat) <- paste0(rld$dex,"-",rld$cell)
heatmap.2(mat, trace="none", col=colors, ColSideColors=sidecols,
labRow=FALSE, mar=c(10,2), scale="row")
We can now see blocks of genes which covary across patients. Note that a set of genes at the top of the heatmap are separating the N061011 cell line from the others. At the bottom of the heatmap, we see a set of genes for which the treated samples have higher gene expression.
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 DESeq2 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")
## 72.63637%
## 5.339835
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. The independent filtering software used inside DESeq2 comes from the genefilter package, which contains a reference to a paper describing the statistical foundation for independent filtering.
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 AnnotationDbi package and the annotation package org.Hs.eg.db:
library("AnnotationDbi")
library("org.Hs.eg.db")
This is the organism annotation package (“org”) for Homo sapiens (“Hs”), organized as an AnnotationDbi database 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"
## [7] "CHR" "CHRLOC" "CHRLOCEND" "ENZYME" "MAP" "PATH"
## [13] "PMID" "REFSEQ" "SYMBOL" "UNIGENE" "ENSEMBL" "ENSEMBLPROT"
## [19] "ENSEMBLTRANS" "GENENAME" "UNIPROT" "GO" "EVIDENCE" "ONTOLOGY"
## [25] "GOALL" "EVIDENCEALL" "ONTOLOGYALL" "OMIM" "UCSCKG"
Converting IDs with the native functions from the AnnotationDbi package is a bit cumbersome, so we provide the following convenience function (without explaining how exactly it works):
convertIDs <- function( ids, from, to, db, ifMultiple=c("putNA", "useFirst")) {
stopifnot( inherits( db, "AnnotationDb" ) )
ifMultiple <- match.arg( ifMultiple )
suppressWarnings( selRes <- AnnotationDbi::select(
db, keys=ids, keytype=from, columns=c(from,to) ) )
if ( ifMultiple == "putNA" ) {
duplicatedIds <- selRes[ duplicated( selRes[,1] ), 1 ]
selRes <- selRes[ ! selRes[,1] %in% duplicatedIds, ]
}
return( selRes[ match( ids, selRes[,1] ), 2 ] )
}
This function takes a list of IDs as first argument and their key type
as the second argument. The third argument is the key type we want to
convert to, the fourth is the AnnotationDb object to use. Finally,
the last 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? 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$entrezgene <- convertIDs(row.names(res), "ENSEMBL", "ENTREZID", org.Hs.eg.db)
Now the results have the desired external gene ids:
resOrdered <- res[order(res$pvalue),]
head(resOrdered)
## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 6 rows and 8 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000152583 997.4398 4.316100 0.1724127 25.03354 2.637881e-138 4.627108e-134
## ENSG00000165995 495.0929 3.188698 0.1277441 24.96160 1.597973e-137 1.401503e-133
## ENSG00000101347 12703.3871 3.618232 0.1499441 24.13054 1.195378e-128 6.441180e-125
## ENSG00000120129 3409.0294 2.871326 0.1190334 24.12201 1.468829e-128 6.441180e-125
## ENSG00000189221 2341.7673 3.230629 0.1373644 23.51868 2.627083e-122 9.216332e-119
## ENSG00000211445 12285.6151 3.552999 0.1589971 22.34631 1.311440e-110 3.833996e-107
## hgnc_symbol entrezgene
## <character> <character>
## ENSG00000152583 SPARCL1 8404
## ENSG00000165995 CACNB2 783
## ENSG00000101347 SAMHD1 25939
## ENSG00000120129 DUSP1 1843
## ENSG00000189221 MAOA 4128
## ENSG00000211445 GPX3 2878
You can easily save the results table in a CSV file, which you can then 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 which can be processed by write.csv.
write.csv(as.data.frame(resOrdered), file="results.csv")
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 location of the genes. We
can therefore easily plot our differential expression results in
genomic space. While the results function by default outputs a
DataFrame, using the format argument, we can ask for GRanges or
GRangesList output.
