Contents

1 Introduction

The GenomicTuples R package defines general purpose containers for storing genomic tuples. It aims to provide functionality for tuples of genomic co-ordinates that are analogous to those available for genomic ranges in the GenomicRanges Bioconductor package.

As you will see, the functionality of the GenomicTuples package is based almost entirely on the wonderful GenomicRanges package. Therefore, I have tried to keep the user interface as similar as possible. This vignette is also heavily based on the vignette “An Introduction to Genomic Ranges Classes”, which is included with the GenomicRanges package1. While not essential, familiarity with the GenomicRanges will be of benefit in understanding the GenomicTuples package.

1.1 What is a genomic tuple?

A genomic tuple is defined by a sequence name (seqnames), a strand (strand) and a tuple (tuples). All positions in a genomic tuple must be on the same strand and sorted in ascending order. Each tuple has an associated size, which is a positive integer. For example, chr1:+:{34, 39, 60} is a 3-tuple (size = 3) of the positions chr1:34, chr1:39 and chr1:60 on the + strand.

When referring to genomic tuples of a general (fixed) size, I will abbreviate these to \(m\)-tuples, where \(m\) = size. I will refer to the first position as \(pos_{1}\) (pos1), the second as \(pos_{2}\) (pos2), \(\ldots{}\), and the final position as \(pos_{m}\) (posm).

The difference between a genomic tuple and a genomic range can be thought of as the difference between a set and an interval. For example, the genomic tuple chr10:-:{800, 900} only includes the positions chr10:-:800 and chr10:-:900 whereas the genomic range chr10:-:[800, 900] includes the positions chr10:-:800, chr10:-:801, chr10:-:802, \(\ldots{}\), chr10:-:900.

1.2 When might you need a genomic tuple?

In short, whenever the co-ordinates of your genomic data are better defined by a set than by an interval.

The original use case for the GTuples class was to store the genomic co-ordinates of “methylation patterns”. I am currently developing these ideas in a separate R package, MethylationTuples, which makes heavy use of the GTuples class. Other genomic data, such as long reads containing multiple variants, may also be better conceptualised as genomic tuples rather than as genomic ranges and therefore may benefit from the GenomicTuples infrastructure.

2 GTuples

The GTuples class represents a collection of genomic tuples, where each tuple has the same size. These objects can be created by using the GTuples constructor function. For example, the following code creates a GTuples object with 10 genomic tuples:

library(GenomicTuples)
#> Loading required package: GenomicRanges
#> Loading required package: stats4
#> Loading required package: BiocGenerics
#> Loading required package: parallel
#> 
#> Attaching package: 'BiocGenerics'
#> The following objects are masked from 'package:parallel':
#> 
#>     clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
#>     clusterExport, clusterMap, parApply, parCapply, parLapply,
#>     parLapplyLB, parRapply, parSapply, parSapplyLB
#> The following objects are masked from 'package:stats':
#> 
#>     IQR, mad, sd, var, xtabs
#> The following objects are masked from 'package:base':
#> 
#>     Filter, Find, Map, Position, Reduce, anyDuplicated, append,
#>     as.data.frame, basename, cbind, colMeans, colSums, colnames,
#>     dirname, do.call, duplicated, eval, evalq, get, grep, grepl,
#>     intersect, is.unsorted, lapply, lengths, mapply, match, mget,
#>     order, paste, pmax, pmax.int, pmin, pmin.int, rank, rbind,
#>     rowMeans, rowSums, rownames, sapply, setdiff, sort, table,
#>     tapply, union, unique, unsplit, which, which.max, which.min
#> Loading required package: S4Vectors
#> 
#> Attaching package: 'S4Vectors'
#> The following object is masked from 'package:base':
#> 
#>     expand.grid
#> Loading required package: IRanges
#> Loading required package: GenomeInfoDb
seqinfo <- Seqinfo(paste0("chr", 1:3), c(1000, 2000, 1500), NA, "mock1")
gt3 <- GTuples(seqnames = Rle(c("chr1", "chr2", "chr1", "chr3"),
                              c(1, 3, 2, 4)),
               tuples = matrix(c(1:10, 2:11, 3:12), ncol = 3),
               strand = Rle(strand(c("-", "+", "*", "+", "-")),
                            c(1, 2, 2, 3, 2)),
               score = 1:10, GC = seq(1, 0, length = 10), seqinfo = seqinfo)
names(gt3) <- letters[1:10]
gt3
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   a     chr1    1    2    3      - |     1                 1
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   c     chr2    3    4    5      + |     3 0.777777777777778
#>   d     chr2    4    5    6      * |     4 0.666666666666667
#>   e     chr1    5    6    7      * |     5 0.555555555555556
#>   f     chr1    6    7    8      + |     6 0.444444444444444
#>   g     chr3    7    8    9      + |     7 0.333333333333333
#>   h     chr3    8    9   10      + |     8 0.222222222222222
#>   i     chr3    9   10   11      - |     9 0.111111111111111
#>   j     chr3   10   11   12      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

The output of the GTuples show method is very similar to that of the show method for GenomicRanges::GRanges objects. Namely, it separates the information into a left and right hand region that are separated by | symbols. The genomic coordinates (seqnames, tuples, 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 GTuples object.

The main difference between a GTuples object and GenomicRanges::GRanges object is that the former uses tuples while the latter uses ranges in the genomic coordinates.

For even more information on the GTuples class, be sure to consult the documentation:

?GTuples

2.1 GTuples methods

Most methods defined for GenomicRanges::GRanges are also defined for GTuples. Those that are not yet defined, which are those that make sense for ranges but generally not for tuples, return error messages.

If you require a method that is not defined for GTuples but is defined for GenomicRanges::GRanges, then this can be achieved by first coercing the GTuples object to a GenomicRanges::GRanges object; Warning: coercing a GTuples object to a GenomicRanges::GRanges is generally a destructive operation.

as(gt3, "GRanges")
#> GRanges object with 10 ranges and 2 metadata columns:
#>     seqnames    ranges strand |     score                GC
#>        <Rle> <IRanges>  <Rle> | <integer>         <numeric>
#>   a     chr1       1-3      - |         1                 1
#>   b     chr2       2-4      + |         2 0.888888888888889
#>   c     chr2       3-5      + |         3 0.777777777777778
#>   d     chr2       4-6      * |         4 0.666666666666667
#>   e     chr1       5-7      * |         5 0.555555555555556
#>   f     chr1       6-8      + |         6 0.444444444444444
#>   g     chr3       7-9      + |         7 0.333333333333333
#>   h     chr3      8-10      + |         8 0.222222222222222
#>   i     chr3      9-11      - |         9 0.111111111111111
#>   j     chr3     10-12      - |        10                 0
#>   -------
#>   seqinfo: 3 sequences from mock1 genome

2.1.1 Basic GTuples accessors

The components of the genomic coordinates within a GTuples object can be extracted using the seqnames, tuples, and strand accessor functions. Warning: The tuples accessor should be used in place of the ranges accessor. While the ranges method is well-defined, namely it accesses \(pos_{1}\) and \(pos_{m}\) of the object, this is not generally what is desired or required.

seqnames(gt3)
#> factor-Rle of length 10 with 4 runs
#>   Lengths:    1    3    2    4
#>   Values : chr1 chr2 chr1 chr3
#> Levels(3): chr1 chr2 chr3
tuples(gt3)
#>       pos1 pos2 pos3
#>  [1,]    1    2    3
#>  [2,]    2    3    4
#>  [3,]    3    4    5
#>  [4,]    4    5    6
#>  [5,]    5    6    7
#>  [6,]    6    7    8
#>  [7,]    7    8    9
#>  [8,]    8    9   10
#>  [9,]    9   10   11
#> [10,]   10   11   12
strand(gt3)
#> factor-Rle of length 10 with 5 runs
#>   Lengths: 1 2 2 3 2
#>   Values : - + * + -
#> Levels(3): + - *

