Some Basic Analysis of ChIP-Seq Data
April 30, 2024
Contents
Our goal is to describe the use of Bioconductor software to perform some basic tasks in the analysis of ChIP-Seq data. We will use several functions in the as-yet-unreleased chipseq package, which provides convenient interfaces to other powerful packages such as ShortRead and IRanges. We will also use the lattice and rtracklayer packages for visualization.
library(chipseq)
library(GenomicFeatures)
library(lattice)1 Example data
The cstest data set is included in the chipseq package
to help demonstrate its capabilities. The dataset contains data for
three chromosomes from Solexa lanes, one from a CTCF mouse ChIP-Seq, and
one from a GFP mouse ChIP-Seq. The raw reads were aligned to the
reference genome (mouse in this case) using an external program (MAQ),
and the results read in using the the readAligned function in the
ShortRead, in conjunction with a filter produced by the
chipseqFilter function. This step filtered the reads to remove
duplicates, to restrict mappings to the canonical, autosomal chromosomes
and ensure that only a single read maps to a given position. A quality
score cutoff was also applied. The remaining data were reduced to a set
of aligned intervals (including orientation). This saves a great deal of
memory, as the sequences, which are unnecessary, are discarded. Finally,
we subset the data for chr10 to chr12, simply for convenience in this
vignette.
We outline this process with this unevaluated code block:
qa_list <- lapply(sampleFiles, qa)
report(do.call(rbind, qa_list))
## spend some time evaluating the QA report, then procede
filter <- compose(chipseqFilter(), alignQualityFilter(15))
cstest <- GenomicRangesList(lapply(sampleFiles, function(file) {
as(readAligned(file, filter), "GRanges")
}))
cstest <- cstest[seqnames(cstest) %in% c("chr10", "chr11", "chr12")]The above step has been performed in advance, and the output has been included as a dataset in this package. We load it now:
data(cstest)
cstest ## GRangesList object of length 2:
## $ctcf
## GRanges object with 450096 ranges and 0 metadata columns:
## seqnames ranges strand
## <Rle> <IRanges> <Rle>
## [1] chr10 3012936-3012959 +
## [2] chr10 3012941-3012964 +
## [3] chr10 3012944-3012967 +
## [4] chr10 3012955-3012978 +
## [5] chr10 3012963-3012986 +
## ... ... ... ...
## [450092] chr12 121239376-121239399 -
## [450093] chr12 121245849-121245872 -
## [450094] chr12 121245895-121245918 -
## [450095] chr12 121246344-121246367 -
## [450096] chr12 121253499-121253522 -
## -------
## seqinfo: 35 sequences from an unspecified genome
##
## $gfp
## GRanges object with 295385 ranges and 0 metadata columns:
## seqnames ranges strand
## <Rle> <IRanges> <Rle>
## [1] chr10 3002512-3002535 +
## [2] chr10 3009093-3009116 +
## [3] chr10 3020716-3020739 +
## [4] chr10 3023026-3023049 +
## [5] chr10 3024629-3024652 +
## ... ... ... ...
## [295381] chr12 121213126-121213149 -
## [295382] chr12 121216905-121216928 -
## [295383] chr12 121216967-121216990 -
## [295384] chr12 121251805-121251828 -
## [295385] chr12 121253426-121253449 -
## -------
## seqinfo: 35 sequences from an unspecified genomecstest is an object of class GRangesList, and has a list-like structure,
each component representing the alignments from one lane, as a GRanges object
of stranded intervals.
cstest$ctcf## GRanges object with 450096 ranges and 0 metadata columns:
## seqnames ranges strand
## <Rle> <IRanges> <Rle>
## [1] chr10 3012936-3012959 +
## [2] chr10 3012941-3012964 +
## [3] chr10 3012944-3012967 +
## [4] chr10 3012955-3012978 +
## [5] chr10 3012963-3012986 +
## ... ... ... ...
## [450092] chr12 121239376-121239399 -
## [450093] chr12 121245849-121245872 -
## [450094] chr12 121245895-121245918 -
## [450095] chr12 121246344-121246367 -
## [450096] chr12 121253499-121253522 -
## -------
## seqinfo: 35 sequences from an unspecified genome2 Extending reads
Solexa gives us the first few (24 in this example) bases of each fragment it sequences, but the actual fragment is longer. By design, the sites of interest (transcription factor binding sites) should be somewhere in the fragment, but not necessarily in its initial part. Although the actual lengths of fragments vary, extending the alignment of the short read by a fixed amount in the appropriate direction, depending on whether the alignment was to the positive or negative strand, makes it more likely that we cover the actual site of interest.
