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\usepackage{rotating}
\title{MethylSeekR}
\author{Lukas Burger, Dimos Gaidatzis, Dirk Sch\"ubeler and Michael Stadler}
\date{Modified: July 25, 2013. Compiled: \today}

\begin{document}

\SweaveOpts{engine=R} 
%\VignetteIndexEntry{MethylSeekR} 
%\VignetteDepends{MethylSeekR, BSgenome.Hsapiens.UCSC.hg18, rtracklayer} 
%\VignetteKeywords{MethylSeekR, segmentPMDs, segmentUMRsLMRs} 
%\VignettePackage{MethylSeekR} 
\maketitle

\tableofcontents

\newpage


\section{Introduction}

This vignette describes how to use \textit{MethylSeekR} to find regulatory
regions from whole-genome bisulfite-sequencing (Bis-seq) methylation
data. The basic ideas of the method were introduced in \cite{Stadler:2011vn}
and the validity of the approach demonstrated on Bis-seq data from mouse
embryonic stem cells and neural progenitors. MethylSeekR represents a refined
and extended version of the inital approach that makes it more robust and
generally applicable and allows much simpler and interactive setting of
segmentation parameters. For details regarding the methodology, we refer the
reader to \cite{Burger2012}. If you use MethylSeekR in a publication, please
cite \cite{Burger2012}. It is important to note that MethylSeekR has been
designed for the segmentation of Bis-seq datasets with a minimal genome-wide
coverage of 10X and we do NOT recommend its use for datasets with lower
coverage.

\section{Prerequisites}

Several functions of \textit{MethylSeekR} require the genome sequence or derived
information such as the chromsome lengths of the reference genome used. To
retrieve this information, \textit{MethylSeekR} makes use of the \textit{BSgenome} package
and the related genome data packages. \textit{BSgenome} can be installed from
Bioconductor (\url{http://www.bioconductor.org}) using the following commands

<<install, eval=FALSE>>=
source("http://www.bioconductor.org/biocLite.R")
biocLite("BSgenome")
@

After the installation, the available genomes can be displayed with 

<<genomes, eval=FALSE>>=
library(BSgenome)
available.genomes()
@

For the example data that comes along with the package, we need the hg18
assembly of the human genome \textit{BSgenome.Hsapiens.UCSC.hg18}. This
genome, and analogously any of the other genomes, can be installed as follows

<<install, eval=FALSE>>=
source("http://www.bioconductor.org/biocLite.R")
biocLite("BSgenome.Hsapiens.UCSC.hg18")
@


\section{Data import and SNP filtering}

We start by loading the \textit{MethylSeekR} package

<<eval=TRUE, results=hide>>=
library(MethylSeekR)
@

One step of the \textit{MethylSeekR} workflow depends on random permutations
of the data (see below), which may lead to slightly different results each
time the calculations are performed. It is thus recommended to set the random
number generator seed at the beginning of the analysis to ensure exact
reproducibility of the results. In R, this can be done e.g. as follows

<<eval=TRUE, results=hide>>=
set.seed(123)
@

In a first step, the Bis-seq data needs to be loaded into
R. The data should be in a tab-delimited file with four columns,
\textit{chromosome}, \textit{position}, \textit{T} and \textit{M}, where
\textit{position} is the coordinate of the cytosine in the CpG on the plus
strand (we assume that the counts have been pooled from the two strands),
\textit{T} is the total number of reads overlapping the cytosine and
\textit{M} the total number of reads without cytosine to thymine conversion
(reflecting methylated cytosines). An example file, containing the
methylation information for $200,000$ CpGs from chromosome 22 of human IMR90
cells \cite{Lister:2009fk}, is part of the package and its path can be
retrieved with the following command

<<eval=FALSE>>=
system.file("extdata", "Lister2009_imr90_hg18_chr22.tab",
package="MethylSeekR")
@

The data can be loaded into R using the \texttt{readMethylome} function.
This function takes two arguments, the name of the file containing the
methylation data and a named vector containing the chromosome lengths of the
reference genome. This vector can be easily created using the
\textit{BSgenome} package of the reference genome. For the example data used
here, we work with the human hg18 assembly.

