1 Introduction

Exon-Intron Split Analysis has been described in (Gaidatzis et al. 2015). It consists of separately quantifying exonic and intronic alignments in RNA-seq data, in order to measure changes in mature RNA and pre-mRNA reads across different experimental conditions. We have shown that this allows quantification of transcriptional and post-transcriptional regulation of gene expression.

The eisaR package contains convenience functions to facilitate the steps in an exon-intron split analysis, which consists of:
1. preparing the annotation (exonic and gene body coordinate ranges, section 3)
2. quantifying RNA-seq alignments in exons and introns (sections 4.1 and 4.2)
3. calculating and comparing exonic and intronic changes across conditions (section 5)
4. visualizing the results (section 6)

For the steps 1. and 2. above, this vignette makes use of Bioconductor annotation and the QuasR package. It is also possible to obtain count tables for exons and introns using some other pipeline or approach, and directly start with step 3.

2 Installation

To install the eisaR package, start R and enter:

# BiocManager is needed to install Bioconductor packages
if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")

# Install eisaR
BiocManager::install("eisaR")

3 Preparing the annotation

As mentioned, eisaR uses gene annotations from Bioconductor. They are provided in the form of TxDb or EnsDb objects, e.g. via packages such as TxDb.Mmusculus.UCSC.mm10.knownGene or EnsDb.Hsapiens.v86. You can see available annotations using the following code:

pkgs <- c(BiocManager::available("TxDb")
          BiocManager::available("EnsDb"))

If you would like to use an alternative source of gene annotations, you might still be able to use eisaR by first converting your annotations into a TxDb or an EnsDb (for creating a TxDb see makeTxDb in the GenomicFeatures package, for creating an EnsDb see makeEnsembldbPackage in the ensembldb package).

For this example, eisaR contains a small TxDb to illustrate how regions are extracted. We will load it from a file. Alternatively, the object would be loaded using library(...), for example using library(TxDb.Mmusculus.UCSC.mm10.knownGene).

# load package
library(eisaR)

# get TxDb object
txdbFile <- system.file("extdata", "hg19sub.sqlite", package = "eisaR")
txdb <- AnnotationDbi::loadDb(txdbFile)

Exon and gene body regions are then extracted from the TxDb:

# extract filtered exonic and gene body regions
regS <- getRegionsFromTxDb(txdb = txdb, strandedData = TRUE)
#> extracting exon coordinates
#> total number of genes/exons: 12/32
#> removing overlapping/single-exon/ambiguous genes (8)
#> creating filtered regions for 4 genes (33.3%) with 20 exons (62.5%)
regU <- getRegionsFromTxDb(txdb = txdb, strandedData = FALSE)
#> extracting exon coordinates
#> total number of genes/exons: 12/32
#> removing overlapping/single-exon/ambiguous genes (9)
#> creating filtered regions for 3 genes (25%) with 17 exons (53.1%)

lengths(regS)
#>      exons genebodies 
#>         20          4
lengths(regU)
#>      exons genebodies 
#>         17          3

regS$exons
#> GRanges object with 20 ranges and 0 metadata columns:
#>                   seqnames      ranges strand
#>                      <Rle>   <IRanges>  <Rle>
#>   ENSG00000078808     chr1 17278-18194      -
#>   ENSG00000078808     chr1 18828-21741      -
#>   ENSG00000078808     chr1 23614-23747      -
#>   ENSG00000078808     chr1 24202-24358      -
#>   ENSG00000078808     chr1 27799-27854      -
#>               ...      ...         ...    ...
#>   ENSG00000186891     chr1   5740-6070      -
#>   ENSG00000186891     chr1   6755-7081      -
#>   ENSG00000254999     chr3   2266-2513      +
#>   ENSG00000254999     chr3 12300-12402      +
#>   ENSG00000254999     chr3 12943-13884      +
#>   -------
#>   seqinfo: 3 sequences from an unspecified genome

As you can see, the filtering procedure removes slightly more genes for unstranded data (strandedData = FALSE), as overlapping genes cannot be discriminated even if they reside on opposite strands.

