EDASeq: Exploratory Data Analysis and Normalization for RNA-Seq
Last modified: May 17, 2018; Compiled: April 26, 2022
Contents
1 Introduction
In this document, we show how to conduct Exploratory Data Analysis
(EDA) and normalization for a typical RNA-Seq experiment using the
package EDASeq.
One can think of EDA for RNA-Seq as a two-step process: “read-level” EDA helps in discovering lanes with low sequencing depths, quality issues, and unusual nucleotide frequencies, while ``gene-level’’ EDA can capture mislabeled lanes, issues with distributional assumptions (e.g., over-dispersion), and GC-content bias.
The package also implements both “within-lane” and “between-lane” normalization procedures, to account, respectively, for within-lane gene-specific (and possibly lane-specific) effects on read counts (e.g., related to gene length or GC-content) and for between-lane distributional differences in read counts (e.g., sequencing depths).
To illustrate the functionality of the EDASeq package, we
make use of the Saccharomyces cerevisiae RNA-Seq data from
(Lee et al. 2008). Briefly, a wild-type strain and three mutant
strains were sequenced using the Solexa 1G Genome Analyzer. For each
strain, there are four technical replicate lanes from the same library
preparation. The reads were aligned using Bowtie
(Langmead et al. 2009), with unique mapping and allowing up to
two mismatches.
The leeBamViews package provides a subset of the aligned
reads in BAM format. In particular, only the reads mapped between
bases 800,000 and 900,000 of chromosome XIII are considered. We use
these reads to illustrate read-level EDA.
The yeastRNASeq package contains gene-level read counts for
four lanes: two replicates of the wild-type strain (“wt”) and
two replicates of one of the mutant strains (“mut”). We use
these data to illustrate gene-level EDA.
library(EDASeq)
library(yeastRNASeq)
library(leeBamViews)2 Reading in unaligned and aligned read data
2.1 Unaligned reads
Unaligned (unmapped) reads stored in FASTQ format may be managed via
the class FastqFileList imported from ShortRead.
Information related to the libraries sequenced in each lane can be
stored in the elementMetadata slot of the
FastqFileList object.
files <- list.files(file.path(system.file(package = "yeastRNASeq"),
"reads"), pattern = "fastq", full.names = TRUE)
names(files) <- gsub("\\.fastq.*", "", basename(files))
met <- DataFrame(conditions=c(rep("mut",2), rep("wt",2)),
row.names=names(files))
fastq <- FastqFileList(files)
elementMetadata(fastq) <- met
fastq## FastqFileList of length 4
## names(4): mut_1_f mut_2_f wt_1_f wt_2_f2.2 Aligned reads
The package can deal with aligned (mapped) reads in BAM format, using
the class BamFileList from Rsamtools. Again, the
elementMetadata slot can be used to store lane-level sample
information.
files <- list.files(file.path(system.file(package = "leeBamViews"), "bam"),
pattern = "bam$", full.names = TRUE)
names(files) <- gsub("\\.bam", "", basename(files))
gt <- gsub(".*/", "", files)
gt <- gsub("_.*", "", gt)
lane <- gsub(".*(.)$", "\\1", gt)
geno <- gsub(".$", "", gt)
pd <- DataFrame(geno=geno, lane=lane,
row.names=paste(geno,lane,sep="."))
bfs <- BamFileList(files)
elementMetadata(bfs) <- pd
bfs## BamFileList of length 8
## names(8): isowt5_13e isowt6_13e ... xrn1_13e xrn2_13e3 Read-level EDA
3.1 Numbers of unaligned and aligned reads
One important check for quality control is to look at the total number of reads produced in each lane, the number and the percentage of reads mapped to a reference genome. A low total number of reads might be a symptom of low quality of the input RNA, while a low mapping percentage might indicate poor quality of the reads (low complexity), problems with the reference genome, or mislabeled lanes.
colors <- c(rep(rgb(1,0,0,alpha=0.7),2),
rep(rgb(0,0,1,alpha=0.7),2),
rep(rgb(0,1,0,alpha=0.7),2),
rep(rgb(0,1,1,alpha=0.7),2))
barplot(bfs,las=2,col=colors)
The figure, produced using the barplot method for the
BamFileList class, displays the number of mapped reads for
the subset of the yeast dataset included in the package
leeBamViews. Unfortunately, leeBamViews does
not provide unaligned reads, but barplots of the total number of reads
can be obtained using the barplot method for the
FastqFileList class. Analogously, one can plot the percentage
of mapped reads with the plot method with signature
c(x="BamFileList", y="FastqFileList"). See the manual pages for
details.
