Introduction

The GenomicRanges package serves as the foundation for representing genomic locations within the Bioconductor project. In the Bioconductor package hierarchy, it builds upon the IRanges (infrastructure) package and provides support for the BSgenome (infrastructure), Rsamtools (I/O), ShortRead (I/O & QA), rtracklayer (I/O), GenomicFeatures (infrastructure), GenomicAlignments (sequence reads), VariantAnnotation (called variants), and many other Bioconductor packages.

This package lays a foundation for genomic analysis by introducing three classes (GRanges, GPos, and GRangesList), which are used to represent genomic ranges, genomic positions, and groups of genomic ranges. This vignette focuses on the GRanges and GRangesList classes and their associated methods.

The GenomicRanges package is available at https://bioconductor.org and can be installed via BiocManager::install:

if (!require("BiocManager"))
    install.packages("BiocManager")
BiocManager::install("GenomicRanges")

A package only needs to be installed once. Load the package into an R session with

library(GenomicRanges)

GRanges: Genomic Ranges

The GRanges class represents a collection of genomic ranges that each have a single start and end location on the genome. It can be used to store the location of genomic features such as contiguous binding sites, transcripts, and exons. These objects can be created by using the GRanges constructor function. For example,

gr <- GRanges(
    seqnames = Rle(c("chr1", "chr2", "chr1", "chr3"), c(1, 3, 2, 4)),
    ranges = IRanges(101:110, end = 111:120, names = head(letters, 10)),
    strand = Rle(strand(c("-", "+", "*", "+", "-")), c(1, 2, 2, 3, 2)),
    score = 1:10,
    GC = seq(1, 0, length=10))
gr

## GRanges object with 10 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1   101-111      - |         1  1.000000
##   b     chr2   102-112      + |         2  0.888889
##   c     chr2   103-113      + |         3  0.777778
##   d     chr2   104-114      * |         4  0.666667
##   e     chr1   105-115      * |         5  0.555556
##   f     chr1   106-116      + |         6  0.444444
##   g     chr3   107-117      + |         7  0.333333
##   h     chr3   108-118      + |         8  0.222222
##   i     chr3   109-119      - |         9  0.111111
##   j     chr3   110-120      - |        10  0.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome; no seqlengths

creates a GRanges object with 10 genomic ranges. The output of the GRanges show method separates the information into a left and right hand region that are separated by | symbols. The genomic coordinates (seqnames, ranges, and strand) are located on the left-hand side and the metadata columns (annotation) are located on the right. For this example, the metadata is comprised of score and GC information, but almost anything can be stored in the metadata portion of a GRanges object.

The components of the genomic coordinates within a GRanges object can be extracted using the seqnames, ranges, and strand accessor functions.

seqnames(gr)

## factor-Rle of length 10 with 4 runs
##   Lengths:    1    3    2    4
##   Values : chr1 chr2 chr1 chr3
## Levels(3): chr1 chr2 chr3

ranges(gr)

## IRanges object with 10 ranges and 0 metadata columns:
##         start       end     width
##     <integer> <integer> <integer>
##   a       101       111        11
##   b       102       112        11
##   c       103       113        11
##   d       104       114        11
##   e       105       115        11
##   f       106       116        11
##   g       107       117        11
##   h       108       118        11
##   i       109       119        11
##   j       110       120        11

strand(gr)

## factor-Rle of length 10 with 5 runs
##   Lengths: 1 2 2 3 2
##   Values : - + * + -
## Levels(3): + - *

The genomic ranges can be extracted without corresponding metadata with granges

granges(gr)

## GRanges object with 10 ranges and 0 metadata columns:
##     seqnames    ranges strand
##        <Rle> <IRanges>  <Rle>
##   a     chr1   101-111      -
##   b     chr2   102-112      +
##   c     chr2   103-113      +
##   d     chr2   104-114      *
##   e     chr1   105-115      *
##   f     chr1   106-116      +
##   g     chr3   107-117      +
##   h     chr3   108-118      +
##   i     chr3   109-119      -
##   j     chr3   110-120      -
##   -------
##   seqinfo: 3 sequences from an unspecified genome; no seqlengths

Annotations for these coordinates can be extracted as a DataFrame object using the mcols accessor.

mcols(gr)

## DataFrame with 10 rows and 2 columns
##       score        GC
##   <integer> <numeric>
## a         1  1.000000
## b         2  0.888889
## c         3  0.777778
## d         4  0.666667
## e         5  0.555556
## f         6  0.444444
## g         7  0.333333
## h         8  0.222222
## i         9  0.111111
## j        10  0.000000

mcols(gr)$score

##  [1]  1  2  3  4  5  6  7  8  9 10

Information about the lengths of the various sequences that the ranges are aligned to can also be stored in the GRanges object. So if this is data from Homo sapiens, we can set the values as:

seqlengths(gr) <- c(249250621, 243199373, 198022430)

And then retrieves as:

seqlengths(gr)

##      chr1      chr2      chr3 
## 249250621 243199373 198022430

Methods for accessing the length and names have also been defined.

