1 Introduction
In this manual, we will show how to use the methylKit package. methylKit is an R package for analysis and annotation of DNA methylation information obtained by high-throughput bisulfite sequencing. The package is designed to deal with sequencing data from RRBS and its variants. But, it can potentially handle whole-genome bisulfite sequencing data if proper input format is provided.
1.1 DNA methylation
DNA methylation in vertebrates typically occurs at CpG dinucleotides, however non-CpG Cs are also methylated in certain tissues such as embryonic stem cells. DNA methylation can act as an epigenetic control mechanism for gene regulation. Methylation can hinder binding of transcription factors and/or methylated bases can be bound by methyl-binding-domain proteins which can recruit chromatin remodeling factors. In both cases, the transcription of the regulated gene will be effected. In addition, aberrant DNA methylation patterns have been associated with many human malignancies and can be used in a predictive manner. In malignant tissues, DNA is either hypo-methylated or hyper-methylated compared to the normal tissue. The location of hyper- and hypo-methylated sites gives a distinct signature to many diseases. Traditionally, hypo-methylation is associated with gene transcription (if it is on a regulatory region such as promoters) and hyper-methylation is associated with gene repression.
1.2 High-throughput bisulfite sequencing
Bisulfite sequencing is a technique that can determine DNA methylation patterns. The major difference from regular sequencing experiments is that, in bisulfite sequencing DNA is treated with bisulfite which converts cytosine residues to uracil, but leaves 5-methylcytosine residues unaffected. By sequencing and aligning those converted DNA fragments it is possible to call methylation status of a base. Usually, the methylation status of a base determined by a high-throughput bisulfite sequencing will not be a binary score, but it will be a percentage. The percentage simply determines how many of the bases that are aligning to a given cytosine location in the genome have actual C bases in the reads. Since bisulfite treatment leaves methylated Cs intact, that percentage will give us percent methylation score on that base. The reasons why we will not get a binary response are:
- the probable sequencing errors in high-throughput sequencing experiments
- incomplete bisulfite conversion
- (and a more likely scenario) is heterogeneity of samples and heterogeneity of paired chromosomes from the same sample
2 Basics
2.1 Reading the methylation call files
We start by reading in the methylation call data from bisulfite sequencing with read function. Reading in the data this way will return a methylRawList object which stores methylation information per sample for each covered base. The methylation call files are basically text files that contain percent methylation score per base. Such input files may be obtained from AMP pipeline developed for aligning RRBS reads or from processBismarkAln function. . However, “cytosineReport” and “coverage” files from Bismark aligner can be read in to methylKit as well.
A typical methylation call file looks like this:
## chrBase chr base strand coverage freqC freqT
## 1 chr21.9764539 chr21 9764539 R 12 25.00 75.00
## 2 chr21.9764513 chr21 9764513 R 12 0.00 100.00
## 3 chr21.9820622 chr21 9820622 F 13 0.00 100.00
## 4 chr21.9837545 chr21 9837545 F 11 0.00 100.00
## 5 chr21.9849022 chr21 9849022 F 124 72.58 27.42Most of the time bisulfite sequencing experiments have test and control samples. The test samples can be from a disease tissue while the control samples can be from a healthy tissue. You can read a set of methylation call files that have test/control conditions giving treatment vector option. For sake of subsequent analysis, file.list, sample.id and treatment option should have the same order. In the following example, first two files are have the sample ids “test1” and “test2” and as determined by treatment vector they belong to the same group. The third and fourth files have sample ids “ctrl1” and “ctrl2” and they belong to the same group as indicated by the treatment vector.
library(methylKit)
file.list=list( system.file("extdata",
"test1.myCpG.txt", package = "methylKit"),
system.file("extdata",
"test2.myCpG.txt", package = "methylKit"),
system.file("extdata",
"control1.myCpG.txt", package = "methylKit"),
system.file("extdata",
"control2.myCpG.txt", package = "methylKit") )
# read the files to a methylRawList object: myobj
myobj=methRead(file.list,
sample.id=list("test1","test2","ctrl1","ctrl2"),
assembly="hg18",
treatment=c(1,1,0,0),
context="CpG"
)In addition to the options we mentioned above, any tab separated text file with a generic format can be read in using methylKit, such as methylation ratio files from BSMAP. See here for an example.
2.2 Reading the methylation call files and store them as flat file database
Sometimes, when dealing with multiple samples and increased sample sizes coming from genome wide bisulfite sequencing experiments, the memory of your computer might not be sufficient enough.
Therefore methylKit offers a new group of classes, that are basically pendants to the original methylKit classes with one important difference: The methylation information, which normally is internally stored as data.frame, is stored in an external bgzipped file and is indexed by tabix (H. Li 2011), to enable fast retrieval of records or regions. This group contains methylRawListDB, methylRawDB, methylBaseDB and methylDiffDB, let us call them methylDB objects.
We can now create a methylRawListDB object, which stores the same content as myobj from above. But the single methylRaw objects retrieve their data from the tabix-file linked under dbpath.
library(methylKit)
file.list=list( system.file("extdata", "test1.myCpG.txt", package = "methylKit"),
system.file("extdata", "test2.myCpG.txt", package = "methylKit"),
system.file("extdata", "control1.myCpG.txt", package = "methylKit"),
system.file("extdata", "control2.myCpG.txt", package = "methylKit") )
# read the files to a methylRawListDB object: myobjDB
# and save in databases in folder methylDB
myobjDB=methRead(file.list,
sample.id=list("test1","test2","ctrl1","ctrl2"),
assembly="hg18",
treatment=c(1,1,0,0),
context="CpG",
dbtype = "tabix",
dbdir = "methylDB"
)
print(myobjDB[[1]]@dbpath)## [1] "/tmp/RtmpTpOekb/Rbuild5ebe4d8329c7/methylKit/vignettes/methylDB/test1.txt.bgz"Most if not all functions in this package will work with methylDB objects the same way as it does with normal methylKit objects. Functions that return methylKit objects, will return a methylDB object if provided, but there are a few exceptions such as the select, the [ and the selectByOverlap functions.
2.3 Reading the methylation calls from sorted Bismark alignments
Alternatively, methylation percentage calls can be calculated from sorted SAM or BAM file(s) from Bismark aligner and read-in to the memory. Bismark is a popular aligner for bisulfite sequencing reads, available here (Krueger and Andrews 2011). processBismarkAln function is designed to read-in Bismark SAM/BAM files as methylRaw or methylRawList objects which store per base methylation calls. SAM files must be sorted by chromosome and read position columns, using ‘sort’ command in unix-like machines will accomplish such a sort easily. BAM files should be sorted and indexed. This could be achieved with samtools (http://www.htslib.org/doc/samtools.html).
The following command reads a sorted SAM file and creates a methylRaw object for CpG methylation.The user has the option to save the methylation call files to a folder given by save.folder option. The saved files can be read-in using the read function when needed.
my.methRaw=processBismarkAln( location =
system.file("extdata",
"test.fastq_bismark.sorted.min.sam",
package = "methylKit"),
sample.id="test1", assembly="hg18",
read.context="CpG",save.folder=getwd())It is also possible to read multiple SAM files at the same time, check processBismarkAln documentation.
2.4 Descriptive statistics on samples
Since we read the methylation data now, we can check the basic stats about the methylation data such as coverage and percent methylation. We now have a methylRawList object which contains methylation information per sample. The following command prints out percent methylation statistics for second sample: “test2”
getMethylationStats(myobj[[2]],plot=FALSE,both.strands=FALSE)## methylation statistics per base
## summary:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 20.00 82.79 63.17 94.74 100.00
## percentiles:
## 0% 10% 20% 30% 40% 50% 60%
## 0.00000 0.00000 0.00000 48.38710 70.00000 82.78556 90.00000
## 70% 80% 90% 95% 99% 99.5% 99.9%
## 93.33333 96.42857 100.00000 100.00000 100.00000 100.00000 100.00000
## 100%
## 100.00000The following command plots the histogram for percent methylation distribution.The figure below is the histogram and numbers on bars denote what percentage of locations are contained in that bin. Typically, percent methylation histogram should have two peaks on both ends. In any given cell, any given base are either methylated or not. Therefore, looking at many cells should yield a similar pattern where we see lots of locations with high methylation and lots of locations with low methylation.
getMethylationStats(myobj[[2]],plot=TRUE,both.strands=FALSE)
We can also plot the read coverage per base information in a similar way, again numbers on bars denote what percentage of locations are contained in that bin. Experiments that are highly suffering from PCR duplication bias will have a secondary peak towards the right hand side of the histogram.
getCoverageStats(myobj[[2]],plot=TRUE,both.strands=FALSE)
2.5 Filtering samples based on read coverage
It might be useful to filter samples based on coverage. Particularly, if our samples are suffering from PCR bias it would be useful to discard bases with very high read coverage. Furthermore, we would also like to discard bases that have low read coverage, a high enough read coverage will increase the power of the statistical tests. The code below filters a methylRawList and discards bases that have coverage below 10X and also discards the bases that have more than 99.9th percentile of coverage in each sample.
filtered.myobj=filterByCoverage(myobj,lo.count=10,lo.perc=NULL,
hi.count=NULL,hi.perc=99.9)3 Comparative analysis
3.1 Merging samples
In order to do further analysis, we will need to get the bases covered in all samples. The following function will merge all samples to one object for base-pair locations that are covered in all samples. Setting destrand=TRUE (the default is FALSE) will merge reads on both strands of a CpG dinucleotide. This provides better coverage, but only advised when looking at CpG methylation (for CpH methylation this will cause wrong results in subsequent analyses). In addition, setting destrand=TRUE will only work when operating on base-pair resolution, otherwise setting this option TRUE will have no effect. The unite() function will return a methylBase object which will be our main object for all comparative analysis. The methylBase object contains methylation information for regions/bases that are covered in all samples.
meth=unite(myobj, destrand=FALSE)Let us take a look at the data content of methylBase object:
head(meth)## chr start end strand coverage1 numCs1 numTs1 coverage2 numCs2
## 1 chr21 9853296 9853296 + 17 10 7 333 268
## 2 chr21 9853326 9853326 + 17 12 5 329 249
## 3 chr21 9860126 9860126 + 39 38 1 83 78
## 4 chr21 9906604 9906604 + 68 42 26 111 97
## 5 chr21 9906616 9906616 + 68 52 16 111 104
## 6 chr21 9906619 9906619 + 68 59 9 111 109
## numTs2 coverage3 numCs3 numTs3 coverage4 numCs4 numTs4
## 1 65 18 16 2 395 341 54
## 2 79 16 14 2 379 284 95
## 3 5 83 83 0 41 40 1
## 4 14 23 18 5 37 33 4
## 5 7 23 14 9 37 27 10
## 6 2 22 18 4 37 29 8By default, unite function produces bases/regions covered in all samples. That requirement can be relaxed using “min.per.group” option in unite function.
