DNA methylation plays critical roles in gene regulation and cellular specification without altering DNA sequences. It is one of the best understood and most intensively studied epigenetic marks in mammalian cells. Treatment of DNA with sodium bisulfite deaminates unmethylated cytosines to uracil while methylated cytosines are resistant to this conversion thus allowing for the discrimination between methylated and unmethylated CpG sites. Sodium bisulfite pre-treatment of DNA coupled with next-generation sequencing has allowed DNA methylation to be studied quantitatively and genome-wide at single cytosine site resolution.
methylSig is a method for testing for differential
methylated cytosines (DMCs) or regions (DMRs) in whole-genome bisulfite
sequencing (WGBS) or reduced representation bisulfite sequencing (RRBS)
experiments. methylSig uses a beta-binomial model to test
for significant differences between groups of samples. Several options
exist for either site-specific or sliding window tests, combining
strands, and for variance estimation.
methylSig is available on GitHub at http://www.github.com/sartorlab/methylSig, and the
easiest way to install it is as follows:
The basic flow of analysis with methylSig is to:
The sections below walk through each step with small test data.
Methylation calls output by either MethylDackel
or Bismark
can be read by the bsseq::read.bismark() function from the
bsseq
R/Bioconductor package.
This function accepts bedGraphs from MethylDackel
and either the coverage or genome-wide cytosine reports from Bismark.
Options to consider when reading data are:
colData, a data.frame or
DataFrame whose rows are samples and columns are phenotype
data. The row ordering should match the ordering of files in
files. This matrix will be needed for downstream
differential methylation testing.strandCollapse, a logical
(TRUE/FALSE) indicating whether or not to
collapse +/- CpG data onto the + strand. Note, this can only be
TRUE when the input type is the genome-wide cytosine report
from Bismark. MethylDackel has an option to destrand data when
methylation calls are made so that the output is already destranded. In
this case, strandCollapse should be
FALSE.For all options, see the bsseq reference
manual, and the section
on reading data in the package vignette.
files = c(
system.file('extdata', 'bis_cov1.cov', package='methylSig'),
system.file('extdata', 'bis_cov2.cov', package='methylSig')
)
bsseq_stranded = bsseq::read.bismark(
files = files,
colData = data.frame(row.names = c('test1','test2')),
rmZeroCov = FALSE,
strandCollapse = FALSE
)The result is a BSseq object. Aspects of the object can
be accessed via:
# pData
bsseq::pData(bsseq_stranded)
#> DataFrame with 2 rows and 0 columns
# GRanges
GenomicRanges::granges(bsseq_stranded)
#> GRanges object with 11 ranges and 0 metadata columns:
#> seqnames ranges strand
#> <Rle> <IRanges> <Rle>
#> [1] chr1 10 *
#> [2] chr1 11 *
#> [3] chr1 25 *
#> [4] chr1 26 *
#> [5] chr1 40 *
#> [6] chr1 41 *
#> [7] chr1 50 *
#> [8] chr1 51 *
#> [9] chr1 60 *
#> [10] chr1 75 *
#> [11] chr1 76 *
#> -------
#> seqinfo: 1 sequence from an unspecified genome; no seqlengths
# Coverage matrix
bsseq::getCoverage(bsseq_stranded, type = 'Cov')
#> test1 test2
#> [1,] 5 10
#> [2,] 5 10
#> [3,] 30 50
#> [4,] 70 50
#> [5,] 10 15
#> [6,] 20 35
#> [7,] 0 5
#> [8,] 0 5
#> [9,] 40 20
#> [10,] 1000 100
#> [11,] 1500 200
# Methylation matrix
bsseq::getCoverage(bsseq_stranded, type = 'M')
#> test1 test2
#> [1,] 4 9
#> [2,] 4 9
#> [3,] 0 1
#> [4,] 5 5
#> [5,] 9 14
#> [6,] 19 34
#> [7,] 0 5
#> [8,] 0 5
#> [9,] 35 15
#> [10,] 900 99
#> [11,] 1400 199After data is loaded, it is good practice to filter loci that have too few or too many reads, and C-to-T and G-to-A SNPs which confound bisulfite conversion.