3.2 Read quality scores
As an additional quality check, one can plot the mean per-base (i.e., per-cycle) quality of the unmapped or mapped reads in every lane.
plotQuality(bfs,col=colors,lty=1)
legend("topright",unique(elementMetadata(bfs)[,1]), fill=unique(colors))
3.3 Individual lane summaries
If one is interested in looking more thoroughly at one lane, it is possible to display the per-base distribution of quality scores for each lane and the number of mapped reads stratified by chromosome or strand. As expected, all the reads are mapped to chromosome XIII.
plotQuality(bfs[[1]],cex.axis=.8)
barplot(bfs[[1]],las=2)
3.4 Read nucleotide distributions
A potential source of bias is related to the sequence composition of
the reads. The function plotNtFrequency plots the
per-base nucleotide frequencies for all the reads in a given
lane.
plotNtFrequency(bfs[[1]])
4 Gene-level EDA
Examining statistics and quality metrics at a read level can help in discovering problematic libraries or systematic biases in one or more lanes. Nevertheless, some biases can be difficult to detect at this scale and gene-level EDA is equally important.
4.1 Classes and methods for gene-level counts
There are several Bioconductor packages for aggregating reads over
genes (or other genomic regions, such as, transcripts and exons) given
a particular genome annotation, e.g., IRanges,
ShortRead, Genominator, Rsubread. See
their respective vignettes for details.
Here, we consider this step done and load the object
geneLevelData from yeastRNASeq, which provides
gene-level counts for 2 wild-type and 2 mutant lanes from the yeast
dataset of lee2008novel (see the Genominator
vignette for an example on the same dataset).
data(geneLevelData)
head(geneLevelData)## mut_1 mut_2 wt_1 wt_2
## YHR055C 0 0 0 0
## YPR161C 38 39 35 34
## YOL138C 31 33 40 26
## YDR395W 55 52 47 47
## YGR129W 29 26 5 5
## YPR165W 189 180 151 180Since it is useful to explore biases related to length and GC-content,
the EDASeq package provides, for illustration purposes,
length and GC-content for S. cerevisiae genes (based on SGD
annotation, version r64 (“Saccharomyces Genome Database,” n.d.)).
Functionality for automated retrieval of gene length and GC-content is introduced in the last section of the vignette.
data(yeastGC)
head(yeastGC)## YAL001C YAL002W YAL003W YAL004W YAL005C YAL007C
## 0.3712317 0.3717647 0.4460548 0.4490741 0.4406428 0.3703704data(yeastLength)
head(yeastLength)## YAL001C YAL002W YAL003W YAL004W YAL005C YAL007C
## 3483 3825 621 648 1929 648First, we filter the non-expressed genes, i.e., we consider only the genes with an average read count greater than 10 across the four lanes and for which we have length and GC-content information.
filter <- apply(geneLevelData,1,function(x) mean(x)>10)
table(filter)## filter
## FALSE TRUE
## 1988 5077common <- intersect(names(yeastGC),
rownames(geneLevelData[filter,]))
length(common)## [1] 4994This leaves us with 4994 genes.
