Contents

R version: R version 4.1.0 (2021-05-18)

Bioconductor version: 3.13

Package: 1.16.0

1 Introduction

Bioconductor has many packages which support analysis of high-throughput sequence data, including RNA sequencing (RNA-seq). The packages which we will use in this workflow include core packages maintained by the Bioconductor core team for working with gene annotations (gene and transcript locations in the genome, as well as gene ID lookup). We will also use contributed packages for statistical analysis and visualization of sequencing data. Through scheduled releases every 6 months, the Bioconductor project ensures that all the packages within a release will work together in harmony (hence the “conductor” metaphor). The packages used in this workflow are loaded with the library function and can be installed by following the Bioconductor package installation instructions.

1.1 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 effects (Himes et al. 2014). 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.

2 Preparing quantification input to DESeq2

As input, the count-based statistical methods, such as DESeq2 (Love, Huber, and Anders 2014), edgeR (Robinson, McCarthy, and Smyth 2009), limma with the voom method (Law et al. 2014), DSS (Wu, Wang, and Wu 2013), EBSeq (Leng et al. 2013) and baySeq (Hardcastle and Kelly 2010), expect input data as obtained, e.g., from RNA-seq or another high-throughput sequencing experiment, in the form of a matrix of un-normalized counts. The value in the i-th row and the j-th column of the matrix tells how many reads (or fragments, for paired-end RNA-seq) can be assigned 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 values in the matrix should be counts or estimated counts of sequencing reads/fragments. This is important for DESeq2’s statistical model to hold, as only counts allow assessing the measurement precision correctly. It is important to never provide counts that were pre-normalized for sequencing depth/library size, as the statistical model is most powerful when applied to un-normalized counts, and is designed to account for library size differences internally.

2.1 Transcript quantification and tximport / tximeta

A previous version of this workflow (including the published version) demonstrated how to align reads to the genome and then count the number of reads that are consistent with gene models. We now recommend a faster, alternative pipeline to genome alignment and read counting. This workflow will demonstrate how to import transcript-level quantification data, aggregating to the gene-level with tximport or tximeta. Transcript quantification methods such as Salmon (Patro et al. 2017), kallisto (Bray et al. 2016), or RSEM (Li and Dewey 2011) perform mapping or alignment of reads to reference transcripts, outputting estimated counts per transcript as well as effective transcript lengths which summarize bias effects. After running one of these tools, the tximport (Soneson, Love, and Robinson 2015) or tximeta (Love et al. 2020) packages can be used to assemble estimated count and offset matrices for use with Bioconductor differential gene expression packages, as will be demonstrated below.

A tutorial on how to use the Salmon software for quantifying transcript abundance can be found here. We recommend using the --gcBias flag which estimates a correction factor for systematic biases commonly present in RNA-seq data (Love, Hogenesch, and Irizarry 2016; Patro et al. 2017), unless you are certain that your data do not contain such bias.

The advantages of using the transcript abundance quantifiers in conjunction with tximport/tximeta to produce gene-level count matrices and normalizing offsets, are: (1) this approach corrects for any potential changes in gene length across samples (e.g. from differential isoform usage) (Trapnell et al. 2013); (2) some of these methods are substantially faster and require less memory and disk usage compared to alignment-based methods; and (3) it is possible to avoid discarding those fragments that can align to multiple genes with homologous sequence (Robert and Watson 2015). Note that transcript abundance quantifiers skip the generation of large files which store read alignments, instead producing smaller files which store estimated abundances, counts, and effective lengths per transcript. For more details, see the manuscript describing this approach (Soneson, Love, and Robinson 2015), and the tximport package vignette for software details.

tximeta (Love et al. 2020) extends tximport, offering the same functionality, plus the additional benefit of automatic addition of annotation metadata for commonly used transcriptomes (GENCODE, Ensembl, RefSeq for human and mouse). See the tximeta vignette package vignette for more details. tximeta produces a SummarizedExperiment that can be loaded easily into DESeq2 using the DESeqDataSet function, which will be demonstrated below. We will also discuss the various possible inputs into DESeq2, whether using tximport, tximeta, htseq (Anders, Pyl, and Huber 2015), or a pre-computed count matrix.

2.2 Quantifying with Salmon

As mentioned above, a short tutorial on how to use Salmon can be found here, so instead we will provide the code that was used to quantify the files used in this workflow. Salmon can be conveniently run on a cluster using the Snakemake workflow management system (Köster and Rahmann 2012).

The following Snakemake file was used to quantify the eight samples that were downloaded from the SRA (the SRR identifier is the run identifier, and there was only one run per sample for these eight samples).

DATASETS = ["SRR1039508",
            "SRR1039509",
            "SRR1039512",
            "SRR1039513",
            "SRR1039516",
            "SRR1039517",
            "SRR1039520",
            "SRR1039521"]

SALMON = "/path/to/salmon_0.14.1/bin/salmon"

rule all:
  input: expand("quants/{dataset}/quant.sf", dataset=DATASETS)

rule salmon_quant:
    input:
        r1 = "fastq/{sample}_1.fastq.gz",
        r2 = "fastq/{sample}_2.fastq.gz",
        index = "/path/to/gencode.v29_salmon_0.14.1"
    output:
        "quants/{sample}/quant.sf"
    params:
        dir = "quants/{sample}"
    shell:
        "{SALMON} quant -i {input.index} -l A -p 6 --validateMappings \
         --gcBias --numGibbsSamples 20 -o {params.dir} \
         -1 {input.r1} -2 {input.r2}"

The last line is the key one which runs Salmon. It says to quantify using a specific index, with automatic library type detection, using 6 threads, with the validate mappings setting (this is default in versions of Salmon \(\ge\) 0.99), with GC bias correction, and writing out 20 Gibbs samples (this is optional). The last three arguments specify the output directory and the two paired read files.

The above Snakemake file requires that an index be created at /path/to/gencode.vVV_salmon_X.Y.Z, where VV and X,Y,Z should help specify the release of the reference transcripts and of Salmon. For human and mouse reference transcripts, we recommend to use GENCODE (Frankish et al. 2018).

The Salmon index can be created easily with the following command:

salmon index -t transcripts.fa.gz -i name_of_index

Note: Salmon can also make use of genomic decoy sequences during indexing, as described in Srivastava et al. (2020), which has been demonstrated to improve quantification accuracy. For further details on how to make use of decoy sequences within the Salmon software please consult this note in the Salmon documentation. Here, we will continue mapping reads to the transcriptome without decoy sequences. During indexing, a note will appear that the Salmon index is being built without any decoy sequences.

If the transcripts are downloaded from GENCODE, it is recommended to use something similar to the following command (which simply helps to strip the extra information from the transcript names):

salmon index --gencode -t gencode.v29.transcripts.fa.gz \
  -i gencode.v29_salmon_X.Y.Z

The above Snakemake file can then be used to execute Snakemake in various ways, including submitting multiple jobs to a compute cluster or in the cloud. The above Snakemake file was executed on a cluster with SLURM scheduling, with the following line in a separate job submitted to the cluster:

snakemake -j 4 --latency-wait 30 --cluster "sbatch -N 1 -n 6"

2.3 Reading in data with tximeta

Later in the workflow, we will load an object that contains the quantification data at the gene-level for all eight samples. However, the airway package also contains two quantification directories output by Salmon, in order to demonstrate reading this data into R/Bioconductor. In order to make the data package smaller, the quant.sf files in the quantification directories have been gzipped, so below where you see quant.sf.gz, you would probably use quant.sf on your own machine.

After we demonstrate importing with tximeta, 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 data object.

We first 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 a number of files, including eight BAM files that were used in the previous version of this workflow demonstrating alignment and counting. We will focus on the two directories that are in the quants directory, which contain the output from Salmon on two 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"          "quants"                           
## [13] "sample_table.csv"
list.files(file.path(dir, "quants"))
## [1] "SRR1039508" "SRR1039509"

Typically, we have a table with detailed information for each of our samples that links samples to the associated FASTQ and Salmon directories. 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")
coldata <- read.csv(csvfile, row.names=1, stringsAsFactors=FALSE)
coldata
##            SampleName    cell   dex albut        Run avgLength Experiment
## SRR1039508 GSM1275862  N61311 untrt untrt SRR1039508       126  SRX384345
## SRR1039509 GSM1275863  N61311   trt untrt SRR1039509       126  SRX384346
## SRR1039512 GSM1275866 N052611 untrt untrt SRR1039512       126  SRX384349
## SRR1039513 GSM1275867 N052611   trt untrt SRR1039513        87  SRX384350
## SRR1039516 GSM1275870 N080611 untrt untrt SRR1039516       120  SRX384353
## SRR1039517 GSM1275871 N080611   trt untrt SRR1039517       126  SRX384354
## SRR1039520 GSM1275874 N061011 untrt untrt SRR1039520       101  SRX384357
## SRR1039521 GSM1275875 N061011   trt untrt SRR1039521        98  SRX384358
##               Sample    BioSample
## SRR1039508 SRS508568 SAMN02422669
## SRR1039509 SRS508567 SAMN02422675
## SRR1039512 SRS508571 SAMN02422678
## SRR1039513 SRS508572 SAMN02422670
## SRR1039516 SRS508575 SAMN02422682
## SRR1039517 SRS508576 SAMN02422673
## SRR1039520 SRS508579 SAMN02422683
## SRR1039521 SRS508580 SAMN02422677

To demonstrate loading Salmon quantifiation data into R, we will just work with the two samples that are provided in the airway package. We create a column called names and a column called files:

coldata <- coldata[1:2,]
coldata$names <- coldata$Run
coldata$files <- file.path(dir, "quants", coldata$names, "quant.sf.gz")
file.exists(coldata$files)
## [1] TRUE TRUE

Now we load the tximeta package and run its main function:

library("tximeta")
se <- tximeta(coldata)
## importing quantifications
## reading in files with read_tsv
## 1 2 
## found matching transcriptome:
## [ GENCODE - Homo sapiens - release 29 ]
## useHub=TRUE: checking for TxDb via 'AnnotationHub'
## snapshotDate(): 2021-05-18
## found matching TxDb via 'AnnotationHub'
## loading from cache
## Loading required package: GenomicFeatures
## Loading required package: AnnotationDbi
## generating transcript ranges

If the reference transcriptome checksum was recognized by tximeta (details on this in the tximeta vignette), and if we have a working internet connection, tximeta will locate and download the relevant annotation data from various sources. A few details: the annotation data is only downloaded and parsed once, subsequently it will used locally cached versions of the metadata as needed (if you load data a second time that was quantified against the same reference transcripts). Also, the very first time that one uses tximeta, it will ask you to approve the default cache location (following the paradigm of the cache location used by other R and Bioconductor packages). You can change this location at any point later.