You can also export the obtained regions into files. This may be useful if you plan to align and/or quantify reads outside of R. For example, you can use rtracklayer to export the regions in regS into .gtf files:

library(rtracklayer)
export(regS$exons, "hg19sub_exons_stranded.gtf")
export(regS$genebodies, "hg19sub_genebodies_stranded.gtf")

4 Quantify RNA-seq alignments in exons and introns

For this example we will use the QuasR package for indexing and alignment of short reads, and a small RNA-seq dataset that is contained in that package. As mentioned, it is also possible to align or also quantify your reads using an alternative aligner/counter, and skip over these steps.

4.1 Align reads

Let’s first copy the sample data from the QuasR package to the current working directory, all contained in a folder named extdata:

library(QuasR)
#> Loading required package: Rbowtie
file.copy(system.file(package = "QuasR", "extdata"), ".", recursive = TRUE)
#> [1] TRUE

We next align the reads to a mini-genome (fasta file extdata/hg19sub.fa) using qAlign:

sampleFile <- "extdata/samples_chip_single.txt"
genomeFile <- "extdata/hg19sub.fa"

proj <- qAlign(sampleFile = "extdata/samples_rna_single.txt", 
               genome = "extdata/hg19sub.fa",
               aligner = "Rhisat2", splicedAlignment = TRUE)
#> Creating .fai file for: /tmp/RtmpNw2WC1/Rbuild1dda2bb23014/eisaR/vignettes/extdata/hg19sub.fa
#> alignment files missing - need to:
#>     create alignment index for the genome
#>     create 4 genomic alignment(s)
#> Creating an Rhisat2 index for /tmp/RtmpNw2WC1/Rbuild1dda2bb23014/eisaR/vignettes/extdata/hg19sub.fa
#> Finished creating index
#> Testing the compute nodes...OK
#> Loading QuasR on the compute nodes...OK
#> Available cores:
#> malbec1: 1
#> Performing genomic alignments for 4 samples. See progress in the log file:
#> /tmp/RtmpNw2WC1/Rbuild1dda2bb23014/eisaR/vignettes/QuasR_log_4fa82aa85589.txt
#> Genomic alignments have been created successfully
alignmentStats(proj)
#>                seqlength mapped unmapped
#> Sample1:genome     95000   5961       43
#> Sample2:genome     95000   5914       86

4.2 Count alignments in exons and gene bodies

Alignments in exons and gene bodies can now be counted using qCount and the regU that we have generated earlier (assuming that the data is unstranded). Intronic counts can then be obtained from the difference between gene bodies and exons:

cntEx <- qCount(proj, regU$exons, orientation = "any")
#> counting alignments...done
#> collapsing counts by sample...done
#> collapsing counts by query name...done
cntGb <- qCount(proj, regU$genebodies, orientation = "any")
#> counting alignments...done
#> collapsing counts by sample...done
cntIn <- cntGb - cntEx
cntEx
#>                 width Sample1 Sample2
#> ENSG00000078808  4837     705    1065
#> ENSG00000186827  1821      37       8
#> ENSG00000186891  1470      26       2
cntIn
#>                 width Sample1 Sample2
#> ENSG00000078808 10307       5      15
#> ENSG00000186827  1012       3       0
#> ENSG00000186891  1734       3       0

As mentioned, both alignments and counts can also be obtained using alternative approaches. It is required that the two resulting exon and intron count tables have identical structure (genes in rows, samples in columns, the same order of rows and columns in both tables).

4.3 Load full count tables

The above example only contains very few genes. For the rest of the vignette, we will use count tables from a real RNA-seq experiment that are provided in the eisaR package. The counts correspond to the raw data used in Figure 3a of (Gaidatzis et al. 2015) and are also available online from the supplementary material:

cntEx <- readRDS(system.file("extdata",
                             "Fig3abc_GSE33252_rawcounts_exonic.rds",
                             package = "eisaR"))
cntIn <- readRDS(system.file("extdata",
                             "Fig3abc_GSE33252_rawcounts_intronic.rds",
                             package = "eisaR"))

5 Run EISA conveniently

All the further steps in exon-intron split analysis can now be performed using a single function runEISA. If you prefer to perform the analysis step-by-step, you can skip now to section 7.