The EDASeq package provides the SeqExpressionSet
class to store gene counts, (lane-level) information on the sequenced
libraries, and (gene-level) feature information. We use the data
frame met created in Section secRead for the
lane-level data. As for the feature data, we use gene length and
GC-content.
feature <- data.frame(gc=yeastGC,length=yeastLength)
data <- newSeqExpressionSet(counts=as.matrix(geneLevelData[common,]),
featureData=feature[common,],
phenoData=data.frame(
conditions=factor(c(rep("mut",2),rep("wt",2))),
row.names=colnames(geneLevelData)))
data## SeqExpressionSet (storageMode: lockedEnvironment)
## assayData: 4994 features, 4 samples
## element names: counts, normalizedCounts, offset
## protocolData: none
## phenoData
## sampleNames: mut_1 mut_2 wt_1 wt_2
## varLabels: conditions
## varMetadata: labelDescription
## featureData
## featureNames: YAL001C YAL002W ... YPR201W (4994
## total)
## fvarLabels: gc length
## fvarMetadata: labelDescription
## experimentData: use 'experimentData(object)'
## Annotation:Note that the row names of counts and featureData
must be the same; likewise for the row names of phenoData
and the column names of counts. The expression values can be accessed with counts, the lane information with pData,
and the feature information with fData.
head(counts(data))## mut_1 mut_2 wt_1 wt_2
## YAL001C 80 83 27 40
## YAL002W 33 38 53 66
## YAL003W 1887 1912 270 270
## YAL004W 90 110 276 295
## YAL005C 325 316 874 935
## YAL007C 27 30 19 24pData(data)## conditions
## mut_1 mut
## mut_2 mut
## wt_1 wt
## wt_2 wthead(fData(data))## gc length
## YAL001C 0.3712317 3483
## YAL002W 0.3717647 3825
## YAL003W 0.4460548 621
## YAL004W 0.4490741 648
## YAL005C 0.4406428 1929
## YAL007C 0.3703704 648The SeqExpressionSet class has two additional slots:
normalizedCounts and offset (matrices of the same dimension as counts),
which may be used to store a matrix of normalized counts and of
normalization offsets, respectively, to be used for subsequent analyses (see Section
and the edgeR vignette for details on the
role of offsets). If not specified, the offset is initialized as a matrix
of zeros.
head(offst(data))## mut_1 mut_2 wt_1 wt_2
## YAL001C 0 0 0 0
## YAL002W 0 0 0 0
## YAL003W 0 0 0 0
## YAL004W 0 0 0 0
## YAL005C 0 0 0 0
## YAL007C 0 0 0 04.2 Between-lane distribution of gene-level counts
One of the main considerations when dealing with gene-level counts is
the difference in count distributions between lanes. The
boxplot method provides an easy way to produce boxplots of
the logarithms of the gene counts in each lane.
boxplot(data,col=colors[1:4])
The MDPlot method produces a mean-difference plot (MD-plot)
of read counts for two lanes.
MDPlot(data,c(1,3))
4.3 Over-dispersion
Although the Poisson distribution is a natural and simple way to model
count data, it has the limitation of assuming equality of the mean and
variance. For this reason, the negative binomial distribution has been
proposed as an alternative when the data show over-dispersion. The
function meanVarPlot can be used to check whether the
count data are over-dispersed (for the Poisson distribution, one would
expect the points in the following Figures to be evenly
scattered around the black line).
meanVarPlot(data[,1:2], log=TRUE, ylim=c(0,16))
meanVarPlot(data, log=TRUE, ylim=c(0,16))
Note that the mean-variance relationship should be examined within replicate lanes only (i.e., conditional on variables expected to contribute to differential expression). For the yeast dataset, it is not surprising to see no evidence of over-dispersion for the two mutant technical replicate lanes; likewise for the two wild-type lanes. However, one expects over-dispersion in the presence of biological variability, when considering at once all four mutant and wild-type lanes (???).
4.4 Gene-specific effects on read counts
Several authors have reported selection biases related to sequence features such as gene length, GC-content, and mappability (Bullard et al. 2010, @hansen2011removing, @oshlack2009transcript, @risso2011gc).
In the following figure, obtained using biasPlot, one can
see the dependence of gene-level counts on GC-content. The same plot
could be created for gene length or mappability instead of GC-content.
biasPlot(data, "gc", log=TRUE, ylim=c(1,5))
To show that GC-content dependence can bias differential expression
analysis, one can produce stratified boxplots of the log-fold-change
of read counts from two lanes using the biasBoxplot method.