We will discuss what is the structure of the se object in the next section, but we can first just consider the dimensions. Note that tximeta imports data at the transcript level.

dim(se)
## [1] 205870      2
head(rownames(se))
## [1] "ENST00000456328.2" "ENST00000450305.2" "ENST00000488147.1"
## [4] "ENST00000619216.1" "ENST00000473358.1" "ENST00000469289.1"

As this workflow is concerned with gene-level analysis, we will now summarize the transcript-level quantifications to the gene level (which internally makes use of the methods in tximport (Soneson, Love, and Robinson 2015)). The correct transcript-to-gene mapping table is automatically created based on the metadata stored within the se object.

gse <- summarizeToGene(se)
## loading existing TxDb created: 2021-05-21 13:03:39
## obtaining transcript-to-gene mapping from database
## generating gene ranges
## summarizing abundance
## summarizing counts
## summarizing length

Now we can check that the dimensions are reduced and the row IDs are now gene IDs:

dim(gse)
## [1] 58294     2
head(rownames(gse))
## [1] "ENSG00000000003.14" "ENSG00000000005.5"  "ENSG00000000419.12"
## [4] "ENSG00000000457.13" "ENSG00000000460.16" "ENSG00000000938.12"

2.4 DESeq2 import functions

While the above section described use of Salmon and tximeta, there are many possible inputs to DESeq2, each of which have their own dedicated import functions. The following tools can be used generate or compile count data for use with DESeq2: tximport (Soneson, Love, and Robinson 2015), tximeta (Love et al. 2020), htseq-count (Anders, Pyl, and Huber 2015), featureCounts (Liao, Smyth, and Shi 2014), summarizeOverlaps (Lawrence et al. 2013).

function package framework output DESeq2 input function
tximport tximport R/Bioconductor list of matrices DESeqDataSetFromTximport
tximeta tximeta R/Bioconductor SummarizedExperiment DESeqDataSet
htseq-count HTSeq Python files DESeqDataSetFromHTSeq
featureCounts Rsubread R/Bioconductor matrix DESeqDataSetFromMatrix
summarizeOverlaps GenomicAlignments R/Bioconductor SummarizedExperiment DESeqDataSet

We will next describe the class of object created by tximeta which was saved above as se and gse, and how to create a DESeqDataSet object from this for use with DESeq2 (the other functions above also create a DESeqDataSet).

2.5 SummarizedExperiment

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).

The SummarizedExperiment container is diagrammed in the Figure above and discussed in the latest Bioconductor paper (Huber et al. 2015). In our case, tximeta has created an object gse with three matrices: “counts” - the estimated fragment counts for each gene and sample, “abundance” - the estimated transcript abundances in TPM, and “length” - the effective gene lengths which include changes in length due to biases as well as due to transcript usage. The names of the assays can be examined with assayNames, and the assays themselves are stored as assays (a list of matrices). The first matrix in the list can be pulled out via assay. The rowRanges for our object is the GRanges of the genes (from the left-most position of all the transcripts to the right-most position of all the transcripts). The component parts of the SummarizedExperiment are accessed with an R function of the same name: assay (or assays), rowRanges and colData.

We now will load the full count matrix corresponding to all samples and all data, which is provided in the airway package, and will continue the analysis with the full data object. We can investigate this SummarizedExperiment object by looking at the matrices in the assays slot, the phenotypic data about the samples in colData slot, and the data about the genes in the rowRanges slot.

data(gse)
gse
## class: RangedSummarizedExperiment 
## dim: 58294 8 
## metadata(6): tximetaInfo quantInfo ... txomeInfo txdbInfo
## assays(3): counts abundance length
## rownames(58294): ENSG00000000003.14 ENSG00000000005.5 ...
##   ENSG00000285993.1 ENSG00000285994.1
## rowData names(1): gene_id
## colnames(8): SRR1039508 SRR1039509 ... SRR1039520 SRR1039521
## colData names(3): names donor condition

The counts are the first matrix, so we can examine them with just assay:

assayNames(gse)
## [1] "counts"    "abundance" "length"
head(assay(gse), 3)
##                    SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516
## ENSG00000000003.14    708.164    467.962    900.992    424.368   1188.295
## ENSG00000000005.5       0.000      0.000      0.000      0.000      0.000
## ENSG00000000419.12    455.000    510.000    604.000    352.000    583.000
##                    SRR1039517 SRR1039520 SRR1039521
## ENSG00000000003.14   1090.668    805.929    599.337
## ENSG00000000005.5       0.000      0.000      0.000
## ENSG00000000419.12    773.999    409.999    499.000
colSums(assay(gse))
## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520 
##   21100805   19298584   26145537   15688246   25268618   31891456   19683767 
## SRR1039521 
##   21813903

The rowRanges, when printed, shows the ranges for the first five and last five genes:

rowRanges(gse)
## GRanges object with 58294 ranges and 1 metadata column:
##                      seqnames              ranges strand |            gene_id
##                         <Rle>           <IRanges>  <Rle> |        <character>
##   ENSG00000000003.14     chrX 100627109-100639991      - | ENSG00000000003.14
##    ENSG00000000005.5     chrX 100584802-100599885      + |  ENSG00000000005.5
##   ENSG00000000419.12    chr20   50934867-50958555      - | ENSG00000000419.12
##   ENSG00000000457.13     chr1 169849631-169894267      - | ENSG00000000457.13
##   ENSG00000000460.16     chr1 169662007-169854080      + | ENSG00000000460.16
##                  ...      ...                 ...    ... .                ...
##    ENSG00000285990.1    chr14   19244904-19269380      - |  ENSG00000285990.1
##    ENSG00000285991.1     chr6 149817937-149896011      - |  ENSG00000285991.1
##    ENSG00000285992.1     chr8   47129262-47132628      + |  ENSG00000285992.1
##    ENSG00000285993.1    chr18   46409197-46410645      - |  ENSG00000285993.1
##    ENSG00000285994.1    chr10   12563151-12567351      + |  ENSG00000285994.1
##   -------
##   seqinfo: 25 sequences (1 circular) from hg38 genome

The rowRanges also contains metadata about the sequences (chromosomes in our case) in the seqinfo slot:

seqinfo(rowRanges(gse))
## Seqinfo object with 25 sequences (1 circular) from hg38 genome:
##   seqnames seqlengths isCircular genome
##   chr1      248956422      FALSE   hg38
##   chr2      242193529      FALSE   hg38
##   chr3      198295559      FALSE   hg38
##   chr4      190214555      FALSE   hg38
##   chr5      181538259      FALSE   hg38
##   ...             ...        ...    ...
##   chr21      46709983      FALSE   hg38
##   chr22      50818468      FALSE   hg38
##   chrX      156040895      FALSE   hg38
##   chrY       57227415      FALSE   hg38
##   chrM          16569       TRUE   hg38

The colData for the SummarizedExperiment reflects the data.frame that was provided to the tximeta function for importing the quantification data. Here we can see that there are columns indicating sample names, as well as the donor ID, and the treatment condition (treated with dexamethasone or untreated).

colData(gse)
## DataFrame with 8 rows and 3 columns
##                 names    donor     condition
##              <factor> <factor>      <factor>
## SRR1039508 SRR1039508  N61311  Untreated    
## SRR1039509 SRR1039509  N61311  Dexamethasone
## SRR1039512 SRR1039512  N052611 Untreated    
## SRR1039513 SRR1039513  N052611 Dexamethasone
## SRR1039516 SRR1039516  N080611 Untreated    
## SRR1039517 SRR1039517  N080611 Dexamethasone
## SRR1039520 SRR1039520  N061011 Untreated    
## SRR1039521 SRR1039521  N061011 Dexamethasone

2.6 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 edgeR (Robinson, McCarthy, and Smyth 2009), limma with the voom method (Law et al. 2014), DSS (Wu, Wang, and Wu 2013), EBSeq (Leng et al. 2013) and baySeq (Hardcastle and Kelly 2010). Schurch et al. (2016) compared performance of different statistical methods for RNA-seq using a large number of biological replicates and can help users to decide which tools make sense to use, and how many biological replicates are necessary to obtain a certain sensitivity. We will continue using DESeq2 (Love, Huber, and Anders 2014). 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.

3 The DESeqDataSet object, sample information and the design formula

Bioconductor software packages often define and use a custom class for storing data that 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. Additionally, the core Bioconductor classes provide useful functionality: for example, subsetting or reordering the rows or columns of a SummarizedExperiment automatically subsets or reorders the associated rowRanges and colData, which can help to prevent accidental sample swaps that would otherwise lead to spurious results. With SummarizedExperiment this is all taken care of behind the scenes.

In DESeq2, the custom class is called DESeqDataSet. It is built on top of the SummarizedExperiment class, and it is easy to convert SummarizedExperiment objects into DESeqDataSet objects, which we show below. One of the two main differences is that the assay slot is instead accessed using the counts accessor function, and the DESeqDataSet 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 columns in the sample information table (colData) specify the experimental design and how these factors should be used in the analysis.