# creates a methylBase object,
# where only CpGs covered with at least 1 sample per group will be returned
# there were two groups defined by the treatment vector,
# given during the creation of myobj: treatment=c(1,1,0,0)
meth.min=unite(myobj,min.per.group=1L)3.2 Sample Correlation
We can check the correlation between samples using getCorrelation. This function will either plot scatter plot and correlation coefficients or just print a correlation matrix
getCorrelation(meth,plot=TRUE)## test1 test2 ctrl1 ctrl2
## test1 1.0000000 0.9252530 0.8767865 0.8737509
## test2 0.9252530 1.0000000 0.8791864 0.8801669
## ctrl1 0.8767865 0.8791864 1.0000000 0.9465369
## ctrl2 0.8737509 0.8801669 0.9465369 1.0000000
3.3 Clustering samples
We can cluster the samples based on the similarity of their methylation profiles. The following function will cluster the samples and draw a dendrogram.
clusterSamples(meth, dist="correlation", method="ward", plot=TRUE)## The "ward" method has been renamed to "ward.D"; note new "ward.D2"
##
## Call:
## hclust(d = d, method = HCLUST.METHODS[hclust.method])
##
## Cluster method : ward.D
## Distance : pearson
## Number of objects: 4Setting the plot=FALSE will return a dendrogram object which can be manipulated by users or fed in to other user functions that can work with dendrograms.
hc = clusterSamples(meth, dist="correlation", method="ward", plot=FALSE)We can also do a PCA analysis on our samples. The following function will plot a scree plot for importance of components.
PCASamples(meth, screeplot=TRUE)
We can also plot PC1 and PC2 axis and a scatter plot of our samples on those axis which will reveal how they cluster.
PCASamples(meth)
3.4 Batch effects
We have implemented some rudimentary functionality for batch effect control. You can check which one of the principal components are statistically associated with the potential batch effects such as batch processing dates, age of subjects, sex of subjects using assocComp. The function gets principal components from the percent methylation matrix derived from the input methylBase object, and checks for association. The tests for association are either via Kruskal-Wallis test or Wilcoxon test for categorical attributes and correlation test for numerical attributes for samples such as age. If you are convinced that some principal components are accounting for batch effects, you can remove those principal components from your data using removeComp.
# make some batch data frame
# this is a bogus data frame
# we don't have batch information
# for the example data
sampleAnnotation=data.frame(batch_id=c("a","a","b","b"),
age=c(19,34,23,40))
as=assocComp(mBase=meth,sampleAnnotation)
as## $pcs
## PC1 PC2 PC3 PC4
## test1 -0.4978699 -0.5220504 0.68923849 -0.06737363
## test2 -0.4990924 -0.4805506 -0.71827964 0.06365693
## ctrl1 -0.5016543 0.4938800 0.08068700 0.70563101
## ctrl2 -0.5013734 0.5026102 -0.05014261 -0.70249091
##
## $vars
## [1] 92.271885 4.525328 1.870950 1.331837
##
## $association
## PC1 PC2 PC3 PC4
## batch_id 0.3333333 0.3333333 1.0000000 1.0000000
## age 0.5864358 0.6794346 0.3140251 0.3467957# construct a new object by removing the first pricipal component
# from percent methylation value matrix
newObj=removeComp(meth,comp=1)In addition to the methods described above, if you have used other ways to correct for batch effects and obtained a corrected percent methylation matrix, you can use reconstruct function to reconstruct a corrected methylBase object. Users have to supply a corrected percent methylation matrix and methylBase object (where the uncorrected percent methylation matrix obtained from) to the reconstruct function. Corrected percent methylation matrix should have the same row and column order as the original percent methylation matrix. All of these functions described in this section work on a methylBase object that does not have missing values (that means all bases in methylBase object should have coverage in all samples).
mat=percMethylation(meth)
# do some changes in the matrix
# this is just a toy example
# ideally you want to correct the matrix
# for batch effects
mat[mat==100]=80
# reconstruct the methylBase from the corrected matrix
newobj=reconstruct(mat,meth)3.5 Tiling windows analysis
For some situations, it might be desirable to summarize methylation information over tiling windows rather than doing base-pair resolution analysis. methylKit provides functionality to do such analysis. The function below tiles the genome with windows 1000bp length and 1000bp step-size and summarizes the methylation information on those tiles. In this case, it returns a methylRawList object which can be fed into unite and calculateDiffMeth functions consecutively to get differentially methylated regions. The tilling function adds up C and T counts from each covered cytosine and returns a total C and T count for each tile.
tiles=tileMethylCounts(myobj,win.size=1000,step.size=1000)
head(tiles[[1]],3)## chr start end strand coverage numCs numTs
## 1 chr21 9764001 9765000 * 24 3 21
## 2 chr21 9820001 9821000 * 13 0 13
## 3 chr21 9837001 9838000 * 11 0 113.6 Finding differentially methylated bases or regions
The calculateDiffMeth() function is the main function to calculate differential methylation. Depending on the sample size per each set it will either use Fisher’s exact or logistic regression to calculate P-values. P-values will be adjusted to Q-values using SLIM method (Wang, Tuominen, and Tsai 2011). If you have replicates, the function will automatically use logistic regression. You can force the calculateDiffMeth() function to use Fisher’s exact test if you pool the replicates when there is only test and control sample groups. This can be achieved with pool() function, see FAQ for more info.
In its simplest form ,where there are no covariates, the logistic regression will try to model the the log odds ratio which is based on methylation proportion of a CpG, \(\pi_i\), using the treatment vector which denotes the sample group membership for the CpGs in the model. Below, the “Treatment” variable is used to predict the log-odds ratio of methylation proportions.
\[ \text{log}\left(\dfrac{\pi_i}{1-\pi_i}\right) =\beta_0 + \beta_1 Treatment_i \]
The logistic regression model is fitted per CpG or per region and we test if treatment vector has any effect on the outcome variable or not. In other words, we are testing if \(log(\pi_i/(1-\pi_i)) = \beta_0 + \beta_1 Treatment_i\) is a “better” model than \(log(\pi_i/(1-\pi_i)) = \beta_0\).
The following code snippet tests for differential methylation. Since the example data has replicates, the logistic regression based modeling and test will be used.
myDiff=calculateDiffMeth(meth)After q-value calculation, we can select the differentially methylated regions/bases based on q-value and percent methylation difference cutoffs. Following bit selects the bases that have q-value<0.01 and percent methylation difference larger than 25%. If you specify type="hyper" or type="hypo" options, you will get hyper-methylated or hypo-methylated regions/bases.
# get hyper methylated bases
myDiff25p.hyper=getMethylDiff(myDiff,difference=25,qvalue=0.01,type="hyper")
#
# get hypo methylated bases
myDiff25p.hypo=getMethylDiff(myDiff,difference=25,qvalue=0.01,type="hypo")
#
#
# get all differentially methylated bases
myDiff25p=getMethylDiff(myDiff,difference=25,qvalue=0.01)We can also visualize the distribution of hypo/hyper-methylated bases/regions per chromosome using the following function. In this case, the example set includes only one chromosome. The list shows percentages of hypo/hyper methylated bases over all the covered bases in a given chromosome.
diffMethPerChr(myDiff,plot=FALSE,qvalue.cutoff=0.01, meth.cutoff=25)## $diffMeth.per.chr
## chr number.of.hypermethylated percentage.of.hypermethylated
## 1 chr21 75 7.788162
## number.of.hypomethylated percentage.of.hypomethylated
## 1 59 6.126687
##
## $diffMeth.all
## number.of.hypermethylated percentage.of.hypermethylated
## 1 75 7.788162
## number.of.hypomethylated percentage.of.hypomethylated
## 1 59 6.1266873.7 Correcting for overdispersion
Overdispersion occurs when there is more variability in the data than assumed by the distribution. In the logistic regression model, the response variable \(meth_i\) (number of methylated CpGs) is expected to have a binomial distribution: \[meth_i \sim Bin(n_i, \pi_i)\] Therefore, the methylated CpGs will have the variance \(n_i \pi_i(1-\pi_i)\) and mean \(\mu_i=n_i \pi_i\). \(n_i\) is the coverage for the CpG or a region and \(\pi_i\) is the underlying methylation proportion.