names(gr)

##  [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"

length(gr)

## [1] 10

Splitting and combining GRanges objects

GRanges objects can be divided into groups using the split method. This produces a GRangesList object, a class that will be discussed in detail in the next section.

sp <- split(gr, rep(1:2, each=5))
sp

## GRangesList object of length 2:
## $`1`
## GRanges object with 5 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1   101-111      - |         1  1.000000
##   b     chr2   102-112      + |         2  0.888889
##   c     chr2   103-113      + |         3  0.777778
##   d     chr2   104-114      * |         4  0.666667
##   e     chr1   105-115      * |         5  0.555556
##   -------
##   seqinfo: 3 sequences from an unspecified genome
## 
## $`2`
## GRanges object with 5 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   f     chr1   106-116      + |         6  0.444444
##   g     chr3   107-117      + |         7  0.333333
##   h     chr3   108-118      + |         8  0.222222
##   i     chr3   109-119      - |         9  0.111111
##   j     chr3   110-120      - |        10  0.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome

Separate GRanges instances can be concatenated by using the c and append methods.

c(sp[[1]], sp[[2]])

## GRanges object with 10 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1   101-111      - |         1  1.000000
##   b     chr2   102-112      + |         2  0.888889
##   c     chr2   103-113      + |         3  0.777778
##   d     chr2   104-114      * |         4  0.666667
##   e     chr1   105-115      * |         5  0.555556
##   f     chr1   106-116      + |         6  0.444444
##   g     chr3   107-117      + |         7  0.333333
##   h     chr3   108-118      + |         8  0.222222
##   i     chr3   109-119      - |         9  0.111111
##   j     chr3   110-120      - |        10  0.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome

Subsetting GRanges objects

GRanges objects act like vectors of ranges, with the expected vector-like subsetting operations available

gr[2:3]

## GRanges object with 2 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   b     chr2   102-112      + |         2  0.888889
##   c     chr2   103-113      + |         3  0.777778
##   -------
##   seqinfo: 3 sequences from an unspecified genome

A second argument to the [ subset operator can be used to specify which metadata columns to extract from the GRanges object. For example,

gr[2:3, "GC"]

## GRanges object with 2 ranges and 1 metadata column:
##     seqnames    ranges strand |        GC
##        <Rle> <IRanges>  <Rle> | <numeric>
##   b     chr2   102-112      + |  0.888889
##   c     chr2   103-113      + |  0.777778
##   -------
##   seqinfo: 3 sequences from an unspecified genome

Elements can also be assigned to the GRanges object. Here is an example where the second row of a GRanges object is replaced with the first row of gr.

singles <- split(gr, names(gr))
grMod <- gr
grMod[2] <- singles[[1]]
head(grMod, n=3)

## GRanges object with 3 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1   101-111      - |         1  1.000000
##   b     chr1   101-111      - |         1  1.000000
##   c     chr2   103-113      + |         3  0.777778
##   -------
##   seqinfo: 3 sequences from an unspecified genome

There are methods to repeat, reverse, or select specific portions of GRanges objects.

rep(singles[[2]], times = 3)

## GRanges object with 3 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   b     chr2   102-112      + |         2  0.888889
##   b     chr2   102-112      + |         2  0.888889
##   b     chr2   102-112      + |         2  0.888889
##   -------
##   seqinfo: 3 sequences from an unspecified genome

rev(gr)

## GRanges object with 10 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   j     chr3   110-120      - |        10  0.000000
##   i     chr3   109-119      - |         9  0.111111
##   h     chr3   108-118      + |         8  0.222222
##   g     chr3   107-117      + |         7  0.333333
##   f     chr1   106-116      + |         6  0.444444
##   e     chr1   105-115      * |         5  0.555556
##   d     chr2   104-114      * |         4  0.666667
##   c     chr2   103-113      + |         3  0.777778
##   b     chr2   102-112      + |         2  0.888889
##   a     chr1   101-111      - |         1  1.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome

head(gr,n=2)

## GRanges object with 2 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1   101-111      - |         1  1.000000
##   b     chr2   102-112      + |         2  0.888889
##   -------
##   seqinfo: 3 sequences from an unspecified genome

tail(gr,n=2)

## GRanges object with 2 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   i     chr3   109-119      - |         9  0.111111
##   j     chr3   110-120      - |        10  0.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome

window(gr, start=2,end=4)

## GRanges object with 3 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   b     chr2   102-112      + |         2  0.888889
##   c     chr2   103-113      + |         3  0.777778
##   d     chr2   104-114      * |         4  0.666667
##   -------
##   seqinfo: 3 sequences from an unspecified genome

gr[IRanges(start=c(2,7), end=c(3,9))]

## GRanges object with 5 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   b     chr2   102-112      + |         2  0.888889
##   c     chr2   103-113      + |         3  0.777778
##   g     chr3   107-117      + |         7  0.333333
##   h     chr3   108-118      + |         8  0.222222
##   i     chr3   109-119      - |         9  0.111111
##   -------
##   seqinfo: 3 sequences from an unspecified genome

Basic interval operations for GRanges objects

Basic interval characteristics of GRanges objects can be extracted using the start, end, width, and range methods.

g <- gr[1:3]
g <- append(g, singles[[10]])
start(g)

## [1] 101 102 103 110

end(g)

## [1] 111 112 113 120

width(g)

## [1] 11 11 11 11

range(g)

## GRanges object with 3 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr1   101-111      -
##   [2]     chr2   102-113      +
##   [3]     chr3   110-120      -
##   -------
##   seqinfo: 3 sequences from an unspecified genome

The GRanges class also has many methods for manipulating the ranges. The methods can be classified as intra-range methods, inter-range methods, and between-range methods.