Low coverage loci (typically those with fewer than 5 reads) should be marked because they adversely affect the variance calculation in downstream differential methylation tests. Very high coverage loci (typically those with more than 500 reads) are likely the result of PCR duplication, and should also be marked.
MethylSig marks such sites by setting their coverage and
methylation matrix entries to 0 for each sample in which this happens.
Prior to testing, these sites can be removed, see below.
As noted above, locations with C-to-T and G-to-A SNPs confound
bisulfite conversion in WGBS and ERRBS. Filtering them out can be
accomplished by constructing a GRanges object with their
location. For now, we leave locating such SNPs to the user.
# Show locations of bs
GenomicRanges::granges(bs)
#> GRanges object with 10000 ranges and 0 metadata columns:
#> seqnames ranges strand
#> <Rle> <IRanges> <Rle>
#> [1] chr21 9411552 *
#> [2] chr21 9411784 *
#> [3] chr21 9412099 *
#> [4] chr21 9412376 *
#> [5] chr21 9412503 *
#> ... ... ... ...
#> [9996] chr21 10831230 *
#> [9997] chr21 10831255 *
#> [9998] chr21 10831310 *
#> [9999] chr21 10831425 *
#> [10000] chr21 10831455 *
#> -------
#> seqinfo: 2 sequences from an unspecified genome; no seqlengths
# Construct GRanges object
remove_gr = GenomicRanges::GRanges(
seqnames = c('chr21', 'chr21', 'chr21'),
ranges = IRanges::IRanges(
start = c(9411552, 9411784, 9412099),
end = c(9411552, 9411784, 9412099)
)
)
bs = filter_loci_by_location(bs = bs, gr = remove_gr)
# Show removal
GenomicRanges::granges(bs)
#> GRanges object with 9997 ranges and 0 metadata columns:
#> seqnames ranges strand
#> <Rle> <IRanges> <Rle>
#> [1] chr21 9412376 *
#> [2] chr21 9412503 *
#> [3] chr21 9412808 *
#> [4] chr21 9413583 *
#> [5] chr21 9413763 *
#> ... ... ... ...
#> [9993] chr21 10831230 *
#> [9994] chr21 10831255 *
#> [9995] chr21 10831310 *
#> [9996] chr21 10831425 *
#> [9997] chr21 10831455 *
#> -------
#> seqinfo: 2 sequences from an unspecified genome; no seqlengthsOne way to increase the power of differential methylation testing is to aggregate the CpG-level data into regions. Regions can take two forms: tiling the entire genome by windows of a certain width or defining a set of regions such as CpG islands or gene promoters.
Given that CpG methylation is strongly correlated over short genomic distances, a reasonable upper threshold might be 500bp. For the example below, in the interest of speed, we tile by larger windows.
windowed_bs = tile_by_windows(bs = bs, win_size = 10000)
# Show tiling
GenomicRanges::granges(windowed_bs)
#> GRanges object with 1085 ranges and 0 metadata columns:
#> seqnames ranges strand
#> <Rle> <IRanges> <Rle>
#> [1] chr21 1-10000 *
#> [2] chr21 10001-20000 *
#> [3] chr21 20001-30000 *
#> [4] chr21 30001-40000 *
#> [5] chr21 40001-50000 *
#> ... ... ... ...
#> [1081] chr21 10800001-10810000 *
#> [1082] chr21 10810001-10820000 *
#> [1083] chr21 10820001-10830000 *
#> [1084] chr21 10830001-10840000 *
#> [1085] chr21 10840001-10841455 *
#> -------
#> seqinfo: 1 sequence from an unspecified genome; no seqlengthsIt may be the case that differential methylation is only relevant at promoter regions of genes for a particular project. In this case, aggregation of methylation calls over these regions may increase power, and decrease computation time.
MethylSig offers three tests for differential
methylation:
diff_binomial()diff_methylsig()diff_dss_fit() and diff_dss_test()Each returns a GRanges object with tested loci and the
corresponding statistics and methylation levels (if applicable). See the
documentation for each function for more information
(?diff_binomial, ?diff_methylsig,
?diff_dss_fit, and ?diff_dss_test).