First, let’s examine the columns of the colData of gse. We can see each of the columns just using the $ directly on the SummarizedExperiment or DESeqDataSet.

gse$donor
## [1] N61311  N61311  N052611 N052611 N080611 N080611 N061011 N061011
## Levels: N052611 N061011 N080611 N61311
gse$condition
## [1] Untreated     Dexamethasone Untreated     Dexamethasone Untreated    
## [6] Dexamethasone Untreated     Dexamethasone
## Levels: Untreated Dexamethasone

We can rename our variables if we want. Let’s use cell to denote the donor cell line, and dex to denote the treatment condition.

gse$cell <- gse$donor
gse$dex <- gse$condition

We can also change the names of the levels. It is critical when one renames levels to not change the order. Here we will rename "Untreated" as "untrt" and "Dexamethasone" as "trt":

levels(gse$dex)
## [1] "Untreated"     "Dexamethasone"
# when renaming levels, the order must be preserved!
levels(gse$dex) <- c("untrt", "trt")

The simplest design formula for differential expression would be ~ condition, where condition is a column in colData(dds) that specifies which of two (or more groups) the samples belong to. For the airway experiment, we will specify ~ cell + dex meaning that we want to test for the effect of dexamethasone (dex) controlling for the effect of different cell line (cell).

Note: it is prefered in R that the first level of a factor be the reference level (e.g. control, or untreated samples). In this case, when the colData table was assembled the untreated samples were already set as the reference, but if this were not the case we could use relevel as shown below. While levels(...) <- above was simply for renaming the character strings associated with levels, relevel is a very different function, which decides how the variables will be coded, and how contrasts will be computed. For a two-group comparison, the use of relevel to change the reference level would flip the sign of a coefficient associated with a contrast between the two groups.

library("magrittr")
gse$dex %<>% relevel("untrt")
gse$dex
## [1] untrt trt   untrt trt   untrt trt   untrt trt  
## Levels: untrt trt

%<>% is the compound assignment pipe-operator from the magrittr package, the above line of code is a concise way of saying:

gse$dex <- relevel(gse$dex, "untrt")

For running DESeq2 models, you can use R’s formula notation to express any fixed-effects experimental design. Note that DESeq2 uses the same formula notation as, for instance, the lm function of base R. If the research aim is to determine for which genes the effect of treatment is different across groups, then interaction terms can be included and tested using a design such as ~ group + treatment + group:treatment. See the manual page for ?results for more examples. We will show how to use an interaction term to test for condition-specific changes over time in a time course example below.

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.

3.1 Starting from SummarizedExperiment

Again, we can quickly check the millions of fragments that could be mapped by Salmon to the genes (the second argument of round tells how many decimal points to keep).

round( colSums(assay(gse)) / 1e6, 1 )
## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520 
##       21.1       19.3       26.1       15.7       25.3       31.9       19.7 
## SRR1039521 
##       21.8

Once we have our fully annotated SummarizedExperiment object, we can construct a DESeqDataSet object from it that will then form the starting point of the analysis. We add an appropriate design for the analysis:

library("DESeq2")
dds <- DESeqDataSet(gse, design = ~ cell + dex)

3.2 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 package (Liao, Smyth, and Shi 2014).

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 <- round(assays(gse)[["counts"]])
head(countdata, 3)
##                    SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516
## ENSG00000000003.14        708        468        901        424       1188
## ENSG00000000005.5           0          0          0          0          0
## ENSG00000000419.12        455        510        604        352        583
##                    SRR1039517 SRR1039520 SRR1039521
## ENSG00000000003.14       1091        806        599
## ENSG00000000005.5           0          0          0
## ENSG00000000419.12        774        410        499

In this count matrix, each row represents a gene, each column a sequenced RNA library, and the values give the estimated counts of fragments that were probabilistically assigned to the respective gene in each library by Salmon. We also have information on each of the samples (the columns of the count matrix). If you’ve imported the count data in some other way, for example loading a pre-computed count matrix, it is very important to check manually that the columns of the count matrix correspond to the rows of the sample information table.

coldata <- colData(gse)

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

  • countdata: a table with the fragment counts
  • coldata: a table with information about the samples

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)

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

4 Exploratory analysis and visualization

There are two separate paths in this workflow; the one we will see first involves transformations of the counts in order to visually explore sample relationships. In the second part, we will go back to the original raw counts for statistical testing. This is critical because the statistical testing methods rely on original count data (not scaled or transformed) for calculating the precision of measurements.

4.1 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 apply the most minimal filtering rule: removing rows of the DESeqDataSet that have no counts, or only a single count across all samples. Additional weighting/filtering to improve power is applied at a later step in the workflow.

nrow(dds)
## [1] 58294
keep <- rowSums(counts(dds)) > 1
dds <- dds[keep,]
nrow(dds)
## [1] 31604

For some datasets, it may make sense to perform additional filtering. For example, one can specify that at least 3 samples have a count of 10 or higher. One recommendation for the number of samples would be set to the smallest group size. Such a rule could be specified by creating a logic vector and subsetting the dds as above. Here is an example of another rule we could have used (here not used for filtering):

# at least 3 samples with a count of 10 or higher
keep <- rowSums(counts(dds) >= 10) >= 3

4.2 The variance stabilizing transformation and the rlog

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 counts, however, the expected variance grows with the mean. For example, if one performs PCA directly on a matrix of counts or normalized counts (e.g. correcting for differences in sequencing depth), the resulting plot typically depends mostly on the genes with highest counts 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 pseudocount of 1; however, depending on the choice of pseudocount, now the genes with the very lowest counts will contribute a great deal of noise to the resulting plot, because taking the logarithm of small counts actually inflates their variance. We can quickly show this property of counts with some simulated data (here, Poisson counts with a range of lambda from 0.1 to 100). We plot the standard deviation of each row (genes) against the mean:

lambda <- 10^seq(from = -1, to = 2, length = 1000)
cts <- matrix(rpois(1000*100, lambda), ncol = 100)
library("vsn")
meanSdPlot(cts, ranks = FALSE)

And for logarithm-transformed counts:

log.cts.one <- log2(cts + 1)
meanSdPlot(log.cts.one, ranks = FALSE)

The logarithm with a small pseudocount amplifies differences when the values are close to 0. The low count genes with low signal-to-noise ratio will overly contribute to sample-sample distances and PCA plots.

As a solution, DESeq2 offers two transformations for count data that stabilize the variance across the mean: the variance stabilizing transformation (VST) for negative binomial data with a dispersion-mean trend (Anders and Huber 2010), implemented in the vst function, and the regularized-logarithm transformation or rlog (Love, Huber, and Anders 2014).

For genes with high counts, both the VST and the rlog will give similar result to the ordinary log2 transformation of normalized counts. For genes with lower counts, however, the values are shrunken towards a middle value. The VST or rlog-transformed data then become approximately homoskedastic (more flat trend in the meanSdPlot), and can be used directly for computing distances between samples, making PCA plots, or as input to downstream methods which perform best with homoskedastic data.

Which transformation to choose? The VST is much faster to compute and is less sensitive to high count outliers than the rlog. The rlog tends to work well on small datasets (n < 30), potentially outperforming the VST when there is a wide range of sequencing depth across samples (an order of magnitude difference). We therefore recommend the VST for medium-to-large datasets (n > 30). You can perform both transformations and compare the meanSdPlot or PCA plots generated, as described below.

Note that the two transformations offered by DESeq2 are 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.

Both vst and rlog return a DESeqTransform object which is based on the SummarizedExperiment class. The transformed values are no longer counts, and are stored in the assay slot. The colData that was attached to dds is still accessible:

vsd <- vst(dds, blind = FALSE)
head(assay(vsd), 3)
##                    SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516
## ENSG00000000003.14  10.105781   9.852029  10.169726   9.991545  10.424865
## ENSG00000000419.12   9.692244   9.923647   9.801921   9.798653   9.763455
## ENSG00000000457.13   9.449592   9.312186   9.362754   9.459168   9.281415
##                    SRR1039517 SRR1039520 SRR1039521
## ENSG00000000003.14  10.194490  10.315814  10.002177
## ENSG00000000419.12   9.874703   9.683211   9.845507
## ENSG00000000457.13   9.395937   9.477971   9.477027
colData(vsd)
## DataFrame with 8 rows and 5 columns
##                 names    donor     condition     cell      dex
##              <factor> <factor>      <factor> <factor> <factor>
## SRR1039508 SRR1039508  N61311  Untreated      N61311     untrt
## SRR1039509 SRR1039509  N61311  Dexamethasone  N61311     trt  
## SRR1039512 SRR1039512  N052611 Untreated      N052611    untrt
## SRR1039513 SRR1039513  N052611 Dexamethasone  N052611    trt  
## SRR1039516 SRR1039516  N080611 Untreated      N080611    untrt
## SRR1039517 SRR1039517  N080611 Dexamethasone  N080611    trt  
## SRR1039520 SRR1039520  N061011 Untreated      N061011    untrt
## SRR1039521 SRR1039521  N061011 Dexamethasone  N061011    trt

Again, for the rlog:

rld <- rlog(dds, blind = FALSE)
head(assay(rld), 3)
##                    SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516
## ENSG00000000003.14   9.482613   9.172197   9.558383   9.346001   9.851349
## ENSG00000000419.12   8.860186   9.150196   9.000042   8.995902   8.951327
## ENSG00000000457.13   8.354790   8.166700   8.236582   8.366693   8.121781
##                    SRR1039517 SRR1039520 SRR1039521
## ENSG00000000003.14   9.587602   9.727248   9.357876
## ENSG00000000419.12   9.091075   8.848782   9.054384
## ENSG00000000457.13   8.282307   8.392384   8.391023

In the above function calls, we specified blind = FALSE, which means that differences between cell lines and treatment (the variables in the design) will not contribute to the expected variance-mean trend of the experiment. 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).