Stored annotations for these coordinates can be extracted as a DataFrame object using the mcols accessor:

mcols(gt3)
#> DataFrame with 10 rows and 2 columns
#>        score                GC
#>    <integer>         <numeric>
#> 1          1                 1
#> 2          2 0.888888888888889
#> 3          3 0.777777777777778
#> 4          4 0.666666666666667
#> 5          5 0.555555555555556
#> 6          6 0.444444444444444
#> 7          7 0.333333333333333
#> 8          8 0.222222222222222
#> 9          9 0.111111111111111
#> 10        10                 0

Seqinfo can be extracted using the seqinfo accessor:

seqinfo(gt3)
#> Seqinfo object with 3 sequences from mock1 genome:
#>   seqnames seqlengths isCircular genome
#>   chr1           1000         NA  mock1
#>   chr2           2000         NA  mock1
#>   chr3           1500         NA  mock1

Methods for accessing the length and names are also defined:

length(gt3)
#> [1] 10
names(gt3)
#>  [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"

2.1.2 Splitting and combining GTuples objects}

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

sp <- split(gt3, rep(1:2, each=5))
sp
#> GTuplesList object of length 2:
#> $1 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   a     chr1    1    2    3      - |     1                 1
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   c     chr2    3    4    5      + |     3 0.777777777777778
#>   d     chr2    4    5    6      * |     4 0.666666666666667
#>   e     chr1    5    6    7      * |     5 0.555555555555556
#> 
#> $2 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   f     chr1    6    7    8      + |     6 0.444444444444444
#>   g     chr3    7    8    9      + |     7 0.333333333333333
#>   h     chr3    8    9   10      + |     8 0.222222222222222
#>   i     chr3    9   10   11      - |     9 0.111111111111111
#>   j     chr3   10   11   12      - |    10                 0
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome

If you then grab the components of this GenomicTuplesList, they can also be combined by using the c and append methods:

c(sp[[1]], sp[[2]])
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   a     chr1    1    2    3      - |     1                 1
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   c     chr2    3    4    5      + |     3 0.777777777777778
#>   d     chr2    4    5    6      * |     4 0.666666666666667
#>   e     chr1    5    6    7      * |     5 0.555555555555556
#>   f     chr1    6    7    8      + |     6 0.444444444444444
#>   g     chr3    7    8    9      + |     7 0.333333333333333
#>   h     chr3    8    9   10      + |     8 0.222222222222222
#>   i     chr3    9   10   11      - |     9 0.111111111111111
#>   j     chr3   10   11   12      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

2.1.3 Subsetting GTuples objects

The expected subsetting operations are also available for GTuples objects:

gt3[2:3]
#> GTuples object with 2 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   c     chr2    3    4    5      + |     3 0.777777777777778
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

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

gt3[2:3, "GC"]
#> GTuples object with 2 x 3-tuples and 1 metadata column:
#>     seqnames pos1 pos2 pos3 strand |                GC
#>   b     chr2    2    3    4      + | 0.888888888888889
#>   c     chr2    3    4    5      + | 0.777777777777778
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

You can also assign into elements of the GTuples object. Here is an example where the 2nd row of a GTuples object is replaced with the 1st row of gt3:

gt3_mod <- gt3
gt3_mod[2] <- gt3[1]
head(gt3_mod, n = 3)
#> GTuples object with 3 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   a     chr1    1    2    3      - |     1                 1
#>   b     chr1    1    2    3      - |     1                 1
#>   c     chr2    3    4    5      + |     3 0.777777777777778
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

There are also methods to repeat, reverse, or select specific portions of GTuples objects:

rep(gt3[2], times = 3)
#> GTuples object with 3 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
rev(gt3)
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   j     chr3   10   11   12      - |    10                 0
#>   i     chr3    9   10   11      - |     9 0.111111111111111
#>   h     chr3    8    9   10      + |     8 0.222222222222222
#>   g     chr3    7    8    9      + |     7 0.333333333333333
#>   f     chr1    6    7    8      + |     6 0.444444444444444
#>   e     chr1    5    6    7      * |     5 0.555555555555556
#>   d     chr2    4    5    6      * |     4 0.666666666666667
#>   c     chr2    3    4    5      + |     3 0.777777777777778
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   a     chr1    1    2    3      - |     1                 1
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
head(gt3, n = 2)
#> GTuples object with 2 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   a     chr1    1    2    3      - |     1                 1
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
tail(gt3, n = 2)
#> GTuples object with 2 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   i     chr3    9   10   11      - |     9 0.111111111111111
#>   j     chr3   10   11   12      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
window(gt3, start = 2, end = 4)
#> GTuples object with 3 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   b     chr2    2    3    4      + |     2 0.888888888888889
#>   c     chr2    3    4    5      + |     3 0.777777777777778
#>   d     chr2    4    5    6      * |     4 0.666666666666667
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

2.1.4 Basic tuple operations for GTuples objects

Basic tuple characteristics of GTuples objects can be extracted using the start, end, and tuples methods. Warning: While the width method is well-defined, namely as \(pos_{m} - pos_{1} + 1\), this may not be what is required. Instead, please see the IPD method that will be discussed in the next section.

start(gt3)
#>  [1]  1  2  3  4  5  6  7  8  9 10
end(gt3)
#>  [1]  3  4  5  6  7  8  9 10 11 12
tuples(gt3)
#>       pos1 pos2 pos3
#>  [1,]    1    2    3
#>  [2,]    2    3    4
#>  [3,]    3    4    5
#>  [4,]    4    5    6
#>  [5,]    5    6    7
#>  [6,]    6    7    8
#>  [7,]    7    8    9
#>  [8,]    8    9   10
#>  [9,]    9   10   11
#> [10,]   10   11   12

2.1.4.1 Intra-tuple operations

Most of the intra-range methods defined for GenomicRanges::GRanges objects are not currently defined via extension for GTuples objects due to the differences between ranges and tuples. Those not currently defined, and which return an error message, are:

  • narrow
  • flank
  • promoters
  • resize
  • Ops

I am happy to add these methods if appropriate, so please contact me if you have suggestions for good definitions.

Both the trim and shift methods are well-defined, although the former is somewhat limited since it will return an error if the internal positions exceed the seqlengths:

shift(gt3, 500)
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   a     chr1  501  502  503      - |     1                 1
#>   b     chr2  502  503  504      + |     2 0.888888888888889
#>   c     chr2  503  504  505      + |     3 0.777777777777778
#>   d     chr2  504  505  506      * |     4 0.666666666666667
#>   e     chr1  505  506  507      * |     5 0.555555555555556
#>   f     chr1  506  507  508      + |     6 0.444444444444444
#>   g     chr3  507  508  509      + |     7 0.333333333333333
#>   h     chr3  508  509  510      + |     8 0.222222222222222
#>   i     chr3  509  510  511      - |     9 0.111111111111111
#>   j     chr3  510  511  512      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
# Raises warning due to tuple being outside of seqlength
x <- shift(gt3[1], 999)
#> Warning in valid.GenomicRanges.seqinfo(x, suggest.trim = TRUE): GRanges object contains 1 out-of-bound range located on sequence
#>   chr1. 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.
x
#> GTuples object with 1 x 3-tuple and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score GC
#>   a     chr1 1000 1001 1002      - |     1  1
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

# Returns an error because internal position exceeds sequence length, resulting 
# in a malformed tuple when trimmed.
trim(x)
#> Error in validObject(object): invalid class "GTuples" object: positions in each tuple must be sorted in strictly increasing order, i.e. 'pos1' < ... < 'pos3'

2.1.4.2 Inter-tuple operations

None of the inter-range methods defined for GenomicRanges::GRanges objects are currently defined via extension for GTuples objects due to the differences between ranges and tuples. Those not currently defined, and which return an error message, are:

  • range
  • reduce
  • gaps
  • disjoin
  • isDisjoint
  • disjointBins

I am happy to add these methods if appropriate, so please contact me if you have suggestions for good definitions.

2.1.4.3 Interval set operations for GTuples objects

None of the interval set operations defined for GenomicRanges::GRanges objects are currently defined via extension for GTuples objects due to the differences between ranges and tuples. Those not currently defined, and which return an error message, are:

  • union
  • intersect
  • setdiff
  • punion
  • pintersect
  • psetdiff

I am happy to add these methods if appropriate, so please contact me if you have suggestions for good definitions.