Intra-range methods operate on each element of a GRanges object independent of the other ranges in the object. For example, the flank method can be used to recover regions flanking the set of ranges represented by the GRanges object. So to get a GRanges object containing the ranges that include the 10 bases upstream of the ranges:

flank(g, 10)

## GRanges object with 4 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1   112-121      - |         1  1.000000
##   b     chr2    92-101      + |         2  0.888889
##   c     chr2    93-102      + |         3  0.777778
##   j     chr3   121-130      - |        10  0.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome

And to include the downstream bases:

flank(g, 10, start=FALSE)

## GRanges object with 4 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1    91-100      - |         1  1.000000
##   b     chr2   113-122      + |         2  0.888889
##   c     chr2   114-123      + |         3  0.777778
##   j     chr3   100-109      - |        10  0.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome

Other examples of intra-range methods include resize and shift. The shift method will move the ranges by a specific number of base pairs, and the resize method will extend the ranges by a specified width.

shift(g, 5)

## GRanges object with 4 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1   106-116      - |         1  1.000000
##   b     chr2   107-117      + |         2  0.888889
##   c     chr2   108-118      + |         3  0.777778
##   j     chr3   115-125      - |        10  0.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome

resize(g, 30)

## GRanges object with 4 ranges and 2 metadata columns:
##     seqnames    ranges strand |     score        GC
##        <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   a     chr1    82-111      - |         1  1.000000
##   b     chr2   102-131      + |         2  0.888889
##   c     chr2   103-132      + |         3  0.777778
##   j     chr3    91-120      - |        10  0.000000
##   -------
##   seqinfo: 3 sequences from an unspecified genome

The GenomicRanges help page ?"intra-range-methods" summarizes these methods.

Inter-range methods involve comparisons between ranges in a single GRanges object. For instance, the reduce method will align the ranges and merge overlapping ranges to produce a simplified set.

reduce(g)

## GRanges object with 3 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr1   101-111      -
##   [2]     chr2   102-113      +
##   [3]     chr3   110-120      -
##   -------
##   seqinfo: 3 sequences from an unspecified genome

Sometimes one is interested in the gaps or the qualities of the gaps between the ranges represented by your GRanges object. The gaps method provides this information: reduced version of your ranges:

gaps(g)

## GRanges object with 12 ranges and 0 metadata columns:
##        seqnames        ranges strand
##           <Rle>     <IRanges>  <Rle>
##    [1]     chr1   1-249250621      +
##    [2]     chr1         1-100      -
##    [3]     chr1 112-249250621      -
##    [4]     chr1   1-249250621      *
##    [5]     chr2         1-101      +
##    ...      ...           ...    ...
##    [8]     chr2   1-243199373      *
##    [9]     chr3   1-198022430      +
##   [10]     chr3         1-109      -
##   [11]     chr3 121-198022430      -
##   [12]     chr3   1-198022430      *
##   -------
##   seqinfo: 3 sequences from an unspecified genome

The disjoin method represents a GRanges object as a collection of non-overlapping ranges:

disjoin(g)

## GRanges object with 5 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr1   101-111      -
##   [2]     chr2       102      +
##   [3]     chr2   103-112      +
##   [4]     chr2       113      +
##   [5]     chr3   110-120      -
##   -------
##   seqinfo: 3 sequences from an unspecified genome

The coverage method quantifies the degree of overlap for all the ranges in a GRanges object.

coverage(g)

## RleList of length 3
## $chr1
## integer-Rle of length 249250621 with 3 runs
##   Lengths:       100        11 249250510
##   Values :         0         1         0
## 
## $chr2
## integer-Rle of length 243199373 with 5 runs
##   Lengths:       101         1        10         1 243199260
##   Values :         0         1         2         1         0
## 
## $chr3
## integer-Rle of length 198022430 with 3 runs
##   Lengths:       109        11 198022310
##   Values :         0         1         0

See the GenomicRanges help page ?"inter-range-methods" for additional help.

Between-range methods involve operations between two GRanges objects; some of these are summarized in the next section.