Overdispersion occurs when the variance of \(meth_i\) is greater than \(n_i \hat{\pi_i}(1-\hat{\pi_i})\), where \(\hat{\pi_i}\) is the estimated methylation proportion from the model. This can be corrected by calculating a scaling parameter \(\phi\) and adjusting the variance as \(\phi n_i \hat{\pi_i}(1-\hat{\pi_i})\). calculateDiffMeth can calculate that scaling parameter and use it in statistical tests to correct for overdispersion. The parameter is calculated as proposed by (McCullagh and Nelder 1989) as follows: \(\hat{\phi}=X^2/(N-P)\), where \(X\) is Pearson goodness-of-fit statistic, \(N\) is the number of samples, and \(P\) is the number of parameters. This scaling parameter also effects the statistical tests and if there is overdispersion correction the tests will be more stringent in general.
By default,this overdispersion correction is not applied. This can be achieved by setting overdispersion="MN". The Chisq-test is used by default only when no overdispersion correction is applied. If overdispersion correction is applied, the function automatically switches to the F-test. The Chisq-test can be manually chosen in this case as well, but the F-test only works with overdispersion correction switched on. In both cases, the procedure tests if the full model (the model where treatment is included as an explanatory variable) explains the data better than the null model (the model with no treatment, just intercept). If there is no effect based on samples being from different groups adding a treatment vector for sample groupings will be no better than not adding the treatment vector. Below, we simulate methylation data and use overdispersion correction for the logistic regression model.
sim.methylBase1<-dataSim(replicates=6,sites=1000,
treatment=c(rep(1,3),rep(0,3)),
sample.ids=c(paste0("test",1:3),paste0("ctrl",1:3))
)
my.diffMeth<-calculateDiffMeth(sim.methylBase1[1:,],
overdispersion="MN",test="Chisq",mc.cores=1)3.8 Accounting for covariates
Covariates can be included in the analysis. The function will then try to separate the influence of the covariates from the treatment effect via the logistic regression model. In this case, we will test if full model (model with treatment and covariates) is better than the model with the covariates only. If there is no effect due to the treatment (sample groups), the full model will not explain the data better than the model with covariates only. In calculateDiffMeth, this is achieved by supplying the covariates argument in the format of a data.frame. Below, we simulate methylation data and add make a data.frame for the age. The data frame can include more columns, and those columns can also be factor variables. The row order of the data.frame should match the order of samples in the methylBase object.
covariates=data.frame(age=c(30,80,34,30,80,40))
sim.methylBase<-dataSim(replicates=6,sites=1000,
treatment=c(rep(1,3),rep(0,3)),
covariates=covariates,
sample.ids=c(paste0("test",1:3),paste0("ctrl",1:3))
)
my.diffMeth3<-calculateDiffMeth(sim.methylBase,
covariates=covariates,
overdispersion="MN",test="Chisq",mc.cores=1)3.9 Finding differentially methylated bases using multiple-cores
The differential methylation calculation speed can be increased substantially by utilizing multiple-cores in a machine if available. Both Fisher’s Exact test and logistic regression based test are able to use multiple-core option.
The following piece of code will run differential methylation calculation using 2 cores.
myDiff=calculateDiffMeth(meth,num.cores=2)4 Annotating differentially methylated bases or regions
We can annotate our differentially methylated regions/bases based on gene annotation using genomation package. In this example, we read the gene annotation from a BED file and annotate our differentially methylated regions with that information using genomation functions. Note that these functions operate on GRanges objects ,so we first coerce methylKit objects to GRanges. This annotation operation will tell us what percentage of our differentially methylated regions are on promoters/introns/exons/intergenic region. In this case we read annotation from a BED file, similar gene annotation information can be fetched using GenomicFeatures package or other packages available from Bioconductor.org.
library(genomation)## Loading required package: grid##
## Attaching package: 'genomation'## The following objects are masked from 'package:methylKit':
##
## getFeatsWithTargetsStats, getFlanks, getMembers,
## getTargetAnnotationStats, plotTargetAnnotation# read the gene BED file
gene.obj=readTranscriptFeatures(system.file("extdata", "refseq.hg18.bed.txt",
package = "methylKit"))## Reading the table...## Calculating intron coordinates...## Calculating exon coordinates...## Calculating TSS coordinates...## Calculating promoter coordinates...## Outputting the final GRangesList...#
# annotate differentially methylated CpGs with
# promoter/exon/intron using annotation data
#
annotateWithGeneParts(as(myDiff25p,"GRanges"),gene.obj)## Summary of target set annotation with genic parts## Rows in target set: 133## -----------------------## percentage of target features overlapping with annotation:## promoter exon intron intergenic
## 27.82 15.04 34.59 57.14##
## percentage of target features overlapping with annotation:## (with promoter > exon > intron precedence):## promoter exon intron intergenic
## 27.82 0.00 15.04 57.14## ## percentage of annotation boundaries with feature overlap:## promoter exon intron
## 0.29 0.03 0.17## ## summary of distances to the nearest TSS:## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5 828 45160 52030 94640 313500## Similarly, we can read the CpG island annotation and annotate our differentially methylated bases/regions with them.
# read the shores and flanking regions and name the flanks as shores
# and CpG islands as CpGi
cpg.obj=readFeatureFlank(system.file("extdata", "cpgi.hg18.bed.txt",
package = "methylKit"),
feature.flank.name=c("CpGi","shores"))
#
# convert methylDiff object to GRanges and annotate
diffCpGann=annotateWithFeatureFlank(as(myDiff25p,"GRanges"),
cpg.obj$CpGi,cpg.obj$shores,
feature.name="CpGi",flank.name="shores")4.1 Regional analysis
We can also summarize methylation information over a set of defined regions such as promoters or CpG islands. The function below summarizes the methylation information over a given set of promoter regions and outputs a methylRaw or methylRawList object depending on the input. We are using the output of genomation functions used above to provide the locations of promoters. For regional summary functions, we need to provide regions of interest as GRanges object.
promoters=regionCounts(myobj,gene.obj$promoters)
head(promoters[[1]])## chr start end strand coverage numCs numTs
## 1 chr21 10011791 10013791 - 7953 6662 1290
## 2 chr21 10119796 10121796 - 1725 1171 554
## 3 chr21 10119808 10121808 - 1725 1171 554
## 4 chr21 13903368 13905368 + 10 10 0
## 5 chr21 14273636 14275636 - 282 220 62
## 6 chr21 14509336 14511336 + 1058 55 10034.2 Convenience functions for annotation objects
After getting the annotation of differentially methylated regions, we can get the distance to TSS and nearest gene name using the getAssociationWithTSS function from genomation package.
diffAnn=annotateWithGeneParts(as(myDiff25p,"GRanges"),gene.obj)
# target.row is the row number in myDiff25p
head(getAssociationWithTSS(diffAnn))## target.row dist.to.feature feature.name feature.strand
## 60 1 106111 NM_199260 -
## 60.1 2 106098 NM_199260 -
## 60.2 3 106092 NM_199260 -
## 60.3 4 105919 NM_199260 -
## 60.4 5 85265 NM_199260 -
## 60.5 6 68287 NM_199260 -It is also desirable to get percentage/number of differentially methylated regions that overlap with intron/exon/promoters
getTargetAnnotationStats(diffAnn,percentage=TRUE,precedence=TRUE)## promoter exon intron intergenic
## 27.82 0.00 15.04 57.14We can also plot the percentage of differentially methylated bases overlapping with exon/intron/promoters
plotTargetAnnotation(diffAnn,precedence=TRUE,
main="differential methylation annotation")
We can also plot the CpG island annotation the same way. The plot below shows what percentage of differentially methylated bases are on CpG islands, CpG island shores and other regions.
plotTargetAnnotation(diffCpGann,col=c("green","gray","white"),
main="differential methylation annotation")
It might be also useful to get percentage of intron/exon/promoters that overlap with differentially methylated bases.
getFeatsWithTargetsStats(diffAnn,percentage=TRUE)## promoter exon intron
## 0.29 0.03 0.175 methylKit convenience functions
5.1 Coercing methylKit objects to GRanges
Most methylKit objects (methylRaw,methylBase and methylDiff), including methylDB objects (methylRawDB,methylBaseDB and methylDiffDB) can be coerced to GRanges objects from GenomicRanges package. Coercing methylKit objects to GRanges will give users additional flexibility when customizing their analyses.