It is possible to estimate the fragment length, through a variety of methods.
There are several implemented by the estimate.mean.fraglen function.
Generally, this only needs to be done for one sample from each experimental
protocol. Here, we use SSISR, the default method:
fraglen <- estimate.mean.fraglen(cstest$ctcf, method="correlation")
fraglen[!is.na(fraglen)] ## chr10 chr11 chr12
## 340 340 340Given the suggestion of \(~190\) nucleotides, we extend all reads to be 200 bases
long. This is done using the resize function, which considers the strand to
determine the direction of extension:
ctcf.ext <- resize (cstest$ctcf, width = 200)
ctcf.ext## GRanges object with 450096 ranges and 0 metadata columns:
## seqnames ranges strand
## <Rle> <IRanges> <Rle>
## [1] chr10 3012936-3013135 +
## [2] chr10 3012941-3013140 +
## [3] chr10 3012944-3013143 +
## [4] chr10 3012955-3013154 +
## [5] chr10 3012963-3013162 +
## ... ... ... ...
## [450092] chr12 121239200-121239399 -
## [450093] chr12 121245673-121245872 -
## [450094] chr12 121245719-121245918 -
## [450095] chr12 121246168-121246367 -
## [450096] chr12 121253323-121253522 -
## -------
## seqinfo: 35 sequences from an unspecified genomeWe now have intervals for the CTCF lane that represent the original fragments that were precipitated.
3 Coverage, islands, and depth
A useful summary of this information is the coverage, that is, how many times each base in the genome was covered by one of these intervals.
cov.ctcf <- coverage(ctcf.ext)
cov.ctcf## RleList of length 35
## $chr1
## integer-Rle of length 197195432 with 1 run
## Lengths: 197195432
## Values : 0
##
## $chr2
## integer-Rle of length 181748087 with 1 run
## Lengths: 181748087
## Values : 0
##
## $chr3
## integer-Rle of length 159599783 with 1 run
## Lengths: 159599783
## Values : 0
##
## $chr4
## integer-Rle of length 155630120 with 1 run
## Lengths: 155630120
## Values : 0
##
## $chr5
## integer-Rle of length 152537259 with 1 run
## Lengths: 152537259
## Values : 0
##
## ...
## <30 more elements>For efficiency, the result is stored in a run-length encoded form.
The regions of interest are contiguous segments of non-zero coverage, also known as islands.
islands <- slice(cov.ctcf, lower = 1)
islands## RleViewsList object of length 35:
## $chr1
## Views on a 197195432-length Rle subject
##
## views: NONE
##
## $chr2
## Views on a 181748087-length Rle subject
##
## views: NONE
##
## $chr3
## Views on a 159599783-length Rle subject
##
## views: NONE
##
## ...
## <32 more elements>For each island, we can compute the number of reads in the island, and the maximum coverage depth within that island.