Interval set operations for GRanges objects

Between-range methods calculate relationships between different GRanges objects. Of central importance are findOverlaps and related operations; these are discussed below. Additional operations treat GRanges as mathematical sets of coordinates; union(g, g2) is the union of the coordinates in g and g2. Here are examples for calculating the union, the intersect and the asymmetric difference (using setdiff).

g2 <- head(gr, n=2)
union(g, g2)

## GRanges object with 3 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr1   101-111      -
##   [2]     chr2   102-113      +
##   [3]     chr3   110-120      -
##   -------
##   seqinfo: 3 sequences from an unspecified genome

intersect(g, g2)

## GRanges object with 2 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr1   101-111      -
##   [2]     chr2   102-112      +
##   -------
##   seqinfo: 3 sequences from an unspecified genome

setdiff(g, g2)

## GRanges object with 2 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr2       113      +
##   [2]     chr3   110-120      -
##   -------
##   seqinfo: 3 sequences from an unspecified genome

Related methods are available when the structure of the GRanges objects are ‘parallel’ to one another, i.e., element 1 of object 1 is related to element 1 of object 2, and so on. These operations all begin with a p, which is short for parallel. The methods then perform element-wise, e.g., the union of element 1 of object 1 with element 1 of object 2, etc. A requirement for these operations is that the number of elements in each GRanges object is the same, and that both of the objects have the same seqnames and strand assignments throughout.

g3 <- g[1:2]
ranges(g3[1]) <- IRanges(start=105, end=112)
punion(g2, g3)

## GRanges object with 2 ranges and 0 metadata columns:
##     seqnames    ranges strand
##        <Rle> <IRanges>  <Rle>
##   a     chr1   101-112      -
##   b     chr2   102-112      +
##   -------
##   seqinfo: 3 sequences from an unspecified genome

pintersect(g2, g3)

## GRanges object with 2 ranges and 3 metadata columns:
##     seqnames    ranges strand |     score        GC       hit
##        <Rle> <IRanges>  <Rle> | <integer> <numeric> <logical>
##   a     chr1   105-111      - |         1  1.000000      TRUE
##   b     chr2   102-112      + |         2  0.888889      TRUE
##   -------
##   seqinfo: 3 sequences from an unspecified genome

psetdiff(g2, g3)

## GRanges object with 2 ranges and 0 metadata columns:
##     seqnames    ranges strand
##        <Rle> <IRanges>  <Rle>
##   a     chr1   101-104      -
##   b     chr2   102-101      +
##   -------
##   seqinfo: 3 sequences from an unspecified genome

For more information on the GRanges class be sure to consult the manual page.

?GRanges

A relatively comprehensive list of available methods is discovered with

methods(class="GRanges")

GRangesList: Groups of Genomic Ranges

Some important genomic features, such as spliced transcripts that are comprised of exons, are inherently compound structures. Such a feature makes much more sense when expressed as a compound object such as a GRangesList. Whenever genomic features consist of multiple ranges that are grouped by a parent feature, they can be represented as a GRangesList object. Consider the simple example of the two transcript GRangesList below created using the GRangesList constructor.

gr1 <- GRanges(
    seqnames = "chr2",
    ranges = IRanges(103, 106),
    strand = "+",
    score = 5L, GC = 0.45)
gr2 <- GRanges(
    seqnames = c("chr1", "chr1"),
    ranges = IRanges(c(107, 113), width = 3),
    strand = c("+", "-"),
    score = 3:4, GC = c(0.3, 0.5))
grl <- GRangesList("txA" = gr1, "txB" = gr2)
grl

## GRangesList object of length 2:
## $txA
## GRanges object with 1 range and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $txB
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   107-109      + |         3       0.3
##   [2]     chr1   113-115      - |         4       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

The show method for a GRangesList object displays it as a named list of GRanges objects, where the names of this list are considered to be the names of the grouping feature. In the example above, the groups of individual exon ranges are represented as separate GRanges objects which are further organized into a list structure where each element name is a transcript name. Many other combinations of grouped and labeled GRanges objects are possible of course, but this example is expected to be a common arrangement.

Basic GRangesList accessors

Just as with GRanges object, the components of the genomic coordinates within a GRangesList object can be extracted using simple accessor methods. Not surprisingly, the GRangesList objects have many of the same accessors as GRanges objects. The difference is that many of these methods return a list since the input is now essentially a list of GRanges objects. Here are a few examples:

seqnames(grl)

## RleList of length 2
## $txA
## factor-Rle of length 1 with 1 run
##   Lengths:    1
##   Values : chr2
## Levels(2): chr2 chr1
## 
## $txB
## factor-Rle of length 2 with 1 run
##   Lengths:    2
##   Values : chr1
## Levels(2): chr2 chr1

ranges(grl)

## IRangesList object of length 2:
## $txA
## IRanges object with 1 range and 0 metadata columns:
##           start       end     width
##       <integer> <integer> <integer>
##   [1]       103       106         4
## 
## $txB
## IRanges object with 2 ranges and 0 metadata columns:
##           start       end     width
##       <integer> <integer> <integer>
##   [1]       107       109         3
##   [2]       113       115         3

strand(grl)

## RleList of length 2
## $txA
## factor-Rle of length 1 with 1 run
##   Lengths: 1
##   Values : +
## Levels(3): + - *
## 
## $txB
## factor-Rle of length 2 with 2 runs
##   Lengths: 1 1
##   Values : + -
## Levels(3): + - *

