RNA-seq workflow: gene-level exploratory analysis and differential expression (original) (raw)
Contents
- 1 Introduction
- 2 Preparing quantification input to DESeq2
- 3 The DESeqDataSet object, sample information and the design formula
- 4 Exploratory analysis and visualization
- 5 Differential expression analysis
- 6 Plotting results
- 7 Annotating and exporting results
- 8 Removing hidden batch effects
- 9 Time course experiments
- 10 Session information
- References
R version: R version 4.5.0 RC (2025-04-04 r88126)
Bioconductor version: 3.21
Package: 1.32.0
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 theBioconductor package installation instructions.
- A published version of this workflow, including reviewer reports and comments is available at F1000Research. The version you are reading now differs from this one, primarily in that we now give code for performing fast transcript quantificationfollowed by import in R/Bioconductor to perform gene-level analysis.
- Another Bioconductor workflow covering differential transcript usage(DTU) is thernaseqDTU workflow, with the published version likewise available atF1000Research.
- If you have questions about this workflow or any Bioconductor software, please post these to theBioconductor support site. If the questions concern a specific package, you can tag the post with the name of the package, or for general questions about the workflow, tag the post with
rnaseqgene. Note theposting guidefor crafting an optimal question for the support site.
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 thePubMed entry 24926665and for raw data see theGEO entry GSE52778.
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.
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 useGENCODE (Frankish et al. 2018).
The Salmon index can be created easily with the following command:
salmon index -t transcripts.fa.gz -i name_of_indexNote: 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 theSalmon 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.ZThe above Snakemake file can then be used toexecute Snakemakein 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"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).
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).
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 colDatalines 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 incolData 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 conditionThe counts are the first matrix, so we can examine them with justassay:
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
## ENSG00000000419.12 773.999 409.999 499.000colSums(assay(gse))## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516 SRR1039517 SRR1039520
## 21100805 19298584 26145537 15688246 25268618 31891456 19683767
## SRR1039521
## 21813903The 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 genomeThe 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 hg38The 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 DexamethasoneBranching 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 performanceof 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.
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$donor## [1] N61311 N61311 N052611 N052611 N080611 N080611 N061011 N061011
## Levels: N052611 N061011 N080611 N61311gse$condition## [1] Untreated Dexamethasone Untreated Dexamethasone Untreated
## [6] Dexamethasone Untreated Dexamethasone
## Levels: Untreated DexamethasoneWe 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$dex <- gse$conditionWe 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 + dexmeaning 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:
- from a SummarizedExperiment object
- from a count matrix and a sample information table
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.
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
## 21.8Once 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)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 499In 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 countscoldata: 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.
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.
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 perform pre-filtering to keep only rows that have a count of at least 10 for a minimal number of samples. The count of 10 is a reasonable choice for bulk RNA-seq. A recommendation for the minimal number of samples is to specify the smallest group size, e.g. here there are 4 samples in each group. If there are not discrete groups, one can use the minimal number of samples where non-zero counts would be considered interesting. Additional weighting/filtering to improve power is applied at a later step in the workflow.
nrow(dds)## [1] 58294smallestGroupSize <- 4
keep <- rowSums(counts(dds) >= 10) >= smallestGroupSize
dds <- dds[keep,]
nrow(dds)## [1] 16637The 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 10.082167 9.828058 10.152774 9.970690 10.410407
## ENSG00000000419.12 9.663489 9.900634 9.779942 9.775148 9.740478
## ENSG00000000457.13 9.417376 9.280001 9.333639 9.430438 9.250501
## SRR1039517 SRR1039520 SRR1039521
## ENSG00000000003.14 10.171994 10.300682 9.976235
## ENSG00000000419.12 9.848458 9.659469 9.817695
## ENSG00000000457.13 9.363013 9.450889 9.444291colData(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 trtAgain, for the rlog:
rld <- rlog(dds, blind = FALSE)
head(assay(rld), 3)## SRR1039508 SRR1039509 SRR1039512 SRR1039513 SRR1039516
## ENSG00000000003.14 9.479269 9.172988 9.561792 9.347935 9.853759
## ENSG00000000419.12 8.856681 9.150490 9.003390 8.997381 8.954032
## ENSG00000000457.13 8.352320 8.165586 8.239148 8.368679 8.122726
## SRR1039517 SRR1039520 SRR1039521
## ENSG00000000003.14 9.584201 9.730416 9.353458
## ENSG00000000419.12 9.088130 8.851863 9.049900
## ENSG00000000457.13 8.279323 8.396402 8.387635In 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 setblind = 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.