viewSums(islands)## IntegerList of length 35
## [["chr1"]] integer(0)
## [["chr2"]] integer(0)
## [["chr3"]] integer(0)
## [["chr4"]] integer(0)
## [["chr5"]] integer(0)
## [["chr6"]] integer(0)
## [["chr7"]] integer(0)
## [["chr8"]] integer(0)
## [["chr9"]] integer(0)
## [["chr10"]] 2400 200 200 200 200 200 200 600 ... 200 200 400 200 200 200 200
## ...
## <25 more elements>viewMaxs(islands)## IntegerList of length 35
## [["chr1"]] integer(0)
## [["chr2"]] integer(0)
## [["chr3"]] integer(0)
## [["chr4"]] integer(0)
## [["chr5"]] integer(0)
## [["chr6"]] integer(0)
## [["chr7"]] integer(0)
## [["chr8"]] integer(0)
## [["chr9"]] integer(0)
## [["chr10"]] 11 1 1 1 1 1 1 3 1 1 1 1 1 1 2 1 ... 1 2 1 1 1 1 3 1 1 1 2 1 1 1 1
## ...
## <25 more elements>nread.tab <- table(viewSums(islands) / 200)
depth.tab <- table(viewMaxs(islands))
nread.tab[,1:10]## 1 2 3 4 5 6 7 8 9 10
## chr1 0 0 0 0 0 0 0 0 0 0
## chr2 0 0 0 0 0 0 0 0 0 0
## chr3 0 0 0 0 0 0 0 0 0 0
## chr4 0 0 0 0 0 0 0 0 0 0
## chr5 0 0 0 0 0 0 0 0 0 0
## chr6 0 0 0 0 0 0 0 0 0 0
## chr7 0 0 0 0 0 0 0 0 0 0
## chr8 0 0 0 0 0 0 0 0 0 0
## chr9 0 0 0 0 0 0 0 0 0 0
## chr10 68101 13352 3019 924 418 246 191 123 133 100
## chr11 71603 15993 4334 1410 619 338 245 199 180 151
## chr12 59141 11279 2613 816 344 175 140 119 84 71
## chr13 0 0 0 0 0 0 0 0 0 0
## chr14 0 0 0 0 0 0 0 0 0 0
## chr15 0 0 0 0 0 0 0 0 0 0
## chr16 0 0 0 0 0 0 0 0 0 0
## chr17 0 0 0 0 0 0 0 0 0 0
## chr18 0 0 0 0 0 0 0 0 0 0
## chr19 0 0 0 0 0 0 0 0 0 0
## chrX 0 0 0 0 0 0 0 0 0 0
## chrY 0 0 0 0 0 0 0 0 0 0
## chrM 0 0 0 0 0 0 0 0 0 0
## chr1_random 0 0 0 0 0 0 0 0 0 0
## chr3_random 0 0 0 0 0 0 0 0 0 0
## chr4_random 0 0 0 0 0 0 0 0 0 0
## chr5_random 0 0 0 0 0 0 0 0 0 0
## chr7_random 0 0 0 0 0 0 0 0 0 0
## chr8_random 0 0 0 0 0 0 0 0 0 0
## chr9_random 0 0 0 0 0 0 0 0 0 0
## chr13_random 0 0 0 0 0 0 0 0 0 0
## chr16_random 0 0 0 0 0 0 0 0 0 0
## chr17_random 0 0 0 0 0 0 0 0 0 0
## chrX_random 0 0 0 0 0 0 0 0 0 0
## chrY_random 0 0 0 0 0 0 0 0 0 0
## chrUn_random 0 0 0 0 0 0 0 0 0 0depth.tab[,1:10]## 1 2 3 4 5 6 7 8 9 10
## chr1 0 0 0 0 0 0 0 0 0 0
## chr2 0 0 0 0 0 0 0 0 0 0
## chr3 0 0 0 0 0 0 0 0 0 0
## chr4 0 0 0 0 0 0 0 0 0 0
## chr5 0 0 0 0 0 0 0 0 0 0
## chr6 0 0 0 0 0 0 0 0 0 0
## chr7 0 0 0 0 0 0 0 0 0 0
## chr8 0 0 0 0 0 0 0 0 0 0
## chr9 0 0 0 0 0 0 0 0 0 0
## chr10 68149 14748 2386 547 256 180 150 129 120 101
## chr11 71677 17945 3527 862 362 268 205 179 181 130
## chr12 59181 12441 2078 482 191 131 131 108 95 77
## chr13 0 0 0 0 0 0 0 0 0 0
## chr14 0 0 0 0 0 0 0 0 0 0
## chr15 0 0 0 0 0 0 0 0 0 0
## chr16 0 0 0 0 0 0 0 0 0 0
## chr17 0 0 0 0 0 0 0 0 0 0
## chr18 0 0 0 0 0 0 0 0 0 0
## chr19 0 0 0 0 0 