# remove "width" column
Rex <- cntEx[, colnames(cntEx) != "width"]
Rin <- cntIn[, colnames(cntIn) != "width"]

# create condition factor (contrast will be TN - ES)
cond <- factor(c("ES", "ES", "TN", "TN"))

# run EISA
res <- runEISA(Rex, Rin, cond)
#> filtering quantifyable genes...keeping 11759 from 20288 (58%)
#> fitting statistical model...done
#> calculating log-fold changes...done

5.1 Alternative implementations of EISA

There are six arguments in runEISA (modelSamples, geneSelection, effects, statFramework, pscnt and sizeFactor) that control gene filtering, calculation of contrasts and the statistical method used, summarized in the bullet list below.

The default values of these arguments correspond to the currently recommended way of running EISA. You can also run EISA exactly as it was described in (Gaidatzis et al. 2015), by setting method = "Gaidatzis2015". This will override the values of the six other arguments and set them according to the published algorithm (as indicated below).

  • modelSamples: Account for individual samples in statistical model? Possible values are:
    • FALSE (method="Gaidatzis2015"): use a model of the form ~ condition * region
    • TRUE (default): use a model adjusting for the baseline differences among samples, and with condition-specific region effects (similar to the model described in section 3.5 of the edgeR user guide)
  • geneSelection: How to select detected genes. Possible values are:
    • "filterByExpr" (default): First, counts are normalized using edgeR::calcNormFactors, treating intronic and exonic counts as individual samples. Then, the edgeR::filterByExpr function is used with default parameters to select quantifiable genes.
    • "none": This will use all the genes provided in the count tables, assuming that an appropriate selection of quantifiable genes has already been done.
    • "Gaidatzis2015" (method="Gaidatzis2015"): First, intronic and exonic counts are linearly scaled to the mean library size (estimated as the sum of all intronic or exonic counts, respectively). Then, quantifiable genes are selected as the genes with counts x that fulfill log2(x + 8) > 5 in both exons and introns.
  • statFramework: The framework within edgeR that is used for the statistical analysis. Possible values are:
    • "QLF" (default): quasi-likelihood F-test using edgeR::glmQLFit and edgeR::glmQLFTest. This framework is highly recommended as it gives stricter error rate control by accounting for the uncertainty in dispersion estimation.
    • "LRT" (method="Gaidatzis2015"): likelihood ratio test using edgeR::glmFit and edgeR::glmLRT.
  • effects: How the effects (log2 fold-changes) are calculated. Possible values are:
    • "predFC" (default): Fold-changes are calculated using the fitted model with edgeR::predFC and the value provided to pscnt. Please note that if a sample factor is included in the statistical model (modelSamples=TRUE), effects cannot be obtained from that model. In that case, effects are obtained from a simpler model without sample effects.
    • "Gaidatzis2015" (method="Gaidatzis2015"): Fold-changes are calculated using the formula log2((x + pscnt)/(y + pscnt)). If pscnt is not set to 8, runEISA will warn that this deviates from the method used in Gaidatzis et al., 2015.

  • pscnt: The pseudocount that is added to normalized counts before log transformation. For geneSelection="Gaidatzis2015", pscnt is used both in gene selection as well as in the calculation of log2 fold-changes. Otherwise, pscnt is only used in the calculation of log2 fold-changes in edgeR::predFC(, prior.count = pscnt).

  • sizeFactor: How size factors (TMM normalization factors and library sizes) are calculated and used within eisaR:
    • "exon" (default): Size factors are calculated for exonic counts and reused for the corresponding intronic counts.
    • "intron": Size factors are calculated for intronic counts and reused for the corresponding exonic counts.
    • "individual" (method="Gaidatzis2015"): Size factors are calculated independently for exonic and intronic counts.

While different values for these arguments typically yield similar results, the defaults are often less stringent compared to method="Gaidatzis2015" when selecting quantifiable genes, but more stringent when calling significant changes (especially with low numbers of replicates).