2.1.5 Additional methods unique to GTuples

GTuples have a few specifically defined methods that do not exist for GenomicRanges::GRanges. These are tuples, size and IPD.

The tuples method we have already seen and is somewhat analogous to the ranges method for GenomicRanges::GRanges, although returning an integer matrix rather than an IRanges::IRanges object:

tuples(gt3)
#>       pos1 pos2 pos3
#>  [1,]    1    2    3
#>  [2,]    2    3    4
#>  [3,]    3    4    5
#>  [4,]    4    5    6
#>  [5,]    5    6    7
#>  [6,]    6    7    8
#>  [7,]    7    8    9
#>  [8,]    8    9   10
#>  [9,]    9   10   11
#> [10,]   10   11   12

The size method returns the size of the tuples stored in the object:

size(gt3)
#> [1] 3

Every m-tuple with \(m \geq 2\) has an associated vector of intra-pair distances (\(IPD\)). This is defined as \(IPD = (pos_{2} - pos_{1}, \ldots, pos_{m} - pos_{m - 1})\). The IPD method returns this as an integer matrix, where the \(i^{th}\) row contains the \(IPD\) for the \(i^{th}\) tuple:

IPD(gt3)
#>       [,1] [,2]
#>  [1,]    1    1
#>  [2,]    1    1
#>  [3,]    1    1
#>  [4,]    1    1
#>  [5,]    1    1
#>  [6,]    1    1
#>  [7,]    1    1
#>  [8,]    1    1
#>  [9,]    1    1
#> [10,]    1    1

2.2 Implementation details

While the GTuples class can be thought of as a matrix-link object, with the number of columns equal to the size of the tuples plus two (one for the seqname and one for the strand), internally, it extends the GenomicRanges::GRanges class. Specifically, the ranges slot stores an IRanges::IRanges object containing \(pos_{1}\) and \(pos_{m}\) and, if size \(> 2\), a matrix is used to store the co-ordinates of the “internal positions”, \(pos_{2}, \ldots, pos_{m - 1}\) in the internalPos slot. If size \(\leq 2\) then the internalPos slot is set to NULL. The size is stored as an integer in the size slot.

While there are arguments for creating stand-alone GTuples and GTuplesList classes, by extending the GenomicRanges::GRanges and GenomicRanges::GRangesList classes we get a lot of very useful functionality “for free” via appropriately defined inheritance.

3 GTuplesList

The GTuplesList class is a container to store a S4Vectors::List of GTuples objects. It extends the GenomicRanges::GRangesList class.

Currently, all GTuples in a GTuplesList must have the same size2. I expect that users will mostly use GTuples objects and have little need to directly use GTuplesList objects.

seqinfo <- Seqinfo(paste0("chr", 1:3), c(1000, 2000, 1500), NA, "mock1")
gt3 <- GTuples(seqnames = Rle(c("chr1", "chr2", "chr1", "chr3"),
                              c(1, 3, 2, 4)),
               tuples = matrix(c(1:10, 2:11, 3:12), ncol = 3),
               strand = Rle(strand(c("-", "+", "*", "+", "-")),
                            c(1, 2, 2, 3, 2)),
               score = 1:10, GC = seq(1, 0, length = 10), seqinfo = seqinfo)
gtl3 <- GTuplesList(A = gt3[1:5], B = gt3[6:10])
gtl3
#> GTuplesList object of length 2:
#> $A 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    1    2    3      - |     1                 1
#>   [2]     chr2    2    3    4      + |     2 0.888888888888889
#>   [3]     chr2    3    4    5      + |     3 0.777777777777778
#>   [4]     chr2    4    5    6      * |     4 0.666666666666667
#>   [5]     chr1    5    6    7      * |     5 0.555555555555556
#> 
#> $B 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    6    7    8      + |     6 0.444444444444444
#>   [2]     chr3    7    8    9      + |     7 0.333333333333333
#>   [3]     chr3    8    9   10      + |     8 0.222222222222222
#>   [4]     chr3    9   10   11      - |     9 0.111111111111111
#>   [5]     chr3   10   11   12      - |    10                 0
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome

For even more information on the GTuplesList class, be sure to consult the documentation:

?GTuplesList

3.1 GTuplesList methods

Most methods defined for GenomicRanges::GRangesList are also applicable to GTuplesList. Those that are not yet defined, which are those that make sense for ranges but generally not for tuples, return error messages.

If a method that is not defined for GTuplesList but is defined for GenomicRanges::GRangesList is truly required, then this can be achieved by first coercing the GTuplesList object to a GenomicRanges::GRangesList object, noting that this is generally a destructive operation:

as(gtl3, "GRangesList")
#> GRangesList object of length 2:
#> $A 
#> GRanges object with 5 ranges and 2 metadata columns:
#>       seqnames    ranges strand |     score                GC
#>          <Rle> <IRanges>  <Rle> | <integer>         <numeric>
#>   [1]     chr1       1-3      - |         1                 1
#>   [2]     chr2       2-4      + |         2 0.888888888888889
#>   [3]     chr2       3-5      + |         3 0.777777777777778
#>   [4]     chr2       4-6      * |         4 0.666666666666667
#>   [5]     chr1       5-7      * |         5 0.555555555555556
#> 
#> $B 
#> GRanges object with 5 ranges and 2 metadata columns:
#>       seqnames ranges strand | score                GC
#>   [1]     chr1    6-8      + |     6 0.444444444444444
#>   [2]     chr3    7-9      + |     7 0.333333333333333
#>   [3]     chr3   8-10      + |     8 0.222222222222222
#>   [4]     chr3   9-11      - |     9 0.111111111111111
#>   [5]     chr3  10-12      - |    10                 0
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome

3.1.1 Basic GTuplesList accessors}

These are very similar to those available for GTuples objects, except that they typically return a list since the input is now essentially a list of GTuples objects:

seqnames(gtl3)
#> RleList of length 2
#> $A
#> factor-Rle of length 5 with 3 runs
#>   Lengths:    1    3    1
#>   Values : chr1 chr2 chr1
#> Levels(3): chr1 chr2 chr3
#> 
#> $B
#> factor-Rle of length 5 with 2 runs
#>   Lengths:    1    4
#>   Values : chr1 chr3
#> Levels(3): chr1 chr2 chr3
# Returns a list of integer matrices
tuples(gtl3)
#> List of length 2
#> names(2): A B
tuples(gtl3)[[1]]
#>      pos1 pos2 pos3
#> [1,]    1    2    3
#> [2,]    2    3    4
#> [3,]    3    4    5
#> [4,]    4    5    6
#> [5,]    5    6    7
strand(gtl3)
#> RleList of length 2
#> $A
#> factor-Rle of length 5 with 3 runs
#>   Lengths: 1 2 2
#>   Values : - + *
#> Levels(3): + - *
#> 
#> $B
#> factor-Rle of length 5 with 2 runs
#>   Lengths: 3 2
#>   Values : + -
#> Levels(3): + - *

The length and names methods will return the length and names of the list, respectively:

length(gtl3)
#> [1] 2
names(gtl3)
#> [1] "A" "B"

Seqinfo can be extracted using the seqinfo accessor:

seqinfo(gtl3)
#> Seqinfo object with 3 sequences from mock1 genome:
#>   seqnames seqlengths isCircular genome
#>   chr1           1000         NA  mock1
#>   chr2           2000         NA  mock1
#>   chr3           1500         NA  mock1

The elementNROWS method returns a list of integers corresponding to the result of calling length on each individual GTuples object contained by the GTuplesList. This is a faster alternative to calling lapply on the GTuplesList:

elementNROWS(gtl3)
#> A B 
#> 5 5

You can also use isEmpty to test if a GTuplesList object contains anything:

isEmpty(gtl3)
#> [1] FALSE
isEmpty(GTuplesList())
#> [1] TRUE

Finally, in the context of a GTuplesList object, the mcols method performs a similar operation to what it does on a GTuples object. However, this metadata now refers to information at the list level instead of the level of the individual GTuples objects:

mcols(gtl3) <- c("Feature A", "Feature B")
mcols(gtl3)
#> DataFrame with 2 rows and 1 column
#>         value
#>   <character>
#> 1   Feature A
#> 2   Feature B

3.1.2 Combining GTuplesList objects

GTuplesList objects can be unlisted to combine the separate GTuples objects that they contain as an expanded GTuples:

ul <- unlist(gtl3)
ul
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>     seqnames pos1 pos2 pos3 strand | score                GC
#>   A     chr1    1    2    3      - |     1                 1
#>   A     chr2    2    3    4      + |     2 0.888888888888889
#>   A     chr2    3    4    5      + |     3 0.777777777777778
#>   A     chr2    4    5    6      * |     4 0.666666666666667
#>   A     chr1    5    6    7      * |     5 0.555555555555556
#>   B     chr1    6    7    8      + |     6 0.444444444444444
#>   B     chr3    7    8    9      + |     7 0.333333333333333
#>   B     chr3    8    9   10      + |     8 0.222222222222222
#>   B     chr3    9   10   11      - |     9 0.111111111111111
#>   B     chr3   10   11   12      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

You can also combine GTuplesList objects together using append or c.