The length and names methods will return the length or names of the list and the seqlengths method will return the set of sequence lengths.

length(grl)

## [1] 2

names(grl)

## [1] "txA" "txB"

seqlengths(grl)

## chr2 chr1 
##   NA   NA

The elementNROWS method returns a list of integers corresponding to the result of calling NROW on each individual GRanges object contained by the GRangesList. This is a faster alternative to calling lapply on the GRangesList.

elementNROWS(grl)

## txA txB 
##   1   2

isEmpty tests if a GRangesList object contains anything.

isEmpty(grl)

## [1] FALSE

In the context of a GRangesList object, the mcols method performs a similar operation to what it does on a GRanges object. However, this metadata now refers to information at the list level instead of the level of the individual GRanges objects.

mcols(grl) <- c("Transcript A","Transcript B")
mcols(grl)

## DataFrame with 2 rows and 1 column
##            value
##      <character>
## txA Transcript A
## txB Transcript B

Element-level metadata can be retrieved by unlisting the GRangesList, and extracting the metadata

mcols(unlist(grl))

## DataFrame with 3 rows and 2 columns
##         score        GC
##     <integer> <numeric>
## txA         5      0.45
## txB         3      0.30
## txB         4      0.50

Combining GRangesList objects

GRangesList objects can be unlisted to combine the separate GRanges objects that they contain as an expanded GRanges.

ul <- unlist(grl)
ul

## GRanges object with 3 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   txA     chr2   103-106      + |         5      0.45
##   txB     chr1   107-109      + |         3      0.30
##   txB     chr1   113-115      - |         4      0.50
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Append lists using append or c.

A support site user had two GRangesList objects with ‘parallel’ elements, and wanted to combined these element-wise into a single GRangesList. One solution is to use pc() – parallel (element-wise) c(). A more general solution is to concatenate the lists and then re-group by some factor, in this case the names of the elements.

grl1 <- GRangesList(
    gr1 = GRanges("chr2", IRanges(3, 6)),
    gr2 = GRanges("chr1", IRanges(c(7,13), width = 3)))
grl2 <- GRangesList(
    gr1 = GRanges("chr2", IRanges(9, 12)),
    gr2 = GRanges("chr1", IRanges(c(25,38), width = 3)))

pc(grl1, grl2)

## GRangesList object of length 2:
## $gr1
## GRanges object with 2 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr2       3-6      *
##   [2]     chr2      9-12      *
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $gr2
## GRanges object with 4 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr1       7-9      *
##   [2]     chr1     13-15      *
##   [3]     chr1     25-27      *
##   [4]     chr1     38-40      *
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

grl3 <- c(grl1, grl2)
regroup(grl3, names(grl3))

## GRangesList object of length 2:
## $gr1
## GRanges object with 2 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr2       3-6      *
##   [2]     chr2      9-12      *
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $gr2
## GRanges object with 4 ranges and 0 metadata columns:
##       seqnames    ranges strand
##          <Rle> <IRanges>  <Rle>
##   [1]     chr1       7-9      *
##   [2]     chr1     13-15      *
##   [3]     chr1     25-27      *
##   [4]     chr1     38-40      *
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Basic interval operations for GRangesList objects

For interval operations, many of the same methods exist for GRangesList objects that exist for GRanges objects.

start(grl)

## IntegerList of length 2
## [["txA"]] 103
## [["txB"]] 107 113

end(grl)

## IntegerList of length 2
## [["txA"]] 106
## [["txB"]] 109 115

width(grl)

## IntegerList of length 2
## [["txA"]] 4
## [["txB"]] 3 3

These operations return a data structure representing, e.g., IntegerList, a list where all elements are integers; it can be convenient to use mathematical and other operations on List objects that work on each element, e.g.,

sum(width(grl))  # sum of widths of each grl element

## txA txB 
##   4   6

Most of the intra-, inter- and between-range methods operate on GRangesList objects, e.g., to shift all the GRanges objects in a GRangesList object, or calculate the coverage. Both of these operations are also carried out across each GRanges list member.

shift(grl, 20)

## GRangesList object of length 2:
## $txA
## GRanges object with 1 range and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   123-126      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $txB
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   127-129      + |         3       0.3
##   [2]     chr1   133-135      - |         4       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

coverage(grl)

## RleList of length 2
## $chr2
## integer-Rle of length 106 with 2 runs
##   Lengths: 102   4
##   Values :   0   1
## 
## $chr1
## integer-Rle of length 115 with 4 runs
##   Lengths: 106   3   3   3
##   Values :   0   1   0   1

Subsetting GRangesList objects

A GRangesList object behaves like a list: [ returns a GRangesList containing a subset of the original object; [[ or $ returns the GRanges object at that location in the list.

grl[1]
grl[[1]]
grl["txA"]
grl$txB

In addition, subsetting a GRangesList also accepts a second parameter to specify which of the metadata columns you wish to select.

grl[1, "score"]