To show the effect of the transformation, in the figure below 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 VST and 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 vst and rlog.

library("dplyr")
library("ggplot2")

dds <- estimateSizeFactors(dds)

df <- bind_rows(
  as_data_frame(log2(counts(dds, normalized=TRUE)[, 1:2]+1)) %>%
         mutate(transformation = "log2(x + 1)"),
  as_data_frame(assay(vsd)[, 1:2]) %>% mutate(transformation = "vst"),
  as_data_frame(assay(rld)[, 1:2]) %>% mutate(transformation = "rlog"))
  
colnames(df)[1:2] <- c("x", "y")  

lvls <- c("log2(x + 1)", "vst", "rlog")
df$transformation <- factor(df$transformation, levels=lvls)

ggplot(df, aes(x = x, y = y)) + geom_hex(bins = 80) +
  coord_fixed() + facet_grid( . ~ transformation)

Scatterplot of transformed counts from two samples. Shown are scatterplots using the log2 transform of normalized counts (left), using the VST (middle), and using the rlog (right). While the rlog is on roughly the same scale as the log2 counts, the VST has a upward shift for the smaller values. It is the differences between samples (deviation from y=x in these scatterplots) which will contribute to the distance calculations and the PCA plot.

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

4.3 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 VST 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(vsd)))
sampleDists
##            SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517
## SRR1039509   39.42362                                                       
## SRR1039512   32.37620   44.93748                                            
## SRR1039513   51.09677   37.18799   41.79886                                 
## SRR1039516   35.59642   47.54671   34.83458   52.05265                      
## SRR1039517   51.26314   41.58572   46.89609   40.67315   39.74268           
## SRR1039520   32.38578   46.96000   30.35980   48.08669   37.07106   50.38349
## SRR1039521   51.49108   37.57383   47.17283   31.45899   52.62276   41.35941
##            SRR1039520
## SRR1039509           
## SRR1039512           
## SRR1039513           
## SRR1039516           
## SRR1039517           
## SRR1039520           
## SRR1039521   43.01502

We visualize the distances in a heatmap in a figure below, using the function pheatmap from the pheatmap package.

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( vsd$dex, vsd$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)

Heatmap of sample-to-sample distances using the variance stabilizing transformed values.

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 (Witten 2011), 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 heatmap in a Figure below.

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

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

4.4 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 below). 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).

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

PCA plot using the VST data. Each unique combination of treatment and cell line is given its own color.

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 package (Wickham 2009). 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.

pcaData <- plotPCA(vsd, intgroup = c( "dex", "cell"), returnData = TRUE)
pcaData
##                   PC1        PC2         group   dex    cell       name
## SRR1039508 -14.311369 -2.6000421  untrt:N61311 untrt  N61311 SRR1039508
## SRR1039509   8.058574 -0.7500532    trt:N61311   trt  N61311 SRR1039509
## SRR1039512  -9.404122 -4.3920761 untrt:N052611 untrt N052611 SRR1039512
## SRR1039513  14.497842 -4.1323833   trt:N052611   trt N052611 SRR1039513
## SRR1039516 -12.365055 11.2109581 untrt:N080611 untrt N080611 SRR1039516
## SRR1039517   9.343946 14.9115160   trt:N080611   trt N080611 SRR1039517
## SRR1039520 -10.852633 -7.7618618 untrt:N061011 untrt N061011 SRR1039520
## SRR1039521  15.032816 -6.4860576   trt:N061011   trt N061011 SRR1039521
percentVar <- round(100 * attr(pcaData, "percentVar"))

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

ggplot(pcaData, aes(x = PC1, y = PC2, color = dex, shape = cell)) +
  geom_point(size =3) +
  xlab(paste0("PC1: ", percentVar[1], "% variance")) +
  ylab(paste0("PC2: ", percentVar[2], "% variance")) +
  coord_fixed() +
  ggtitle("PCA with VST data")

PCA plot using the VST values with custom ggplot2 code. Here we specify cell line (plotting symbol) and dexamethasone treatment (color).

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.

4.5 PCA plot using Generalized PCA

Another technique for performing dimension reduction on data that is not Normally distributed (e.g. over-dispersed count data) is generalized principal component analysis, or GLM-PCA, (Townes et al. 2019) as implemented in the CRAN package glmpca. This package takes as input the count matrix, as well as the number of latent dimensions to fit (here, we specify 2). As stated by Townes et al. (2019):

…we propose the use of GLM-PCA, a generalization of PCA to exponential family likelihoods. GLM-PCA operates on raw counts, avoiding the pitfalls of normalization. We also demonstrate that applying PCA to deviance or Pearson residuals provides a useful and fast approximation to GLM-PCA.

library("glmpca")
gpca <- glmpca(counts(dds), L=2)
gpca.dat <- gpca$factors
gpca.dat$dex <- dds$dex
gpca.dat$cell <- dds$cell
ggplot(gpca.dat, aes(x = dim1, y = dim2, color = dex, shape = cell)) +
  geom_point(size =3) + coord_fixed() + ggtitle("glmpca - Generalized PCA")

4.6 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 VST data and plot these in a figure below.

mds <- as.data.frame(colData(vsd))  %>%
         cbind(cmdscale(sampleDistMatrix))
ggplot(mds, aes(x = `1`, y = `2`, color = dex, shape = cell)) +
  geom_point(size = 3) + coord_fixed() + ggtitle("MDS with VST data")

MDS plot using VST data.

In a figure below we show the same plot for the PoissonDistance:

mdsPois <- as.data.frame(colData(dds)) %>%
   cbind(cmdscale(samplePoisDistMatrix))
ggplot(mdsPois, aes(x = `1`, y = `2`, color = dex, shape = cell)) +
  geom_point(size = 3) + coord_fixed() + ggtitle("MDS with PoissonDistances")

MDS plot using the Poisson Distance.

5 Differential expression analysis

5.1 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.

5.2 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. The comparison is printed at the top of the output: dex trt vs untrt.

res <- results(dds)
res
## log2 fold change (MLE): dex trt vs untrt 
## Wald test p-value: dex trt vs untrt 
## DataFrame with 31604 rows and 6 columns
##                      baseMean log2FoldChange     lfcSE      stat      pvalue
##                     <numeric>      <numeric> <numeric> <numeric>   <numeric>
## ENSG00000000003.14 739.940717     -0.3611537  0.106869 -3.379419 0.000726392
## ENSG00000000419.12 511.735722      0.2063147  0.128665  1.603509 0.108822318
## ENSG00000000457.13 314.194855      0.0378308  0.158633  0.238479 0.811509461
## ENSG00000000460.16  79.793622     -0.1152590  0.314991 -0.365912 0.714430444
## ENSG00000000938.12   0.307267     -1.3691185  3.503764 -0.390757 0.695977205
## ...                       ...            ...       ...       ...         ...
## ENSG00000285979.1   38.353886      0.3423657  0.359511  0.952310    0.340940
## ENSG00000285987.1    1.562508      0.7064145  1.547295  0.456548    0.647996
## ENSG00000285990.1    0.642315      0.3647333  3.433276  0.106235    0.915396
## ENSG00000285991.1   11.276284     -0.1165515  0.748601 -0.155692    0.876275
## ENSG00000285994.1    3.651041     -0.0960094  1.068660 -0.089841    0.928414
##                          padj
##                     <numeric>
## ENSG00000000003.14 0.00531137
## ENSG00000000419.12 0.29318870
## ENSG00000000457.13 0.92255697
## ENSG00000000460.16 0.87298038
## ENSG00000000938.12         NA
## ...                       ...
## ENSG00000285979.1    0.600750
## ENSG00000285987.1          NA
## ENSG00000285990.1          NA
## ENSG00000285991.1    0.952921
## ENSG00000285994.1          NA

We could have equivalently produced this results table with the following more specific command. Because dex is the last variable in the design, we could optionally leave off the contrast argument to extract the comparison of the two levels of dex.

res <- results(dds, contrast=c("dex","trt","untrt"))

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 c..
## log2FoldChange      results log2 fold change (ML..
## lfcSE               results standard error: dex ..
## stat                results Wald statistic: dex ..
## pvalue              results Wald test p-value: d..
## padj                results   BH adjusted p-values

The first column, baseMean, is a just the average of the normalized count values, divided by the 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 \(2^{1.5} \approx 2.82\).

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 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 31604 with nonzero total read count
## adjusted p-value < 0.1
## LFC > 0 (up)       : 2373, 7.5%
## LFC < 0 (down)     : 1949, 6.2%
## outliers [1]       : 0, 0%
## low counts [2]     : 14706, 47%
## (mean count < 9)
## [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:

  • lower the false discovery rate threshold (the threshold on padj in the results table)
  • raise the log2 fold change threshold from 0 using the lfcThreshold argument of results

If we lower the false discovery rate threshold, we should also inform the results() function about it, so that the function can use this threshold for the optimal independent filtering that it performs:

res.05 <- results(dds, alpha = 0.05)
table(res.05$padj < 0.05)
## 
## FALSE  TRUE 
## 13357  3541

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 \(2^1 = 2\).

resLFC1 <- results(dds, lfcThreshold=1)
table(resLFC1$padj < 0.1)
## 
## FALSE  TRUE 
## 16687   211

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.