Prior to applying any test function, loci without a minimum number of samples having appropriate coverage should be removed to avoid testing loci where one sample dominates the test.
# Look a the phenotype data for bs
bsseq::pData(bs)
#> DataFrame with 6 rows and 2 columns
#> Type Pair
#> <character> <character>
#> C1 cancer pair1
#> C2 cancer pair2
#> C3 cancer pair3
#> N1 normal pair1
#> N2 normal pair2
#> N3 normal pair3
# Require at least two samples from cancer and two samples from normal
bs = filter_loci_by_group_coverage(
bs = bs,
group_column = 'Type',
c('cancer' = 2, 'normal' = 2))diff_binomial() is a binomial test based on that in the
methylKit
R/Bioconductor package. This was included for benchmarking purposes in
the publication. It does not take into account the variability among
samples being compared.
# Test cancer versus normal
diff_gr = diff_binomial(
bs = bs,
group_column = 'Type',
comparison_groups = c('case' = 'cancer', 'control' = 'normal'))
diff_gr
#> GRanges object with 1358 ranges and 7 metadata columns:
#> seqnames ranges strand | meth_case meth_control meth_diff
#> <Rle> <IRanges> <Rle> | <numeric> <numeric> <numeric>
#> [1] chr21 9413763 * | 0.00 6.45 -6.45
#> [2] chr21 9416731 * | 63.64 100.00 -36.36
#> [3] chr21 9417127 * | 22.22 47.06 -24.84
#> [4] chr21 9419355 * | 15.38 64.52 -49.14
#> [5] chr21 9420237 * | 14.29 26.32 -12.03
#> ... ... ... ... . ... ... ...
#> [1354] chr21 10831159 * | 50.00 50.00 0.00
#> [1355] chr21 10831205 * | 31.03 37.93 -6.90
#> [1356] chr21 10831230 * | 56.52 76.00 -19.48
#> [1357] chr21 10831425 * | 86.14 90.66 -4.52
#> [1358] chr21 10831455 * | 78.55 84.46 -5.91
#> direction pvalue fdr log_lik_ratio
#> <character> <numeric> <numeric> <numeric>
#> [1] normal 1.37950e-01 0.280229141 2.200680
#> [2] normal 1.11483e-02 0.050296774 6.441531
#> [3] normal 1.19314e-01 0.253169711 2.426301
#> [4] normal 1.65661e-05 0.000523179 18.548211
#> [5] normal 3.95560e-01 0.559564440 0.721783
#> ... ... ... ... ...
#> [1354] cancer 1.0000000 1.0000000 0.000000
#> [1355] normal 0.5803640 0.7317868 0.305646
#> [1356] normal 0.1513080 0.2943785 2.059015
#> [1357] normal 0.0170048 0.0659787 5.695877
#> [1358] normal 0.0806182 0.1961998 3.052395
#> -------
#> seqinfo: 2 sequences from an unspecified genome; no seqlengthsThe diff_methylsig() is a beta-binomial test which takes
into account the variability among samples being compared. It can
perform group versus group comparisons with no covariates.
# Test cancer versus normal with dispersion from both groups
diff_gr = diff_methylsig(
bs = bs,
group_column = 'Type',
comparison_groups = c('case' = 'cancer', 'control' = 'normal'),
disp_groups = c('case' = TRUE, 'control' = TRUE),
local_window_size = 0,
t_approx = TRUE,
n_cores = 1)
diff_gr
#> GRanges object with 1358 ranges and 9 metadata columns:
#> seqnames ranges strand | meth_case meth_control meth_diff
#> <Rle> <IRanges> <Rle> | <numeric> <numeric> <numeric>
#> [1] chr21 9413763 * | 0.0000 6.49751 -6.49751
#> [2] chr21 9416731 * | 63.4272 100.00000 -36.57276
#> [3] chr21 9417127 * | 22.2200 47.05888 -24.83887
#> [4] chr21 9419355 * | 15.3828 64.51513 -49.13232
#> [5] chr21 9420237 * | 14.2857 26.31581 -12.03013
#> ... ... ... ... . ... ... ...