0 0 0 0 0
## chrX 0 0 0 0 0 0 0 0 0 0
## chrY 0 0 0 0 0 0 0 0 0 0
## chrM 0 0 0 0 0 0 0 0 0 0
## chr1_random 0 0 0 0 0 0 0 0 0 0
## chr3_random 0 0 0 0 0 0 0 0 0 0
## chr4_random 0 0 0 0 0 0 0 0 0 0
## chr5_random 0 0 0 0 0 0 0 0 0 0
## chr7_random 0 0 0 0 0 0 0 0 0 0
## chr8_random 0 0 0 0 0 0 0 0 0 0
## chr9_random 0 0 0 0 0 0 0 0 0 0
## chr13_random 0 0 0 0 0 0 0 0 0 0
## chr16_random 0 0 0 0 0 0 0 0 0 0
## chr17_random 0 0 0 0 0 0 0 0 0 0
## chrX_random 0 0 0 0 0 0 0 0 0 0
## chrY_random 0 0 0 0 0 0 0 0 0 0
## chrUn_random 0 0 0 0 0 0 0 0 0 04 Processing multiple lanes
Although data from one lane is often a natural analytical unit, we typically want to apply any procedure to all lanes. Here is a simple summary function that computes the frequency distribution of the number of reads.
islandReadSummary <- function(x)
{
g <- resize(x, 200)
s <- slice(coverage(g), lower = 1)
tab <- table(viewSums(s) / 200)
df <- DataFrame(tab)
colnames(df) <- c("chromosome", "nread", "count")
df$nread <- as.integer(df$nread)
df
}Applying it to our test-case, we get
head(islandReadSummary(cstest$ctcf)) ## DataFrame with 6 rows and 3 columns
## chromosome nread count
## <factor> <integer> <integer>
## 1 chr1 1 0
## 2 chr2 1 0
## 3 chr3 1 0
## 4 chr4 1 0
## 5 chr5 1 0
## 6 chr6 1 0We can now use it to summarize the full dataset, flattening the returned
DataFrameList with the stack function.
nread.islands <- DataFrameList(lapply(cstest, islandReadSummary))
nread.islands <- stack(nread.islands, "sample")
nread.islands ## DataFrame with 4025 rows and 4 columns
## sample chromosome nread count
## <Rle> <factor> <integer> <integer>
## 1 ctcf chr1 1 0
## 2 ctcf chr2 1 0
## 3 ctcf chr3 1 0
## 4 ctcf chr4 1 0
## 5 ctcf chr5 1 0
## ... ... ... ... ...
## 4021 gfp chr16_random 34 0
## 4022 gfp chr17_random 34 0
## 4023 gfp chrX_random 34 0
## 4024 gfp chrY_random 34 0
## 4025 gfp chrUn_random 34 0xyplot(log(count) ~ nread | sample, as.data.frame(nread.islands),
subset = (chromosome == "chr10" & nread <= 40),
layout = c(1, 2), pch = 16, type = c("p", "g"))
If reads were sampled randomly from the genome, then the null distribution number of reads per island would have a geometric distribution; that is,
\[P(X = k) = p^{k-1} (1-p)\]
In other words, \(\log P(X = k)\) is linear in \(k\). Although our samples are not random, the islands with just one or two reads may be representative of the null distribution.
xyplot(log(count) ~ nread | sample, data = as.data.frame(nread.islands),
subset = (chromosome == "chr10" & nread <= 40),
layout = c(1, 2), pch = 16, type = c("p", "g"),
panel = function(x, y, ...) {
panel.lmline(x[1:2], y[1:2], col = "black")
panel.xyplot(x, y, ...)