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 37.77776
## SRR1039512 30.25948 43.38127
## SRR1039513 49.66501 34.84097 40.18573
## SRR1039516 33.62914 46.11028 32.89674 50.61885
## SRR1039517 50.13559 39.95782 45.59332 38.73688 38.49412
## SRR1039520 29.92878 45.27463 27.72834 46.25456 34.97574 48.96752
## SRR1039521 50.08387 35.35988 45.51074 28.48458 51.19216 39.62934
## SRR1039520
## SRR1039509
## SRR1039512
## SRR1039513
## SRR1039516
## SRR1039517
## SRR1039520
## SRR1039521 41.45015We 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_distanceargument 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.
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 documentationfor more details on using ggplot.
pcaData <- plotPCA(vsd, intgroup = c( "dex", "cell"), returnData = TRUE)
pcaData## PC1 PC2 group name names donor
## SRR1039508 -14.427794 -3.057906 untrt:N61311 SRR1039508 SRR1039508 N61311
## SRR1039509 8.144808 -1.422929 trt:N61311 SRR1039509 SRR1039509 N61311
## SRR1039512 -9.476223 -4.414224 untrt:N052611 SRR1039512 SRR1039512 N052611
## SRR1039513 14.628644 -4.290437 trt:N052611 SRR1039513 SRR1039513 N052611
## SRR1039516 -12.425251 11.397272 untrt:N080611 SRR1039516 SRR1039516 N080611
## SRR1039517 9.475669 15.097249 trt:N080611 SRR1039517 SRR1039517 N080611
## SRR1039520 -10.965862 -7.197057 untrt:N061011 SRR1039520 SRR1039520 N061011
## SRR1039521 15.046009 -6.111969 trt:N061011 SRR1039521 SRR1039521 N061011
## condition cell dex
## SRR1039508 Untreated N61311 untrt
## SRR1039509 Dexamethasone N61311 trt
## SRR1039512 Untreated N052611 untrt
## SRR1039513 Dexamethasone N052611 trt
## SRR1039516 Untreated N080611 untrt
## SRR1039517 Dexamethasone N080611 trt
## SRR1039520 Untreated N061011 untrt
## SRR1039521 Dexamethasone N061011 trtpercentVar <- 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.
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$cell <- dds$cellggplot(gpca.dat, aes(x = dim1, y = dim2, color = dex, shape = cell)) +
geom_point(size =3) + coord_fixed() + ggtitle("glmpca - Generalized PCA")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.
Running the differential expression pipeline
As we have already specified an experimental design when we created the DESeqDataSet, we can run the differential expression pipeline on the raw counts with a single call to the function DESeq:
dds <- DESeq(dds)This function will print out a message for the various steps it performs. These are described in more detail in the manual page for_DESeq_, which can be accessed by typing ?DESeq. Briefly these are: the estimation of size factors (controlling for differences in the sequencing depth of the samples), the estimation of dispersion values for each gene, and fitting a generalized linear model.
A DESeqDataSet is returned that contains all the fitted parameters within it, and the following section describes how to extract out results tables of interest from this object.