5.3 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 (MLE): cell N061011 vs N61311 
## Wald test p-value: cell N061011 vs N61311 
## DataFrame with 31604 rows and 6 columns
##                      baseMean log2FoldChange     lfcSE       stat    pvalue
##                     <numeric>      <numeric> <numeric>  <numeric> <numeric>
## ENSG00000000003.14 739.940717       0.270945  0.152171   1.780534 0.0749886
## ENSG00000000419.12 511.735722      -0.071831  0.182817  -0.392912 0.6943842
## ENSG00000000457.13 314.194855       0.179881  0.225122   0.799036 0.4242696
## ENSG00000000460.16  79.793622      -0.119482  0.441594  -0.270570 0.7867217
## ENSG00000000938.12   0.307267       0.000000  4.997580   0.000000 1.0000000
## ...                       ...            ...       ...        ...       ...
## ENSG00000285979.1   38.353886      0.0589757  0.512391  0.1150989  0.908367
## ENSG00000285987.1    1.562508      1.0216804  2.201861  0.4640078  0.642642
## ENSG00000285990.1    0.642315     -3.0956404  4.852715 -0.6379193  0.523526
## ENSG00000285991.1   11.276284     -0.8779628  1.046963 -0.8385804  0.401705
## ENSG00000285994.1    3.651041     -0.0192351  1.513236 -0.0127112  0.989858
##                         padj
##                    <numeric>
## ENSG00000000003.14  0.378828
## ENSG00000000419.12  0.936703
## ENSG00000000457.13  0.820733
## ENSG00000000460.16  0.960662
## ENSG00000000938.12        NA
## ...                      ...
## ENSG00000285979.1    0.98371
## ENSG00000285987.1         NA
## ENSG00000285990.1         NA
## ENSG00000285991.1         NA
## ENSG00000285994.1         NA

There are additional ways to build results tables for certain comparisons after running DESeq once. If results for an interaction term are desired, the name argument of results should be used. Please see the help page for the results function for details on the additional ways to build results tables. In particular, the Examples section of the help page for results gives some pertinent examples.

5.4 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 5170 genes with a p value below 0.05 among the 31604 genes for which the test succeeded in reporting a p value:

sum(res$pvalue < 0.05, na.rm=TRUE)
## [1] 5170
sum(!is.na(res$pvalue))
## [1] 31604

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 1580 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 1580 / 5170 = 31% false positives.

DESeq2 uses the Benjamini-Hochberg (BH) adjustment (Benjamini and Hochberg 1995) 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] 4322

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 (MLE): dex trt vs untrt 
## Wald test p-value: dex trt vs untrt 
## DataFrame with 6 rows and 6 columns
##                    baseMean log2FoldChange     lfcSE      stat      pvalue
##                   <numeric>      <numeric> <numeric> <numeric>   <numeric>
## ENSG00000216490.3   42.3007       -5.72483  1.475652  -3.87952 1.04661e-04
## ENSG00000267339.5   30.5206       -5.39781  0.773017  -6.98278 2.89390e-12
## ENSG00000257542.5   10.0399       -5.25991  1.282001  -4.10289 4.08015e-05
## ENSG00000146006.7   61.6448       -4.49504  0.663821  -6.77147 1.27484e-11
## ENSG00000108700.4   14.6324       -4.09069  0.941842  -4.34328 1.40369e-05
## ENSG00000213240.8   12.0962       -3.87313  1.274133  -3.03981 2.36725e-03
##                          padj
##                     <numeric>
## ENSG00000216490.3 9.87853e-04
## ENSG00000267339.5 9.45863e-11
## ENSG00000257542.5 4.30646e-04
## ENSG00000146006.7 3.82632e-10
## ENSG00000108700.4 1.66687e-04
## ENSG00000213240.8 1.44987e-02

…and with the strongest up-regulation:

head(resSig[ order(resSig$log2FoldChange, decreasing = TRUE), ])
## log2 fold change (MLE): dex trt vs untrt 
## Wald test p-value: dex trt vs untrt 
## DataFrame with 6 rows and 6 columns
##                     baseMean log2FoldChange     lfcSE      stat      pvalue
##                    <numeric>      <numeric> <numeric> <numeric>   <numeric>
## ENSG00000254692.1    62.2302       10.20714   3.37706   3.02250 2.50700e-03
## ENSG00000179593.15   67.0895        9.50515   1.07705   8.82513 1.09334e-18
## ENSG00000268173.3    46.4370        8.40438   3.38506   2.48279 1.30358e-02
## ENSG00000224712.12   35.5607        7.16686   2.16476   3.31070 9.30628e-04
## ENSG00000109906.13  438.1940        6.37750   0.31381  20.32276 8.08934e-92
## ENSG00000257663.1    24.3946        6.34758   2.09531   3.02942 2.45024e-03
##                           padj
##                      <numeric>
## ENSG00000254692.1  1.52167e-02
## ENSG00000179593.15 6.81746e-17
## ENSG00000268173.3  5.94385e-02
## ENSG00000224712.12 6.55240e-03
## ENSG00000109906.13 1.24267e-88
## ENSG00000257663.1  1.49151e-02

6 Plotting results

6.1 Counts plot

A quick way to visualize the counts for a particular gene is to use the plotCounts function that takes as arguments the DESeqDataSet, a gene name, and the group over which to plot the counts (figure below).

topGene <- rownames(res)[which.min(res$padj)]
plotCounts(dds, gene = topGene, intgroup=c("dex"))

Normalized counts for a single gene over treatment group.

We can also make custom plots using the ggplot function from the ggplot2 package (figures below).

library("ggbeeswarm")
geneCounts <- plotCounts(dds, gene = topGene, intgroup = c("dex","cell"),
                         returnData = TRUE)
ggplot(geneCounts, aes(x = dex, y = count, color = cell)) +
  scale_y_log10() +  geom_beeswarm(cex = 3)

ggplot(geneCounts, aes(x = dex, y = count, color = cell, group = cell)) +
  scale_y_log10() + geom_point(size = 3) + geom_line()

Normalized counts with lines connecting cell lines. Note that the DESeq test actually takes into account the cell line effect, so this figure more closely depicts the difference being tested.

6.2 MA-plot

An MA-plot (Dudoit et al. 2002) provides a useful overview for the distribution of the estimated coefficients in the model, e.g. the comparisons of interest, across all genes. On the y-axis, the “M” stands for “minus” – subtraction of log values is equivalent to the log of the ratio – and on the x-axis, the “A” stands for “average”. You may hear this plot also referred to as a mean-difference plot, or a Bland-Altman plot.

Before making the MA-plot, we use the lfcShrink function to shrink the log2 fold changes for the comparison of dex treated vs untreated samples. There are three types of shrinkage estimators in DESeq2, which are covered in the DESeq2 vignette. Here we specify the apeglm method for shrinking coefficients, which is good for shrinking the noisy LFC estimates while giving low bias LFC estimates for true large differences (Zhu, Ibrahim, and Love 2018). To use apeglm we specify a coefficient from the model to shrink, either by name or number as the coefficient appears in resultsNames(dds).

library("apeglm")
resultsNames(dds)
## [1] "Intercept"               "cell_N061011_vs_N052611"
## [3] "cell_N080611_vs_N052611" "cell_N61311_vs_N052611" 
## [5] "dex_trt_vs_untrt"
res <- lfcShrink(dds, coef="dex_trt_vs_untrt", type="apeglm")
plotMA(res, ylim = c(-5, 5))

If it is necessary to specify a contrast not represented in resultsNames(dds), either of the other two shrinkage methods can be used, or in some cases, re-factoring the relevant variables and running nbinomWaldTest followed by lfcShrink is sufficient. See the DESeq2 vignette for more details.

An MA-plot of changes induced by treatment. 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. 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 uses a Bayesian procedure to moderate (or “shrink”) log2 fold changes from genes with very low counts and highly variable counts, as can be seen by the narrowing of the vertical spread of points on the left side of the MA-plot. As shown above, the lfcShrink function performs this operation. For a detailed explanation of the rationale of moderated fold changes, please see the DESeq2 paper (Love, Huber, and Anders 2014).

If we had not used statistical moderation to shrink the noisy log2 fold changes, we would have instead seen the following plot:

res.noshr <- results(dds, name="dex_trt_vs_untrt")
plotMA(res.noshr, ylim = c(-5, 5))

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))
topGene <- rownames(res)[which.min(res$padj)]
with(res[topGene, ], {
  points(baseMean, log2FoldChange, col="dodgerblue", cex=2, lwd=2)
  text(baseMean, log2FoldChange, topGene, pos=2, col="dodgerblue")
})

Another useful diagnostic plot is the histogram of the p values (figure below). This plot is best formed by excluding genes with very small counts, which otherwise generate spikes in the histogram.

hist(res$pvalue[res$baseMean > 1], breaks = 0:20/20,
     col = "grey50", border = "white")

Histogram of p values for genes with mean normalized count larger than 1.

6.3 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 VST data.

library("genefilter")
topVarGenes <- head(order(rowVars(assay(vsd)), 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 below). We provide a data.frame that instructs the pheatmap function how to label the columns.

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

Heatmap of relative VST-transformed values across samples. Treatment status and cell line information are shown with colored bars at the top of the heatmap. Blocks of genes that covary across patients. Note that a set of genes in the heatmap are separating the N061011 cell line from the others, and there is another set of genes for which the dexamethasone treated samples have higher gene expression.

6.4 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 below).

qs <- c(0, quantile(resLFC1$baseMean[resLFC1$baseMean > 0], 0:6/6))
bins <- cut(resLFC1$baseMean, qs)
levels(bins) <- paste0("~", round(signif((qs[-1] + qs[-length(qs)])/2, 2)))
fractionSig <- tapply(resLFC1$pvalue, bins, function(p)
                          mean(p < .05, na.rm = TRUE))
barplot(fractionSig, xlab = "mean normalized count",
                     ylab = "fraction of small p values")

The ratio of small p values for genes binned by mean normalized count. The p values are from a test of log2 fold change greater than 1 or less than -1. This plot demonstrates that genes with very low mean count have little or no power, and are best excluded from testing.

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 filtering (Bourgon, Gentleman, and Huber 2010).