3.1.3 Subsetting GTuplesList objects

Subsetting of GTuplesList objects is identical to subsetting of GenomicRanges::GRangesList objects:

gtl3[1]
#> GTuplesList object of length 1:
#> $A 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    1    2    3      - |     1                 1
#>   [2]     chr2    2    3    4      + |     2 0.888888888888889
#>   [3]     chr2    3    4    5      + |     3 0.777777777777778
#>   [4]     chr2    4    5    6      * |     4 0.666666666666667
#>   [5]     chr1    5    6    7      * |     5 0.555555555555556
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome
gtl3[[1]]
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    1    2    3      - |     1                 1
#>   [2]     chr2    2    3    4      + |     2 0.888888888888889
#>   [3]     chr2    3    4    5      + |     3 0.777777777777778
#>   [4]     chr2    4    5    6      * |     4 0.666666666666667
#>   [5]     chr1    5    6    7      * |     5 0.555555555555556
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
gtl3["A"]
#> GTuplesList object of length 1:
#> $A 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    1    2    3      - |     1                 1
#>   [2]     chr2    2    3    4      + |     2 0.888888888888889
#>   [3]     chr2    3    4    5      + |     3 0.777777777777778
#>   [4]     chr2    4    5    6      * |     4 0.666666666666667
#>   [5]     chr1    5    6    7      * |     5 0.555555555555556
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome
gtl3$B
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    6    7    8      + |     6 0.444444444444444
#>   [2]     chr3    7    8    9      + |     7 0.333333333333333
#>   [3]     chr3    8    9   10      + |     8 0.222222222222222
#>   [4]     chr3    9   10   11      - |     9 0.111111111111111
#>   [5]     chr3   10   11   12      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

When subsetting a GTuplesList, you can also pass in a second parameter (as with a GTuples object) to again specify which of the metadata columns you wish to select:

gtl3[1, "score"]
#> GTuplesList object of length 1:
#> $A 
#> GTuples object with 5 x 3-tuples and 1 metadata column:
#>       seqnames pos1 pos2 pos3 strand | score
#>   [1]     chr1    1    2    3      - |     1
#>   [2]     chr2    2    3    4      + |     2
#>   [3]     chr2    3    4    5      + |     3
#>   [4]     chr2    4    5    6      * |     4
#>   [5]     chr1    5    6    7      * |     5
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome
gtl3["B", "GC"]
#> GTuplesList object of length 1:
#> $B 
#> GTuples object with 5 x 3-tuples and 1 metadata column:
#>       seqnames pos1 pos2 pos3 strand |                GC
#>   [1]     chr1    6    7    8      + | 0.444444444444444
#>   [2]     chr3    7    8    9      + | 0.333333333333333
#>   [3]     chr3    8    9   10      + | 0.222222222222222
#>   [4]     chr3    9   10   11      - | 0.111111111111111
#>   [5]     chr3   10   11   12      - |                 0
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome

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 GTuples elements:

rep(gtl3[[1]], times = 3)
#> GTuples object with 15 x 3-tuples and 2 metadata columns:
#>        seqnames pos1 pos2 pos3 strand | score                GC
#>    [1]     chr1    1    2    3      - |     1                 1
#>    [2]     chr2    2    3    4      + |     2 0.888888888888889
#>    [3]     chr2    3    4    5      + |     3 0.777777777777778
#>    [4]     chr2    4    5    6      * |     4 0.666666666666667
#>    [5]     chr1    5    6    7      * |     5 0.555555555555556
#>    ...      ...  ...  ...  ...    ... .   ...               ...
#>   [11]     chr1    1    2    3      - |     1                 1
#>   [12]     chr2    2    3    4      + |     2 0.888888888888889
#>   [13]     chr2    3    4    5      + |     3 0.777777777777778
#>   [14]     chr2    4    5    6      * |     4 0.666666666666667
#>   [15]     chr1    5    6    7      * |     5 0.555555555555556
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
rev(gtl3)
#> GTuplesList object of length 2:
#> $B 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    6    7    8      + |     6 0.444444444444444
#>   [2]     chr3    7    8    9      + |     7 0.333333333333333
#>   [3]     chr3    8    9   10      + |     8 0.222222222222222
#>   [4]     chr3    9   10   11      - |     9 0.111111111111111
#>   [5]     chr3   10   11   12      - |    10                 0
#> 
#> $A 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    1    2    3      - |     1                 1
#>   [2]     chr2    2    3    4      + |     2 0.888888888888889
#>   [3]     chr2    3    4    5      + |     3 0.777777777777778
#>   [4]     chr2    4    5    6      * |     4 0.666666666666667
#>   [5]     chr1    5    6    7      * |     5 0.555555555555556
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome
head(gtl3, n = 1)
#> GTuplesList object of length 1:
#> $A 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    1    2    3      - |     1                 1
#>   [2]     chr2    2    3    4      + |     2 0.888888888888889
#>   [3]     chr2    3    4    5      + |     3 0.777777777777778
#>   [4]     chr2    4    5    6      * |     4 0.666666666666667
#>   [5]     chr1    5    6    7      * |     5 0.555555555555556
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome
tail(gtl3, n = 1)
#> GTuplesList object of length 1:
#> $B 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    6    7    8      + |     6 0.444444444444444
#>   [2]     chr3    7    8    9      + |     7 0.333333333333333
#>   [3]     chr3    8    9   10      + |     8 0.222222222222222
#>   [4]     chr3    9   10   11      - |     9 0.111111111111111
#>   [5]     chr3   10   11   12      - |    10                 0
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome
window(gtl3, start = 1, end = 1)
#> GTuplesList object of length 1:
#> $A 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    1    2    3      - |     1                 1
#>   [2]     chr2    2    3    4      + |     2 0.888888888888889
#>   [3]     chr2    3    4    5      + |     3 0.777777777777778
#>   [4]     chr2    4    5    6      * |     4 0.666666666666667
#>   [5]     chr1    5    6    7      * |     5 0.555555555555556
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome

3.1.4 Basic tuple operations for GTuplesList objects

Basic tuple characteristics of GTuplesList objects can be extracted using the start, end, and tuples methods. These are very similar to those available for GTuples objects, except that they typically return a list since the input is now essentially a list of GTuples objects.

WARNING: While the width method is well-defined, namely it returns an IntegerList of \(pos_{m} - pos_{1} + 1\), this is not generally what is desired or required. Instead, please see the IPD method that is discussed later.

start(gtl3)
#> IntegerList of length 2
#> [["A"]] 1 2 3 4 5
#> [["B"]] 6 7 8 9 10
end(gtl3)
#> IntegerList of length 2
#> [["A"]] 3 4 5 6 7
#> [["B"]] 8 9 10 11 12
tuples(gtl3)
#> List of length 2
#> names(2): A B

3.1.4.1 Intra-tuple operations

Most of the intra-range methods defined for GenomicRanges::GRangesList objects are not currently defined via extension for GTuples objects due to the differences between ranges and tuples. Those not currently defined, and which return an error message, are:

  • flank
  • promoters
  • resize
  • restrict

I am happy to add these methods if appropriate, so please contact me if you have suggestions for good definitions.