#> [1354] chr21 10831159 * | 43.5065 52.9219 -9.41540
#> [1355] chr21 10831205 * | 31.0346 37.9314 -6.89683
#> [1356] chr21 10831230 * | 54.8027 78.3147 -23.51194
#> [1357] chr21 10831425 * | 86.3300 90.5347 -4.20472
#> [1358] chr21 10831455 * | 78.5454 84.4641 -5.91865
#> direction pvalue fdr disp_est log_lik_ratio df
#> <character> <numeric> <numeric> <numeric> <numeric> <numeric>
#> [1] normal 0.26498356 0.526114 8.12977e+00 1.511133 6
#> [2] normal 0.06962183 0.342560 4.58693e+01 6.056174 4
#> [3] normal 0.19431108 0.468936 1.00000e+06 2.426293 4
#> [4] normal 0.00505542 0.269846 1.00000e+06 18.547969 6
#> [5] normal 0.43434258 0.667774 1.00000e+06 0.721783 5
#> ... ... ... ... ... ... ...
#> [1354] normal 0.7252207 0.875422 4.12922e+00 0.138296 5
#> [1355] normal 0.6003419 0.800849 1.00000e+06 0.305642 6
#> [1356] normal 0.2250738 0.489277 9.82992e+00 1.828248 6
#> [1357] normal 0.0909511 0.374278 9.82979e+02 4.046584 6
#> [1358] normal 0.1312360 0.414624 1.00000e+06 3.051969 6
#> -------
#> seqinfo: 2 sequences from an unspecified genome; no seqlengthsdiff_dss_fit() and diff_dss_test() are
tests supporting general models, and are wrappers for functions in the
DSS
R/Bioconductor package. We have added the ability to recover group
methylation for group comparisons, or top/bottom 25 percentile
methylation rates based on a continuous covariate.
The DSS style test is in two stages similar to tests in
the edgeR or limma R/Bioconductor packages.
The first stage is a fit, and the second stage is a test on a
contrast.
First we add a numerical covariate to the pData(bs) so
that we can give an example of such a test.
Fit the simplest group versus group model on just the type.
diff_fit_simple = diff_dss_fit(
bs = bs,
design = bsseq::pData(bs),
formula = as.formula('~ Type'))
#> Fitting DML model for CpG site:Fit a paired model where cancer and normal samples are paired by patient.
# Paired-test
diff_fit_paired = diff_dss_fit(
bs = bs,
design = bsseq::pData(bs),
formula = '~ Type + Pair')
#> Fitting DML model for CpG site:Fit a model on the numerical covariate.
# Numerical covariate test
diff_fit_num = diff_dss_fit(
bs = bs,
design = bsseq::pData(bs),
formula = '~ num_covariate')
#> Fitting DML model for CpG site:The result of diff_dss_fit() is a list with
the following structure with elements:
gr, the GRanges of the fit loci.design, the phenotype matrix passed via the
design parameter.formula, the formula used in conjunction with
design to create the model matrix.X, the result of model.matrix with
design and formula.fit, the beta and var.beta
matrices.Prior to calling diff_fit_test(), it may help to look at
the model matrix used for fitting in order to build the contrast.
diff_fit_simple$X
#> (Intercept) Typenormal
#> C1 1 0
#> C2 1 0
#> C3 1 0
#> N1 1 1
#> N2 1 1
#> N3 1 1
#> attr(,"assign")
#> [1] 0 1
#> attr(,"contrasts")
#> attr(,"contrasts")$Type
#> [1] "contr.treatment"
diff_fit_paired$X
#> (Intercept) Typenormal Pairpair2 Pairpair3
#> C1 1 0 0 0
#> C2 1 0 1 0
#> C3 1 0 0 1
#> N1 1 1 0 0
#> N2 1 1 1 0
#> N3 1 1 0 1
#> attr(,"assign")
#> [1] 0 1 2 2
#> attr(,"contrasts")
#> attr(,"contrasts")$Type
#> [1] "contr.treatment"
#>
#> attr(,"contrasts")$Pair
#> [1] "contr.treatment"
diff_fit_num$X
#> (Intercept) num_covariate
#> C1 1 84
#> C2 1 96
#> C3 1 93
#> N1 1 10
#> N2 1 18
#> N3 1 9
#> attr(,"assign")
#> [1] 0 1The contrast passed to diff_fit_test() should be a
column vector or a matrix whose rows correspond to the columns of the
model matrix above. See the DSS
user guide for more information.