Again, the same type of plots can be created
for gene length or mappability.
lfc <- log(counts(data)[,3]+0.1) - log(counts(data)[,1]+0.1)
biasBoxplot(lfc, fData(data)$gc)
5 Normalization
Following (Risso et al. 2011), we consider two main types of effects
on gene-level counts: (1) within-lane gene-specific (and possibly
lane-specific) effects, e.g., related to gene length or GC-content,
and (2) effects related to between-lane distributional differences,
e.g., sequencing depth. Accordingly,
withinLaneNormalization and
betweenLaneNormalization adjust for the first and second
type of effects, respectively. We recommend to normalize for
within-lane effects prior to between-lane normalization.
We implemented four within-lane normalization methods, namely: loess
robust local regression of read counts (log) on a gene feature such as
GC-content (loess), global-scaling between feature strata
using the median (median), global-scaling between feature
strata using the upper-quartile (upper), and full-quantile
normalization between feature strata (full). For a discussion
of these methods in context of GC-content normalization see
(Risso et al. 2011).
dataWithin <- withinLaneNormalization(data,"gc", which="full")
dataNorm <- betweenLaneNormalization(dataWithin, which="full")Regarding between-lane normalization, the package implements three of
the methods introduced in (Bullard et al. 2010):
global-scaling using the median (median), global-scaling using
the upper-quartile (upper), and full-quantile normalization
(full).
The next figure shows how after full-quantile within- and between-lane normalization, the GC-content bias is reduced and the distribution of the counts is the same in each lane.
biasPlot(dataNorm, "gc", log=TRUE, ylim=c(1,5))
boxplot(dataNorm, col=colors)
5.1 Offset
Some authors have argued that it is better to leave the count data
unchanged to preserve their sampling properties and instead use an
offset for normalization purposes in the statistical model for read
counts
(???). This
can be achieved easily using the argument offset in both
normalization functions.
dataOffset <- withinLaneNormalization(data,"gc",
which="full",offset=TRUE)
dataOffset <- betweenLaneNormalization(dataOffset,
which="full",offset=TRUE)Note that the dataOffset object will have both normalized
counts and offset stored in their respective slots.
6 Differential expression analysis
One of the main applications of RNA-Seq is differential expression
analysis. The normalized counts (or the original counts and the
offset) obtained using the EDASeq package can be supplied
to packages such as edgeR (Robinson, McCarthy, and Smyth 2010) or
DESeq2 (Love, Huber, and Anders 2014) to find differentially
expressed genes. This section should be considered only as an
illustration of the compatibility of the results of EDASeq
with two of the most widely used packages for differential expression;
we refer ther reader to the edgeR’s user guide and to the DESeq2 vignettes for more details on the methods implemented there.
6.1 edgeR
We can perform a differential expression analysis with
edgeR based on the original counts by passing an offset to
the generalized linear model. See the edgeR vignette for details
about how to perform a differential expression analysis with more complex designs or more robust approaches.
library(edgeR)
design <- model.matrix(~conditions, data=pData(dataOffset))
y <- DGEList(counts=counts(dataOffset),
group=pData(dataOffset)$conditions)
y$offset <- -offst(dataOffset)
y <- estimateDisp(y, design)
fit <- glmFit(y, design)
lrt <- glmLRT(fit, coef=2)
topTags(lrt)## Coefficient: conditionswt
## logFC logCPM LR PValue
## YPL198W -7.424994 10.437912 2135.344 0.000000e+00
## YMR013W-A -6.236270 9.920053 1678.226 0.000000e+00
## YGL088W -5.554418 11.444995 3001.192 0.000000e+00
## YAL003W -2.991238 11.609151 2899.918 0.000000e+00
## YCL040W 1.938459 13.172063 3286.985 0.000000e+00
## YFL014W -1.492220 13.156236 2724.811 0.000000e+00
## YGL076C -4.206623 9.966608 1420.289 8.198093e-311
## YLR110C -1.079939 13.004727 1320.927 3.202620e-289
## YLR167W -2.009235 11.080563 1299.033 1.833950e-284
## YNL036W -2.403393 10.350078 1079.020 1.199052e-236
## FDR
## YPL198W 0.000000e+00
## YMR013W-A 0.000000e+00
## YGL088W 0.000000e+00
## YAL003W 0.000000e+00
## YCL040W 0.000000e+00
## YFL014W 0.000000e+00
## YGL076C 5.848754e-308
## YLR110C 1.999235e-286
## YLR167W 1.017638e-281
## YNL036W 5.988065e-2346.2 DESeq2
We can perform the same differential expression analysis with
DESeq2.