The shift method is well-defined:

shift(gtl3, 500)
#> GTuplesList object of length 2:
#> $A 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1  501  502  503      - |     1                 1
#>   [2]     chr2  502  503  504      + |     2 0.888888888888889
#>   [3]     chr2  503  504  505      + |     3 0.777777777777778
#>   [4]     chr2  504  505  506      * |     4 0.666666666666667
#>   [5]     chr1  505  506  507      * |     5 0.555555555555556
#> 
#> $B 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1  506  507  508      + |     6 0.444444444444444
#>   [2]     chr3  507  508  509      + |     7 0.333333333333333
#>   [3]     chr3  508  509  510      + |     8 0.222222222222222
#>   [4]     chr3  509  510  511      - |     9 0.111111111111111
#>   [5]     chr3  510  511  512      - |    10                 0
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome
shift(gtl3, IntegerList(A = 300L, B = 500L))
#> GTuplesList object of length 2:
#> $A 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1  301  302  303      - |     1                 1
#>   [2]     chr2  302  303  304      + |     2 0.888888888888889
#>   [3]     chr2  303  304  305      + |     3 0.777777777777778
#>   [4]     chr2  304  305  306      * |     4 0.666666666666667
#>   [5]     chr1  305  306  307      * |     5 0.555555555555556
#> 
#> $B 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1  506  507  508      + |     6 0.444444444444444
#>   [2]     chr3  507  508  509      + |     7 0.333333333333333
#>   [3]     chr3  508  509  510      + |     8 0.222222222222222
#>   [4]     chr3  509  510  511      - |     9 0.111111111111111
#>   [5]     chr3  510  511  512      - |    10                 0
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome

3.1.4.2 Inter-tuple operations

None of the inter-range methods defined for GenomicRanges::GRangesList objects are currently defined via extension for GTuplesList objects due to the differences between ranges and tuples. Those not currently defined, and which return an error message, are:

  • range
  • reduce
  • disjoin
  • isDisjoint

I am happy to add these methods if appropriate, so please contact me if you have suggestions for good definitions.

3.1.4.3 Interval set operations for GTuplesList objects

None of the interval set operations defined for GenomicRanges::GRangesList objects are currently defined via extension for GTuplesList objects due to the differences between ranges and tuples. Those not currently defined, and which return an error message, are:

  • punion
  • pintersect
  • psetdiff

I am happy to add these methods if appropriate, so please contact me if you have suggestions for good definitions.

3.1.5 Looping over GTuplesList objects

Like for GenomicRanges::GRangesList objects, for GTuplesList objects there is a family of apply methods. These include lapply, sapply, mapply, endoapply, mendoapply, Map, and Reduce. The different looping methods defined for GTuplesList 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(gtl3, length)
#> $A
#> [1] 5
#> 
#> $B
#> [1] 5
sapply(gtl3, length)
#> A B 
#> 5 5

As with GenomicRanges::GRangesList objects, there is also a multivariate version of sapply, called mapply, defined for GTuplesList 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:

gtl3_shift <- shift(gtl3, 10)
names(gtl3) <- c("shiftA", "shiftB")
mapply(c, gtl3, gtl3_shift)
#> $shiftA
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>        seqnames pos1 pos2 pos3 strand | score                GC
#>    [1]     chr1    1    2    3      - |     1                 1
#>    [2]     chr2    2    3    4      + |     2 0.888888888888889
#>    [3]     chr2    3    4    5      + |     3 0.777777777777778
#>    [4]     chr2    4    5    6      * |     4 0.666666666666667
#>    [5]     chr1    5    6    7      * |     5 0.555555555555556
#>    [6]     chr1   11   12   13      - |     1                 1
#>    [7]     chr2   12   13   14      + |     2 0.888888888888889
#>    [8]     chr2   13   14   15      + |     3 0.777777777777778
#>    [9]     chr2   14   15   16      * |     4 0.666666666666667
#>   [10]     chr1   15   16   17      * |     5 0.555555555555556
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
#> 
#> $shiftB
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>        seqnames pos1 pos2 pos3 strand | score                GC
#>    [1]     chr1    6    7    8      + |     6 0.444444444444444
#>    [2]     chr3    7    8    9      + |     7 0.333333333333333
#>    [3]     chr3    8    9   10      + |     8 0.222222222222222
#>    [4]     chr3    9   10   11      - |     9 0.111111111111111
#>    [5]     chr3   10   11   12      - |    10                 0
#>    [6]     chr1   16   17   18      + |     6 0.444444444444444
#>    [7]     chr3   17   18   19      + |     7 0.333333333333333
#>    [8]     chr3   18   19   20      + |     8 0.222222222222222
#>    [9]     chr3   19   20   21      - |     9 0.111111111111111
#>   [10]     chr3   20   21   22      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
Map(c, gtl3, gtl3_shift)
#> $shiftA
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>        seqnames pos1 pos2 pos3 strand | score                GC
#>    [1]     chr1    1    2    3      - |     1                 1
#>    [2]     chr2    2    3    4      + |     2 0.888888888888889
#>    [3]     chr2    3    4    5      + |     3 0.777777777777778
#>    [4]     chr2    4    5    6      * |     4 0.666666666666667
#>    [5]     chr1    5    6    7      * |     5 0.555555555555556
#>    [6]     chr1   11   12   13      - |     1                 1
#>    [7]     chr2   12   13   14      + |     2 0.888888888888889
#>    [8]     chr2   13   14   15      + |     3 0.777777777777778
#>    [9]     chr2   14   15   16      * |     4 0.666666666666667
#>   [10]     chr1   15   16   17      * |     5 0.555555555555556
#>   ---
#>   seqinfo: 3 sequences from mock1 genome
#> 
#> $shiftB
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>        seqnames pos1 pos2 pos3 strand | score                GC
#>    [1]     chr1    6    7    8      + |     6 0.444444444444444
#>    [2]     chr3    7    8    9      + |     7 0.333333333333333
#>    [3]     chr3    8    9   10      + |     8 0.222222222222222
#>    [4]     chr3    9   10   11      - |     9 0.111111111111111
#>    [5]     chr3   10   11   12      - |    10                 0
#>    [6]     chr1   16   17   18      + |     6 0.444444444444444
#>    [7]     chr3   17   18   19      + |     7 0.333333333333333
#>    [8]     chr3   18   19   20      + |     8 0.222222222222222
#>    [9]     chr3   19   20   21      - |     9 0.111111111111111
#>   [10]     chr3   20   21   22      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

The endoapply method will return the results as a GTuplesList object rather than as a list:

endoapply(gtl3, rev)
#> GTuplesList object of length 2:
#> $shiftA 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr1    5    6    7      * |     5 0.555555555555556
#>   [2]     chr2    4    5    6      * |     4 0.666666666666667
#>   [3]     chr2    3    4    5      + |     3 0.777777777777778
#>   [4]     chr2    2    3    4      + |     2 0.888888888888889
#>   [5]     chr1    1    2    3      - |     1                 1
#> 
#> $shiftB 
#> GTuples object with 5 x 3-tuples and 2 metadata columns:
#>       seqnames pos1 pos2 pos3 strand | score                GC
#>   [1]     chr3   10   11   12      - |    10                 0
#>   [2]     chr3    9   10   11      - |     9 0.111111111111111
#>   [3]     chr3    8    9   10      + |     8 0.222222222222222
#>   [4]     chr3    7    8    9      + |     7 0.333333333333333
#>   [5]     chr1    6    7    8      + |     6 0.444444444444444
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome

There is also a multivariate version of the endoapply method in the form of the mendoapply method:

mendoapply(c, gtl3, gtl3_shift)
#> GTuplesList object of length 2:
#> $shiftA 
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>        seqnames pos1 pos2 pos3 strand | score                GC
#>    [1]     chr1    1    2    3      - |     1                 1
#>    [2]     chr2    2    3    4      + |     2 0.888888888888889
#>    [3]     chr2    3    4    5      + |     3 0.777777777777778
#>    [4]     chr2    4    5    6      * |     4 0.666666666666667
#>    [5]     chr1    5    6    7      * |     5 0.555555555555556
#>    [6]     chr1   11   12   13      - |     1                 1
#>    [7]     chr2   12   13   14      + |     2 0.888888888888889
#>    [8]     chr2   13   14   15      + |     3 0.777777777777778
#>    [9]     chr2   14   15   16      * |     4 0.666666666666667
#>   [10]     chr1   15   16   17      * |     5 0.555555555555556
#> 
#> $shiftB 
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>        seqnames pos1 pos2 pos3 strand | score                GC
#>    [1]     chr1    6    7    8      + |     6 0.444444444444444
#>    [2]     chr3    7    8    9      + |     7 0.333333333333333
#>    [3]     chr3    8    9   10      + |     8 0.222222222222222
#>    [4]     chr3    9   10   11      - |     9 0.111111111111111
#>    [5]     chr3   10   11   12      - |    10                 0
#>    [6]     chr1   16   17   18      + |     6 0.444444444444444
#>    [7]     chr3   17   18   19      + |     7 0.333333333333333
#>    [8]     chr3   18   19   20      + |     8 0.222222222222222
#>    [9]     chr3   19   20   21      - |     9 0.111111111111111
#>   [10]     chr3   20   21   22      - |    10                 0
#> 
#> -------
#> seqinfo: 3 sequences from mock1 genome

Finally, the Reduce method will allow the GTuples objects to be collapsed across the whole of the GTuplesList object:

Reduce(c, gtl3)
#> GTuples object with 10 x 3-tuples and 2 metadata columns:
#>        seqnames pos1 pos2 pos3 strand | score                GC
#>    [1]     chr1    1    2    3      - |     1                 1
#>    [2]     chr2    2    3    4      + |     2 0.888888888888889
#>    [3]     chr2    3    4    5      + |     3 0.777777777777778
#>    [4]     chr2    4    5    6      * |     4 0.666666666666667
#>    [5]     chr1    5    6    7      * |     5 0.555555555555556
#>    [6]     chr1    6    7    8      + |     6 0.444444444444444
#>    [7]     chr3    7    8    9      + |     7 0.333333333333333
#>    [8]     chr3    8    9   10      + |     8 0.222222222222222
#>    [9]     chr3    9   10   11      - |     9 0.111111111111111
#>   [10]     chr3   10   11   12      - |    10                 0
#>   ---
#>   seqinfo: 3 sequences from mock1 genome

3.1.6 Additional methods unique to GTuplesList

Like GTuples, GTuplesList have a few specifically defined methods that do not exist for GenomicRanges::GRangesList. These are tuples, size and IPD. These are identical to the methods for GTuples, except that they typically return a list since the input is now essentially a List of GTuples objects.

tuples(gtl3)
#> List of length 2
#> names(2): shiftA shiftB
tuples(gtl3)[[1]]
#>      pos1 pos2 pos3
#> [1,]    1    2    3
#> [2,]    2    3    4
#> [3,]    3    4    5
#> [4,]    4    5    6
#> [5,]    5    6    7
size(gtl3)
#> [1] 3
IPD(gtl3)
#> List of length 2
#> names(2): shiftA shiftB
IPD(gtl3)[[1]]
#>      [,1] [,2]
#> [1,]    1    1
#> [2,]    1    1
#> [3,]    1    1
#> [4,]    1    1
#> [5,]    1    1

3.2 Implementation details

The GTuplesList class extends the GenomicRanges::GRangesList class.

4 findOverlaps-based methods

The definition of what constitutes an “overlap” between genomic tuples, or between genomic tuples and genomic ranges, lies at the heart of all findOverlaps-based methods3 for GTuples and GTuplesList objects.

I have chosen a definition that matches my intuition of what constitutes an “overlap” between genomic tuples or between genomic tuples and genomic ranges. However, I am open to suggestions on amending or extending this behaviour in future versions of GenomicTuples.

4.1 Definition of overlapping genomic tuples

I consider two genomic tuples to be equal (type = "equal") if they have identical sequence names (seqnames), strands (strand) and tuples (tuples). For 1-tuples and 2-tuples, this means we can simply defer to the findOverlaps-based methods for GenomicRanges::GRanges and GenomicRanges::GRangesList objects via inheritance. However, we cannot do the same for m-tuples with \(m > 2\) since this would ignore the “internal positions”. Therefore, I have implemented a special case of the findOverlaps method for when size \(> 2\) and type = "equal", which ensures that the “internal positions” are also checked for equality.

In all other cases genomic tuples are treated as genomic ranges. This means that when type = "any", type = "start", type = "end" or type = "within" then the genomic tuples are treated as if they were genomic ranges. Specifically, GTuples (resp. GTuplesList) are treated as though they were GenomicRanges::GRanges (resp. GenomicRanges::GRangesList) with pos1 = start and posm = end.

4.2 Definition of overlapping genomic tuples and ranges

Genomic tuples are always treated as genomic ranges when searching for overlaps between genomic tuples and genomic ranges.

4.3 Examples

It is easiest to understand the above definitions by studying a few examples.

Firstly, for 1-tuples where the GTuples methods use the GenomicRanges::GRanges methods:

# Construct example 1-tuples
gt1 <- GTuples(seqnames = c('chr1', 'chr1', 'chr1', 'chr2'), 
               tuples = matrix(c(10L, 10L, 10L, 10L), ncol = 1), 
               strand = c('+', '-', '*', '+'))
# GRanges version of gt1
gr1 <- as(gt1, "GRanges")
findOverlaps(gt1, gt1, type = 'any')
#> Hits object with 8 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         1           3
#>   [3]         2           2
#>   [4]         2           3
#>   [5]         3           1
#>   [6]         3           2
#>   [7]         3           3
#>   [8]         4           4
#>   -------
#>   queryLength: 4 / subjectLength: 4
# GTuples and GRanges methods identical
identical(findOverlaps(gt1, gt1, type = 'any'), 
          findOverlaps(gr1, gr1, type = 'any'))
#> [1] TRUE
findOverlaps(gt1, gt1, type = 'start')
#> Hits object with 8 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         1           3
#>   [3]         2           2
#>   [4]         2           3
#>   [5]         3           1
#>   [6]         3           2
#>   [7]         3           3
#>   [8]         4           4
#>   -------
#>   queryLength: 4 / subjectLength: 4
# GTuples and GRanges methods identical
identical(findOverlaps(gt1, gt1, type = 'start'), 
          findOverlaps(gr1, gr1, type = 'start'))
#> [1] TRUE
findOverlaps(gt1, gt1, type = 'end')
#> Hits object with 8 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         1           3
#>   [3]         2           2
#>   [4]         2           3
#>   [5]         3           1
#>   [6]         3           2
#>   [7]         3           3
#>   [8]         4           4
#>   -------
#>   queryLength: 4 / subjectLength: 4
# GTuples and GRanges methods identical
identical(findOverlaps(gt1, gt1, type = 'end'), 
          findOverlaps(gr1, gr1, type = 'end'))
#> [1] TRUE
findOverlaps(gt1, gt1, type = 'within')
#> Hits object with 8 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         1           3
#>   [3]         2           2
#>   [4]         2           3
#>   [5]         3           1
#>   [6]         3           2
#>   [7]         3           3
#>   [8]         4           4
#>   -------
#>   queryLength: 4 / subjectLength: 4
# GTuples and GRanges methods identical
identical(findOverlaps(gt1, gt1, type = 'within'), 
          findOverlaps(gr1, gr1, type = 'within'))
#> [1] TRUE
findOverlaps(gt1, gt1, type = 'equal')
#> Hits object with 8 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         1           3
#>   [3]         2           2
#>   [4]         2           3
#>   [5]         3           1
#>   [6]         3           2
#>   [7]         3           3
#>   [8]         4           4
#>   -------
#>   queryLength: 4 / subjectLength: 4
# GTuples and GRanges methods identical
identical(findOverlaps(gt1, gt1, type = 'equal'), 
          findOverlaps(gr1, gr1, type = 'equal'))
#> [1] TRUE
# Can pass other arguments, such as select and ignore.strand
findOverlaps(gt1, gt1, type = 'equal', ignore.strand = TRUE, select = 'last')
#> [1] 3 3 3 4