})
We can create a similar plot of the distribution of depths.
islandDepthSummary <- function(x)
{
g <- resize(x, 200)
s <- slice(coverage(g), lower = 1)
tab <- table(viewMaxs(s) / 200)
df <- DataFrame(tab)
colnames(df) <- c("chromosome", "depth", "count")
df$depth <- as.integer(df$depth)
df
}
depth.islands <- DataFrameList(lapply(cstest, islandDepthSummary))
depth.islands <- stack(depth.islands, "sample")
plt <- xyplot(log(count) ~ depth | sample, as.data.frame(depth.islands),
subset = (chromosome == "chr10" & depth <= 20),
layout = c(1, 2), pch = 16, type = c("p", "g"),
panel = function(x, y, ...){
lambda <- 2 * exp(y[2]) / exp(y[1])
null.est <- function(xx) {
xx * log(lambda) - lambda - lgamma(xx + 1)
}
log.N.hat <- null.est(1) - y[1]
panel.lines(1:10, -log.N.hat + null.est(1:10), col = "black")
panel.xyplot(x, y, ...)
})
## depth.islands <- summarizeReads(cstest, summary.fun = islandDepthSummary)
The above plot is very useful for detecting peaks, discussed in the next
section. As a convenience, it can be created for the coverage over all
chromosomes for a single sample by calling the islandDepthPlot
function:
islandDepthPlot(cov.ctcf)5 Peaks
To obtain a set of putative binding sites, i.e., peaks, we need to find
those regions that are significantly above the noise level. Using the
same Poisson-based approach for estimating the noise distribution as in
the plot above, the peakCutoff function returns a cutoff value for a
specific FDR:
peakCutoff(cov.ctcf, fdr = 0.0001) ## [1] 6.959837Considering the above calculation of \(7\) at an FDR of \(0.0001\), and looking at the above plot, we might choose \(8\) as a conservative peak cutoff:
peaks.ctcf <- slice(cov.ctcf, lower = 8)
peaks.ctcf ## RleViewsList object of length 35:
## $chr1
## Views on a 197195432-length Rle subject
##
## views: NONE
##
## $chr2
## Views on a 181748087-length Rle subject
##
## views: NONE
##
## $chr3
## Views on a 159599783-length Rle subject
##
## views: NONE
##
## ...
## <32 more elements>To summarize the peaks for exploratory analysis, we call the
peakSummary function:
peaks <- peakSummary(peaks.ctcf) The result is a GRanges object with two columns: the view maxs and the view sums. Beyond that, this object is often useful as a scaffold for adding additional statistics.
It is meaningful to ask about the contribution of each strand to each peak, as the sequenced region of pull-down fragments would be on opposite sides of a binding site depending on which strand it matched. We can compute strand-specific coverage, and look at the individual coverages under the combined peaks as follows:
peak.depths <- viewMaxs(peaks.ctcf)
cov.pos <- coverage(ctcf.ext[strand(ctcf.ext) == "+"])
cov.neg <- coverage(ctcf.ext[strand(ctcf.ext) == "-"])
peaks.pos <- Views(cov.pos, ranges(peaks.ctcf))
peaks.neg <- Views(cov.neg, ranges(peaks.ctcf))
wpeaks <- tail(order(peak.depths$chr10), 4)
wpeaks## [1] 971 989 1079 922Below, we plot the four highest peaks on chromosome 10.
coverageplot(peaks.pos$chr10[wpeaks[1]], peaks.neg$chr10[wpeaks[1]])
coverageplot(peaks.pos$chr10[wpeaks[2]], peaks.neg$chr10[wpeaks[2]])
coverageplot(peaks.pos$chr10[wpeaks[3]], peaks.neg$chr10[wpeaks[3]])
coverageplot(peaks.pos$chr10[wpeaks[4]], peaks.neg$chr10[wpeaks[4]])
6 Differential peaks
One common question is: which peaks are different in two samples? One simple strategy is the following: combine the two peak sets, and compare the two samples by calculating summary statistics for the combined peaks on top of each coverage vector.