class(meth)## [1] "methylBase"
## attr(,"package")
## [1] "methylKit"as(meth,"GRanges")## GRanges object with 963 ranges and 12 metadata columns:
## seqnames ranges strand | coverage1 numCs1
## <Rle> <IRanges> <Rle> | <integer> <numeric>
## [1] chr21 [9853296, 9853296] + | 17 10
## [2] chr21 [9853326, 9853326] + | 17 12
## [3] chr21 [9860126, 9860126] + | 39 38
## [4] chr21 [9906604, 9906604] + | 68 42
## [5] chr21 [9906616, 9906616] + | 68 52
## ... ... ... ... . ... ...
## [959] chr21 [19855690, 19855690] + | 27 26
## [960] chr21 [19855706, 19855706] + | 27 27
## [961] chr21 [19855711, 19855711] + | 18 18
## [962] chr21 [19943653, 19943653] + | 12 12
## [963] chr21 [19943695, 19943695] + | 12 11
## numTs1 coverage2 numCs2 numTs2 coverage3 numCs3
## <numeric> <integer> <numeric> <numeric> <integer> <numeric>
## [1] 7 333 268 65 18 16
## [2] 5 329 249 79 16 14
## [3] 1 83 78 5 83 83
## [4] 26 111 97 14 23 18
## [5] 16 111 104 7 23 14
## ... ... ... ... ... ... ...
## [959] 1 19 17 2 34 34
## [960] 0 19 19 0 34 34
## [961] 0 18 15 3 34 34
## [962] 0 32 30 2 26 25
## [963] 1 32 32 0 26 26
## numTs3 coverage4 numCs4 numTs4
## <numeric> <integer> <numeric> <numeric>
## [1] 2 395 341 54
## [2] 2 379 284 95
## [3] 0 41 40 1
## [4] 5 37 33 4
## [5] 9 37 27 10
## ... ... ... ... ...
## [959] 0 12 12 0
## [960] 0 12 11 1
## [961] 0 12 12 0
## [962] 1 24 22 2
## [963] 0 27 24 3
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengthsclass(myDiff)## [1] "methylDiff"
## attr(,"package")
## [1] "methylKit"as(myDiff,"GRanges")## GRanges object with 963 ranges and 2 metadata columns:
## seqnames ranges strand | qvalue
## <Rle> <IRanges> <Rle> | <numeric>
## [1] chr21 [9853296, 9853296] + | 0.0215658126063664
## [2] chr21 [9853326, 9853326] + | 0.592173028310101
## [3] chr21 [9860126, 9860126] + | 0.0697808391745445
## [4] chr21 [9906604, 9906604] + | 0.259453089661393
## [5] chr21 [9906616, 9906616] + | 0.00432220069940914
## ... ... ... ... . ...
## [959] chr21 [19855690, 19855690] + | 0.0660274910679262
## [960] chr21 [19855706, 19855706] + | 0.282958728725395
## [961] chr21 [19855711, 19855711] + | 0.0446545923565475
## [962] chr21 [19943653, 19943653] + | 0.592173028310101
## [963] chr21 [19943695, 19943695] + | 0.396045532748492
## meth.diff
## <numeric>
## [1] -7.01210653753027
## [2] 0.209135938359928
## [3] -4.11158117398203
## [4] -7.34636871508379
## [5] 18.8175046554935
## ... ...
## [959] -6.52173913043478
## [960] 2.17391304347826
## [961] -8.33333333333334
## [962] 1.45454545454546
## [963] 3.38765008576329
## -------
## seqinfo: 1 sequence from an unspecified genome; no seqlengths5.2 Converting methylKit objects to methylDB objects and vice versa
methylDB objects (methylRawDB, methylBaseDB and methylDiffDB) can be coerced to normal methylKit objects. This might speed up the analysis if sufficient computing resources are available. This can be done via “as()” function.
class(myobjDB[[1]])## [1] "methylRawDB"
## attr(,"package")
## [1] "methylKit"as(myobjDB[[1]],"methylRaw")## chr start end strand coverage numCs numTs
## 1 chr21 9764513 9764513 - 12 0 12
## 2 chr21 9764539 9764539 - 12 3 9
## 3 chr21 9820622 9820622 + 13 0 13
## 4 chr21 9837545 9837545 + 11 0 11
## 5 chr21 9849022 9849022 + 124 90 34
## 6 chr21 9853296 9853296 + 17 10 7
## 7 chr21 9853326 9853326 + 17 12 5
## 8 chr21 9860126 9860126 + 39 38 1
## 9 chr21 9874553 9874553 + 12 12 0
## 10 chr21 9882409 9882409 + 10 7 3
## 11 chr21 9882434 9882434 + 10 0 10
## 12 chr21 9906604 9906604 + 68 42 26
## 13 chr21 9906616 9906616 + 68 52 16
## 14 chr21 9906619 9906619 + 68 59 9
## 15 chr21 9906634 9906634 + 68 56 12
## 16 chr21 9906635 9906635 - 37 24 13
## 17 chr21 9906640 9906640 + 67 6 61
## 18 chr21 9906641 9906641 - 36 4 32
## 19 chr21 9906644 9906644 + 68 63 5
## 20 chr21 9906645 9906645 - 36 30 6
## 21 chr21 9906655 9906655 - 37 26 11
## 22 chr21 9906657 9906657 - 37 4 33
## 23 chr21 9906660 9906660 - 37 24 13
## 24 chr21 9906663 9906663 - 37 25 12
## 25 chr21 9906676 9906676 + 21 17 4
## 26 chr21 9906677 9906677 - 37 28 9
## 27 chr21 9906681 9906681 + 21 12 9
## 28 chr21 9906694 9906694 + 21 9 12
## 29 chr21 9906700 9906700 + 13 6 7
## 30 chr21 9906714 9906714 + 14 3 11
## 31 chr21 9906846 9906846 + 14 13 1
## 32 chr21 9906864 9906864 + 14 10 4
## 33 chr21 9906869 9906869 + 14 4 10
## 34 chr21 9906873 9906873 + 12 8 4
## 35 chr21 9906884 9906884 + 14 1 13
## 36 chr21 9906889 9906889 + 11 0 11
## 37 chr21 9906933 9906933 + 20 17 3
## 38 chr21 9906949 9906949 + 20 14 6
## 39 chr21 9906952 9906952 + 20 15 5
## 40 chr21 9906954 9906954 + 20 15 5
## 41 chr21 9906957 9906957 + 20 17 3
## 42 chr21 9911433 9911433 - 19 7 12
## 43 chr21 9911447 9911447 - 19 17 2
## 44 chr21 9913543 9913543 + 36 26 10
## 45 chr21 9913575 9913575 + 35 30 5
## 46 chr21 9927527 9927527 + 17 5 12
## 47 chr21 9944505 9944505 + 37 2 35
## 48 chr21 9944663 9944663 - 61 19 42
## 49 chr21 9959407 9959407 + 44 17 27
## 50 chr21 9959541 9959541 - 26 12 14
## 51 chr21 9959569 9959569 - 25 17 8
## 52 chr21 9959577 9959577 - 25 25 0
## 53 chr21 9959644 9959644 - 21 0 21
## 54 chr21 9959650 9959650 - 21 6 15
## 55 chr21 9967634 9967634 - 10 0 10
## 56 chr21 10011833 10011833 + 174 173 1
## 57 chr21 10011841 10011841 + 173 164 9
## 58 chr21 10011855 10011855 + 175 175 0
## 59 chr21 10011858 10011858 + 175 131 44
## 60 chr21 10011861 10011861 + 174 147 27
## 61 chr21 10011872 10011872 + 167 160 7
## 62 chr21 10011876 10011876 + 160 148 12
## 63 chr21 10011878 10011878 + 150 134 16
## 64 chr21 10011925 10011925 - 120 65 55
## 65 chr21 10011938 10011938 - 134 127 7
## 66 chr21 10011954 10011954 - 133 131 2
## 67 chr21 10011964 10011964 - 139 110 29
## 68 chr21 10011974 10011974 - 139 106 33
## 69 chr21 10011987 10011987 + 224 214 10
## 70 chr21 10011990 10011990 + 224 184 40
## 71 chr21 10012008 10012008 + 229 91 138
## 72 chr21 10012030 10012030 + 229 180 49
## 73 chr21 10012069 10012069 + 94 88 6
## 74 chr21 10012075 10012075 + 95 93 2
## 75 chr21 10012079 10012079 + 94 88 6
## 76 chr21 10012089 10012089 + 94 80 14
## 77 chr21 10012095 10012095 + 94 89 5
## 78 chr21 10012101 10012101 + 98 96 2
## 79 chr21 10012316 10012316 - 14 11 3
## 80 chr21 10012318 10012318 - 14 14 0
## 81 chr21 10012321 10012321 - 14 14 0
## 82 chr21 10012324 10012324 - 14 14 0
## 83 chr21 10012328 10012328 - 14 13 1
## 84 chr21 10012425 10012425 - 70 48 22
## 85 chr21 10012428 10012428 - 69 52 17
## 86 chr21 10012430 10012430 - 70 54 16
## 87 chr21 10012442 10012442 - 67 50 17
## 88 chr21 10012454 10012454 - 70 65 5
## 89 chr21 10012465 10012465 - 70 56 14
## 90 chr21 10012587 10012587 - 39 8 31
## 91 chr21 10012606 10012606 - 43 4 39
## 92 chr21 10012609 10012609 + 162 148 14
## 93 chr21 10012610 10012610 - 44 41 3
## 94 chr21 10012636 10012636 + 158 115 43
## 95 chr21 10012637 10012637 - 136 88 48
## 96 chr21 10012640 10012640 + 156 129 27
## 97 chr21 10012641 10012641 - 136 111 25
## 98 chr21 10012642 10012642 + 155 146 9
## 99 chr21 10012643 10012643 - 136 130 6
## 100 chr21 10012658 10012658 + 