Here is an illustration of how the results differ between method="Gaidatzis2015" and the defaults:

res1 <- runEISA(Rex, Rin, cond, method = "Gaidatzis2015")
#> setting parameters according to Gaidatzis et al., 2015
#> filtering quantifyable genes...keeping 8481 from 20288 (41.8%)
#> fitting statistical model...done
#> calculating log-fold changes...done
res2 <- runEISA(Rex, Rin, cond)
#> filtering quantifyable genes...keeping 11759 from 20288 (58%)
#> fitting statistical model...done
#> calculating log-fold changes...done

# number of quantifiable genes
nrow(res1$DGEList)
#> [1] 8481
nrow(res2$DGEList)
#> [1] 11759

# number of genes with significant post-transcriptional regulation
sum(res1$tab.ExIn$FDR < 0.05)
#> [1] 458
sum(res2$tab.ExIn$FDR < 0.05)
#> [1] 114

# method="Gaidatzis2015" results contain most of default results
summary(rownames(res2$contrasts)[res2$tab.ExIn$FDR < 0.05] %in%
        rownames(res1$contrasts)[res1$tab.ExIn$FDR < 0.05])
#>    Mode   FALSE    TRUE 
#> logical      35      79

# comparison of deltas
ids <- intersect(rownames(res1$DGEList), rownames(res2$DGEList))
cor(res1$contrasts[ids,"Dex"], res2$contrasts[ids,"Dex"])
#> [1] 0.9897309
cor(res1$contrasts[ids,"Din"], res2$contrasts[ids,"Din"])
#> [1] 0.9893341
cor(res1$contrasts[ids,"Dex.Din"], res2$contrasts[ids,"Dex.Din"])
#> [1] 0.9673152
plot(res1$contrasts[ids,"Dex.Din"], res2$contrasts[ids,"Dex.Din"], pch = "*",
     xlab = expression(paste(Delta, "exon", -Delta, "intron for method='Gaidatzis2015'")),
     ylab = expression(paste(Delta, "exon", -Delta, "intron for default parameters")))

5.2 On the estimation of interactions in a split-plot design experiment

The calculation of the significance of interactions (here whether the fold-changes differ between exonic or intronic data) is well defined for experimental designs were all samples are independent from one another. Within EISA, this is not the case (each sample yields two data points, one for exons and one for introns). That results in a dependency between data points: If a sample is affected by a problem in the experiment, it might at the same time give rise to outlier values in both exonic and intronic counts.

In statistics, such an experimental design is often referred to as a split-plot design, and a recommended way to analyze interactions in such experiments would be to use a mixed effect model with the plot (in our case, the sample) as a random effect. The disadvantage here however would be that available packages for mixed effect models are not designed for count data, and we therefore use an alternative approach to explicitly model the sample dependency, by introducing sample-specific columns into the design matrix (for modelSamples=TRUE). That sample factor is nested in the condition factor (no sample can belong to more than one condition). Thus, we are in the situation described in section 3.5 (‘Comparisons both between and within subjects’) of the edgeR user guide, and we use the approach described there to define a design matrix with sample-specific baseline effects as well as condition-specific region effects.

This has no impact on the effects (the log2 fold-changes of modelSamples=TRUE and modelSamples=FALSE are nearly identical). However, in the presence of sample effects, modelSamples=TRUE increases the sensitivity of detecting genes with significant interactions. Here is a comparison of the EISA results with and without accounting for the sample in the model:

res3 <- runEISA(Rex, Rin, cond, modelSamples = FALSE)
#> filtering quantifyable genes...keeping 11034 from 20288 (54.4%)
#> fitting statistical model...done
#> calculating log-fold changes...done
res4 <- runEISA(Rex, Rin, cond, modelSamples = TRUE)
#> filtering quantifyable genes...keeping 11759 from 20288 (58%)
#> fitting statistical model...done
#> calculating log-fold changes...done
ids <- intersect(rownames(res3$contrasts), rownames(res4$contrasts))

# number of genes with significant post-transcriptional regulation
sum(res3$tab.ExIn$FDR < 0.05)
#> [1] 6
sum(res4$tab.ExIn$FDR < 0.05)
#> [1] 114

# modelSamples=TRUE results are a super-set of
# modelSamples=FALSE results
summary(rownames(res3$contrasts)[res3$tab.ExIn$FDR < 0.05] %in%
        rownames(res4$contrasts)[res4$tab.ExIn$FDR < 0.05])
#>    Mode    TRUE 
#> logical       6