(resGR <- results(dds, format="GRanges"))
## GRanges object with 64102 ranges and 6 metadata columns:
## seqnames ranges strand | baseMean log2FoldChange
## <Rle> <IRanges> <Rle> | <numeric> <numeric>
## ENSG00000000003 X [ 99883667, 99894988] - | 708.602169691234 -0.374249979536954
## ENSG00000000005 X [ 99839799, 99854882] + | 0 <NA>
## ENSG00000000419 20 [ 49551404, 49575092] - | 520.297900552084 0.202155505693114
## ENSG00000000457 1 [169818772, 169863408] - | 237.163036796015 0.036248256467167
## ENSG00000000460 1 [169631245, 169823221] + | 57.9326331250967 -0.0852337113734982
## ... ... ... ... ... ... ...
## LRG_94 LRG_94 [5001, 10428] + | 0 <NA>
## LRG_96 LRG_96 [5001, 91210] + | 0 <NA>
## LRG_97 LRG_97 [5001, 23996] + | 0 <NA>
## LRG_98 LRG_98 [5001, 16750] + | 0 <NA>
## LRG_99 LRG_99 [4975, 11294] + | 0 <NA>
## lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric>
## ENSG00000000003 0.0987310651630226 -3.7906000398051 0.000150283787045845 0.00121761104321994
## ENSG00000000005 <NA> <NA> <NA> <NA>
## ENSG00000000419 0.109298992984101 1.84956421073815 0.0643763851119363 0.188306353032025
## ENSG00000000457 0.136842577842801 0.264890190162943 0.79109405560077 0.907203244592907
## ENSG00000000460 0.24654402419601 -0.345713961842916 0.729557690510272 0.87442237439294
## ... ... ... ... ...
## LRG_94 <NA> <NA> <NA> <NA>
## LRG_96 <NA> <NA> <NA> <NA>
## LRG_97 <NA> <NA> <NA> <NA>
## LRG_98 <NA> <NA> <NA> <NA>
## LRG_99 <NA> <NA> <NA> <NA>
## -------
## seqinfo: 722 sequences (1 circular) from an unspecified genome
resGR$symbol <- convertIDs(names(resGR), "ENSEMBL", "SYMBOL", org.Hs.eg.db)
We will use the Gviz package for plotting the GRanges and associated metadata: the log fold changes due to dexamethasone treatment.
library("Gviz")
The following code chunk specifies a window of 1 million base pairs upstream and downstream from the gene with the smallest p value. We create a subset of our full results, for genes within the window which have a fold change (exclude genes with no counts). We add the gene symbol as a name, if the symbol exists or is not duplicated in our subset.
window <- resGR[topGene] + 1e6
strand(window) <- "*"
hasLFC <- !is.na(resGR$log2FoldChange)
resGRsub <- resGR[resGR %over% window & hasLFC]
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(is.na(resGRsub$padj) | resGRsub$padj > .1,"notsig","sig"))
We can then plot the results using Gviz functions. We create an axis track specifying our location in the genome, a track which will show the genes and their names, colored by significance, and a data track which 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.
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="lightblue", sig="pink")
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 which might be affecting many or all of the genes in the dataset. We can use statistical methods from the sva package to detect such groupings of the samples, and then we can add these to the DESeqDataSet's design, in order to account for them. The SVA software uses the term surrogate variables for the estimated variables which we want to account for in our analysis.
library("sva")
Below we get a matrix of 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
\Robject{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 help at ?svaseq.
idx <- rowMeans(counts(dds)) > 1
dat <- counts(dds)[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$sv
## [,1] [,2]
## [1,] 0.06377538 -0.55406974
## [2,] 0.19103550 -0.56800484
## [3,] -0.11163748 0.01350373
## [4,] 0.51995353 0.12602098
## [5,] -0.43575316 0.06501056
## [6,] -0.63526037 0.09416419
## [7,] 0.20315165 0.37816883
## [8,] 0.20473493 0.44520630
Because we actually do know the cell lines, we can see how well the SVA method did at recovering these variables:
par(mfrow=c(2,1),mar=c(5,5,1,1))
stripchart(svseq$sv[,1] ~ dds$cell,vertical=TRUE)
abline(h=0)
stripchart(svseq$sv[,2] ~ dds$cell,vertical=TRUE)
abline(h=0)
Finally, in order to use SVA to remove any effect on the counts from our surrogate variables, we simply add these two as columns to the DESeqDataSet and add them to the design.