## find peaks for GFP control
cov.gfp <- coverage(resize(cstest$gfp, 200))
peaks.gfp <- slice(cov.gfp, lower = 8)
peakSummary <- diffPeakSummary(peaks.gfp, peaks.ctcf)
plt <- xyplot(asinh(sums2) ~ asinh(sums1) | seqnames,
data = as.data.frame(peakSummary),
panel = function(x, y, ...) {
panel.xyplot(x, y, ...)
panel.abline(median(y - x), 1)
},
type = c("p", "g"), alpha = 0.5, aspect = "iso")
We use a simple cutoff to flag peaks that are different.
mcols(peakSummary) <-
within(mcols(peakSummary),
{
diffs <- asinh(sums2) - asinh(sums1)
resids <- (diffs - median(diffs)) / mad(diffs)
up <- resids > 2
down <- resids < -2
change <- ifelse(up, "up", ifelse(down, "down", "flat"))
})7 Placing peaks in genomic context
Locations of individual peaks may be of interest. Alternatively, a
global summary might look at classifying the peaks of interest in the
context of genomic features such as promoters, upstream regions, etc.
The GenomicFeatures package facilitates obtaining gene
annotations from different data sources. We could download the UCSC gene
predictions for the mouse genome and generate a GRanges object with
the transcript regions (from the first to last exon, contiguous) using
makeTxDbFromUCSC; here we use a library containing a recent snapshot.
library(TxDb.Mmusculus.UCSC.mm9.knownGene)
gregions <- transcripts(TxDb.Mmusculus.UCSC.mm9.knownGene)
gregions ## GRanges object with 55419 ranges and 2 metadata columns:
## seqnames ranges strand | tx_id tx_name
## <Rle> <IRanges> <Rle> | <integer> <character>
## [1] chr1 4797974-4832908 + | 1 uc007afg.1
## [2] chr1 4797974-4836816 + | 2 uc007afh.1
## [3] chr1 4847775-4887990 + | 3 uc007afi.2
## [4] chr1 4847775-4887990 + | 4 uc011wht.1
## [5] chr1 4848409-4887990 + | 5 uc011whu.1
## ... ... ... ... . ... ...
## [55415] chrUn_random 2204169-2216886 - | 55415 uc009sjw.2
## [55416] chrUn_random 2674945-2678407 - | 55416 uc009skb.2
## [55417] chrUn_random 2889607-2891056 - | 55417 uc009ske.1
## [55418] chrUn_random 3830796-3837247 - | 55418 uc009skg.1
## [55419] chrUn_random 4677114-4677187 - | 55419 uc009skh.1
## -------
## seqinfo: 35 sequences (1 circular) from mm9 genomeWe can now estimate the promoter for each transcript:
promoters <- flank(gregions, 1000, both = TRUE) And count the peaks that fall into a promoter:
peakSummary$inPromoter <- peakSummary %over% promoters
xtabs(~ inPromoter + change, peakSummary) ## change
## inPromoter down flat
## FALSE 21 5158
## TRUE 2 625or somewhere upstream or in a gene:
peakSummary$inUpstream <- peakSummary %over% flank(gregions, 20000)## Warning in valid.GenomicRanges.seqinfo(x, suggest.trim = TRUE): GRanges object contains 7 out-of-bound ranges located on sequences
## chr13, chr16, chr5_random, and chr13_random. Note that ranges located
## on a sequence whose length is unknown (NA) or on a circular sequence
## are not considered out-of-bound (use seqlengths() and isCircular() to
## get the lengths and circularity flags of the underlying sequences). You
## can use trim() to trim these ranges. See ?`trim,GenomicRanges-method`
## for more information.peakSummary$inGene <- peakSummary %over% gregionssumtab <-
as.data.frame(rbind(total = xtabs(~ change, peakSummary),
promoter = xtabs(~ change,
subset(peakSummary, inPromoter)),
upstream = xtabs(~ change,
subset(peakSummary, inUpstream)),
gene = xtabs(~ change, subset(peakSummary, inGene))))
## cbind(sumtab, ratio = round(sumtab[, "down"] / sumtab[, "up"], 3))8 Visualizing peaks in genomic context
While it is generally informative to calculate statistics incorporating the genomic context, eventually one wants a picture. The traditional genome browser view is an effective method of visually integrating multiple annotations with experimental data along the genome.