Building the results table
Calling results without any arguments will extract the estimated log2 fold changes and p values for the last variable in the design formula. If there are more than 2 levels for this variable, _results_will extract the results table for a comparison of the last level over the first level. 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 16637 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue
## <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000000003.14 740.1093 -0.365327 0.1073385 -3.403501 6.65282e-04
## ENSG00000000419.12 511.6990 0.202232 0.1278579 1.581694 1.13720e-01
## ENSG00000000457.13 314.1680 0.033792 0.1552106 0.217717 8.27650e-01
## ENSG00000000460.16 79.7988 -0.120633 0.3055270 -0.394836 6.92964e-01
## ENSG00000000971.15 5715.3064 0.442982 0.0904089 4.899766 9.59508e-07
## ... ... ... ... ... ...
## ENSG00000285953.1 29.5747 -1.920562 0.649661 -2.956253 0.00311401
## ENSG00000285967.1 181.1650 -0.325885 0.179340 -1.817132 0.06919688
## ENSG00000285976.1 875.4424 0.262132 0.142980 1.833351 0.06675037
## ENSG00000285979.1 38.3502 0.338383 0.348445 0.971124 0.33148631
## ENSG00000285991.1 11.2772 -0.115472 0.723139 -0.159681 0.87313221
## padj
## <numeric>
## ENSG00000000003.14 4.63552e-03
## ENSG00000000419.12 2.88125e-01
## ENSG00000000457.13 9.21718e-01
## ENSG00000000460.16 8.48743e-01
## ENSG00000000971.15 1.36387e-05
## ... ...
## ENSG00000285953.1 0.0171889
## ENSG00000285967.1 0.2019448
## ENSG00000285976.1 0.1965808
## ENSG00000285979.1 0.5713913
## ENSG00000285991.1 NAWe 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-valuesThe 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 16637 with nonzero total read count
## adjusted p-value < 0.1
## LFC > 0 (up) : 2362, 14%
## LFC < 0 (down) : 2019, 12%
## outliers [1] : 0, 0%
## low counts [2] : 646, 3.9%
## (mean count < 12)
## [1] see 'cooksCutoff' argument of ?results
## [2] see 'independentFiltering' argument of ?resultsNote 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
padjin the results table) - raise the log2 fold change threshold from 0 using the
lfcThresholdargument 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
## 12712 3602If 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 specifyinglfcThreshold = 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
## 16397 240Sometimes 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 typingcitation("pkgName"), where you would substitute the name of the package for pkgName. Citing methods papers helps to support and reward the individuals who put time into open source software for genomic data analysis.
Other comparisons
In general, the results for a comparison of any two levels of a variable can be extracted using the contrast argument to_results_. The user should specify three values: the name of the variable, the name of the level for the numerator, and the name of the level for the denominator. Here we extract results for the log2 of the fold change of one cell line over another:
results(dds, contrast = c("cell", "N061011", "N61311"))## log2 fold change (MLE): cell N061011 vs N61311