ddssva <- dds
ddssva$SV1 <- svseq$sv[,1]
ddssva$SV2 <- svseq$sv[,2]
design(ddssva) <- ~ SV1 + SV2 + dex
ddssva <- DESeq(ddssva)
head(results(ddssva), 4)
## log2 fold change (MAP): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 4 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000000003 708.6022 -0.34279935 0.1201619 -2.8528131 0.004333409 0.02618765
## ENSG00000000005 0.0000 NA NA NA NA NA
## ENSG00000000419 520.2979 0.21224825 0.1167970 1.8172405 0.069180295 0.21557002
## ENSG00000000457 237.1630 0.02046694 0.1443496 0.1417873 0.887248007 0.95484386
DESeq2 can be used to analyze time series experiments, for example
to find those genes which react in a condition specific manner over
time. Here we demontrate a basic time series analysis with the
fission data package,
which contains gene counts for an RNA-Seq time course of fission
yeast. The yeast were exposed to oxidative stress, and half of the
samples contain a deletion of the gene atf21.
We use a design which models the strain difference at time 0,
the difference over time, and any strain-specific differences over
time (the interaction term strain:minute).
library("fission")
data("fission")
ddsTC <- DESeqDataSet(fission, ~ strain + minute + strain:minute)
The following chunk performs a likelihood ratio test, where we remove the strain-specific differences over time. Genes with small p values from this test are those which, at one or more time points after time 0 showed a strain-specific effect. Note therefore that this will not give small p values to genes which moved up or down over time in the same way in both strains.
ddsTC <- DESeq(ddsTC, test="LRT", reduced = ~ strain + minute)
resTC <- results(ddsTC)
resTC$symbol <- mcols(ddsTC)$symbol
head(resTC[order(resTC$pvalue),],4)
## log2 fold change (MLE): strainmut.minute180
## LRT p-value: '~ strain + minute + strain:minute' vs '~ strain + minute'
## DataFrame with 4 rows and 7 columns
## baseMean log2FoldChange lfcSE stat pvalue padj symbol
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <character>
## SPBC2F12.09c 174.6712 -2.65763737 0.7498270 99.23199 7.671942e-20 5.184698e-16 atf21
## SPAC1002.18 444.5050 -0.05118463 0.2030554 57.72116 3.590886e-11 1.213360e-07 urg3
## SPAC1002.19 336.3732 -0.39267927 0.5749887 43.26296 3.268243e-08 7.362263e-05 urg1
## SPAC1002.17c 261.7731 -1.13882844 0.6072772 39.13718 2.228530e-07 3.765101e-04 urg2
This is just one of the tests which can be applied to time series data. Another option would be to model the counts as a smooth function of time, and to include an interaction term of the condition with the smooth function. It is possible to build such a model using spline basis functions within R.
We can plot the counts for the groups over time using ggplot2, for the gene with the smallest p value, testing for condition-dependent time profile and accounting for differences at time 0. Keep in mind that the interaction terms are the difference between the two groups at a given time after accounting for the difference at time 0.
data <- plotCounts(ddsTC, which.min(resTC$pvalue),
intgroup=c("minute","strain"), returnData=TRUE)
ggplot(data, aes(x=minute, y=count, color=strain, group=strain)) +
geom_point() + stat_smooth(se=FALSE,method="loess") + scale_y_log10()
Wald tests for the log2 fold changes at individual time points can be
investigated using the test argument to results:
resultsNames(ddsTC)
## [1] "Intercept" "strain_mut_vs_wt" "minute_15_vs_0" "minute_30_vs_0"
## [5] "minute_60_vs_0" "minute_120_vs_0" "minute_180_vs_0" "strainmut.minute15"
## [9] "strainmut.minute30" "strainmut.minute60" "strainmut.minute120" "strainmut.minute180"
res30 <- results(ddsTC, name="strainmut.minute30", test="Wald")
res30[which.min(resTC$pvalue),]
## log2 fold change (MLE): strainmut.minute30
## Wald test p-value: strainmut.minute30
## DataFrame with 1 row and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## SPBC2F12.09c 174.6712 -2.601034 0.6314737 -4.11899 3.805364e-05 0.2571665
We can further more cluster significant genes by their profiles.