library(DESeq2)
dds <- DESeqDataSetFromMatrix(countData = counts(dataOffset),
colData = pData(dataOffset),
design = ~ conditions)
normFactors <- exp(-1 * offst(dataOffset))
normFactors <- normFactors / exp(rowMeans(log(normFactors)))
normalizationFactors(dds) <- normFactors
dds <- DESeq(dds)
res <- results(dds)
res## log2 fold change (MLE): conditions wt vs mut
## Wald test p-value: conditions wt vs mut
## DataFrame with 4994 rows and 6 columns
## baseMean log2FoldChange lfcSE stat
## <numeric> <numeric> <numeric> <numeric>
## YAL001C 56.0099 -1.101637 0.378950 -2.90708
## YAL002W 53.3486 1.614092 0.386722 4.17377
## YAL003W 1136.8612 -2.991780 0.146400 -20.43569
## YAL004W 178.9912 0.990713 0.233707 4.23912
## YAL005C 560.4825 0.814788 0.164510 4.95281
## ... ... ... ... ...
## YPR196W 10.61537 0.597979 0.810533 0.737760
## YPR197C 18.52248 0.905072 0.620132 1.459483
## YPR198W 62.69788 0.607913 0.347310 1.750348
## YPR199C 33.25060 -1.192572 0.485729 -2.455222
## YPR201W 9.56508 0.165297 0.862888 0.191562
## pvalue padj
## <numeric> <numeric>
## YAL001C 3.64821e-03 2.57142e-02
## YAL002W 2.99595e-05 4.37100e-04
## YAL003W 8.05405e-93 1.93297e-89
## YAL004W 2.24395e-05 3.40854e-04
## YAL005C 7.31511e-07 1.59602e-05
## ... ... ...
## YPR196W 0.4606602 NA
## YPR197C 0.1444323 0.3593960
## YPR198W 0.0800583 0.2442976
## YPR199C 0.0140797 0.0725916
## YPR201W 0.8480851 NA7 Definitions and conventions
7.1 Rounding
After either within-lane or between-lane normalization, the expression values are not counts anymore. However, their distribution still shows some typical features of counts distribution (e.g., the variance depends on the mean). Hence, for most applications, it is useful to round the normalized values to recover count-like values, which we refer to as “pseudo-counts”.
By default, both
withinLaneNormalization and
betweenLaneNormalization round the normalized values to
the closest integer. This behavior can be changed by specifying
round=FALSE. This gives the user more flexibility and assures
that rounding approximations do not affect subsequent computations
(e.g., recovering the offset from the normalized counts).
7.2 Zero counts
To avoid problems in the computation of logarithms (e.g. in log-fold-changes), we add a small positive constant (namely \(0.1\)) to the counts. For instance, the log-fold-change between \(y_1\) and \(y_2\) is defined as \[\begin{equation*} \frac{\log(y_1 + 0.1)}{\log(y_2 + 0.1)}. \end{equation*}\]
7.3 Offset
We define an offset in the normalization as \[\begin{equation*} o = \log(y_{norm} + 0.1) - \log(y_{raw} + 0.1), \end{equation*}\] where \(y_{norm}\) and \(y_{raw}\) are the normalized and raw counts, respectively.