# Test the simplest model for cancer vs normal
# Note, 2 rows corresponds to 2 columns in diff_fit_simple$X
simple_contrast = matrix(c(0,1), ncol = 1)
# Test the paired model for cancer vs normal
# Note, 4 rows corresponds to 4 columns in diff_fit_paired$X
paired_contrast = matrix(c(0,1,0,0), ncol = 1)
# Test the numerical covariate
num_contrast = matrix(c(0,1), ncol = 1)The diff_fit_test() function enables the recovery of
group methylation rates via the optional
methylation_group_column and
methylation_groups parameters.
The simple, group versus group, test.
diff_simple_gr = diff_dss_test(
bs = bs,
diff_fit = diff_fit_simple,
contrast = simple_contrast,
methylation_group_column = 'Type',
methylation_groups = c('case' = 'cancer', 'control' = 'normal'))
diff_simple_gr
#> GRanges object with 1358 ranges and 7 metadata columns:
#> seqnames ranges strand | meth_case meth_control meth_diff
#> <Rle> <IRanges> <Rle> | <numeric> <numeric> <numeric>
#> [1] chr21 9413763 * | 0.00 6.45 -6.45
#> [2] chr21 9416731 * | 63.64 100.00 -36.36
#> [3] chr21 9417127 * | 22.22 47.06 -24.84
#> [4] chr21 9419355 * | 15.38 64.52 -49.13
#> [5] chr21 9420237 * | 14.29 26.32 -12.03
#> ... ... ... ... . ... ... ...
#> [1354] chr21 10831159 * | 50.00 50.00 0.00
#> [1355] chr21 10831205 * | 31.03 37.93 -6.90
#> [1356] chr21 10831230 * | 56.52 76.00 -19.48
#> [1357] chr21 10831425 * | 86.14 90.66 -4.53
#> [1358] chr21 10831455 * | 78.55 84.46 -5.92
#> direction stat pvalue fdr
#> <character> <numeric> <numeric> <numeric>
#> [1] normal 0.729474 4.65711e-01 0.7261035
#> [2] normal 2.365831 1.79896e-02 0.1285786
#> [3] normal 1.687860 9.14381e-02 0.3151597
#> [4] normal 4.396071 1.10228e-05 0.0011392
#> [5] normal 1.138130 2.55066e-01 0.5200900
#> ... ... ... ... ...
#> [1354] cancer 0.453781 0.6499867 0.848938
#> [1355] normal 0.587070 0.5571567 0.784061
#> [1356] normal 1.198860 0.2305825 0.498198
#> [1357] normal 0.944001 0.3451693 0.607963
#> [1358] normal 1.698473 0.0894185 0.312965
#> -------
#> seqinfo: 2 sequences from an unspecified genome; no seqlengthsThe paired test.
diff_paired_gr = diff_dss_test(
bs = bs,
diff_fit = diff_fit_paired,
contrast = paired_contrast,
methylation_group_column = 'Type',
methylation_groups = c('case' = 'cancer', 'control' = 'normal'))
#> 93 loci were dropped due to insufficient degrees of freedom.
diff_paired_gr
#> GRanges object with 1265 ranges and 7 metadata columns:
#> seqnames ranges strand | meth_case meth_control meth_diff
#> <Rle> <IRanges> <Rle> | <numeric> <numeric> <numeric>
#> [1] chr21 9413763 * | 0.00 6.45 -6.45
#> [2] chr21 9419355 * | 15.38 64.52 -49.13
#> [3] chr21 9420237 * | 14.29 26.32 -12.03
#> [4] chr21 9420952 * | 57.14 65.52 -8.37
#> [5] chr21 9580059 * | 71.43 84.09 -12.66
#> ... ... ... ... . ... ... ...