148 125 22
## 101 chr21 10012659 10012659 - 136 109 27
## 102 chr21 10012662 10012662 - 136 133 3
## 103 chr21 10012696 10012696 + 148 147 1
## 104 chr21 10012699 10012699 + 148 140 8
## 105 chr21 10012862 10012862 - 10 9 1
## 106 chr21 10012876 10012876 + 29 28 1
## 107 chr21 10012877 10012877 - 10 9 1
## 108 chr21 10012881 10012881 + 30 0 30
## 109 chr21 10012883 10012883 + 29 29 0
## 110 chr21 10012887 10012887 + 30 27 3
## 111 chr21 10012891 10012891 + 30 29 1
## 112 chr21 10012894 10012894 + 30 23 7
## 113 chr21 10012898 10012898 + 20 20 0
## 114 chr21 10012900 10012900 + 24 22 2
## 115 chr21 10012902 10012902 + 24 24 0
## 116 chr21 10012921 10012921 + 23 23 0
## 117 chr21 10012924 10012924 + 23 23 0
## 118 chr21 10012934 10012934 - 84 82 2
## 119 chr21 10012938 10012938 - 119 116 3
## 120 chr21 10012940 10012940 - 118 118 0
## 121 chr21 10012942 10012942 - 128 126 2
## 122 chr21 10012944 10012944 - 130 123 7
## 123 chr21 10012947 10012947 - 137 134 3
## 124 chr21 10012961 10012961 - 143 136 7
## 125 chr21 10012975 10012975 - 149 107 42
## 126 chr21 10012981 10012981 + 18 13 5
## 127 chr21 10012982 10012982 - 152 150 2
## 128 chr21 10012989 10012989 + 18 15 3
## 129 chr21 10012994 10012994 + 18 13 5
## 130 chr21 10013000 10013000 + 12 6 6
## 131 chr21 10013039 10013039 - 106 0 106
## 132 chr21 10013060 10013060 - 109 56 53
## 133 chr21 10013062 10013062 - 111 55 56
## 134 chr21 10013072 10013072 - 111 97 14
## 135 chr21 10013086 10013086 - 112 106 6
## 136 chr21 10013594 10013594 - 11 4 7
## 137 chr21 10013827 10013827 - 16 14 2
## 138 chr21 10022131 10022131 - 17 7 10
## 139 chr21 10022157 10022157 - 17 8 9
## 140 chr21 10022165 10022165 - 17 16 1
## 141 chr21 10065022 10065022 + 26 26 0
## 142 chr21 10065061 10065061 + 25 12 13
## 143 chr21 10077699 10077699 + 47 10 37
## 144 chr21 10077705 10077705 + 47 12 35
## 145 chr21 10077904 10077904 - 17 10 7
## 146 chr21 10081627 10081627 + 12 2 10
## 147 chr21 10081638 10081638 + 14 6 8
## 148 chr21 10081652 10081652 + 11 3 8
## 149 chr21 10086785 10086785 + 20 8 12
## 150 chr21 10087014 10087014 - 10 3 7
## 151 chr21 10099942 10099942 + 13 13 0
## 152 chr21 10099950 10099950 + 13 10 3
## 153 chr21 10114305 10114305 - 12 2 10
## 154 chr21 10114343 10114343 - 13 8 5
## 155 chr21 10114345 10114345 - 13 5 8
## 156 chr21 10114351 10114351 - 13 6 7
## 157 chr21 10118483 10118483 + 12 0 12
## 158 chr21 10120564 10120564 - 25 15 10
## 159 chr21 10120584 10120584 - 27 8 19
## 160 chr21 10120599 10120599 + 84 78 6
## 161 chr21 10120600 10120600 - 27 21 6
## 162 chr21 10120603 10120603 + 94 12 82
## 163 chr21 10120634 10120634 + 99 14 85
## 164 chr21 10120643 10120643 + 97 18 79
## 165 chr21 10121028 10121028 + 11 11 0
## 166 chr21 10121033 10121033 + 11 9 2
## 167 chr21 10121126 10121126 + 818 686 132
## 168 chr21 10121171 10121171 + 406 284 122
## 169 chr21 10121198 10121198 + 26 15 11
## 170 chr21 10122567 10122567 + 14 14 0
## 171 chr21 10128590 10128590 + 310 275 35
## 172 chr21 10128601 10128601 + 306 270 36
## 173 chr21 10128603 10128603 + 308 284 24
## 174 chr21 10128609 10128609 + 309 292 17
## 175 chr21 10128617 10128617 + 307 255 51
## 176 chr21 10128639 10128639 + 527 227 300
## 177 chr21 10128659 10128659 + 237 159 78
## 178 chr21 10128660 10128660 - 135 90 45
## 179 chr21 10128661 10128661 + 236 196 40
## 180 chr21 10128662 10128662 - 136 115 17
## 181 chr21 10128670 10128670 + 237 225 12
## 182 chr21 10128671 10128671 - 138 117 21
## 183 chr21 10128673 10128673 + 227 194 33
## 184 chr21 10128674 10128674 - 139 126 13
## 185 chr21 10128682 10128682 + 145 2 142
## 186 chr21 10128683 10128683 - 101 39 62
## 187 chr21 10128702 10128702 + 87 87 0
## 188 chr21 10128705 10128705 + 87 86 1
## 189 chr21 10128706 10128706 - 49 47 2
## 190 chr21 10128707 10128707 + 87 84 3
## 191 chr21 10128708 10128708 - 50 47 3
## 192 chr21 10128710 10128710 + 87 85 2
## 193 chr21 10128711 10128711 - 50 48 2
## 194 chr21 10128720 10128720 + 87 83 4
## 195 chr21 10128721 10128721 - 50 48 2
## 196 chr21 10128734 10128734 + 260 201 59
## 197 chr21 10128735 10128735 - 50 48 2
## 198 chr21 10128738 10128738 + 286 223 63
## 199 chr21 10128745 10128745 + 292 168 124
## 200 chr21 10128748 10128748 + 294 258 36
## 201 chr21 10128758 10128758 + 192 108 84
## 202 chr21 10128775 10128775 + 204 161 43
## 203 chr21 10128839 10128839 + 518 472 46
## 204 chr21 10128850 10128850 + 514 395 119
## 205 chr21 10128867 10128867 + 522 487 35
## 206 chr21 10128881 10128881 + 515 463 52
## 207 chr21 10128883 10128883 + 511 465 46
## 208 chr21 10128964 10128964 - 68 40 28
## 209 chr21 10128980 10128980 - 70 38 32
## 210 chr21 10128989 10128989 - 70 62 8
## 211 chr21 10128991 10128991 - 70 39 31
## 212 chr21 10129002 10129002 + 78 77 1
## 213 chr21 10129003 10129003 - 71 60 11
## 214 chr21 10129032 10129032 + 80 61 19
## 215 chr21 10129036 10129036 + 81 79 2
## 216 chr21 10129044 10129044 + 80 78 2
## 217 chr21 10129181 10129181 + 34 28 6
## 218 chr21 10129546 10129546 + 36 35 1
## 219 chr21 10129550 10129550 + 36 26 10
## 220 chr21 10131969 10131969 + 14 14 0
## 221 chr21 10132033 10132033 + 12 7 5
## 222 chr21 10132081 10132081 - 29 27 2
## 223 chr21 10132089 10132089 - 29 25 4
## 224 chr21 10132094 10132094 + 35 28 7
## 225 chr21 10132095 10132095 - 29 15 14
## 226 chr21 10132122 10132122 + 36 24 12
## 227 chr21 10132130 10132130 + 136 92 44
## 228 chr21 10132131 10132131 - 16 12 4
## 229 chr21 10132177 10132177 + 108 41 67
## 230 chr21 10132398 10132398 + 19 14 5
## 231 chr21 10132406 10132406 + 19 14 5
## 232 chr21 10132418 10132418 + 19 8 11
## 233 chr21 10133048 10133048 + 133 105 28
## 234 chr21 10133056 10133056 + 132 94 38
## 235 chr21 10133080 10133080 + 131 73 58
## 236 chr21 10133091 10133091 + 124 41 83
## 237 chr21 10133092 10133092 - 16 1 15
## 238 chr21 10133111 10133111 - 74 47 27
## 239 chr21 10133159 10133159 + 50 24 26
## 240 chr21 10133160 10133160 - 114 60 54
## 241 chr21 10133401 10133401 + 17 9 8
## 242 chr21 10133402 10133402 - 26 12 14
## 243 chr21 10136614 10136614 + 97 79 18
## 244 chr21 10136632 10136632 + 133 9 124
## 245 chr21 10136648 10136648 + 138 29 109
## 246 chr21 10136731 10136731 - 145 97 48
## 247 chr21 10136737 10136737 - 144 114 30
## 248 chr21 10136755 10136755 - 143 113 30
## 249 chr21 10136772 10136772 + 20 11 9
## 250 chr21 10136773 10136773 - 142 76 66
## 251 chr21 10136966 10136966 - 11 0 11
## 252 chr21 10145439 10145439 + 32 16 16
## 253 chr21 10145470 10145470 + 32 24 8
## 254 chr21 10145471 10145471 - 39 17 22
## 255 chr21 10145507 10145507 - 41 24 17
## 256 chr21 10148190 10148190 + 16 11 5
## 257 chr21 10148224 10148224 + 17 14 3
## 258 chr21 10148396 10148396 - 16 4 12
## 259 chr21 10151952 10151952 - 11 7 4
## 260 chr21 10151967 10151967 + 12 5 7
## 261 chr21 10151968 10151968 - 11 9 2
## 262 chr21 10152050 10152050 - 17 14 3
## 263 chr21 10154024 10154024 - 19 18 1
## 264 chr21 10154062 10154062 - 19 9 10
## 265 chr21 10154072 10154072 - 19 19 0
## 266 chr21 10154210 10154210 - 57 49 8
## 267 chr21 10154226 10154226 - 57 43 14
## 268 