<<eval=TRUE>>=
library("BSgenome.Hsapiens.UCSC.hg18")
sLengths=seqlengths(Hsapiens)
head(sLengths)
@ 

\texttt{readMethylome} will directly create a GRanges object containing the
methylation data. GRanges objects (as defined in the \textit{GenomicRanges}
package) represent general purpose containers for storing genomic intervals
and allow for very efficient overlap/intersection operations. To use
\textit{MethylSeekR}, it is not necessary to understand how GRanges objects
work, and we refer the interested reader to
\texttt{help(package="GenomicRanges")}.



To read in the methylation data of our example data, we can use the following
commands.

<<eval=TRUE>>=
methFname <- system.file("extdata", 
"Lister2009_imr90_hg18_chr22.tab", package="MethylSeekR")
meth.gr <- readMethylome(FileName=methFname, seqLengths=sLengths)
head(meth.gr)
@ 


Each element of the \texttt{meth.gr} object stands for one CpG and the
corresponding metadata (columns on the right) contains its counts $T$ and
$M$.


In cases where the genomic background of the sample differs from the
reference genome which the methylation data has been aligned against, CpGs
overlapping SNPs should be removed from the methylation table
\cite{Stadler:2011vn, Burger2012}. To this end, \texttt{MethylSeekR} provides
functions to both load a SNP table and remove the SNP-overlapping CpGs from
the methylation GRanges object (the following four code chunks can be
skipped if the genomic background of the sample is identical to the reference
genome).


Similary to the methylation data, the SNP table can be loaded using the
\texttt{readSNPTable} function. The SNP data should be in a tab-delimited
text file with two columns corresponding to the chromosome and position of
the SNPs. The path to an example SNP file with data downloaded from dbSNP
\cite{Sherry:2001fk} for hg18 (and prefiltered to keep the file size small)
can be retrieved as follows

<<eval=FALSE>>=
system.file("extdata", "SNVs_hg18_chr22.tab",
package="MethylSeekR")
@ 

To read in the SNPs from our example file, we can thus use the following
commands


<<eval=TRUE>>=
snpFname <- system.file("extdata", "SNVs_hg18_chr22.tab",
package="MethylSeekR")
snps.gr <- readSNPTable(FileName=snpFname, seqLengths=sLengths)
head(snps.gr)
@

Here, \texttt{seqLengths} is the same named vector with chromsome lengths as
needed for the \texttt{readMethylome} function. \texttt{readSNPTable}
directly returns a GRanges object containing the coordinates of the
SNPs. Using this object, the CpGs overlapping SNPs can now be removed from
the methylation object using the \texttt{removeSNPs} function.


<<>>=
meth.gr <- removeSNPs(meth.gr, snps.gr)
@


\section{Segmentation of partially methylated domains}


Some methylomes contain large regions of seemingly disordered methylation
which have been termed partially methylated domains (PMDs,
\cite{Lister:2009fk}). These regions need to be identified and masked prior
to the segmentation of regulatory regions. To decide whether a methylome
contains PMDs, we can first calculate the distribution of $\alpha$-values for
one selected chromosome. $\alpha$ characterizes the distribution of
methylation levels in sliding windows containing 100 consecutive CpGs along
the genome. $\alpha$-values smaller than 1 reflect a polarized distribution,
favoring low and high methylation (as in regulatory regions and background
methylation levels respectively), whereas $\alpha$-values equal to 1 or
larger indicate distributions that are rather uniform or polarized towards
intermediate methylation levels (as in PMDs). The distribution of
$\alpha$-values for one selected chromosome can be determined as follows,



<<fig=TRUE, width=5, height=5>>=
plotAlphaDistributionOneChr(m=meth.gr, chr.sel="chr22", 
num.cores=1)
@

\texttt{chr.sel} denotes the chromosome for which the statistic is
calculated. Generally, the $\alpha$ distribution of different chromosomes are
very similar, but we recommend using a small autosome to minimize the
computing time and to avoid sex-specific
biases. \texttt{plotAlphaDistributionOneChr} generates a figure showing the
inferred $\alpha$ distribution. This figure is by default printed to the
screen but can also be saved in a pdf file if a filename is provided via the
\texttt{pdfFilename} argument. \texttt{num.cores} is the number of cores that
are used for the calculation. By default, all functions of
\textit{MethylSeekR} perform their calculations on a single core. However,
almost all functions can be run in parallel (by setting \texttt{num.cores} to
a number larger than one, only availabe on unix and mac) and we recommend
the user to use multiple cores in order to speed up the calculations. To
determine the number of cores of the machine used, use the following commands

<<eval=FALSE>>=
library(parallel)
detectCores()
@

Generally, there is evidence for PMDs if the distribution of $\alpha$-values
is bimodal or long-tailed with a significant fraction of $\alpha$ values
larger or equal $1$. In the example here, the
distribution is clearly bimodal and we thus, in a next step, run a Hidden
Markov Model (HMM) to identify PMDs genome-wide (in cases where the $\alpha$
distribution is unimodal (for examples see \cite{Burger2012}), there is no
evidence for PMDs and the following three code chunks can be omitted).