## Wald test p-value: cell N061011 vs N61311
## DataFrame with 16637 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue
## <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000000003.14 740.1093 0.2725914 0.152831 1.783618 7.44857e-02
## ENSG00000000419.12 511.6990 -0.0707901 0.181681 -0.389640 6.96803e-01
## ENSG00000000457.13 314.1680 0.1816517 0.220300 0.824567 4.09618e-01
## ENSG00000000460.16 79.7988 -0.1180515 0.428104 -0.275754 7.82737e-01
## ENSG00000000971.15 5715.3064 0.8234461 0.128134 6.426459 1.30610e-10
## ... ... ... ... ... ...
## ENSG00000285953.1 29.5747 1.3094223 0.891768 1.468344 0.1420107
## ENSG00000285967.1 181.1650 -0.5347871 0.254739 -2.099355 0.0357856
## ENSG00000285976.1 875.4424 -0.0932084 0.202503 -0.460281 0.6453144
## ENSG00000285979.1 38.3502 0.0604501 0.496866 0.121663 0.9031662
## ENSG00000285991.1 11.2772 -0.8779643 1.010832 -0.868556 0.3850901
## padj
## <numeric>
## ENSG00000000003.14 3.72420e-01
## ENSG00000000419.12 9.34643e-01
## ENSG00000000457.13 8.04500e-01
## ENSG00000000460.16 9.57685e-01
## ENSG00000000971.15 1.61144e-08
## ... ...
## ENSG00000285953.1 0.517887
## ENSG00000285967.1 0.241459
## ENSG00000285976.1 0.916522
## ENSG00000285979.1 0.981312
## ENSG00000285991.1 NAThere are additional ways to build results tables for certain comparisons after running DESeq once. If results for an interaction term are desired, the nameargument 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.
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 5069 genes with a p value below 0.05 among the 16637 genes for which the test succeeded in reporting a p value:
sum(res$pvalue < 0.05, na.rm=TRUE)## [1] 5069sum(!is.na(res$pvalue))## [1] 16637Now, assume for a moment that the null hypothesis is true for all genes, i.e., no gene is affected by the treatment with dexamethasone. Then, by the definition of the p value, we expect up to 5% of the genes to have a p value below 0.05. This amounts to 832 genes. If we just considered the list of genes with a p value below 0.05 as differentially expressed, this list should therefore be expected to contain up to 832 / 5069 = 16% false positives.
DESeq2 uses the Benjamini-Hochberg (BH) adjustment (Benjamini and Hochberg 1995) as implemented in the base R p.adjust function; in brief, this method calculates for each gene an adjusted p value that answers the following question: if one called significant all genes with an adjusted p value less than or equal to this gene’s adjusted p value threshold, what would be the fraction of false positives (the false discovery rate, FDR) among them, in the sense of the calculation outlined above? These values, called the BH-adjusted p values, are given in the column padj of the resobject.
The FDR is a useful statistic for many high-throughput experiments, as we are often interested in reporting or focusing on a set of interesting genes, and we would like to put an upper bound on the percent of false positives in this set.
Hence, if we consider a fraction of 10% false positives acceptable, we can consider all genes with an adjusted p value below 10% = 0.1 as significant. How many such genes are there?
sum(res$padj < 0.1, na.rm=TRUE)## [1] 4381We 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$log2FoldChange), ])## log2 fold change (MLE): dex trt vs untrt
## Wald test p-value: dex trt vs untrt
## DataFrame with 6 rows and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue
## <numeric> <numeric> <numeric> <numeric> <numeric>
## ENSG00000216490.3 42.3457 -5.72709 1.474282 -3.88466 1.02473e-04
## ENSG00000267339.5 30.5903 -5.39692 0.754323 -7.15465 8.38861e-13
## ENSG00000146006.7 61.6555 -4.48259 0.643341 -6.96767 3.22240e-12
## ENSG00000155897.9 23.9892 -3.87698 0.809195 -4.79115 1.65824e-06
## ENSG00000213240.8 12.1002 -3.79153 1.221385 -3.10429 1.90737e-03
## ENSG00000162692.11 505.5613 -3.67636 0.201427 -18.25164 2.00779e-74
## padj
## <numeric>
## ENSG00000216490.3 9.14426e-04
## ENSG00000267339.5 2.76013e-11
## ENSG00000146006.7 9.83385e-11
## ENSG00000155897.9 2.25676e-05
## ENSG00000213240.8 1.14064e-02
## ENSG00000162692.11 2.00666e-71…and with the strongest up-regulation:
head(resSig[ order(resSig$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 62.1517 10.20327 3.377058 3.02135 2.51651e-03
## ENSG00000179593.15 66.9666 9.50105 1.070620 8.87435 7.03444e-19
## ENSG00000224712.12 35.5516 7.16466 2.164701 3.30977 9.33725e-04
## ENSG00000109906.13 437.5025 6.37252 0.309988 20.55731 6.62052e-94
## ENSG00000257663.1 24.3615 6.34094 2.094868 3.02689 2.47081e-03
## ENSG00000250978.5 45.6682 5.91333 0.710469 8.32314 8.56661e-17
## padj
## <numeric>
## ENSG00000254692.1 1.44165e-02
## ENSG00000179593.15 4.22886e-17
## ENSG00000224712.12 6.18525e-03
## ENSG00000109906.13 1.17632e-90
## ENSG00000257663.1 1.42176e-02
## ENSG00000250978.5 4.32141e-15Plotting results
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.