betas <- coef(ddsTC)
colnames(betas)
## [1] "Intercept" "strain_mut_vs_wt" "minute_15_vs_0" "minute_30_vs_0"
## [5] "minute_60_vs_0" "minute_120_vs_0" "minute_180_vs_0" "strainmut.minute15"
## [9] "strainmut.minute30" "strainmut.minute60" "strainmut.minute120" "strainmut.minute180"
mat <- betas[,-c(1,2)]
mat[mat < -5] <- -5
mat[mat > 5] <- 5
topGenes <- head(order(resTC$pvalue),40)
colors <- colorRampPalette( rev(brewer.pal(9, "PuOr")) )(255)
heatmap.2(mat[ topGenes, ], trace="none", dendrogram="row",
Colv=FALSE, col=colors, mar=c(12,8))
As last part of this document, we call the function sessionInfo, which reports the version numbers of R and all the packages used in this session. It is good practice to always keep such a record as it will help to trace down what has happened in case that an R script ceases to work because the functions have been changed in a newer version of a package. The session information should also always be included in any emails to the Bioconductor support site along with all code used in the analysis.
sessionInfo()
## R version 3.1.1 (2014-07-10)
## Platform: x86_64-unknown-linux-gnu (64-bit)
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8
## [4] LC_COLLATE=C LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C
## [10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] grid stats4 parallel stats graphics grDevices utils datasets methods
## [10] base
##
## other attached packages:
## [1] fission_0.99.4 sva_3.12.0
## [3] mgcv_1.8-3 nlme_3.1-118
## [5] Gviz_1.10.1 ggplot2_1.0.0
## [7] PoiClaClu_1.0.2 RColorBrewer_1.0-5
## [9] gplots_2.14.2 DESeq2_1.6.1
## [11] RcppArmadillo_0.4.450.1.0 Rcpp_0.11.3
## [13] org.Hs.eg.db_3.0.0 RSQLite_1.0.0
## [15] DBI_0.3.1 ShortRead_1.24.0
## [17] BiocParallel_1.0.0 VariantAnnotation_1.12.2
## [19] RNAseqData.HNRNPC.bam.chr14_0.3.2 GenomicAlignments_1.2.0
## [21] Rsamtools_1.18.1 genefilter_1.48.1
## [23] BSgenome.Hsapiens.UCSC.hg19_1.4.0 BSgenome_1.34.0
## [25] rtracklayer_1.26.1 airway_0.99.5
## [27] ALL_1.7.1 TxDb.Hsapiens.UCSC.hg19.knownGene_3.0.0
## [29] GenomicFeatures_1.18.1 AnnotationDbi_1.28.0
## [31] Biobase_2.26.0 GenomicRanges_1.18.1
## [33] GenomeInfoDb_1.2.2 Biostrings_2.34.0
## [35] XVector_0.6.0 IRanges_2.0.0
## [37] S4Vectors_0.4.0 BiocGenerics_0.12.0
## [39] BiocStyle_1.4.1 LearnBioconductor_0.1.6
##
## loaded via a namespace (and not attached):
## [1] BBmisc_1.7 BatchJobs_1.4 BiocInstaller_1.16.0 Formula_1.1-2
## [5] Hmisc_3.14-5 KernSmooth_2.23-13 MASS_7.3-35 Matrix_1.1-4
## [9] R.methodsS3_1.6.1 RCurl_1.95-4.3 XML_3.98-1.1 acepack_1.3-3.3
## [13] annotate_1.44.0 base64enc_0.1-2 biomaRt_2.22.0 biovizBase_1.14.0
## [17] bitops_1.0-6 brew_1.0-6 caTools_1.17.1 checkmate_1.5.0
## [21] cluster_1.15.3 codetools_0.2-9 colorspace_1.2-4 dichromat_2.0-0
## [25] digest_0.6.4 evaluate_0.5.5 fail_1.2 foreach_1.4.2
## [29] foreign_0.8-61 formatR_1.0 gdata_2.13.3 geneplotter_1.44.0
## [33] gtable_0.1.2 gtools_3.4.1 hwriter_1.3.2 iterators_1.0.7
## [37] knitr_1.7 labeling_0.3 lattice_0.20-29 latticeExtra_0.6-26
## [41] locfit_1.5-9.1 markdown_0.7.4 matrixStats_0.10.3 mime_0.2
## [45] munsell_0.4.2 nnet_7.3-8 plyr_1.8.1 proto_0.3-10
## [49] reshape2_1.4 rpart_4.1-8 scales_0.2.4 sendmailR_1.2-1
## [53] splines_3.1.1 stringr_0.6.2 survival_2.37-7 tools_3.1.1
## [57] xtable_1.7-4 zlibbioc_1.12.0