6.5 Independent Hypothesis Weighting

A generalization of the idea of p value filtering is to weight hypotheses to optimize power. A Bioconductor package, IHW is available that implements the method of Independent Hypothesis Weighting (Ignatiadis et al. 2016). See the DESeq2 package vignette for an example of using IHW in combination with DESeq2. In particular, the following (here, un-evaluated) code chunk can be used to perform IHW in lieu of independent filtering described above.

library("IHW")
res.ihw <- results(dds, filterFun=ihw)

7 Annotating and exporting results

Our result table so far only contains the Ensembl gene IDs, but alternative gene names may be more informative for interpretation. 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] "ACCNUM"       "ALIAS"        "ENSEMBL"      "ENSEMBLPROT"  "ENSEMBLTRANS"
##  [6] "ENTREZID"     "ENZYME"       "EVIDENCE"     "EVIDENCEALL"  "GENENAME"    
## [11] "GENETYPE"     "GO"           "GOALL"        "IPI"          "MAP"         
## [16] "OMIM"         "ONTOLOGY"     "ONTOLOGYALL"  "PATH"         "PFAM"        
## [21] "PMID"         "PROSITE"      "REFSEQ"       "SYMBOL"       "UCSCKG"      
## [26] "UNIPROT"

We can use the mapIds function to add individual columns to our results table. We provide the row names of our results table as a key, and specify that keytype=ENSEMBL. The column argument tells the mapIds function which information we want, and the multiVals argument tells the function what to do if there are multiple possible values for a single input value. Here we ask to just give us back the first one that occurs in the database. To add the gene symbol and Entrez ID, we call mapIds twice.

ens.str <- substr(rownames(res), 1, 15)
res$symbol <- mapIds(org.Hs.eg.db,
                     keys=ens.str,
                     column="SYMBOL",
                     keytype="ENSEMBL",
                     multiVals="first")
res$entrez <- mapIds(org.Hs.eg.db,
                     keys=ens.str,
                     column="ENTREZID",
                     keytype="ENSEMBL",
                     multiVals="first")

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 7 columns
##                     baseMean log2FoldChange     lfcSE       pvalue         padj
##                    <numeric>      <numeric> <numeric>    <numeric>    <numeric>
## ENSG00000189221.9   2373.805        3.38765  0.136985 1.84494e-137 3.11758e-133
## ENSG00000120129.5   3420.727        2.96335  0.120850 6.35042e-135 5.36547e-131
## ENSG00000101347.9  14125.584        3.74129  0.157927 2.88983e-127 1.62775e-123
## ENSG00000196136.17  2710.217        3.23518  0.143951 3.68488e-114 1.55668e-110
## ENSG00000152583.12   974.737        4.48641  0.201276 2.94551e-113 9.95466e-110
## ENSG00000211445.11 12512.792        3.75875  0.169536 2.36246e-112 6.65348e-109
##                         symbol      entrez
##                    <character> <character>
## ENSG00000189221.9         MAOA        4128
## ENSG00000120129.5        DUSP1        1843
## ENSG00000101347.9       SAMHD1       25939
## ENSG00000196136.17    SERPINA3          12
## ENSG00000152583.12     SPARCL1        8404
## ENSG00000211445.11        GPX3        2878

7.1 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")

A more sophisticated way for exporting results the Bioconductor package ReportingTools (Huntley et al. 2013). 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)

7.2 Plotting fold changes in genomic space

If we have used the tximeta function to read in the quantification data, then our DESeqDataSet object is built on top of ready-to-use Bioconductor objects specifying the genomic coordinates of the genes. We can therefore easily plot our differential expression results in genomic space. While the results or lfcShrink functions by default return a DataFrame, using the format argument, we can ask for GRanges or GRangesList output (the latter is only possible if we use the addExons function from the tximeta package upstream of creating a DESeqDataSet).

resGR <- lfcShrink(dds, coef="dex_trt_vs_untrt", type="apeglm", format="GRanges")
resGR
## GRanges object with 31604 ranges and 5 metadata columns:
##                      seqnames              ranges strand |   baseMean
##                         <Rle>           <IRanges>  <Rle> |  <numeric>
##   ENSG00000000003.14     chrX 100627109-100639991      - | 739.940717
##   ENSG00000000419.12    chr20   50934867-50958555      - | 511.735722
##   ENSG00000000457.13     chr1 169849631-169894267      - | 314.194855
##   ENSG00000000460.16     chr1 169662007-169854080      + |  79.793622
##   ENSG00000000938.12     chr1   27612064-27635277      - |   0.307267
##                  ...      ...                 ...    ... .        ...
##    ENSG00000285979.1    chr16   57177349-57181390      + |  38.353886
##    ENSG00000285987.1     chr9   84316514-84657077      + |   1.562508
##    ENSG00000285990.1    chr14   19244904-19269380      - |   0.642315
##    ENSG00000285991.1     chr6 149817937-149896011      - |  11.276284
##    ENSG00000285994.1    chr10   12563151-12567351      + |   3.651041
##                      log2FoldChange     lfcSE      pvalue       padj
##                           <numeric> <numeric>   <numeric>  <numeric>
##   ENSG00000000003.14     -0.3360046  0.105909 0.000726392 0.00531137
##   ENSG00000000419.12      0.1783789  0.122440 0.108822318 0.29318870
##   ENSG00000000457.13      0.0299361  0.141095 0.811509461 0.92255697
##   ENSG00000000460.16     -0.0555061  0.222787 0.714430444 0.87298038
##   ENSG00000000938.12     -0.0115799  0.304740 0.695977205         NA
##                  ...            ...       ...         ...        ...
##    ENSG00000285979.1     0.15284386  0.257070    0.340940   0.600750
##    ENSG00000285987.1     0.02551527  0.300687    0.647996         NA
##    ENSG00000285990.1    -0.00018563  0.304465    0.915396         NA
##    ENSG00000285991.1    -0.01507882  0.283931    0.876275   0.952921
##    ENSG00000285994.1    -0.00684681  0.293399    0.928414         NA
##   -------
##   seqinfo: 25 sequences (1 circular) from hg38 genome

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

ens.str <- substr(names(resGR), 1, 15)
resGR$symbol <- mapIds(org.Hs.eg.db, ens.str, "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 and 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 value of padj.

status <- factor(ifelse(resGRsub$padj < 0.05 & !is.na(resGRsub$padj),
                        "sig", "notsig"))

We can then plot the results using Gviz functions (figure below). 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.

options(ucscChromosomeNames = FALSE)
g <- GenomeAxisTrack()
a <- AnnotationTrack(resGRsub, name = "gene ranges", feature = status)
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")

log2 fold changes in genomic region surrounding the gene with smallest adjusted p value. Genes highlighted in pink have adjusted p value less than 0.1.

8 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 package (Leek 2014) or the RUVSeq package (Risso et al. 2014) in Bioconductor 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, while the RUV package uses the terms factors of unwanted variation with the acronym “Remove Unwanted Variation” explaining the package title. We first use SVA to find hidden batch effects and then RUV following.

8.1 Using SVA with DESeq2

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,]  0.2465669 -0.51599084
## [2,]  0.2588137 -0.59462876
## [3,]  0.1384516  0.24920662
## [4,]  0.2179075  0.37716083
## [5,] -0.6042910 -0.06305844
## [6,] -0.6138795 -0.03623320
## [7,]  0.1821306  0.30328185
## [8,]  0.1743002  0.28026195

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

par(mfrow = c(2, 1), mar = c(3,5,3,1))
for (i in 1:2) {
  stripchart(svseq$sv[, i] ~ dds$cell, vertical = TRUE, main = paste0("SV", i))
  abline(h = 0)
 }

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 a source of variation which is correlated with cell line.

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.

8.2 Using RUV with DESeq2

We can also use the RUV method in the RUVSeq package to detect the hidden batch effects.

library("RUVSeq")

We can use the RUVg function to estimate factors of unwanted variation, analogous to SVA’s surrogate variables. A difference compared to the SVA procedure above, is that we first would run DESeq and results to obtain the p-values for the analysis without knowing about the batches, e.g. just ~ dex. Supposing that we have this results table res, we then pull out a set of empirical control genes by looking at the genes that do not have a small p-value.

set <- newSeqExpressionSet(counts(dds))
idx  <- rowSums(counts(set) > 5) >= 2
set  <- set[idx, ]
set <- betweenLaneNormalization(set, which="upper")
not.sig <- rownames(res)[which(res$pvalue > .1)]
empirical <- rownames(set)[ rownames(set) %in% not.sig ]
set <- RUVg(set, empirical, k=2)
pData(set)
##                     W_1         W_2
## SRR1039508 -0.224881168  0.42992983
## SRR1039509 -0.249022928  0.53858506
## SRR1039512  0.001460949  0.01437385
## SRR1039513 -0.175547525  0.08408354
## SRR1039516  0.599387535 -0.02512358
## SRR1039517  0.590516825 -0.02549392
## SRR1039520 -0.241071948 -0.50369551
## SRR1039521 -0.300841739 -0.51265927

We can plot the factors estimated by RUV:

par(mfrow = c(2, 1), mar = c(3,5,3,1))
for (i in 1:2) {
  stripchart(pData(set)[, i] ~ dds$cell, vertical = TRUE, main = paste0("W", i))
  abline(h = 0)
 }

Factors of unwanted variation plotted over cell line.

As before, if we wanted to control for these factors, we simply add them to the DESeqDataSet and to the design:

ddsruv <- dds
ddsruv$W1 <- set$W_1
ddsruv$W2 <- set$W_2
design(ddsruv) <- ~ W1 + W2 + dex

We would then run DESeq with the new design to re-estimate the parameters and results.

9 Time course experiments

DESeq2 can be used to analyze time course experiments, for example to find those genes that react in a condition-specific manner over time, compared to a set of baseline samples. Here we demonstrate a basic time course analysis with the fission data package, which contains gene counts for an RNA-seq time course of fission yeast (Leong et al. 2014). The yeast were exposed to oxidative stress, and half of the samples contained a deletion of the gene atf21. We use a design formula that 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 of code 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 that 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$padj),], 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
##              <numeric>      <numeric> <numeric> <numeric>   <numeric>
## SPBC2F12.09c   174.671     -2.6567195  0.752261   97.2834 1.97415e-19
## SPAC1002.18    444.505     -0.0509321  0.204299   56.9536 5.16955e-11
## SPAC1002.19    336.373     -0.3927490  0.573494   43.5339 2.87980e-08
## SPAC1002.17c   261.773     -1.1387648  0.606129   39.3158 2.05137e-07
##                     padj      symbol
##                <numeric> <character>
## SPBC2F12.09c 1.33453e-15       atf21
## SPAC1002.18  1.74731e-07        urg3
## SPAC1002.19  6.48916e-05        urg1
## SPAC1002.17c 3.46682e-04        urg2

This is just one of the tests that 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, and another, more modern approach is using Gaussian processes (Tonner et al. 2017).