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 theDESeq2 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 inresultsNames(dds), either of the other two shrinkage methods can be used, or in some cases, re-factoring the relevant variables and runningnbinomWaldTest 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 andlog2FoldChange 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.
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.
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).
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)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 multiValsargument 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 2371.265 3.38410 0.136340 2.47518e-138 3.95806e-134
## ENSG00000120129.5 3417.255 2.95871 0.121485 3.44226e-133 2.75226e-129
## ENSG00000101347.9 14106.720 3.73919 0.157542 1.66892e-127 8.89591e-124
## ENSG00000152583.12 973.479 4.48318 0.199191 2.26145e-115 9.04071e-112
## ENSG00000196136.17 2708.309 3.22904 0.144707 1.23286e-112 3.94293e-109
## ENSG00000211445.11 12502.886 3.75413 0.170078 2.52549e-111 6.73085e-108
## symbol entrez
## <character> <character>
## ENSG00000189221.9 MAOA 4128
## ENSG00000120129.5 DUSP1 1843
## ENSG00000101347.9 SAMHD1 25939
## ENSG00000152583.12 SPARCL1 8404
## ENSG00000196136.17 SERPINA3 12
## ENSG00000211445.11 GPX3 2878Exporting 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")More sophisticated ways for exporting results are described in the DESeq2 vignette, including links to other Bioconductor packages that facilitate visualization and report building.
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 16637 ranges and 5 metadata columns:
## seqnames ranges strand | baseMean
## <Rle> <IRanges> <Rle> | <numeric>
## ENSG00000000003.14 chrX 100627109-100639991 - | 740.1093
## ENSG00000000419.12 chr20 50934867-50958555 - | 511.6990
## ENSG00000000457.13 chr1 169849631-169894267 - | 314.1680
## ENSG00000000460.16 chr1 169662007-169854080 + | 79.7988
## ENSG00000000971.15 chr1 196651878-196747504 + | 5715.3064
## ... ... ... ... . ...
## ENSG00000285953.1 chr7 92131774-92245924 - | 29.5747
## ENSG00000285967.1 chr5 36864425-36876700 - | 181.1650
## ENSG00000285976.1 chr6 63572012-63583587 + | 875.4424
## ENSG00000285979.1 chr16 57177349-57181390 + | 38.3502
## ENSG00000285991.1 chr6 149817937-149896011 - | 11.2772
## log2FoldChange lfcSE pvalue padj
## <numeric> <numeric> <numeric> <numeric>
## ENSG00000000003.14 -0.3401220 0.1063304 6.65282e-04 4.63552e-03
## ENSG00000000419.12 0.1770178 0.1218213 1.13720e-01 2.88125e-01
## ENSG00000000457.13 0.0269533 0.1394669 8.27650e-01 9.21718e-01
## ENSG00000000460.16 -0.0616870 0.2231260 6.92964e-01 8.48743e-01
## ENSG00000000971.15 0.4206549 0.0903614 9.59508e-07 1.36387e-05
## ... ... ... ... ...
## ENSG00000285953.1 -1.2313653 0.916996 0.00311401 0.0171889
## ENSG00000285967.1 -0.2623422 0.169901 0.06919688 0.2019448
## ENSG00000285976.1 0.2247352 0.136898 0.06675037 0.1965808
## ENSG00000285979.1 0.1614980 0.257628 0.33148631 0.5713913
## ENSG00000285991.1 -0.0168702 0.290081 0.87313221 NA
## -------
## seqinfo: 25 sequences (1 circular) from hg38 genomeWe 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.
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$padj),], 4)## log2 fold change (MLE): strainmut.minute180
## LRT p-value: '~ strain + minute + strain:minute' vs '~ strain + minute'
## DataFrame with 4 rows and 7 columns
## baseMean log2FoldChange lfcSE stat pvalue
## <numeric> <numeric> <numeric> <numeric> <numeric>
## SPBC2F12.09c 174.671 -2.6567195 0.752261 97.2834 1.97415e-19
## SPAC1002.18 444.505 -0.0509321 0.204299 56.9536 5.16955e-11
## SPAC1002.19 336.373 -0.3927490 0.573494 43.5339 2.87980e-08
## SPAC1002.17c 261.773 -1.1387648 0.606129 39.3158 2.05137e-07
## padj symbol
## <numeric> <character>
## SPBC2F12.09c 1.33453e-15 atf21
## SPAC1002.18 1.74731e-07 urg3
## SPAC1002.19 6.48916e-05 urg1
## SPAC1002.17c 3.46682e-04 urg2This is just one of the tests that can be applied to time series data. Another option would be to model the counts as a smooth function of time, and to include an interaction term of the condition with the smooth function. It is possible to build such a model using spline basis functions within R, and another, more modern approach is using Gaussian processes (Tonner et al. 2017).
We can plot the counts for the groups over time using_ggplot2, for the gene with the smallest adjusted p value, testing for condition-dependent time profile and accounting for differences at time 0 (figure below). Keep in mind that the interaction terms are the_difference between the two groups at a given time after accounting for the difference at time 0.
fiss <- plotCounts(ddsTC, which.min(resTC$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(res30$padj),]## log2 fold change (MLE): strainmut.minute30
## Wald test p-value: strainmut.minute30
## DataFrame with 1 row and 6 columns
## baseMean log2FoldChange lfcSE stat pvalue padj
## <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
## SPBC2F12.09c 174.671 -2.60047 0.634343 -4.09947 4.14099e-05 0.279931We can furthermore cluster significant genes by their profiles. We extract a matrix of the log2 fold changes using the _coef_function. Note that these are the maximum likelihood estimates (MLE). For shrunken LFC, one must obtain them one coefficient at a time using lfcShrink.
betas <- coef(ddsTC)
colnames(betas)## [1] "Intercept" "strain_mut_vs_wt" "minute_15_vs_0"
## [4] "minute_30_vs_0" "minute_60_vs_0" "minute_120_vs_0"
## [7] "minute_180_vs_0" "strainmut.minute15" "strainmut.minute30"
## [10] "strainmut.minute60" "strainmut.minute120" "strainmut.minute180"We can now plot the log2 fold changes in a heatmap (figure below).
topGenes <- head(order(resTC$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).
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 theBioconductor support site along with all code used in the analysis.