<<fig=TRUE, width=5, height=5>>=
PMDsegments.gr <- segmentPMDs(m=meth.gr, chr.sel="chr22", 
seqLengths=sLengths, num.cores=1)
head(PMDsegments.gr)
@

Here, as above, \texttt{chr.sel} is the chromosome used to train the
HMM. \texttt{segmentPMDs} generates a GRanges object which partitions the
genome into PMDs and regions outside of PMDs (notPMD) as indicated in the
first column of the metadata (\texttt{type}). The second column
(\texttt{nCG}) of the metadata indicates the number of covered (by at least
one read) CpGs in each region. The function creates a figure (which is by
default printed to the screen or saved in a pdf file if a filename is
provided via the \texttt{pdfFilename} argument) which shows the same alpha
distribution as in the previous figure, but including the fitted Gaussian
emission distributions of the HMM in red and green. If the HMM fitting works
properly, the two Gaussians should correspond to the two peaks of the bimodal
distribution (or the main peak and the tail if the alpha distribution is
long-tailed), as illustrated for the example dataset. As a control, we may
want to recalculate the distribution of $\alpha$-values using only the
methylation values outside of the predicted PMDs.

<<fig=TRUE, width=5, height=5>>=
plotAlphaDistributionOneChr(m=subsetByOverlaps(meth.gr, 
PMDsegments.gr[values(PMDsegments.gr)$type=="notPMD"]), chr.sel="chr22", 
num.cores=1)
@ 

Clearly, we have managed to remove the second mode of the distribution. Such
a unimodal distribution with most $\alpha$-values below 1 is also what is
typically seen in methylomes without PMDs. Note that the distribution of
$\alpha$-values is not only influenced by the presence of PMDs, but also by
the variability in background methylation levels outside of regulatory
regions. In methylomes that do not contain PMDs, but show large variability,
a substantial fraction of $\alpha$-values (10-20\%) may be larger than
one. However, if there are no PMDs, the shape of the $\alpha$-distribution
should still be unimodal. It is thus rather the shape of the distribution
(bimodal versus unimodal) that indicates the presence or absence of PMDs and
not the fraction of $\alpha$-values larger 1. In any case, the resulting PMD
segmentation should be visually inspected to assess its validity. This can
easily be done for randomly chosen regions of the genome using the
\texttt{plotPMDSegmentation} function.

<<myfig1, fig=TRUE, width=15, height=10, include=FALSE, results=hide>>=
plotPMDSegmentation(m=meth.gr, segs=PMDsegments.gr)
@

\centerline{\includegraphics[angle=90, scale=1.8]{MethylSeekR-myfig1}}


The resulting figure is either printed to the screen (default) or saved in a
pdf file if a filename is provided via the \texttt{pdfFilename} argument. It
is also possible to plot multiple regions and save them in a multi-page pdf
file if both the argument \texttt{pdfFilename} and \texttt{numRegions} are
provided. The randomly chosen region that is displayed is broken up into 6
panels and in each panel, the raw (ie unsmoothed) methylation levels of all
CpGs with a minimal coverage of 5 reads are shown. PMDs are indicated as
green bars, extending over the entire PMD.


The PMD segmentation can be saved both as a GRanges object and as a
tab-delimited file.

<<eval=FALSE>>=
savePMDSegments(PMDs=PMDsegments.gr, 
GRangesFilename="PMDs.gr.rds", TableFilename="PMDs.tab")
@

\texttt{GRangesFilename} is the filename for the GRanges object and the
\texttt{TableFilename} the filename for the tab-delimited file (only of the
two filenames is required).