We can plot the counts for the groups over time using ggplot2, for the gene with the smallest adjusted p value, testing for condition-dependent time profile and accounting for differences at time 0 (figure below). 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.

fiss <- plotCounts(ddsTC, which.min(resTC$padj), 
                   intgroup = c("minute","strain"), returnData = TRUE)
fiss$minute <- as.numeric(as.character(fiss$minute))
ggplot(fiss,
  aes(x = minute, y = count, color = strain, group = strain)) + 
  geom_point() + stat_summary(fun.y=mean, geom="line") +
  scale_y_log10()

Normalized counts for a gene with condition-specific changes over time.

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"     
##  [4] "minute_30_vs_0"      "minute_60_vs_0"      "minute_120_vs_0"    
##  [7] "minute_180_vs_0"     "strainmut.minute15"  "strainmut.minute30" 
## [10] "strainmut.minute60"  "strainmut.minute120" "strainmut.minute180"
res30 <- results(ddsTC, name="strainmut.minute30", test="Wald")
res30[which.min(resTC$padj),]
## 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   174.671       -2.60047  0.634343  -4.09947 4.14099e-05  0.279931

We can furthermore cluster significant genes by their profiles. We extract a matrix of the log2 fold changes using the coef function. Note that these are the maximum likelihood estimates (MLE). For shrunken LFC, one must obtain them one coefficient at a time using lfcShrink.

betas <- coef(ddsTC)
colnames(betas)
##  [1] "Intercept"           "strain_mut_vs_wt"    "minute_15_vs_0"     
##  [4] "minute_30_vs_0"      "minute_60_vs_0"      "minute_120_vs_0"    
##  [7] "minute_180_vs_0"     "strainmut.minute15"  "strainmut.minute30" 
## [10] "strainmut.minute60"  "strainmut.minute120" "strainmut.minute180"

We can now plot the log2 fold changes in a heatmap (figure below).

topGenes <- head(order(resTC$padj),20)
mat <- betas[topGenes, -c(1,2)]
thr <- 3 
mat[mat < -thr] <- -thr
mat[mat > thr] <- thr
pheatmap(mat, breaks=seq(from=-thr, to=thr, length=101),
         cluster_col=FALSE)

Heatmap of log2 fold changes for genes with smallest adjusted p value. The bottom set of genes show strong induction of expression for the baseline samples in minutes 15-60 (red boxes in the bottom left corner), but then have slight differences for the mutant strain (shown in the boxes in the bottom right corner).

10 Session information

As the 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 of this as it will help to track down what has happened in case an R script ceases to work or gives different results because the functions have been changed in a newer version of one of your packages. By including it at the bottom of a script, your reports will become more reproducible.

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 4.1.0 (2021-05-18)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.2 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.13-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.13-bioc/R/lib/libRlapack.so
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
##  [1] grid      parallel  stats4    stats     graphics  grDevices utils    
##  [8] datasets  methods   base     
## 
## other attached packages:
##  [1] fission_1.11.1              RUVSeq_1.26.0              
##  [3] edgeR_3.34.0                limma_3.48.0               
##  [5] EDASeq_2.26.0               ShortRead_1.50.0           
##  [7] GenomicAlignments_1.28.0    Rsamtools_2.8.0            
##  [9] Biostrings_2.60.0           XVector_0.32.0             
## [11] sva_3.40.0                  BiocParallel_1.26.0        
## [13] mgcv_1.8-35                 nlme_3.1-152               
## [15] Gviz_1.36.0                 org.Hs.eg.db_3.13.0        
## [17] genefilter_1.74.0           apeglm_1.14.0              
## [19] ggbeeswarm_0.6.0            glmpca_0.2.0               
## [21] PoiClaClu_1.0.2.1           RColorBrewer_1.1-2         
## [23] pheatmap_1.0.12             ggplot2_3.3.3              
## [25] dplyr_1.0.6                 vsn_3.60.0                 
## [27] DESeq2_1.32.0               magrittr_2.0.1             
## [29] GenomicFeatures_1.44.0      AnnotationDbi_1.54.0       
## [31] tximeta_1.10.0              airway_1.11.1              
## [33] SummarizedExperiment_1.22.0 Biobase_2.52.0             
## [35] GenomicRanges_1.44.0        GenomeInfoDb_1.28.0        
## [37] IRanges_2.26.0              S4Vectors_0.30.0           
## [39] BiocGenerics_0.38.0         MatrixGenerics_1.4.0       
## [41] matrixStats_0.58.0          rmarkdown_2.8              
## [43] knitr_1.33                  BiocStyle_2.20.0           
## 
## loaded via a namespace (and not attached):
##   [1] utf8_1.2.1                    R.utils_2.10.1               
##   [3] tidyselect_1.1.1              RSQLite_2.2.7                
##   [5] htmlwidgets_1.5.3             munsell_0.5.0                
##   [7] preprocessCore_1.54.0         withr_2.4.2                  
##   [9] colorspace_2.0-1              filelock_1.0.2               
##  [11] highr_0.9                     rstudioapi_0.13              
##  [13] labeling_0.4.2                tximport_1.20.0              
##  [15] bbmle_1.0.23.1                GenomeInfoDbData_1.2.6       
##  [17] hwriter_1.3.2                 bit64_4.0.5                  
##  [19] farver_2.1.0                  coda_0.19-4                  
##  [21] vctrs_0.3.8                   generics_0.1.0               
##  [23] xfun_0.23                     biovizBase_1.40.0            
##  [25] BiocFileCache_2.0.0           R6_2.5.0                     
##  [27] locfit_1.5-9.4                AnnotationFilter_1.16.0      
##  [29] bitops_1.0-7                  cachem_1.0.5                 
##  [31] DelayedArray_0.18.0           assertthat_0.2.1             
##  [33] promises_1.2.0.1              BiocIO_1.2.0                 
##  [35] scales_1.1.1                  nnet_7.3-16                  
##  [37] beeswarm_0.3.1                gtable_0.3.0                 
##  [39] affy_1.70.0                   ensembldb_2.16.0             
##  [41] rlang_0.4.11                  splines_4.1.0                
##  [43] rtracklayer_1.52.0            lazyeval_0.2.2               
##  [45] dichromat_2.0-0               hexbin_1.28.2                
##  [47] checkmate_2.0.0               BiocManager_1.30.15          
##  [49] yaml_2.2.1                    backports_1.2.1              
##  [51] httpuv_1.6.1                  Hmisc_4.5-0                  
##  [53] tools_4.1.0                   bookdown_0.22                
##  [55] affyio_1.62.0                 ellipsis_0.3.2               
##  [57] jquerylib_0.1.4               Rcpp_1.0.6                   
##  [59] plyr_1.8.6                    base64enc_0.1-3              
##  [61] progress_1.2.2                zlibbioc_1.38.0              
##  [63] purrr_0.3.4                   RCurl_1.98-1.3               
##  [65] prettyunits_1.1.1             rpart_4.1-15                 
##  [67] cluster_2.1.2                 data.table_1.14.0            
##  [69] magick_2.7.2                  mvtnorm_1.1-1                
##  [71] ProtGenerics_1.24.0           aroma.light_3.22.0           
##  [73] hms_1.1.0                     mime_0.10                    
##  [75] evaluate_0.14                 xtable_1.8-4                 
##  [77] XML_3.99-0.6                  emdbook_1.3.12               
##  [79] jpeg_0.1-8.1                  gridExtra_2.3                
##  [81] compiler_4.1.0                biomaRt_2.48.0               
##  [83] bdsmatrix_1.3-4               tibble_3.1.2                 
##  [85] crayon_1.4.1                  R.oo_1.24.0                  
##  [87] htmltools_0.5.1.1             later_1.2.0                  
##  [89] Formula_1.2-4                 geneplotter_1.70.0           
##  [91] DBI_1.1.1                     dbplyr_2.1.1                 
##  [93] MASS_7.3-54                   rappdirs_0.3.3               
##  [95] Matrix_1.3-3                  readr_1.4.0                  
##  [97] R.methodsS3_1.8.1             pkgconfig_2.0.3              
##  [99] numDeriv_2016.8-1.1           foreign_0.8-81               
## [101] annotate_1.70.0               vipor_0.4.5                  
## [103] bslib_0.2.5.1                 stringr_1.4.0                
## [105] VariantAnnotation_1.38.0      digest_0.6.27                
## [107] htmlTable_2.2.1               restfulr_0.0.13              
## [109] curl_4.3.1                    shiny_1.6.0                  
## [111] rjson_0.2.20                  lifecycle_1.0.0              
## [113] jsonlite_1.7.2                BSgenome_1.60.0              
## [115] fansi_0.4.2                   pillar_1.6.1                 
## [117] lattice_0.20-44               KEGGREST_1.32.0              
## [119] fastmap_1.1.0                 httr_1.4.2                   
## [121] survival_3.2-11               interactiveDisplayBase_1.30.0
## [123] glue_1.4.2                    png_0.1-7                    
## [125] BiocVersion_3.13.1            bit_4.0.4                    
## [127] stringi_1.6.2                 sass_0.4.0                   
## [129] blob_1.2.1                    AnnotationHub_3.0.0          
## [131] latticeExtra_0.6-29           memoise_2.0.0

References

Anders, Simon, and Wolfgang Huber. 2010. “Differential expression analysis for sequence count data.” Genome Biology 11 (10): R106+. https://doi.org/10.1186/gb-2010-11-10-r106.

Anders, Simon, Paul T. Pyl, and Wolfgang Huber. 2015. “HTSeq – a Python framework to work with high-throughput sequencing data.” Bioinformatics 31 (2): 166–69. https://doi.org/10.1093/bioinformatics/btu638.