sessionInfo()## R version 4.5.0 RC (2025-04-04 r88126)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.2 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.21-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.12.0 LAPACK version 3.12.0
##
## 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
##
## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] grid stats4 stats graphics grDevices utils datasets
## [8] methods base
##
## other attached packages:
## [1] fission_1.28.0 RUVSeq_1.42.0
## [3] edgeR_4.6.1 limma_3.64.0
## [5] EDASeq_2.42.0 ShortRead_1.66.0
## [7] GenomicAlignments_1.44.0 Rsamtools_2.24.0
## [9] Biostrings_2.76.0 XVector_0.48.0
## [11] sva_3.56.0 BiocParallel_1.42.0
## [13] mgcv_1.9-3 nlme_3.1-168
## [15] Gviz_1.52.0 org.Hs.eg.db_3.21.0
## [17] genefilter_1.90.0 apeglm_1.30.0
## [19] ggbeeswarm_0.7.2 glmpca_0.2.0
## [21] PoiClaClu_1.0.2.1 RColorBrewer_1.1-3
## [23] pheatmap_1.0.12 ggplot2_3.5.2
## [25] dplyr_1.1.4 vsn_3.76.0
## [27] DESeq2_1.48.0 magrittr_2.0.3
## [29] GenomicFeatures_1.60.0 AnnotationDbi_1.70.0
## [31] tximeta_1.26.0 airway_1.28.0
## [33] SummarizedExperiment_1.38.0 Biobase_2.68.0
## [35] GenomicRanges_1.60.0 GenomeInfoDb_1.44.0
## [37] IRanges_2.42.0 S4Vectors_0.46.0
## [39] BiocGenerics_0.54.0 generics_0.1.3
## [41] MatrixGenerics_1.20.0 matrixStats_1.5.0
## [43] rmarkdown_2.29 knitr_1.50
## [45] BiocStyle_2.36.0
##
## loaded via a namespace (and not attached):
## [1] splines_4.5.0 BiocIO_1.18.0 bitops_1.0-9
## [4] filelock_1.0.3 R.oo_1.27.0 tibble_3.2.1
## [7] preprocessCore_1.70.0 rpart_4.1.24 XML_3.99-0.18
## [10] lifecycle_1.0.4 httr2_1.1.2 pwalign_1.4.0
## [13] lattice_0.22-7 vroom_1.6.5 ensembldb_2.32.0
## [16] MASS_7.3-65 backports_1.5.0 Hmisc_5.2-3
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## [22] DBI_1.2.3 abind_1.4-8 R.utils_2.13.0
## [25] purrr_1.0.4 AnnotationFilter_1.32.0 biovizBase_1.56.0
## [28] RCurl_1.98-1.17 nnet_7.3-20 VariantAnnotation_1.54.0
## [31] rappdirs_0.3.3 GenomeInfoDbData_1.2.14 annotate_1.86.0
## [34] codetools_0.2-20 DelayedArray_0.34.1 xml2_1.3.8
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## [40] BiocFileCache_2.16.0 base64enc_0.1-3 jsonlite_2.0.0
## [43] Formula_1.2-5 survival_3.8-3 bbmle_1.0.25.1
## [46] tools_4.5.0 progress_1.2.3 Rcpp_1.0.14
## [49] glue_1.8.0 gridExtra_2.3 SparseArray_1.8.0
## [52] xfun_0.52 withr_3.0.2 numDeriv_2016.8-1.1
## [55] BiocManager_1.30.25 fastmap_1.2.0 latticeExtra_0.6-30
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## [70] htmlwidgets_1.6.4 prettyunits_1.2.0 httr_1.4.7
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## [76] blob_1.2.4 hwriter_1.3.2.1 htmltools_0.5.8.1
## [79] bookdown_0.43 ProtGenerics_1.40.0 scales_1.3.0
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## [100] xtable_1.8-4 cluster_2.1.8.1 htmlTable_2.4.3
## [103] archive_1.1.12 beeswarm_0.4.0 tximport_1.36.0
## [106] evaluate_1.0.3 readr_2.1.5 tinytex_0.57
## [109] magick_2.8.6 mvtnorm_1.3-3 cli_3.6.4
## [112] locfit_1.5-9.12 compiler_4.5.0 rlang_1.1.6
## [115] crayon_1.5.3 labeling_0.4.3 aroma.light_3.38.0
## [118] interp_1.1-6 emdbook_1.3.13 affy_1.86.0
## [121] plyr_1.8.9 stringi_1.8.7 deldir_2.0-4
## [124] txdbmaker_1.4.0 munsell_0.5.1 lazyeval_0.2.2
## [127] Matrix_1.7-3 BSgenome_1.76.0 hms_1.1.3
## [130] bit64_4.6.0-1 KEGGREST_1.48.0 statmod_1.5.0
## [133] AnnotationHub_3.16.0 memoise_2.0.1 affyio_1.78.0
## [136] bslib_0.9.0 bit_4.6.0References
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