Next, for 2-tuples where the GTuples methods use the GenomicRanges::GRanges methods:

# Construct example 2-tuples
gt2 <- GTuples(seqnames = c('chr1', 'chr1', 'chr1', 'chr1', 'chr2'), 
               tuples = matrix(c(10L, 10L, 10L, 10L, 10L, 20L, 20L, 20L, 25L, 
                                 20L), ncol = 2), 
               strand = c('+', '-', '*', '+', '+'))
# GRanges version of gt2
gr2 <- as(gt2, "GRanges")
findOverlaps(gt2, gt2, type = 'any')
#> Hits object with 13 hits and 0 metadata columns:
#>        queryHits subjectHits
#>        <integer>   <integer>
#>    [1]         1           4
#>    [2]         1           1
#>    [3]         1           3
#>    [4]         2           2
#>    [5]         2           3
#>    ...       ...         ...
#>    [9]         3           3
#>   [10]         4           4
#>   [11]         4           1
#>   [12]         4           3
#>   [13]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt2, gt2, type = 'any'), 
          findOverlaps(gr2, gr2, type = 'any'))
#> [1] TRUE
findOverlaps(gt2, gt2, type = 'start')
#> Hits object with 13 hits and 0 metadata columns:
#>        queryHits subjectHits
#>        <integer>   <integer>
#>    [1]         1           4
#>    [2]         1           1
#>    [3]         1           3
#>    [4]         2           2
#>    [5]         2           3
#>    ...       ...         ...
#>    [9]         3           3
#>   [10]         4           4
#>   [11]         4           1
#>   [12]         4           3
#>   [13]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt2, gt2, type = 'start'), 
          findOverlaps(gr2, gr2, type = 'start'))
#> [1] TRUE
findOverlaps(gt2, gt2, type = 'end')
#> Hits object with 9 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         1           3
#>   [3]         2           2
#>   [4]         2           3
#>   [5]         3           1
#>   [6]         3           2
#>   [7]         3           3
#>   [8]         4           4
#>   [9]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt2, gt2, type = 'end'), 
          findOverlaps(gr2, gr2, type = 'end'))
#> [1] TRUE
findOverlaps(gt2, gt2, type = 'within')
#> Hits object with 11 hits and 0 metadata columns:
#>        queryHits subjectHits
#>        <integer>   <integer>
#>    [1]         1           4
#>    [2]         1           1
#>    [3]         1           3
#>    [4]         2           2
#>    [5]         2           3
#>    [6]         3           4
#>    [7]         3           1
#>    [8]         3           2
#>    [9]         3           3
#>   [10]         4           4
#>   [11]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt2, gt2, type = 'within'), 
          findOverlaps(gr2, gr2, type = 'within'))
#> [1] TRUE
findOverlaps(gt2, gt2, type = 'equal')
#> Hits object with 9 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         1           3
#>   [3]         2           2
#>   [4]         2           3
#>   [5]         3           1
#>   [6]         3           2
#>   [7]         3           3
#>   [8]         4           4
#>   [9]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt2, gt2, type = 'equal'), 
          findOverlaps(gr2, gr2, type = 'equal'))
#> [1] TRUE
# Can pass other arguments, such as select and ignore.strand
findOverlaps(gt2, gt2, type = 'equal', ignore.strand = TRUE, select = 'last')
#> [1] 3 3 3 4 5

Finally, for m-tuples with \(m > 2\) where GTuples methods use the GenomicRanges::GRanges methods unless type = "equal":

# Construct example 3-tuples
gt3 <- GTuples(seqnames = c('chr1', 'chr1', 'chr1', 'chr1', 'chr2'), 
               tuples = matrix(c(10L, 10L, 10L, 10L, 10L, 20L, 20L, 20L, 25L, 
                                 20L, 30L, 30L, 35L, 30L, 30L), ncol = 3), 
               strand = c('+', '-', '*', '+', '+'))
# GRanges version of gt3
gr3 <- as(gt3, "GRanges")
findOverlaps(gt3, gt3, type = 'any')
#> Warning in .local(query, subject, maxgap, minoverlap, type, select, ...):
#> 'type' is not 'equal' so coercing 'query' and 'subject' to 'GRanges' objects
#> (see docs for details)
#> Hits object with 13 hits and 0 metadata columns:
#>        queryHits subjectHits
#>        <integer>   <integer>
#>    [1]         1           3
#>    [2]         1           1
#>    [3]         1           4
#>    [4]         2           3
#>    [5]         2           2
#>    ...       ...         ...
#>    [9]         3           4
#>   [10]         4           3
#>   [11]         4           1
#>   [12]         4           4
#>   [13]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt3, gt3, type = 'any'), 
          findOverlaps(gr3, gr3, type = 'any')) # TRUE
#> Warning in .local(query, subject, maxgap, minoverlap, type, select, ...):
#> 'type' is not 'equal' so coercing 'query' and 'subject' to 'GRanges' objects
#> (see docs for details)
#> [1] TRUE

findOverlaps(gt3, gt3, type = 'start')
#> Warning in .local(query, subject, maxgap, minoverlap, type, select, ...):
#> 'type' is not 'equal' so coercing 'query' and 'subject' to 'GRanges' objects
#> (see docs for details)
#> Hits object with 13 hits and 0 metadata columns:
#>        queryHits subjectHits
#>        <integer>   <integer>
#>    [1]         1           3
#>    [2]         1           1
#>    [3]         1           4
#>    [4]         2           3
#>    [5]         2           2
#>    ...       ...         ...
#>    [9]         3           4
#>   [10]         4           3
#>   [11]         4           1
#>   [12]         4           4
#>   [13]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt3, gt3, type = 'start'), 
          findOverlaps(gr3, gr3, type = 'start')) # TRUE
#> Warning in .local(query, subject, maxgap, minoverlap, type, select, ...):
#> 'type' is not 'equal' so coercing 'query' and 'subject' to 'GRanges' objects
#> (see docs for details)
#> [1] TRUE

findOverlaps(gt3, gt3, type = 'end')
#> Warning in .local(query, subject, maxgap, minoverlap, type, select, ...):
#> 'type' is not 'equal' so coercing 'query' and 'subject' to 'GRanges' objects
#> (see docs for details)
#> Hits object with 7 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         1           4
#>   [3]         2           2
#>   [4]         3           3
#>   [5]         4           1
#>   [6]         4           4
#>   [7]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt3, gt3, type = 'end'), 
          findOverlaps(gr3, gr3, type = 'end')) # TRUE
#> Warning in .local(query, subject, maxgap, minoverlap, type, select, ...):
#> 'type' is not 'equal' so coercing 'query' and 'subject' to 'GRanges' objects
#> (see docs for details)
#> [1] TRUE

findOverlaps(gt3, gt3, type = 'within')
#> Warning in .local(query, subject, maxgap, minoverlap, type, select, ...):
#> 'type' is not 'equal' so coercing 'query' and 'subject' to 'GRanges' objects
#> (see docs for details)
#> Hits object with 10 hits and 0 metadata columns:
#>        queryHits subjectHits
#>        <integer>   <integer>
#>    [1]         1           3
#>    [2]         1           1
#>    [3]         1           4
#>    [4]         2           3
#>    [5]         2           2
#>    [6]         3           3
#>    [7]         4           3
#>    [8]         4           1
#>    [9]         4           4
#>   [10]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods identical
identical(findOverlaps(gt3, gt3, type = 'within'), 
          findOverlaps(gr3, gr3, type = 'within')) # TRUE
#> Warning in .local(query, subject, maxgap, minoverlap, type, select, ...):
#> 'type' is not 'equal' so coercing 'query' and 'subject' to 'GRanges' objects
#> (see docs for details)
#> [1] TRUE

findOverlaps(gt3, gt3, type = 'equal')
#> Hits object with 5 hits and 0 metadata columns:
#>       queryHits subjectHits
#>       <integer>   <integer>
#>   [1]         1           1
#>   [2]         2           2
#>   [3]         3           3
#>   [4]         4           4
#>   [5]         5           5
#>   -------
#>   queryLength: 5 / subjectLength: 5
# GTuples and GRanges methods **not** identical because  GRanges method ignores 
# "internal positions".
identical(findOverlaps(gt3, gt3, type = 'equal'), 
          findOverlaps(gr3, gr3, type = 'equal')) # FALSE
#> [1] FALSE
# Can pass other arguments, such as select and ignore.strand
findOverlaps(gt3, gt3, type = 'equal', ignore.strand = TRUE, select = 'last')
#> [1] 2 2 3 4 5

5 Comparison of genomic tuples

I have chosen a definition that matches my intuition of what constitutes a
comparison between genomic tuples. However, I am open to suggestions on amending or extending this behaviour in future versions of GenomicTuples.