Using the rtracklayer package, we can upload our coverage and peaks for both samples to the UCSC Genome Browser:
library(rtracklayer)
session <- browserSession()
genome(session) <- "mm9"
session$gfpCov <- cov.gfp
session$gfpPeaks <- peaks.gfp
session$ctcfCov <- cov.ctcf
session$ctcfPeaks <- peaks.ctcf Once the tracks are uploaded, we can choose a region to view, such as the tallest peak on chr10 in the CTCF data:
peak.ord <- order(unlist(peak.depths), decreasing=TRUE)
peak.sort <- as(peaks.ctcf, "GRanges")[peak.ord]
view <- browserView(session, peak.sort[1], full = c("gfpCov", "ctcfCov")) We coerce to GRanges so that we can sort the ranges across chromosomes. By
passing the full parameter to browserView we instruct UCSC to display the
coverage tracks as a bar chart. Next, we might programmatically display a view
for the top 5 tallest peaks:
views <- browserView(session, head(peak.sort, 5), full = c("gfpCov", "ctcfCov")) 9 Version information
sessionInfo() ## R version 4.4.0 beta (2024-04-15 r86425)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 22.04.4 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.19-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
## [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] stats4 stats graphics grDevices utils datasets methods
## [8] base
##
## other attached packages:
## [1] TxDb.Mmusculus.UCSC.mm9.knownGene_3.2.2
## [2] lattice_0.22-6
## [3] GenomicFeatures_1.56.0
## [4] AnnotationDbi_1.66.0
## [5] chipseq_1.54.0
## [6] ShortRead_1.62.0
## [7] GenomicAlignments_1.40.0
## [8] SummarizedExperiment_1.34.0
## [9] Biobase_2.64.0
## [10] MatrixGenerics_1.16.0
## [11] matrixStats_1.3.0
## [12] Rsamtools_2.20.0
## [13] Biostrings_2.72.0
## [14] XVector_0.44.0
## [15] BiocParallel_1.38.0
## [16] GenomicRanges_1.56.0
## [17] GenomeInfoDb_1.40.0
## [18] IRanges_2.38.0
## [19] S4Vectors_0.42.0
## [20] BiocGenerics_0.50.0
## [21] BiocStyle_2.32.0
##
## loaded via a namespace (and not attached):
## [1] KEGGREST_1.44.0 rjson_0.2.21 xfun_0.43
## [4] bslib_0.7.0 hwriter_1.3.2.1 latticeExtra_0.6-30
## [7] vctrs_0.6.5 tools_4.4.0 bitops_1.0-7
## [10] curl_5.2.1 parallel_4.4.0 RSQLite_2.3.6
## [13] highr_0.10 blob_1.2.4 pkgconfig_2.0.3
## [16] Matrix_1.7-0 RColorBrewer_1.1-3 lifecycle_1.0.4
## [19] GenomeInfoDbData_1.2.12 compiler_4.4.0 deldir_2.0-4
## [22] tinytex_0.50 codetools_0.2-20 htmltools_0.5.8.1
## [25] sass_0.4.9 RCurl_1.98-1.14 yaml_2.3.8
## [28] crayon_1.5.2 jquerylib_0.1.4 DelayedArray_0.30.0
## [31] cachem_1.0.8 magick_2.8.3 abind_1.4-5
## [34] digest_0.6.35 restfulr_0.0.15 bookdown_0.39
## [37] fastmap_1.1.1 grid_4.4.0 cli_3.6.2
## [40] SparseArray_1.4.0 magrittr_2.0.3 S4Arrays_1.4.0
## [43] XML_3.99-0.16.1 UCSC.utils_1.0.0 bit64_4.0.5
## [46] rmarkdown_2.26 pwalign_1.0.0 httr_1.4.7
## [49] jpeg_0.1-10 bit_4.0.5 interp_1.1-6
## [52] png_0.1-8 memoise_2.0.1 evaluate_0.23
## [55] knitr_1.46 BiocIO_1.14.0 rtracklayer_1.64.0
## [58] rlang_1.1.3 Rcpp_1.0.12 DBI_1.2.2
## [61] BiocManager_1.30.22 jsonlite_1.8.8 R6_2.5.1
## [64] zlibbioc_1.50.0