chr21 10154246 10154246 - 57 48 9
## 269 chr21 10154306 10154306 - 98 82 14
## 270 chr21 10154872 10154872 + 49 24 25
## 271 chr21 10154873 10154873 - 28 22 6
## 272 chr21 10154893 10154893 + 49 32 17
## 273 chr21 10154894 10154894 - 28 19 9
## 274 chr21 10154897 10154897 + 43 0 43
## 275 chr21 10154898 10154898 - 27 0 27
## 276 chr21 10154916 10154916 - 29 24 5
## 277 chr21 10156390 10156390 + 13 7 6
## 278 chr21 10156406 10156406 + 13 10 3
## 279 chr21 10156434 10156434 + 11 11 0
## 280 chr21 10156485 10156485 - 13 10 3
## 281 chr21 10156496 10156496 - 14 13 1
## 282 chr21 10156520 10156520 + 148 77 71
## 283 chr21 10156521 10156521 - 14 7 7
## 284 chr21 10157440 10157440 - 68 42 26
## 285 chr21 10158020 10158020 + 10 8 2
## 286 chr21 10158023 10158023 + 10 8 2
## 287 chr21 10160749 10160749 - 11 9 2
## 288 chr21 10160753 10160753 - 11 7 4
## 289 chr21 10162951 10162951 + 12 0 12
## 290 chr21 10166512 10166512 - 12 12 0
## 291 chr21 10166531 10166531 - 12 0 12
## 292 chr21 10176577 10176577 - 68 37 31
## 293 chr21 10176592 10176592 - 68 52 16
## 294 chr21 10186386 10186386 - 52 39 13
## 295 chr21 10186452 10186452 + 13 10 3
## 296 chr21 10186507 10186507 - 54 42 12
## 297 chr21 10186519 10186519 - 76 24 52
## 298 chr21 10186541 10186541 - 70 5 65
## 299 chr21 10187865 10187865 - 13 10 3
## 300 chr21 10190503 10190503 - 293 224 69
## 301 chr21 10190515 10190515 + 47 43 4
## 302 chr21 10190516 10190516 - 297 249 48
## 303 chr21 10190523 10190523 + 47 37 10
## 304 chr21 10190524 10190524 - 22 19 3
## 305 chr21 10190541 10190541 + 50 49 1
## 306 chr21 10190542 10190542 - 25 22 3
## 307 chr21 10190546 10190546 + 47 34 13
## 308 chr21 10190547 10190547 - 25 21 4
## 309 chr21 10190550 10190550 + 35 33 2
## 310 chr21 10190551 10190551 - 24 21 3
## 311 chr21 10190555 10190555 + 48 42 6
## 312 chr21 10190556 10190556 - 25 22 3
## 313 chr21 10190563 10190563 + 47 38 9
## 314 chr21 10190574 10190574 + 45 34 11
## 315 chr21 10190582 10190582 + 44 0 44
## 316 chr21 10190583 10190583 - 113 92 21
## 317 chr21 10190586 10190586 + 24 19 5
## 318 chr21 10190587 10190587 - 116 111 5
## 319 chr21 10190611 10190611 - 118 0 118
## 320 chr21 10190622 10190622 - 118 97 21
## 321 chr21 10190627 10190627 - 118 38 80
## 322 chr21 10190629 10190629 + 91 82 9
## 323 chr21 10190630 10190630 - 117 101 16
## 324 chr21 10190633 10190633 + 91 67 24
## 325 chr21 10190658 10190658 + 91 83 8
## 326 chr21 10190669 10190669 + 87 83 4
## 327 chr21 10190676 10190676 + 81 70 11
## 328 chr21 10190754 10190754 + 11 9 2
## 329 chr21 10190787 10190787 + 10 10 0
## 330 chr21 10190834 10190834 - 17 11 6
## 331 chr21 10190852 10190852 - 17 7 10
## 332 chr21 10190868 10190868 - 17 5 12
## 333 chr21 10190881 10190881 + 296 152 144
## 334 chr21 10190882 10190882 - 16 7 9
## 335 chr21 10190896 10190896 + 293 239 54
## 336 chr21 10190897 10190897 - 344 266 78
## 337 chr21 10190924 10190924 + 204 195 9
## 338 chr21 10190925 10190925 - 387 373 14
## 339 chr21 10190929 10190929 + 175 129 46
## 340 chr21 10190930 10190930 - 390 248 142
## 341 chr21 10190937 10190937 - 381 351 30
## 342 chr21 10190944 10190944 - 390 366 24
## 343 chr21 10190970 10190970 + 17 17 0
## 344 chr21 10190983 10190983 + 18 18 0
## 345 chr21 10190985 10190985 + 18 17 1
## 346 chr21 10190995 10190995 + 17 13 4
## 347 chr21 10191023 10191023 - 153 88 65
## 348 chr21 10191062 10191062 - 154 110 44
## 349 chr21 10191089 10191089 - 48 41 7
## 350 chr21 10191109 10191109 - 48 42 6
## 351 chr21 10191112 10191112 - 47 33 14
## 352 chr21 10191118 10191118 - 48 46 2
## 353 chr21 10191326 10191326 - 69 40 29
## 354 chr21 10191348 10191348 - 64 51 13
## 355 chr21 10191408 10191408 - 238 54 184
## 356 chr21 10191430 10191430 - 237 54 183
## 357 chr21 10191769 10191769 + 46 21 25
## 358 chr21 10191770 10191770 - 190 152 38
## 359 chr21 10191773 10191773 + 45 28 17
## 360 chr21 10191786 10191786 + 45 25 20
## 361 chr21 10191818 10191818 + 45 36 9
## 362 chr21 10191819 10191819 - 304 160 144
## 363 chr21 10191824 10191824 - 307 181 126
## 364 chr21 10191830 10191830 - 310 259 51
## 365 chr21 10191838 10191838 - 309 235 74
## 366 chr21 10191851 10191851 - 310 218 92
## 367 chr21 10191878 10191878 + 309 289 20
## 368 chr21 10191899 10191899 + 305 250 55
## 369 chr21 10191900 10191900 - 299 242 57
## 370 chr21 10191906 10191906 + 308 191 117
## 371 chr21 10191907 10191907 - 311 216 95
## 372 chr21 10191923 10191923 + 262 200 61
## 373 chr21 10191924 10191924 - 313 223 90
## 374 chr21 10191940 10191940 - 328 237 90
## 375 chr21 10192279 10192279 + 245 138 107
## 376 chr21 10192318 10192318 + 230 122 107
## 377 chr21 10192319 10192319 - 178 141 37
## 378 chr21 10192322 10192322 + 241 190 51
## 379 chr21 10192323 10192323 - 249 203 46
## 380 chr21 10192331 10192331 - 248 163 85
## 381 chr21 10192334 10192334 + 11 7 4
## 382 chr21 10192335 10192335 - 254 188 66
## 383 chr21 10192368 10192368 + 10 7 3
## 384 chr21 10192378 10192378 + 11 9 2
## 385 chr21 13282433 13282433 + 63 41 22
## 386 chr21 13282440 13282440 + 62 20 42
## 387 chr21 13294742 13294742 + 20 20 0
## 388 chr21 13294755 13294755 + 21 21 0
## 389 chr21 13294757 13294757 + 21 21 0
## 390 chr21 13294785 13294785 + 22 19 3
## 391 chr21 13306319 13306319 - 30 21 9
## 392 chr21 13306339 13306339 - 30 30 0
## 393 chr21 13306349 13306349 - 30 22 8
## 394 chr21 13490512 13490512 + 23 17 6
## 395 chr21 13490521 13490521 + 23 11 12
## 396 chr21 13490535 13490535 + 22 19 2
## 397 chr21 13490540 13490540 + 23 21 2
## 398 chr21 13490561 13490561 + 10 8 2
## 399 chr21 13662766 13662766 + 11 11 0
## 400 chr21 13664888 13664888 + 20 10 10
## 401 chr21 13664889 13664889 - 71 38 33
## 402 chr21 13666397 13666397 - 61 45 16
## 403 chr21 13666553 13666553 - 10 7 3
## 404 chr21 13673290 13673290 + 17 17 0
## 405 chr21 13673294 13673294 + 17 17 0
## 406 chr21 13673713 13673713 + 10 10 0
## 407 chr21 13673740 13673740 + 10 9 1
## 408 chr21 13673754 13673754 + 10 9 1
## 409 chr21 13673865 13673865 + 13 13 0
## 410 chr21 13719180 13719180 - 11 5 6
## 411 chr21 13719188 13719188 - 11 0 11
## 412 chr21 13786212 13786212 + 20 10 10
## 413 chr21 13808881 13808881 - 11 8 3
## 414 chr21 13808911 13808911 - 12 10 2
## 415 chr21 13866816 13866816 + 11 3 8
## 416 chr21 13866838 13866838 + 11 7 4
## 417 chr21 13877808 13877808 - 10 6 4
## 418 chr21 13878804 13878804 - 11 9 2
## 419 chr21 13903783 13903783 - 10 10 0
## 420 chr21 13958077 13958077 - 18 12 6
## 421 chr21 13958080 13958080 - 17 15 2
## 422 chr21 13958094 13958094 - 17 14 3
## 423 chr21 13958107 13958107 - 18 13 5
## 424 chr21 13958266 13958266 - 20 15 5
## 425 chr21 13958466 13958466 + 11 5 6
## 426 chr21 13960041 13960041 + 16 10 6
## 427 chr21 13960067 13960067 + 16 14 2
## 428 chr21 13960069 13960069 + 15 14 1
## 429 chr21 13960080 13960080 + 16 14 2
## 430 chr21 13960088 13960088 + 16 14 2
## 431 chr21 13989277 13989277 + 48 47 1
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## 1802 chr21 18539117 18539117 + 25 0 25