\section{Identification of UMRs and LMRs}


Once we have identified PMDs (if there are any), we can proceed to the
segmentation of regulatory regions. These come in two distinct groups,
unmethylated regions (UMRs) which correspond mostly to unmethylated CpG
islands (including promoters) and low-methylated regions (LMRs) which
correspond to distal regulatory regions \cite{Stadler:2011vn, Burger2012}. We
identify these regions by a fairly straightforward procedure. We first smooth
methylation levels over $3$ consecutive CpGs to reduce the sampling noise and
then identify hypo-methylated regions as regions of consecutive CpGs with
smoothed methylation levels below a fixed cut-off $m$, containing a minimal
number of CpGs $n$. The identified regions are then further classified into
UMRs and LMRs based on the number of CpGs they contain. The parameters $m$
and $n$ must be determined prior to segmentation, which can be done via false
discovery rate (FDR) considerations. This approach will naturally take into
account the variability of methylation levels in the methylome
studied. Briefly, for each set of parameters ($m$, $n$), we determine the
number of regions with methylation levels below $m$ and with a minimal number
of CpGs $n$ in both the original methylome, $n_o$, and a randomized
methylome, $n_r$. The FDR is then defined as the ratio
$\frac{n_r}{n_o}$. Given a user-defined cut-off on the FDR, we can then
determine reasonable sets of values for $m$ and $n$.


To calculate FDRs with \texttt{MethylSeekR}, we can use the function
\texttt{calculateFDRs}. Since the FDR calculation is based on the
randomization of methylation levels outside of CpG islands \cite{Burger2012},
we first need to create a GRanges object containing the CpG islands, which is
then passed on to \texttt{calculateFDRs}. CpG island annotation can for
example be retrieved from UCSC using the package \texttt{rtracklayer}

<<eval=TRUE>>=
library(rtracklayer)
session <- browserSession()
genome(session) <- "hg18"
query <- ucscTableQuery(session, "cpgIslandExt")
CpGislands.gr <- track(query)
genome(CpGislands.gr) <- NA
@ 

If other genome assemblies than hg18 are used, hg18 in the code above needs
to be replaced by the corresponding assembly.

Next, we extend the CpG islands to 5kb to make sure that all unmethylated
CpGs lying in CpG islands are excluded from the FDR calculation.

%results=hide
<<eval=TRUE>>=
CpGislands.gr <- 
suppressWarnings(resize(CpGislands.gr, 5000, fix="center"))
@ 

We can now calculate the FDRs

<<fig=TRUE, width=8, height=4, eval=TRUE>>=
stats <- calculateFDRs(m=meth.gr, CGIs=CpGislands.gr,
PMDs=PMDsegments.gr, num.cores=1)
stats
@

%\centerline{\includegraphics[scale=2]{MethylSeekR-myfig2}}

Since the FDR calculation also masks PMDs, the PMDs need to be passed to the
function as well. In the case of methylomes without PMDs, the \texttt{PMDs}
argument can be omitted. The function creates a figure (which is, again, by
default printed to the screen or saved in a pdf file if a filename is
provided via the \texttt{pdfFilename} argument) which illustrates the
relationship between FDR (cut at 20\% if larger than 20\%), $m$, $n$ and the
number of identified segments. Additionally, the function returns a list
containing a matrix with FDR values (in percent) and a matrix with the number
of inferred segments in the original methylome for each $m$ (rows) and $n$
(columns). Since the parameters $m$ and $n$ are partially redundant, we need
to set one parameter by hand. $m=0.5$ ($50\%$ methylation) appears to be a
reasonable choice for most methylomes (leading to high accuracy at a good
sensitivity when overlapping the identified regions with DNase hypersensitive
sites \cite{Stadler:2011vn, Burger2012}) and we thus set $m=0.5$ and
determine $n$ by choosing the smallest $n$ such that the FDR is below a given
cut-off (here $5\%$).


<<eval=TRUE>>=
FDR.cutoff <- 5 
m.sel <- 0.5 
n.sel=as.integer(names(stats$FDRs[as.character(m.sel), ]
[stats$FDRs[as.character(m.sel), ]<FDR.cutoff])[1])
n.sel
@

Once the parameters $m$ (\texttt{m.sel}) and $n$ (\texttt{n.sel}) have been
set, we can call \texttt{segmentUMRsLMRs} to identify UMRs and LMRs.