# comparison of contrasts
diag(cor(res3$contrasts[ids, ], res4$contrasts[ids, ]))
#>       Dex       Din   Dex.Din 
#> 0.9931251 0.9872626 0.9912877
plot(res3$contrasts[ids, 3], res4$contrasts[ids, 3], pch = "*",
     xlab = "Interaction effects for modelSamples=FALSE",
     ylab = "Interaction effects for modelSamples=TRUE")


# comparison of interaction significance
plot(-log10(res3$tab.ExIn[ids, "FDR"]), -log10(res4$tab.ExIn[ids, "FDR"]), pch = "*",
     xlab = "-log10(FDR) for modelSamples=FALSE",
     ylab = "-log10(FDR) for modelSamples=TRUE")
abline(a = 0, b = 1, col = "gray")
legend("bottomright", "y = x", bty = "n", lty = 1, col = "gray")

6 Visualize EISA results

We can now visualize the results by plotting intronic changes versus exonic changes (genes with significant interactions, which are likely to be post-transcriptionally regulated, are color coded):

plotEISA(res)
#> identified 114 genes to highlight

7 Run EISA step-by-step

As an alternative to runEISA (section 5) and plotEISA (section 6) described above, you can also analyze the data step-by-step as described in (Gaidatzis et al. 2015). This may be preferable to understand each individual step and be able to access intermediate results.

The results obtained in this way are identical to what you get with runEISA(..., method = "Gaidatzis2015"), so if you are happy with runEISA you can skip the rest of the vignette.

7.1 Normalization

Normalization is performed separately on exonic and intronic counts, assuming that varying exon over intron ratios between samples are of technical origin.

# remove column "width"
Rex <- cntEx[,colnames(cntEx) != "width"]
Rin <- cntIn[,colnames(cntIn) != "width"]
Rall <- Rex + Rin
fracIn <- colSums(Rin)/colSums(Rall)
summary(fracIn)
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#>  0.2696  0.2977  0.3105  0.3459  0.3587  0.4929

# scale counts to the mean library size,
# separately for exons and introns
Nex <- t(t(Rex) / colSums(Rex) * mean(colSums(Rex)))
Nin <- t(t(Rin) / colSums(Rin) * mean(colSums(Rin)))

# log transform (add a pseudocount of 8)
NLex <- log2(Nex + 8)
NLin <- log2(Nin + 8)

7.2 Identify quantifiable genes

Genes with very low counts in either exons or introns are better removed, as they will be too noisy to yield useful results. We use here a fixed cut-off on the normalized, log-transformed intron and exonic counts:

quantGenes <- rownames(Rex)[ rowMeans(NLex) > 5.0 & rowMeans(NLin) > 5.0 ]
length(quantGenes)
#> [1] 8481

7.3 Calculate \(\Delta I\), \(\Delta E\) and \(\Delta E - \Delta I\)

The count tables were obtained from a total RNA-seq experiments in mouse embryonic stem (MmES) cells and derived terminal neurons (MmTN), with two replicates for each condition.

We will now calculate the changes between neurons and ES cells in introns (\(\Delta I\)), in exons (\(\Delta E\)), and the difference between the two (\(\Delta E - \Delta I\)):

Dex <- NLex[,c("MmTN_RNA_total_a","MmTN_RNA_total_b")] - NLex[,c("MmES_RNA_total_a","MmES_RNA_total_b")]
Din <- NLin[,c("MmTN_RNA_total_a","MmTN_RNA_total_b")] - NLin[,c("MmES_RNA_total_a","MmES_RNA_total_b")]
Dex.Din <- Dex - Din

cor(Dex[quantGenes,1], Dex[quantGenes,2])
#> [1] 0.9379397
cor(Din[quantGenes,1], Din[quantGenes,2])
#> [1] 0.8449252
cor(Dex.Din[quantGenes,1], Dex.Din[quantGenes,2])
#> [1] 0.5518187

Both exonic and intronic changes are correlated across replicates, and so are the differences, indicating a reproducible signal for post-transcriptional regulation.