## GRangesList object of length 1:
## $txA
## GRanges object with 1 range and 1 metadata column:
##       seqnames    ranges strand |     score
##          <Rle> <IRanges>  <Rle> | <integer>
##   [1]     chr2   103-106      + |         5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

grl["txB", "GC"]

## GRangesList object of length 1:
## $txB
## GRanges object with 2 ranges and 1 metadata column:
##       seqnames    ranges strand |        GC
##          <Rle> <IRanges>  <Rle> | <numeric>
##   [1]     chr1   107-109      + |       0.3
##   [2]     chr1   113-115      - |       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

The head, tail, rep, rev, and window methods all behave as you would expect them to for a list object. For example, the elements referred to by window are now list elements instead of GRanges elements.

rep(grl[[1]], times = 3)

## GRanges object with 3 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   [2]     chr2   103-106      + |         5      0.45
##   [3]     chr2   103-106      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

rev(grl)

## GRangesList object of length 2:
## $txB
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   107-109      + |         3       0.3
##   [2]     chr1   113-115      - |         4       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $txA
## GRanges object with 1 range and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

head(grl, n=1)

## GRangesList object of length 1:
## $txA
## GRanges object with 1 range and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

tail(grl, n=1)

## GRangesList object of length 1:
## $txB
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   107-109      + |         3       0.3
##   [2]     chr1   113-115      - |         4       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

window(grl, start=1, end=1)

## GRangesList object of length 1:
## $txA
## GRanges object with 1 range and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

grl[IRanges(start=2, end=2)]

## GRangesList object of length 1:
## $txB
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   107-109      + |         3       0.3
##   [2]     chr1   113-115      - |         4       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Looping over GRangesList objects

For GRangesList objects there is also a family of apply methods. These include lapply, sapply, mapply, endoapply, mendoapply, Map, and Reduce.

The different looping methods defined for GRangesList objects are useful for returning different kinds of results. The standard lapply and sapply behave according to convention, with the lapply method returning a list and sapply returning a more simplified output.

lapply(grl, length)

## $txA
## [1] 1
## 
## $txB
## [1] 2

sapply(grl, length)

## txA txB 
##   1   2

As with IRanges objects, there is also a multivariate version of sapply, called mapply, defined for GRangesList objects. And, if you don’t want the results simplified, you can call the Map method, which does the same things as mapply but without simplifying the output.

grl2 <- shift(grl, 10)
names(grl2) <- c("shiftTxA", "shiftTxB")

mapply(c, grl, grl2)

## $txA
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   [2]     chr2   113-116      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $txB
## GRanges object with 4 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   107-109      + |         3       0.3
##   [2]     chr1   113-115      - |         4       0.5
##   [3]     chr1   117-119      + |         3       0.3
##   [4]     chr1   123-125      - |         4       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Map(c, grl, grl2)

## $txA
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   [2]     chr2   113-116      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $txB
## GRanges object with 4 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   107-109      + |         3       0.3
##   [2]     chr1   113-115      - |         4       0.5
##   [3]     chr1   117-119      + |         3       0.3
##   [4]     chr1   123-125      - |         4       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Sometimes you will want to get back a modified version of the GRangesList that you originally passed in.

An endomorphism is a transformation of an object to another instance of the same class . This is achieved using the endoapply method, which will return the results as a GRangesList object.

endoapply(grl, rev)

## GRangesList object of length 2:
## $txA
## GRanges object with 1 range and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $txB
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   113-115      - |         4       0.5
##   [2]     chr1   107-109      + |         3       0.3
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

mendoapply(c, grl, grl2)

## GRangesList object of length 2:
## $txA
## GRanges object with 2 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   [2]     chr2   113-116      + |         5      0.45
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $txB
## GRanges object with 4 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr1   107-109      + |         3       0.3
##   [2]     chr1   113-115      - |         4       0.5
##   [3]     chr1   117-119      + |         3       0.3
##   [4]     chr1   123-125      - |         4       0.5
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

The Reduce method will allow the GRanges objects to be collapsed across the whole of the GRangesList object. % Again, this seems like a sub-optimal example to me.

Reduce(c, grl)

## GRanges object with 3 ranges and 2 metadata columns:
##       seqnames    ranges strand |     score        GC
##          <Rle> <IRanges>  <Rle> | <integer> <numeric>
##   [1]     chr2   103-106      + |         5      0.45
##   [2]     chr1   107-109      + |         3      0.30
##   [3]     chr1   113-115      - |         4      0.50
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Explicit element-wise operations (lapply() and friends) on GRangesList objects with many elements can be slow. It is therefore beneficial to explore operations that work on List objects directly (e.g., many of the ‘group generic’ operators, see ?S4groupGeneric, and the set and parallel set operators (e.g., union, punion). A useful and fast strategy is to unlist the GRangesList to a GRanges object, operate on the GRanges object, then relist the result, e.g.,

gr <- unlist(grl)
gr$log_score <- log(gr$score)
grl <- relist(gr, grl)
grl

## GRangesList object of length 2:
## $txA
## GRanges object with 1 range and 3 metadata columns:
##       seqnames    ranges strand |     score        GC log_score
##          <Rle> <IRanges>  <Rle> | <integer> <numeric> <numeric>
##   txA     chr2   103-106      + |         5      0.45   1.60944
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths
## 
## $txB
## GRanges object with 2 ranges and 3 metadata columns:
##       seqnames    ranges strand |     score        GC log_score
##          <Rle> <IRanges>  <Rle> | <integer> <numeric> <numeric>
##   txB     chr1   107-109      + |         3       0.3   1.09861
##   txB     chr1   113-115      - |         4       0.5   1.38629
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Interval overlaps involving GRanges and GRangesList objects