## 1803 chr21 18539131 18539131 + 25 1 24
## 1804 chr21 18539148 18539148 + 25 0 25
## 1805 chr21 18539208 18539208 - 75 45 30
## 1806 chr21 18539218 18539218 - 79 37 42
## 1807 chr21 18539220 18539220 - 79 32 47
## 1808 chr21 18539222 18539222 - 80 28 52
## 1809 chr21 18539231 18539231 - 79 38 41
## 1810 chr21 18539233 18539233 - 80 24 56
## 1811 chr21 18539240 18539240 - 77 14 63
## 1812 chr21 18539249 18539249 + 96 45 51
## 1813 chr21 18539250 18539250 - 77 39 38
## 1814 chr21 18539253 18539253 + 94 51 43
## 1815 chr21 18539259 18539259 + 90 19 71
## 1816 chr21 18539264 18539264 + 94 22 72
## 1817 chr21 18539265 18539265 - 71 15 56
## 1818 chr21 18539266 18539266 + 93 50 43
## 1819 chr21 18539267 18539267 - 71 39 32
## 1820 chr21 18539276 18539276 + 96 7 89
## 1821 chr21 18539277 18539277 - 72 3 69
## 1822 chr21 18539290 18539290 + 89 2 87
## 1823 chr21 18539291 18539291 - 73 3 70
## 1824 chr21 18539294 18539294 + 68 7 61
## 1825 chr21 18539295 18539295 - 73 6 67
## 1826 chr21 18539297 18539297 + 27 2 25
## 1827 chr21 18539298 18539298 - 73 1 72
## 1828 chr21 18539310 18539310 + 18 0 18
## 1829 chr21 18539311 18539311 - 73 2 71
## 1830 chr21 18539344 18539344 + 18 3 15
## 1831 chr21 18539346 18539346 + 16 0 16
## 1832 chr21 18539353 18539353 + 16 1 15
## 1833 chr21 18539540 18539540 - 11 0 11
## 1834 chr21 18539545 18539545 - 10 0 10
## 1835 chr21 18539547 18539547 - 11 0 11
## 1836 chr21 18539550 18539550 - 11 1 10
## 1837 chr21 18539565 18539565 - 12 0 12
## 1838 chr21 18539569 18539569 - 12 0 12
## 1839 chr21 18539580 18539580 - 12 0 12
## 1840 chr21 18539585 18539585 - 10 0 10
## 1841 chr21 18539612 18539612 + 17 0 17
## 1842 chr21 18539613 18539613 - 10 0 10
## 1843 chr21 18539622 18539622 + 16 0 16
## 1844 chr21 18539801 18539801 - 21 2 19
## 1845 chr21 18539804 18539804 + 124 14 110
## 1846 chr21 18539805 18539805 - 21 0 21
## 1847 chr21 18539838 18539838 + 80 4 76
## 1848 chr21 18539933 18539933 - 111 62 49
## 1849 chr21 18539960 18539960 - 116 37 79
## 1850 chr21 18539970 18539970 - 111 4 107
## 1851 chr21 18539976 18539976 - 117 17 100
## 1852 chr21 18550887 18550887 + 15 8 7
## 1853 chr21 18572834 18572834 + 10 8 2
## 1854 chr21 18572866 18572866 + 10 10 0
## 1855 chr21 18576141 18576141 + 15 15 0
## 1856 chr21 18576145 18576145 + 14 12 2
## 1857 chr21 18576157 18576157 + 14 14 0
## 1858 chr21 18576178 18576178 + 11 11 0
## 1859 chr21 18576179 18576179 - 11 11 0
## 1860 chr21 18576203 18576203 - 11 5 6
## 1861 chr21 18576211 18576211 - 11 11 0
## 1862 chr21 18582970 18582970 + 18 12 6
## 1863 chr21 18582975 18582975 + 18 11 7
## 1864 chr21 18615698 18615698 - 24 16 8
## 1865 chr21 18713624 18713624 + 12 11 1
## 1866 chr21 18713634 18713634 + 12 12 0
## 1867 chr21 18713648 18713648 + 12 8 4
## 1868 chr21 18737675 18737675 + 12 7 5
## 1869 chr21 18737730 18737730 - 13 8 5
## 1870 chr21 18763228 18763228 + 11 0 11
## 1871 chr21 18763284 18763284 - 10 0 10
## 1872 chr21 18957876 18957876 + 16 9 7
## 1873 chr21 19280741 19280741 + 10 8 2
## 1874 chr21 19282009 19282009 + 11 11 0
## 1875 chr21 19390691 19390691 - 14 8 6
## 1876 chr21 19390694 19390694 - 14 9 5
## 1877 chr21 19422671 19422671 - 17 15 2
## 1878 chr21 19539486 19539486 - 10 7 3
## 1879 chr21 19539511 19539511 - 12 8 4
## 1880 chr21 19539528 19539528 - 12 12 0
## 1881 chr21 19579289 19579289 + 23 10 13
## 1882 chr21 19579345 19579345 - 10 8 2
## 1883 chr21 19579352 19579352 - 12 6 6
## 1884 chr21 19579357 19579357 - 12 10 2
## 1885 chr21 19579361 19579361 - 12 10 2
## 1886 chr21 19626227 19626227 - 25 22 3
## 1887 chr21 19626384 19626384 - 22 22 0
## 1888 chr21 19711774 19711774 + 10 2 8
## 1889 chr21 19739452 19739452 + 10 9 1
## 1890 chr21 19788073 19788073 - 45 42 3
## 1891 chr21 19788076 19788076 - 44 42 2
## 1892 chr21 19788089 19788089 - 45 45 0
## 1893 chr21 19788093 19788093 - 45 45 0
## 1894 chr21 19788113 19788113 - 46 46 0
## 1895 chr21 19788117 19788117 - 46 46 0
## 1896 chr21 19788122 19788122 - 46 43 3
## 1897 chr21 19834041 19834041 + 10 10 0
## 1898 chr21 19834070 19834070 + 10 3 7
## 1899 chr21 19855659 19855659 + 10 10 0
## 1900 chr21 19855690 19855690 + 27 26 1
## 1901 chr21 19855706 19855706 + 27 27 0
## 1902 chr21 19855711 19855711 + 18 18 0
## 1903 chr21 19943653 19943653 + 12 12 0
## 1904 chr21 19943695 19943695 + 12 11 1You can also convert methylDB objects to their in-memory equivalents. Since that requires an additional parameter (the directory where the files will be located), we have a different function, named makeMethylDB to achieve this goal. Below, we convert a methylBase object to methylBaseDB and saving it at “exMethylDB” directory.
data(methylKit)
objDB=makeMethylDB(methylBase.obj,"exMethylDB")5.3 Selection: subsetting methylKit Objects
We can also select rows from methylRaw, methylBase and methylDiff objects and methylDB pendants with select function. An appropriate methylKit object will be returned as a result of select function. Or you can use the '[' notation to subset the methylKit objects.
select(meth,1:5) # get first 10 rows of a methylBase object## chr start end strand coverage1 numCs1 numTs1 coverage2 numCs2
## 1 chr21 9853296 9853296 + 17 10 7 333 268
## 2 chr21 9853326 9853326 + 17 12 5 329 249
## 3 chr21 9860126 9860126 + 39 38 1 83 78
## 4 chr21 9906604 9906604 + 68 42 26 111 97
## 5 chr21 9906616 9906616 + 68 52 16 111 104
## numTs2 coverage3 numCs3 numTs3 coverage4 numCs4 numTs4
## 1 65 18 16 2 395 341 54
## 2 79 16 14 2 379 284 95
## 3 5 83 83 0 41 40 1
## 4 14 23 18 5 37 33 4
## 5 7 23 14 9 37 27 10myDiff[21:25,] # get 5 rows of a methylDiff object## chr start end strand pvalue qvalue meth.diff
## 21 chr21 9913543 9913543 + 1.254379e-02 2.632641e-02 -13.343109
## 22 chr21 9913575 9913575 + 2.755448e-01 3.161628e-01 -5.442623
## 23 chr21 9927527 9927527 + 1.120126e-07 9.257475e-07 -46.109840
## 24 chr21 9944505 9944505 + 7.907909e-20 7.515975e-18 -51.017943
## 25 chr21 9944663 9944663 - 1.790779e-05 7.678302e-05 -28.099911Important: Using select or '[' on methylDB objects will return its normal methylKit pendant, to avoid overhead of database operations.
5.3.1 selectByOverlap
We can select rows from any methylKit object, that lie inside the ranges of a GRanges object from GenomicRanges package with selectByOverlap function. An appropriate methylKit object will be returned as a result of selectByOverlap function.
library(GenomicRanges)
my.win=GRanges(seqnames="chr21",
ranges=IRanges(start=seq(from=9764513,by=10000,length.out=20),width=5000) )
# selects the records that lie inside the regions
selectByOverlap(myobj[[1]],my.win)Important: Using selectByOverlap on methylDB objects will return its normal methylKit pendant, to avoid overhead of database operations.
5.4 reorganize(): reorganizing samples and treatment vector within methylKit objects
The methylBase and methylRawList, as well as methylDB pendants can be reorganized by reorganize function. The function can subset the objects based on provided sample ids, it also creates a new treatment vector determining which samples belong to which group. Order of sample ids should match the treatment vector order.