<<fig=TRUE, width=4, height=4, eval=TRUE>>=
UMRLMRsegments.gr <- segmentUMRsLMRs(m=meth.gr, meth.cutoff=m.sel,
nCpG.cutoff=n.sel, PMDs=PMDsegments.gr, 
num.cores=1, myGenomeSeq=Hsapiens, 
seqLengths=sLengths)
head(UMRLMRsegments.gr)
@ 


If the methylome under consideration contains no PMDs, the \texttt{PMDs}
argument can be omitted. The argument \texttt{myGenomeSeq} takes as input a
BSgenome object of the genome assembly used, here Hsapiens, as defined in the
package \texttt{BSgenome.Hsapiens.UCSC.hg18} (the genome object is directly
loaded with the package and corresponds to the species name in the package
name). The genome sequence is needed to retrieve the number of CpGs in the
genome per identified region, which is further used to classifiy the regions
into UMRs and LMRs. \texttt{segmentUMRsLMRs} returns a GRanges object
containing the identified regions. The metadata includes the number of
covered CpGs (by at least $5$ reads) per region ($nCG.segmentation$) , the
number of CpGs in the genome per region ($nCG$), the total number of reads
overlapping CpGs ($T$), the total number of tags overlapping CpGs without
conversion event ($M$), the mean methylation ($pmeth=\frac{M}{T}$), the
median methylation ($median.meth$, median over the methylation levels of each
single CpG) and $type$, which classifies the region into UMR or LMR. For the
calculation of $T$, $M$, $pmeth$ and $median.meth$, only CpG that are covered
by at least $5$ reads are used. \texttt{segmentUMRsLMRs} also creates a
figure (by default printed to the screen or saved in a pdf file if a filename
is provided via the \texttt{pdfFilename} argument) which shows the number of
CpGs per region versus its median methylation level. Typically, as in the
example here, this figure should show a clear separation into unmethylated,
CpG-rich regions (UMRs) versus low-methylated, CpG-poor regions (LMRs). The
dashed line is at 30 CpGs and represents the cut-off used for the
classification.



Analogously to the PMD segmentation, the result of this final segmentation
can be visualized for a randomly selected region.

<<myfig3, fig=TRUE, width=12, height=6, include=FALSE, eval=TRUE, results=hide>>=
plotFinalSegmentation(m=meth.gr, segs=UMRLMRsegments.gr,
PMDs=PMDsegments.gr,meth.cutoff=m.sel)
@ 

If the methylome under study does not contain any PMDs, the \texttt{PMDs}
argument can be omitted. The resulting figure is either printed to the screen
(default) or saved in a pdf file if a filename is provided via the
\texttt{pdfFilename} argument. It is also possible to plot multiple regions
and save them in a multi-page pdf file if both the argument
\texttt{pdfFilename} and \texttt{numRegions} are provided. The randomly
chosen region that is displayed is broken up into 3 pairs of panels, where in
each pair the same region is shown twice, once with raw methylation levels
(top) and once with methylation levels smoothed over 3 consecutive CpGs
(bottom). In both cases only CpGs with a coverage of at least $5$ reads are
shown. The raw data best illustrates the disordered nature of methylation
levels in PMDs, whereas the smoothed methylation levels more clearly show
UMRs and LMRs. In all figures, UMRs are shown as blue squares (placed at the
middle of the identified segment), LMRs as red triangles (placed at the
middle of the identified segment) and PMDs as green bars (extending over the
entire PMD). The cut-off on methylation to determine UMRs and LMRs is shown
as a grey dashed line. Note that UMRs and LMRs can partially overlap with
PMDs as only UMRs and LMRs that are fully contained in PMDs are filtered
out by the algorithm. 


\centerline{\includegraphics[angle=90, scale=1.8]{MethylSeekR-myfig3}}



Finally, the segmentation of UMRs and LMRs can be saved both as a GRanges object and a
tab-delimited file as follows,

<<eval=FALSE>>=
saveUMRLMRSegments(segs=UMRLMRsegments.gr, 
GRangesFilename="UMRsLMRs.gr.rds", TableFilename="UMRsLMRs.tab")
@

Here, \texttt{GRangesFilename} is the filename for the GRanges object and
the \texttt{TableFilename} the filename for the tab-delimited file (only one of the
two filenames is required).


\bibliography{refs}
\bibliographystyle{unsrt}
%\bibliographystyle{plain}

\end{document}