Benjamini, Yoav, and Yosef Hochberg. 1995. “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.” Journal of the Royal Statistical Society. Series B (Methodological) 57 (1): 289–300. http://www.jstor.org/stable/2346101.

Bourgon, R., R. Gentleman, and W. Huber. 2010. “Independent filtering increases detection power for high-throughput experiments.” Proceedings of the National Academy of Sciences 107 (21): 9546–51. https://doi.org/10.1073/pnas.0914005107.

Bray, Nicolas, Harold Pimentel, Pall Melsted, and Lior Pachter. 2016. “Near-Optimal Probabilistic Rna-Seq Quantification.” Nature Biotechnology 34: 525–27. http://dx.doi.org/10.1038/nbt.3519.

Dudoit, Rine, Yee H. Yang, Matthew J. Callow, and Terence P. Speed. 2002. “Statistical methods for identifying differentially expressed genes in replicated cDNA microarray experiments.” Statistica Sinica, 111–39.

Frankish, Adam, Alexandra Bignell, Andrew Berry, Andrew Yates, Anne Parker, Bianca M Schmitt, Bronwen Aken, et al. 2018. “GENCODE reference annotation for the human and mouse genomes.” Nucleic Acids Research 47 (D1): D766–D773.

Hardcastle, Thomas, and Krystyna Kelly. 2010. “baySeq: Empirical Bayesian methods for identifying differential expression in sequence count data.” BMC Bioinformatics 11 (1): 422+. https://doi.org/10.1186/1471-2105-11-422.

Himes, Blanca E., Xiaofeng Jiang, Peter Wagner, Ruoxi Hu, Qiyu Wang, Barbara Klanderman, Reid M. Whitaker, et al. 2014. “RNA-Seq transcriptome profiling identifies CRISPLD2 as a glucocorticoid responsive gene that modulates cytokine function in airway smooth muscle cells.” PloS One 9 (6). https://doi.org/10.1371/journal.pone.0099625.

Huber, Wolfgang, Vincent J. Carey, Robert Gentleman, Simon Anders, Marc Carlson, Benilton S. Carvalho, Hector Corrada C. Bravo, et al. 2015. “Orchestrating high-throughput genomic analysis with Bioconductor.” Nature Methods 12 (2): 115–21. https://doi.org/10.1038/nmeth.3252.

Huntley, Melanie A., Jessica L. Larson, Christina Chaivorapol, Gabriel Becker, Michael Lawrence, Jason A. Hackney, and Joshua S. Kaminker. 2013. “ReportingTools: an automated result processing and presentation toolkit for high-throughput genomic analyses.” Bioinformatics 29 (24): 3220–1. https://doi.org/10.1093/bioinformatics/btt551.

Ignatiadis, Nikolaos, Bernd Klaus, Judith Zaugg, and Wolfgang Huber. 2016. “Data-Driven Hypothesis Weighting Increases Detection Power in Genome-Scale Multiple Testing.” Nature Methods. http://dx.doi.org/10.1038/nmeth.3885.

Köster, Johannes, and Sven Rahmann. 2012. “Snakemake - A scalable bioinformatics workflow engine.” Bioinformatics. https://doi.org/10.1093/bioinformatics/bts480.

Law, Charity W., Yunshun Chen, Wei Shi, and Gordon K. Smyth. 2014. “Voom: precision weights unlock linear model analysis tools for RNA-seq read counts.” Genome Biology 15 (2): R29+. https://doi.org/10.1186/gb-2014-15-2-r29.

Lawrence, Michael, Wolfgang Huber, Hervé Pagès, Patrick Aboyoun, Marc Carlson, Robert Gentleman, Martin T. Morgan, and Vincent J. Carey. 2013. “Software for Computing and Annotating Genomic Ranges.” Edited by Andreas Prlic. PLoS Computational Biology 9 (8): e1003118+. https://doi.org/10.1371/journal.pcbi.1003118.

Leek, Jeffrey T. 2014. “svaseq: removing batch effects and other unwanted noise from sequencing data.” Nucleic Acids Research 42 (21): 000. https://doi.org/10.1093/nar/gku864.

Leng, N., J. A. Dawson, J. A. Thomson, V. Ruotti, A. I. Rissman, B. M. G. Smits, J. D. Haag, M. N. Gould, R. M. Stewart, and C. Kendziorski. 2013. “EBSeq: an empirical Bayes hierarchical model for inference in RNA-seq experiments.” Bioinformatics 29 (8): 1035–43. https://doi.org/10.1093/bioinformatics/btt087.

Leong, Hui S., Keren Dawson, Chris Wirth, Yaoyong Li, Yvonne Connolly, Duncan L. Smith, Caroline R. Wilkinson, and Crispin J. Miller. 2014. “A global non-coding RNA system modulates fission yeast protein levels in response to stress.” Nature Communications 5. https://doi.org/10.1038/ncomms4947.

Li, Bo, and Colin N. Dewey. 2011. “RSEM: accurate transcript quantification from RNA-Seq data with or without a reference genome.” BMC Bioinformatics 12: 323+. https://doi.org/10.1186/1471-2105-12-3231.

Liao, Y., G. K. Smyth, and W. Shi. 2014. “featureCounts: an efficient general purpose program for assigning sequence reads to genomic features.” Bioinformatics 30 (7): 923–30. https://doi.org/10.1093/bioinformatics/btt656.

Love, Michael I., John B. Hogenesch, and Rafael A. Irizarry. 2016. “Modeling of Rna-Seq Fragment Sequence Bias Reduces Systematic Errors in Transcript Abundance Estimation.” Nature Biotechnology 34 (12): 1287–91. http://dx.doi.org/10.1038/nbt.3682.

Love, Michael I., Wolfgang Huber, and Simon Anders. 2014. “Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2.” Genome Biology 15 (12): 550+. https://doi.org/10.1186/s13059-014-0550-8.

Love, Michael I., Charlotte Soneson, Peter F. Hickey, Lisa K. Johnson, N. Tessa Pierce, Lori Shepherd, Martin Morgan, and Rob Patro. 2020. “Tximeta: Reference sequence checksums for provenance identification in RNA-seq.” PLOS Computational Biology. https://doi.org/10.1371/journal.pcbi.1007664.

Patro, Rob, Geet Duggal, Michael I. Love, Rafael A. Irizarry, and Carl Kingsford. 2017. “Salmon Provides Fast and Bias-Aware Quantification of Transcript Expression.” Nature Methods. http://dx.doi.org/10.1038/nmeth.4197.

Risso, Davide, John Ngai, Terence P. Speed, and Sandrine Dudoit. 2014. “Normalization of RNA-seq data using factor analysis of control genes or samples.” Nature Biotechnology 32 (9): 896–902. https://doi.org/10.1038/nbt.2931.

Robert, Christelle, and Mick Watson. 2015. “Errors in RNA-Seq quantification affect genes of relevance to human disease.” Genome Biology. https://doi.org/10.1186/s13059-015-0734-x.

Robinson, M. D., D. J. McCarthy, and G. K. Smyth. 2009. “edgeR: a Bioconductor package for differential expression analysis of digital gene expression data.” Bioinformatics 26 (1): 139–40. https://doi.org/10.1093/bioinformatics/btp616.

Schurch, Nicholas J., Pieta Schofield, Marek Gierlinski, Christian Cole, Alexander Sherstnev, Vijender Singh, Nicola Wrobel, et al. 2016. “How Many Biological Replicates Are Needed in an Rna-Seq Experiment and Which Differential Expression Tool Should You Use?” 22 (6): 839–51. https://doi.org/10.1261/rna.053959.115.

Soneson, Charlotte, Michael I. Love, and Mark Robinson. 2015. “Differential analyses for RNA-seq: transcript-level estimates improve gene-level inferences.” F1000Research 4 (1521). https://doi.org/10.12688/f1000research.7563.1.

Srivastava, Avi, Laraib Malik, Hirak Sarkar, Mohsen Zakeri, Fatemeh Almodaresi, Charlotte Soneson, Michael I. Love, Carl Kingsford, and Rob Patro. 2020. “Alignment and Mapping Methodology Influence Transcript Abundance Estimation.” Genome Biology 21 (1): 239. https://doi.org/10.1186/s13059-020-02151-8.

Tonner, Peter D, Cynthia L Darnell, Barbara E Engelhardt, and Amy K Schmid. 2017. “Detecting differential growth of microbial populations with Gaussian process regression.” Genome Research 27: 320–33. https://doi.org/10.1101/gr.210286.116.

Townes, F. William, Stephanie C. Hicks, Martin J. Aryee, and Rafael A. Irizarry. 2019. “Feature selection and dimension reduction for single-cell RNA-Seq based on a multinomial model.” Genome Biology 20 (1): 295. https://doi.org/10.1186/s13059-019-1861-6.

Trapnell, Cole, David G Hendrickson, Martin Sauvageau, Loyal Goff, John L Rinn, and Lior Pachter. 2013. “Differential analysis of gene regulation at transcript resolution with RNA-seq.” Nature Biotechnology. https://doi.org/10.1038/nbt.2450.

Wickham, Hadley. 2009. ggplot2. New York, NY: Springer New York. https://doi.org/10.1007/978-0-387-98141-3.

Witten, Daniela M. 2011. “Classification and clustering of sequencing data using a Poisson model.” The Annals of Applied Statistics 5 (4): 2493–2518. https://doi.org/10.1214/11-AOAS493.

Wu, Hao, Chi Wang, and Zhijin Wu. 2013. “A new shrinkage estimator for dispersion improves differential expression detection in RNA-seq data.” Biostatistics 14 (2): 232–43. https://doi.org/10.1093/biostatistics/kxs033.

Zhu, Anqi, Joseph G. Ibrahim, and Michael I. Love. 2018. “Heavy-Tailed Prior Distributions for Sequence Count Data: Removing the Noise and Preserving Large Differences.” Bioinformatics. https://doi.org/10.1093/bioinformatics/bty895.