#> [1261] chr21 10831159 * | 50.00 50.00 0.00
#> [1262] chr21 10831205 * | 31.03 37.93 -6.90
#> [1263] chr21 10831230 * | 56.52 76.00 -19.48
#> [1264] chr21 10831425 * | 86.14 90.66 -4.53
#> [1265] chr21 10831455 * | 78.55 84.46 -5.92
#> direction stat pvalue fdr
#> <character> <numeric> <numeric> <numeric>
#> [1] normal 0.724620 4.68685e-01 0.70439772
#> [2] normal 4.032480 5.51913e-05 0.00188695
#> [3] normal 0.697177 4.85692e-01 0.72174449
#> [4] normal 0.355852 7.21952e-01 0.87938305
#> [5] normal 1.247730 2.12130e-01 0.46426373
#> ... ... ... ... ...
#> [1261] cancer 0.657701 0.510730 0.740911
#> [1262] normal 0.426110 0.670028 0.846738
#> [1263] normal 1.229273 0.218970 0.472342
#> [1264] normal 0.637471 0.523818 0.748735
#> [1265] normal 1.420936 0.155335 0.392214
#> -------
#> seqinfo: 2 sequences from an unspecified genome; no seqlengthsThe numerical covariate test. Note, here the
methylation_groups parameter is omitted because there are
no groups. By giving the numerical covariate column, we will group
samples by the top/bottom 25 percentile over the covariate, and compute
mean methylation within those groups of samples.
diff_num_gr = diff_dss_test(
bs = bs,
diff_fit = diff_fit_num,
contrast = num_contrast,
methylation_group_column = 'num_covariate')
diff_num_gr
#> GRanges object with 1358 ranges and 7 metadata columns:
#> seqnames ranges strand | meth_case meth_control meth_diff
#> <Rle> <IRanges> <Rle> | <numeric> <numeric> <numeric>
#> [1] chr21 9413763 * | 11.11 0.00 11.11
#> [2] chr21 9416731 * | 100.00 63.64 36.36
#> [3] chr21 9417127 * | 50.00 22.22 27.78
#> [4] chr21 9419355 * | 63.64 10.34 53.29
#> [5] chr21 9420237 * | 27.27 14.29 12.99
#> ... ... ... ... . ... ... ...
#> [1354] chr21 10831159 * | 83.33 40.00 43.33
#> [1355] chr21 10831205 * | 33.33 22.22 11.11
#> [1356] chr21 10831230 * | 93.75 46.15 47.60
#> [1357] chr21 10831425 * | 89.02 84.39 4.63
#> [1358] chr21 10831455 * | 81.65 78.38 3.27
#> direction stat pvalue fdr
#> <character> <numeric> <numeric> <numeric>
#> [1] Hyper -0.84328 3.99072e-01 0.650587695
#> [2] Hyper -2.32367 2.01430e-02 0.128928038
#> [3] Hyper -1.79346 7.28996e-02 0.274231889
#> [4] Hyper -4.47274 7.72224e-06 0.000813826
#> [5] Hyper -1.09861 2.71939e-01 0.525272220
#> ... ... ... ... ...
#> [1354] Hyper -0.597314 0.550298 0.773607
#> [1355] Hyper -0.636270 0.524601 0.755469
#> [1356] Hyper -1.449572 0.147178 0.380700
#> [1357] Hyper -1.097767 0.272306 0.525272
#> [1358] Hyper -1.563098 0.118030 0.334685
#> -------
#> seqinfo: 2 sequences from an unspecified genome; no seqlengthssessionInfo()
#> R version 4.4.1 (2024-06-14)
#> 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] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] methylSig_1.19.0 BiocStyle_2.35.0
#>
#> loaded via a namespace (and not attached):
#> [1] SummarizedExperiment_1.35.5 rjson_0.2.23
#> [3] xfun_0.48 bslib_0.8.0
#> [5] rhdf5_2.49.0 Biobase_2.67.0
#> [7] lattice_0.22-6 bitops_1.0-9
#> [9] rhdf5filters_1.17.0 tools_4.4.1
#> [11] curl_5.2.3 stats4_4.4.1
#> [13] parallel_4.4.1 R.oo_1.26.0
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