7.4 Statistical analysis

Finally, we use the replicate measurement in the edgeR framework to calculate the significance of the changes:

# create DGEList object with exonic and intronic counts
library(edgeR)
#> Loading required package: limma
#> 
#> Attaching package: 'limma'
#> The following object is masked from 'package:BiocGenerics':
#> 
#>     plotMA
cnt <- data.frame(Ex = Rex, In = Rin)
y <- DGEList(counts = cnt, genes = data.frame(ENTREZID = rownames(cnt)))

# select quantifiable genes and normalize
y <- y[quantGenes, ]
y <- calcNormFactors(y)

# design matrix with interaction term
region <- factor(c("ex","ex","ex","ex","in","in","in","in"), levels = c("in", "ex"))
cond <- rep(factor(c("ES","ES","TN","TN")), 2)
design <- model.matrix(~ region * cond)
rownames(design) <- colnames(cnt)
design
#>                     (Intercept) regionex condTN regionex:condTN
#> Ex.MmES_RNA_total_a           1        1      0               0
#> Ex.MmES_RNA_total_b           1        1      0               0
#> Ex.MmTN_RNA_total_a           1        1      1               1
#> Ex.MmTN_RNA_total_b           1        1      1               1
#> In.MmES_RNA_total_a           1        0      0               0
#> In.MmES_RNA_total_b           1        0      0               0
#> In.MmTN_RNA_total_a           1        0      1               0
#> In.MmTN_RNA_total_b           1        0      1               0
#> attr(,"assign")
#> [1] 0 1 2 3
#> attr(,"contrasts")
#> attr(,"contrasts")$region
#> [1] "contr.treatment"
#> 
#> attr(,"contrasts")$cond
#> [1] "contr.treatment"

# estimate model parameters
y <- estimateDisp(y, design)
fit <- glmFit(y, design)

# calculate likelihood-ratio between full and reduced models
lrt <- glmLRT(fit)

# create results table
tt <- topTags(lrt, n = nrow(y), sort.by = "none")
head(tt$table[order(tt$table$FDR, decreasing = FALSE), ])
#>        ENTREZID    logFC   logCPM       LR       PValue          FDR
#> 14680     14680 6.375699 6.554051 95.79494 1.274210e-22 1.080658e-18
#> 75209     75209 5.341413 6.400361 85.66167 2.135122e-20 9.053983e-17
#> 268354   268354 9.854778 8.402066 53.71350 2.319637e-13 6.557614e-10
#> 17957     17957 4.342644 6.864176 51.63948 6.668718e-13 1.413935e-09
#> 93765     93765 3.849670 6.603142 51.08555 8.842689e-13 1.499897e-09
#> 68666     68666 4.536512 5.872792 48.29846 3.660400e-12 5.173976e-09

7.5 Visualize the results

Finally, we visualize the results by plotting intronic changes versus exonic changes (genes with significant interactions, which are likely to be post-transcriptionally regulated, are color coded):

sig     <- tt$table$FDR < 0.05
sum(sig)
#> [1] 490
sig.dir <- sign(tt$table$logFC[sig])
cols <- ifelse(sig, ifelse(tt$table$logFC > 0, "#E41A1CFF", "#497AB3FF"), "#22222244")

# volcano plot
plot(tt$table$logFC, -log10(tt$table$FDR), col = cols, pch = 20,
     xlab = expression(paste("RNA change (log2 ",Delta,"exon/",Delta,"intron)")),
     ylab = "Significance (-log10 FDR)")
abline(h = -log10(0.05), lty = 2)
abline(v = 0, lty = 2)
text(x = par("usr")[1] + 3 * par("cxy")[1], y = par("usr")[4], adj = c(0,1),
     labels = sprintf("n=%d", sum(sig.dir == -1)), col = "#497AB3FF")
text(x = par("usr")[2] - 3 * par("cxy")[1], y = par("usr")[4], adj = c(1,1),
     labels = sprintf("n=%d", sum(sig.dir ==  1)), col = "#E41A1CFF")


# Delta I vs. Delta E
plot(rowMeans(Din)[quantGenes], rowMeans(Dex)[quantGenes], pch = 20, col = cols,
     xlab = expression(paste(Delta,"intron (log2 TN/ES)")),
     ylab = expression(paste(Delta,"exon (log2 TN/ES)")))
legend(x = "bottomright", bty = "n", pch = 20, col = c("#E41A1CFF","#497AB3FF"),
       legend = sprintf("%s (%d)", c("Up","Down"), c(sum(sig.dir == 1), sum(sig.dir == -1))))