5.1 Definition of comparison methods for genomic tuples

The comparison of two genomic tuples, x and y, is done by first comparing the seqnames(x) to seqnames(y), then strand(x) to strand(y) and finally tuples(x) to tuples(y).

Ordering of seqnames and strand is as implemented GenomicRanges::GRanges. Ordering of tuples is element-wise, i.e. \(pos_{1}, \ldots, pos_{m}\) are compared in turn. For example, chr1:+:10, 20, 30 is considered less than chr1:+:10, 20, 40. This defines what I will refer to as the “natural order” of genomic tuples.

The above is implemented in the pcompare method for GTuples, which performs “generalized range-wise comparison” of two GTuples objects, x and y. That is, pcompare(x, y) returns an integer vector where the \(i^{th}\) element is a code describing how the \(i^{th}\) element in x is qualitatively positioned relatively to the \(i^{th}\) element in y. A code that is < 0, = 0, or > 0, corresponds to x[i] < y[i], x[i] == y[i], or x[i] > y[i], respectively.

The 6 traditional binary comparison operators (==, !=, <=, >=, <, and >), other comparison operators (match, order, sort, and rank) and duplicate-based methods (duplicated and unique) all use this “natural order”.

5.2 Examples

It is easiest to understand the above definitions by studying a few examples, here using 3-tuples:

# Construct example 3-tuples
gt3 <- GTuples(seqnames = c('chr1', 'chr1', 'chr1', 'chr1', 'chr2', 'chr1', 
                            'chr1'), 
               tuples = matrix(c(10L, 10L, 10L, 10L, 10L, 5L, 10L, 20L, 20L, 
                                 20L, 25L, 20L, 20L, 20L, 30L, 30L, 35L, 30L, 
                                 30L, 30L, 35L), 
                               ncol = 3), 
               strand = c('+', '-', '*', '+', '+', '+', '+'))
gt3
#> GTuples object with 7 x 3-tuples and 0 metadata columns:
#>       seqnames pos1 pos2 pos3 strand
#>   [1]     chr1   10   20   30      +
#>   [2]     chr1   10   20   30      -
#>   [3]     chr1   10   20   35      *
#>   [4]     chr1   10   25   30      +
#>   [5]     chr2   10   20   30      +
#>   [6]     chr1    5   20   30      +
#>   [7]     chr1   10   20   35      +
#>   ---
#>   seqinfo: 2 sequences from an unspecified genome; no seqlengths

# pcompare each tuple to itself
pcompare(gt3, gt3)
#> [1] 0 0 0 0 0 0 0
gt3 < gt3
#> [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
gt3 > gt3
#> [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
gt3 == gt3
#> [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE

# pcompare the third tuple to all tuples
pcompare(gt3[3], gt3)
#> [1]  2  1  0  2 -1  2  2
gt3[3] < gt3
#> [1] FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
gt3[3] > gt3
#> [1]  TRUE  TRUE FALSE  TRUE FALSE  TRUE  TRUE
gt3[3] == gt3
#> [1] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE

## Some comparisons where tuples differ only in one coordinate

# Ordering of seqnames 
# 'chr1' < 'chr2' for tuples with otherwise identical coordinates
gt3[1] < gt3[5] # TRUE
#> [1] TRUE

# Ordering of strands
# '+' < '-' < '*' for tuples with otherwise identical coordiantes
gt3[1] < gt3[2] # TRUE
#> [1] TRUE
gt3[1] < gt3[2] # TRUE
#> [1] TRUE
gt3[1] < unstrand(gt3[2]) # TRUE
#> [1] TRUE
gt3[2] < unstrand(gt3[2]) # TRUE
#> [1] TRUE

# Ordering of tuples
# Tuples checked sequentially from pos1, ..., posm for tuples with otherwise
# identical coordinates
gt3[6] < gt3[1] # TRUE due to pos1
#> [1] TRUE
gt3[2] < gt3[4] # TRUE due to pos2
#> [1] FALSE
gt3[1] < gt3[7] # TRUE due to pos3
#> [1] TRUE

# Sorting of tuples
# Sorted first by seqnames, then by strand, then by tuples
sort(gt3)
#> GTuples object with 7 x 3-tuples and 0 metadata columns:
#>       seqnames pos1 pos2 pos3 strand
#>   [1]     chr1    5   20   30      +
#>   [2]     chr1   10   20   30      +
#>   [3]     chr1   10   20   35      +
#>   [4]     chr1   10   25   30      +
#>   [5]     chr1   10   20   30      -
#>   [6]     chr1   10   20   35      *
#>   [7]     chr2   10   20   30      +
#>   ---
#>   seqinfo: 2 sequences from an unspecified genome; no seqlengths

# Duplicate tuples
# Duplicate tuples must have identical seqnames, strand and positions (tuples)
duplicated(c(gt3, gt3[1:3]))
#>  [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
unique(c(gt3, gt3[1:3]))
#> GTuples object with 7 x 3-tuples and 0 metadata columns:
#>       seqnames pos1 pos2 pos3 strand
#>   [1]     chr1   10   20   30      +
#>   [2]     chr1   10   20   30      -
#>   [3]     chr1   10   20   35      *
#>   [4]     chr1   10   25   30      +
#>   [5]     chr2   10   20   30      +
#>   [6]     chr1    5   20   30      +
#>   [7]     chr1   10   20   35      +
#>   ---
#>   seqinfo: 2 sequences from an unspecified genome; no seqlengths

6 Acknowledgements

I am very grateful to all the Bioconductor developers but particularly wish to thank the developers of GenomicRanges (Lawrence, M. et al. Software for computing and annotating genomic ranges. PLoS Comput. Biol. 9, e1003118 (2013).), which GenomicTuples uses heavily and is based upon. A special thanks to Hervé Pagès for his assistance and fixes when making upstream changes to GenomicRanges.

7 Session info

Here is the output of sessionInfo on the system on which this document was compiled:

sessionInfo()
#> R version 3.5.0 (2018-04-23)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 16.04.4 LTS
#> 
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.7-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.7-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] parallel  stats4    stats     graphics  grDevices utils     datasets 
#> [8] methods   base     
#> 
#> other attached packages:
#> [1] GenomicTuples_1.14.0 GenomicRanges_1.32.0 GenomeInfoDb_1.16.0 
#> [4] IRanges_2.14.0       S4Vectors_0.18.0     BiocGenerics_0.26.0 
#> [7] BiocStyle_2.8.0     
#> 
#> loaded via a namespace (and not attached):
#>  [1] Rcpp_0.12.16           knitr_1.20             XVector_0.20.0        
#>  [4] magrittr_1.5           zlibbioc_1.26.0        stringr_1.3.0         
#>  [7] tools_3.5.0            data.table_1.10.4-3    xfun_0.1              
#> [10] htmltools_0.3.6        yaml_2.1.18            rprojroot_1.3-2       
#> [13] digest_0.6.15          bookdown_0.7           GenomeInfoDbData_1.1.0
#> [16] bitops_1.0-6           RCurl_1.95-4.10        evaluate_0.10.1       
#> [19] rmarkdown_1.9          stringi_1.1.7          compiler_3.5.0        
#> [22] backports_1.1.2

8 References