Interval overlapping is the process of comparing the ranges in two objects to determine if and when they overlap. As such, it is perhaps the most common operation performed on GRanges and GRangesList objects. To this end, the GenomicRanges package provides a family of interval overlap functions. The most general of these functions is findOverlaps, which takes a query and a subject as inputs and returns a Hits object containing the index pairings for the overlapping elements.

findOverlaps(gr, grl)

## Hits object with 3 hits and 0 metadata columns:
##       queryHits subjectHits
##       <integer>   <integer>
##   [1]         1           1
##   [2]         2           2
##   [3]         3           2
##   -------
##   queryLength: 3 / subjectLength: 2

As suggested in the sections discussing the nature of the GRanges and GRangesList classes, the index in the above Hits object for a GRanges object is a single range while for a GRangesList object it is the set of ranges that define a “feature”.

Another function in the overlaps family is countOverlaps, which tabulates the number of overlaps for each element in the query.

countOverlaps(gr, grl)

## txA txB txB 
##   1   1   1

A third function in this family is subsetByOverlaps, which extracts the elements in the query that overlap at least one element in the subject.

subsetByOverlaps(gr,grl)

## GRanges object with 3 ranges and 3 metadata columns:
##       seqnames    ranges strand |     score        GC log_score
##          <Rle> <IRanges>  <Rle> | <integer> <numeric> <numeric>
##   txA     chr2   103-106      + |         5      0.45   1.60944
##   txB     chr1   107-109      + |         3      0.30   1.09861
##   txB     chr1   113-115      - |         4      0.50   1.38629
##   -------
##   seqinfo: 2 sequences from an unspecified genome; no seqlengths

Finally, you can use the select argument to get the index of the first overlapping element in the subject for each element in the query.

findOverlaps(gr, grl, select="first")

## [1] 1 2 2

findOverlaps(grl, gr, select="first")

## [1] 1 2

Finding the nearest genomic position in GRanges objects

The GenomicRanges package provides multiple functions to facilitate the indentification of neighboring genomic positions. For the following examples, we define an arbitrary GRanges object for x and we define the GRanges object subject as the collection of genes in TxDb.Hsapiens.UCSC.hg38.knownGene extracted using the genes method from the GenomicFeatures package.

library(TxDb.Hsapiens.UCSC.hg38.knownGene)

## Loading required package: GenomicFeatures

## Loading required package: AnnotationDbi

## Loading required package: Biobase

## Welcome to Bioconductor
## 
##     Vignettes contain introductory material; view with
##     'browseVignettes()'. To cite Bioconductor, see
##     'citation("Biobase")', and for packages 'citation("pkgname")'.

txdb <- TxDb.Hsapiens.UCSC.hg38.knownGene
broads <- GenomicFeatures::genes(txdb)

##   2162 genes were dropped because they have exons located on both strands of
##   the same reference sequence or on more than one reference sequence, so cannot
##   be represented by a single genomic range.
##   Use 'single.strand.genes.only=FALSE' to get all the genes in a GRangesList
##   object, or use suppressMessages() to suppress this message.

x <- GRanges(
    seqnames = Rle(c("chr1", "chr2", "chr1", "chr3"), c(1, 3, 2, 4)),
    ranges = IRanges(101:110, end = 111:120, names = head(letters, 10)),
    strand = Rle(strand(c("-", "+", "*", "+", "-")), c(1, 2, 2, 3, 2)),
    score = 1:10, GC = seq(1, 0, length=10))
subject <- broads[ seqnames(broads) %in% seqlevels(gr) ]

The nearest method performs conventional nearest neighbor finding. It finds the nearest neighbor range in subject for each range in x. Overlaps are included. If subject is not given as an argument, x will also be treated as the subject.

nearest(x, subject)

##  [1] 4316 3659 3659 4177   96   96   NA   NA   NA   NA

nearest(x)

##  [1]  5  4  4  3  6  5  8  7 10  9

The precede method will return the index of the range in subject that is preceded by the range in x. Overlaps are excluded.

precede(x, subject)

##  [1]   NA 3659 3659 3659   96   96   NA   NA   NA   NA

The follow method will return the index of the range in subject that is followed by the range in x.

follow(x, subject)

##  [1] 4316   NA   NA 4177 4316   NA   NA   NA   NA   NA

The nearestKNeighbors method performs conventional k-nearest neighbor finding. For each range in x, it will find the index of the k-nearest neighbors in subject. The argument k can be specified to identify more than one nearest neighbor. Overlaps are included. If subject is not given as an argument, x will also be treated as the subject.