8 Session information

The output in this vignette was produced under:

sessionInfo()
#> R version 4.0.3 (2020-10-10)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 18.04.5 LTS
#> 
#> Matrix products: default
#> BLAS:   /home/biocbuild/bbs-3.12-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.12-bioc/R/lib/libRlapack.so
#> 
#> locale:
#>  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
#>  [3] LC_TIME=en_US.UTF-8        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    parallel  stats     graphics  grDevices utils     datasets 
#> [8] methods   base     
#> 
#> other attached packages:
#>  [1] edgeR_3.32.0           limma_3.46.0           QuasR_1.30.0          
#>  [4] Rbowtie_1.30.0         rtracklayer_1.50.0     GenomicFeatures_1.42.0
#>  [7] AnnotationDbi_1.52.0   Biobase_2.50.0         GenomicRanges_1.42.0  
#> [10] GenomeInfoDb_1.26.0    IRanges_2.24.0         S4Vectors_0.28.0      
#> [13] BiocGenerics_0.36.0    eisaR_1.2.0            BiocStyle_2.18.0      
#> 
#> loaded via a namespace (and not attached):
#>  [1] MatrixGenerics_1.2.0        httr_1.4.2                 
#>  [3] splines_4.0.3               bit64_4.0.5                
#>  [5] GenomicFiles_1.26.0         assertthat_0.2.1           
#>  [7] askpass_1.1                 BiocManager_1.30.10        
#>  [9] BiocFileCache_1.14.0        latticeExtra_0.6-29        
#> [11] blob_1.2.1                  BSgenome_1.58.0            
#> [13] GenomeInfoDbData_1.2.4      Rsamtools_2.6.0            
#> [15] yaml_2.2.1                  progress_1.2.2             
#> [17] pillar_1.4.6                RSQLite_2.2.1              
#> [19] lattice_0.20-41             glue_1.4.2                 
#> [21] digest_0.6.27               RColorBrewer_1.1-2         
#> [23] XVector_0.30.0              htmltools_0.5.0            
#> [25] Matrix_1.2-18               XML_3.99-0.5               
#> [27] pkgconfig_2.0.3             ShortRead_1.48.0           
#> [29] biomaRt_2.46.0              magick_2.5.0               
#> [31] bookdown_0.21               zlibbioc_1.36.0            
#> [33] purrr_0.3.4                 jpeg_0.1-8.1               
#> [35] BiocParallel_1.24.0         tibble_3.0.4               
#> [37] openssl_1.4.3               generics_0.0.2             
#> [39] ellipsis_0.3.1              SummarizedExperiment_1.20.0
#> [41] magrittr_1.5                crayon_1.3.4               
#> [43] memoise_1.1.0               evaluate_0.14              
#> [45] hwriter_1.3.2               xml2_1.3.2                 
#> [47] tools_4.0.3                 prettyunits_1.1.1          
#> [49] hms_0.5.3                   lifecycle_0.2.0            
#> [51] matrixStats_0.57.0          stringr_1.4.0              
#> [53] locfit_1.5-9.4              DelayedArray_0.16.0        
#> [55] Biostrings_2.58.0           compiler_4.0.3             
#> [57] rlang_0.4.8                 grid_4.0.3                 
#> [59] RCurl_1.98-1.2              VariantAnnotation_1.36.0   
#> [61] rappdirs_0.3.1              bitops_1.0-6               
#> [63] rmarkdown_2.5               DBI_1.1.0                  
#> [65] curl_4.3                    R6_2.4.1                   
#> [67] GenomicAlignments_1.26.0    knitr_1.30                 
#> [69] dplyr_1.0.2                 bit_4.0.4                  
#> [71] stringi_1.5.3               Rcpp_1.0.5                 
#> [73] png_0.1-7                   vctrs_0.3.4                
#> [75] dbplyr_1.4.4                tidyselect_1.1.0           
#> [77] xfun_0.18

References

Gaidatzis, D., L. Burger, M. Florescu, and M.B. Stadler. 2015. “Analysis of Intronic and Exonic Reads in Rna-Seq Data Characterizes Transcriptional and Post-Transcriptional Regulation.” Nature Biotechnology 33 (7):722–29. https://doi.org/10.1038/nbt.3269.