One can easily recover the normalized data from the raw counts and offset, as shown here:
dataNorm <- betweenLaneNormalization(data, round=FALSE, offset=TRUE)
norm1 <- normCounts(dataNorm)
norm2 <- exp(log(counts(dataNorm) + 0.1 ) + offst(dataNorm)) - 0.1
head(norm1 - norm2)## mut_1 mut_2 wt_1
## YAL001C -1.421085e-14 -1.421085e-14 0.000000e+00
## YAL002W 3.552714e-15 -7.105427e-15 -2.131628e-14
## YAL003W 4.547474e-13 -2.273737e-13 1.136868e-13
## YAL004W -2.842171e-14 -1.421085e-14 5.684342e-14
## YAL005C -1.136868e-13 5.684342e-14 -3.410605e-13
## YAL007C 3.552714e-15 3.552714e-15 -3.552714e-15
## wt_2
## YAL001C 0.000000e+00
## YAL002W 0.000000e+00
## YAL003W -5.684342e-14
## YAL004W -5.684342e-14
## YAL005C -1.136868e-13
## YAL007C 3.552714e-15Note that the small constant added in the definition of offset does not matter when pseudo-counts are considered, i.e.,
head(round(normCounts(dataNorm)) - round(counts(dataNorm) * exp(offst(dataNorm))))## mut_1 mut_2 wt_1 wt_2
## YAL001C 0 0 0 0
## YAL002W 0 0 0 0
## YAL003W 0 0 0 0
## YAL004W 0 0 0 0
## YAL005C 0 0 0 0
## YAL007C 0 0 0 0We defined the offset as the log-ratio between normalized and raw
counts. However, the edgeR functions expect as offset
argument the log-ratio between raw and normalized counts. One must use
-offst(offsetData) as the offset argument of edgeR.
8 Retrieving gene length and GC-content
Two essential features the gene-level EDA normalizes for are gene length and
GC-content. As users might wish to automatically retrieve this information, we
provide the function getGeneLengthAndGCContent. Given selected
ENTREZ or ENSEMBL gene IDs and the organism under investigation, this can be
done either based on BioMart (default) or using BioC annotation utilities.
getGeneLengthAndGCContent(id=c("ENSG00000012048", "ENSG00000139618"), org="hsa")Accordingly, we can retrieve the precalculated yeast data that has been used throughout the vignette via
fData(data) <- getGeneLengthAndGCContent(featureNames(data),
org="sacCer3", mode="org.db")9 SessionInfo
sessionInfo()## R version 4.2.0 RC (2022-04-19 r82224)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.4 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.15-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.15-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] stats4 stats graphics grDevices utils
## [6] datasets methods base
##
## other attached packages:
## [1] DESeq2_1.36.0 edgeR_3.38.0
## [3] limma_3.52.0 leeBamViews_1.31.1
## [5] BSgenome_1.64.0 rtracklayer_1.56.0
## [7] yeastRNASeq_0.33.0 EDASeq_2.30.0
## [9] ShortRead_1.54.0 GenomicAlignments_1.32.0
## [11] SummarizedExperiment_1.26.0 MatrixGenerics_1.8.0
## [13] matrixStats_0.62.0 Rsamtools_2.12.0
## [15] GenomicRanges_1.48.0 Biostrings_2.64.0
## [17] GenomeInfoDb_1.32.0 XVector_0.36.0
## [19] IRanges_2.30.0 S4Vectors_0.34.0
## [21] BiocParallel_1.30.0 Biobase_2.56.0
## [23] BiocGenerics_0.42.0 knitr_1.38
## [25] BiocStyle_2.24.0
##
## loaded via a namespace (and not attached):
## [1] colorspace_2.0-3 