# creates a new methylRawList object
myobj2=reorganize(myobj,sample.ids=c("test1","ctrl2"),treatment=c(1,0) )
# creates a new methylBase object
meth2 =reorganize(meth,sample.ids=c("test1","ctrl2"),treatment=c(1,0) )5.5 percMethylation(): Getting percent methylation matrix from methylBase objects
Percent methylation values can be extracted from methylBase object by using percMethylation function.
# creates a matrix containing percent methylation values
perc.meth=percMethylation(meth)5.6 methSeg(): segmentation of methylation or differential methylation profiles
Methylation or differential methylation profiles can be segmented to sections that contain similar CpGs with respect to their methylation profiles. This kind of segmentation could help us find interesting regions. For example, segmentation analysis will usually reveal high or low methylated regions, where low methylated regions could be interesting for gene regulation. The algorithm first finds segments that have CpGs with similar methylation levels, then those segments are classified to segment groups based on their mean methylation levels. This enables us to group segments with similar methylation levels to the same class.
See more at http://zvfak.blogspot.de/2015/06/segmentation-of-methylation-profiles.html
download.file("https://dl.dropboxusercontent.com/u/1373164/H1.chr21.chr22.rds",
destfile="H1.chr21.chr22.rds",method="curl")
mbw=readRDS("H1.chr21.chr22.rds")
# it finds the optimal number of componets as 6
res=methSeg(mbw,diagnostic.plot=TRUE,maxInt=100,minSeg=10)
# however the BIC stabilizes after 4, we can also try 4 componets
res=methSeg(mbw,diagnostic.plot=TRUE,maxInt=100,minSeg=10,G=1:4)
# get segments to BED file
methSeg2bed(res,filename="H1.chr21.chr22.trial.seg.bed")6 Frequently Asked Questions
Detailed answers to some of the frequently asked questions and various HOW-TO’s can be found at http://zvfak.blogspot.com/search/label/methylKit. In addition, http://code.google.com/p/methylkit/ has online documentation and links to tutorials and other related material. You can also check methylKit Q&A forum for answers https://groups.google.com/forum/#!forum/methylkit_discussion.
Apart from those here are some of the frequently asked questions.
6.0.1 How can I select certain regions/bases from methylRaw or methylBase objects ?
See ?select or help("[", package = "methylKit")
6.0.2 How can I find if my regions of interest overlap with exon/intron/promoter/CpG island etc.?
Currently, we will be able to tell you if your regions/bases overlap with the genomic features or not. See ?getMembers.
6.0.3 How can I find the nearest TSS associated with my CpGs ?
See ?genomation::getAssociationWithTSS
6.0.4 How do you define promoters and CpG island shores ?
Promoters are defined by options at genomation::readTranscriptFeatures function. The default option is to take -1000,+1000bp around the TSS and you can change that. Same goes for CpG islands when reading them in via genomation::readFeatureFlank function. Default is to take 2000bp flanking regions on each side of the CpG island as shores. But you can change that as well.
6.0.5 What does Bismark SAM output look like, where can I get more info ?
Check the Bismark (Krueger and Andrews 2011) website and there are also example files that ship with the package. Look at their formats and try to run different variations of processBismarkAln() command on the example files.
6.0.6 How can I reorder or remove samples at/from methylRawList or methylBase objects ?
See ?reorganize
6.0.7 Should I normalize my data ?
methylKit comes with a simple normalizeCoverage() function to normalize read coverage distributions between samples. Ideally, you should first filter bases with extreme coverage to account for PCR bias using filterByCoverage() function, then run normalizeCoverage() function to normalize coverage between samples. These two functions will help reduce the bias in the statistical tests that might occur due to systematic over-sampling of reads in certain samples.
6.0.8 How can I force methylKit to use Fisher’s exact test ?
methylKit decides which test to use based on number of samples per group. In order to use Fisher’s exact there must be one sample in each of the test and control groups. So if you have multiple samples for group, the package will employ Logistic Regression based test. However, you can use pool() function to pool samples in each group so that you have one representative sample per group. pool() function will sum up number of Cs and Ts in each group. We recommend using filterByCoverage() and normalizeCoverage() functions prior to using pool(). See ?pool
6.0.9 Can use data from other aligners than Bismark in methylKit ?
Yes, you can. methylKit can read any generic methylation percentage/ratio file as long as that text file contains columns for chromosome, start, end, strand, coverage and number of methylated cytosines. However, methylKit can only process SAM files from Bismark. For other aligners, you need to get a text file containing the minimal information described above. Some aligners will come with scripts or built-in tools to provide such files. See http://zvfak.blogspot.com/2012/10/how-to-read-bsmap-methylation-ratio.html for how to read methylation ratio files from BSMAP (Xi and Li 2009) aligner.
6.0.10 Can I transform an methylKit object into an methylDB object ?
Yes, you can. Many functions of the analysis workflow provide an save.db argument, which allows you to save the output as methylDB object. For example see ?unite and also check the ... argument section for further details.
7 Acknowledgements
This package is initially developed at Weill Cornell Medical College by Altuna Akalin with important code contributions from Matthias Kormaksson(mk375@cornell.edu) and Sheng Li (shl2018@med.cornell.edu). We wish to thank especially Maria E. Figueroa, Francine Garret-Bakelman, Christopher Mason and Ari Melnick for their contribution of ideas, data and support. Their support and discussions lead to development of methylKit.
7.1 Full list of contributors
- Altuna Akalin (main design and development)
- Matthias Kormaksson (initial differential methylation tests)
- Sheng Li (adding PCA and clustering)
- Adrian Bierling (methylation simulation, covariate and over-dispersion correction)
- Alexander Gosdschan (C++ based BAM parsing and tabix based classes )
- Arsene Webo (methylation segmentation)
8 R session info
sessionInfo() ## R version 3.3.1 (2016-06-21)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 16.04.1 LTS
##
## 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] grid parallel stats4 stats graphics grDevices utils
## [8] datasets methods base
##
## other attached packages:
## [1] genomation_1.6.0 methylKit_1.0.0 GenomicRanges_1.26.0
## [4] GenomeInfoDb_1.10.0 IRanges_2.8.0 S4Vectors_0.12.0
## [7] BiocGenerics_0.20.0
##
## loaded via a namespace (and not attached):
## [1] SummarizedExperiment_1.4.0 qvalue_2.6.0
## [3] gtools_3.5.0 reshape2_1.4.1
## [5] splines_3.3.1 lattice_0.20-34
## [7] seqPattern_1.6.0 colorspace_1.2-7
## [9] htmltools_0.3.5 rtracklayer_1.34.0
## [11] yaml_2.1.13 chron_2.3-47
## [13] XML_3.98-1.4 R.oo_1.20.0
## [15] R.utils_2.4.0 BiocParallel_1.8.0
## [17] fastseg_1.20.0 matrixStats_0.51.0
## [19] plyr_1.8.4 stringr_1.1.0
## [21] zlibbioc_1.20.0 Biostrings_2.42.0
## [23] munsell_0.4.3 gtable_0.2.0
## [25] R.methodsS3_1.7.1 coda_0.18-1
## [27] evaluate_0.10 Biobase_2.34.0
## [29] knitr_1.14 Rcpp_0.12.7
## [31] readr_1.0.0 KernSmooth_2.23-15
## [33] scales_0.4.0 BSgenome_1.42.0
## [35] formatR_1.4 plotrix_3.6-3
## [37] limma_3.30.0 XVector_0.14.0
## [39] Rsamtools_1.26.0 impute_1.48.0
## [41] ggplot2_2.1.0 digest_0.6.10
## [43] stringi_1.1.2 numDeriv_2016.8-1
## [45] tools_3.3.1 bitops_1.0-6
## [47] bbmle_1.0.18 magrittr_1.5
## [49] RCurl_1.95-4.8 tibble_1.2
## [51] MASS_7.3-45 Matrix_1.2-7.1
## [53] gridBase_0.4-7 data.table_1.9.6
## [55] assertthat_0.1 rmarkdown_1.1
## [57] emdbook_1.3.9 mclust_5.2
## [59] GenomicAlignments_1.10.0References
Krueger, Felix, and Simon R Andrews. 2011. “Bismark: a flexible aligner and methylation caller for Bisulfite-Seq applications.” Bioinformatics (Oxford, England) 27 (11): 1571–2. doi:10.1093/bioinformatics/btr167.
Li, Heng. 2011. “Tabix: Fast Retrieval of Sequence Features from Generic TAB-Delimited Files.” Bioinformatics 27 (5): 718–19. doi:10.1093/bioinformatics/btq671.
McCullagh, P., and John A. Nelder. 1989. Generalized Linear Models, Second Edition (Chapman & Hall/CRC Monographs on Statistics & Applied Probability). Chapman; Hall/CRC. http://www.amazon.com/Generalized-Chapman-Monographs-Statistics-Probability/dp/0412317605%3FSubscriptionId%3D0JYN1NVW651KCA56C102%26tag%3Dtechkie-20%26linkCode%3Dxm2%26camp%3D2025%26creative%3D165953%26creativeASIN%3D0412317605.
Wang, Hong-Qiang, Lindsey K Tuominen, and Chung-Jui Tsai. 2011. “SLIM: a sliding linear model for estimating the proportion of true null hypotheses in datasets with dependence structures.” Bioinformatics (Oxford, England) 27 (2): 225–31. doi:10.1093/bioinformatics/btq650.
Xi, Yuanxin, and Wei Li. 2009. “BSMAP: whole genome bisulfite sequence MAPping program.” BMC Bioinformatics 10 (1): 232. doi:10.1186/1471-2105-10-232.
Author of the vignette. See Acknowledgements for a list of contributors.↩