nearestKNeighbors(x, subject)

## IntegerList of length 10
## [[1]] 4316
## [[2]] 3659
## [[3]] 3659
## [[4]] 4177
## [[5]] 96
## [[6]] 96
## [[7]] <NA>
## [[8]] <NA>
## [[9]] <NA>
## [[10]] <NA>

nearestKNeighbors(x, subject, k=10)

## IntegerList of length 10
## [[1]] 4316 779 4219 1736 4511 430 765 2035 1790 1595
## [[2]] 3659 505 1904 1017 439 513 1018 1019 1046 4449
## [[3]] 3659 505 1904 1017 439 513 1018 1019 1046 4449
## [[4]] 4177 3659 505 1904 1017 439 513 1018 1019 1046
## [[5]] 96 779 1456 129 4611 850 1240 1791 3306 4194
## [[6]] 96 1456 129 4611 850 1240 1791 3306 4194 1402
## [[7]] <NA>
## [[8]] <NA>
## [[9]] <NA>
## [[10]] <NA>

nearestKNeighbors(x)

## IntegerList of length 10
## [[1]] 5
## [[2]] 3
## [[3]] 2
## [[4]] 2
## [[5]] 1
## [[6]] 5
## [[7]] 8
## [[8]] 7
## [[9]] 10
## [[10]] 9

nearestKNeighbors(x, k=10)

## IntegerList of length 10
## [[1]] 5 5
## [[2]] 3 4
## [[3]] 2 4
## [[4]] 2 3
## [[5]] 1 6 1
## [[6]] 5
## [[7]] 8
## [[8]] 7
## [[9]] 10 10
## [[10]] 9 9

Session Information

All of the output in this vignette was produced under the following conditions:

sessionInfo()

## R version 4.4.2 (2024-10-31)
## Platform: x86_64-pc-linux-gnu
## Running under: Ubuntu 24.04.1 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
## 
## 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       
## 
## time zone: Etc/UTC
## tzcode source: system (glibc)
## 
## attached base packages:
## [1] stats4    stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] TxDb.Hsapiens.UCSC.hg38.knownGene_3.20.0
##  [2] GenomicFeatures_1.59.1                  
##  [3] AnnotationDbi_1.69.0                    
##  [4] Biobase_2.67.0                          
##  [5] GenomicRanges_1.59.1                    
##  [6] GenomeInfoDb_1.43.2                     
##  [7] IRanges_2.41.2                          
##  [8] S4Vectors_0.45.2                        
##  [9] BiocGenerics_0.53.3                     
## [10] generics_0.1.3                          
## [11] BiocStyle_2.35.0                        
## 
## loaded via a namespace (and not attached):
##  [1] KEGGREST_1.47.0             SummarizedExperiment_1.37.0
##  [3] rjson_0.2.23                xfun_0.49                  
##  [5] bslib_0.8.0                 lattice_0.22-6             
##  [7] vctrs_0.6.5                 tools_4.4.2                
##  [9] bitops_1.0-9                curl_6.0.1                 
## [11] parallel_4.4.2              RSQLite_2.3.9              
## [13] blob_1.2.4                  pkgconfig_2.0.3            
## [15] Matrix_1.7-1                lifecycle_1.0.4            
## [17] GenomeInfoDbData_1.2.13     compiler_4.4.2             
## [19] Rsamtools_2.23.1            Biostrings_2.75.3          
## [21] codetools_0.2-20            htmltools_0.5.8.1          
## [23] sys_3.4.3                   buildtools_1.0.0           
## [25] sass_0.4.9                  RCurl_1.98-1.16            
## [27] yaml_2.3.10                 crayon_1.5.3               
## [29] jquerylib_0.1.4             BiocParallel_1.41.0        
## [31] DelayedArray_0.33.3         cachem_1.1.0               
## [33] abind_1.4-8                 digest_0.6.37              
## [35] restfulr_0.0.15             maketools_1.3.1            
## [37] grid_4.4.2                  fastmap_1.2.0              
## [39] SparseArray_1.7.2           cli_3.6.3                  
## [41] S4Arrays_1.7.1              XML_3.99-0.17              
## [43] UCSC.utils_1.3.0            bit64_4.5.2                
## [45] rmarkdown_2.29              XVector_0.47.0             
## [47] httr_1.4.7                  matrixStats_1.4.1          
## [49] bit_4.5.0.1                 png_0.1-8                  
## [51] memoise_2.0.1               evaluate_1.0.1             
## [53] knitr_1.49                  BiocIO_1.17.1              
## [55] rtracklayer_1.67.0          rlang_1.1.4                
## [57] DBI_1.2.3                   BiocManager_1.30.25        
## [59] jsonlite_1.8.9              R6_2.5.1                   
## [61] MatrixGenerics_1.19.0       GenomicAlignments_1.43.0   
## [63] zlibbioc_1.52.0

An Introduction to the GenomicRanges Package