rjson_0.2.21
## [3] hwriter_1.3.2.1 ellipsis_0.3.2
## [5] bit64_4.0.5 AnnotationDbi_1.58.0
## [7] fansi_1.0.3 xml2_1.3.3
## [9] splines_4.2.0 R.methodsS3_1.8.1
## [11] cachem_1.0.6 geneplotter_1.74.0
## [13] jsonlite_1.8.0 annotate_1.74.0
## [15] dbplyr_2.1.1 png_0.1-7
## [17] R.oo_1.24.0 BiocManager_1.30.17
## [19] compiler_4.2.0 httr_1.4.2
## [21] assertthat_0.2.1 Matrix_1.4-1
## [23] fastmap_1.1.0 cli_3.3.0
## [25] htmltools_0.5.2 prettyunits_1.1.1
## [27] tools_4.2.0 gtable_0.3.0
## [29] glue_1.6.2 GenomeInfoDbData_1.2.8
## [31] dplyr_1.0.8 rappdirs_0.3.3
## [33] Rcpp_1.0.8.3 jquerylib_0.1.4
## [35] vctrs_0.4.1 xfun_0.30
## [37] stringr_1.4.0 lifecycle_1.0.1
## [39] restfulr_0.0.13 XML_3.99-0.9
## [41] scales_1.2.0 zlibbioc_1.42.0
## [43] aroma.light_3.26.0 hms_1.1.1
## [45] parallel_4.2.0 RColorBrewer_1.1-3
## [47] yaml_2.3.5 curl_4.3.2
## [49] memoise_2.0.1 ggplot2_3.3.5
## [51] sass_0.4.1 biomaRt_2.52.0
## [53] latticeExtra_0.6-29 stringi_1.7.6
## [55] RSQLite_2.2.12 highr_0.9
## [57] genefilter_1.78.0 BiocIO_1.6.0
## [59] GenomicFeatures_1.48.0 filelock_1.0.2
## [61] rlang_1.0.2 pkgconfig_2.0.3
## [63] bitops_1.0-7 evaluate_0.15
## [65] lattice_0.20-45 purrr_0.3.4
## [67] bit_4.0.4 tidyselect_1.1.2
## [69] magrittr_2.0.3 bookdown_0.26
## [71] R6_2.5.1 magick_2.7.3
## [73] generics_0.1.2 DelayedArray_0.22.0
## [75] DBI_1.1.2 pillar_1.7.0
## [77] survival_3.3-1 KEGGREST_1.36.0
## [79] RCurl_1.98-1.6 tibble_3.1.6
## [81] crayon_1.5.1 KernSmooth_2.23-20
## [83] utf8_1.2.2 BiocFileCache_2.4.0
## [85] rmarkdown_2.14 jpeg_0.1-9
## [87] progress_1.2.2 locfit_1.5-9.5
## [89] grid_4.2.0 blob_1.2.3
## [91] digest_0.6.29 xtable_1.8-4
## [93] R.utils_2.11.0 munsell_0.5.0
## [95] bslib_0.3.1References
Bullard, James H, Elizabeth Purdom, Kasper D Hansen, and Sandrine Dudoit. 2010. “Evaluation of Statistical Methods for Normalization and Differential Expression in mRNA-Seq Experiments.” BMC Bioinformatics 11 (1): 94.
Langmead, Ben, Cole Trapnell, Mihai Pop, and Steven L Salzberg. 2009. “Ultrafast and Memory-Efficient Alignment of Short Dna Sequences to the Human Genome.” Genome Biology 10 (3): R25.
Lee, Albert, Kasper Daniel Hansen, James Bullard, Sandrine Dudoit, and Gavin Sherlock. 2008. “Novel Low Abundance and Transient Rnas in Yeast Revealed by Tiling Microarrays and Ultra High–Throughput Sequencing Are Not Conserved Across Closely Related Yeast Species.” PLoS Genetics 4 (12): e1000299.
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.
Oshlack, Alicia, and Matthew J Wakefield. 2009. “Transcript Length Bias in Rna-Seq Data Confounds Systems Biology.” Biology Direct 4 (1): 14.
Risso, Davide, Katja Schwartz, Gavin Sherlock, and Sandrine Dudoit. 2011. “GC-Content Normalization for Rna-Seq Data.” BMC Bioinformatics 12 (1): 480.
Robinson, Mark D, Davis J McCarthy, and Gordon K Smyth. 2010. “EdgeR: A Bioconductor Package for Differential Expression Analysis of Digital Gene Expression Data.” Bioinformatics 26 (1): 139–40.
“Saccharomyces Genome Database.” n.d. http://www.yeastgenome.org.