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\begin{document}

\title{\texttt{htSeqTools}: quality control, visualization and processing high-throughput sequencing data}
\small
\author{Evarist Planet \footnote{Bioinformatics \& Biostatistics Unit, IRB Barcelona}, 
  Camille Stephan-Otto \footnotemark[1], Oscar Reina \footnotemark[1], \\
  Oscar Flores \footnote{IRB-BSC Joint Research Program on Computational Biology, IRB Barcelona},
  David Rossell \footnotemark[1]}
\normalsize
\date{}  %comment to include current date

\maketitle


\section{Introduction}
\label{sec:intro}

The \texttt{htSeqTools} package provides an easy-to-use toolset 
to efficiently perform a variety of tasks with high-throughput
sequencing data. 
Although relatively simple-minded, we found the tools to be
extremely helpful in quality control assessment,
routine pre-processing and analysis steps
and in producing useful visualizations.

Emphasis is placed on ChIP-Seq alike experiments,
but many functions are also useful for other kinds of sequencing experiments.

Many routines allow performing computations in parallel 
by specifying an argument \texttt{mc.cores}, which uses
package \texttt{multicore}.
As this package is not available in all platforms,
in this manual we do not use parallel computing.
Please see the help page for each function for more details.

We start by loading the package and a ChIP-Seq dataset
which we will use for illustration purposes.

\footnotesize
<<import1>>=
options(width=70)
library(htSeqTools)
data(htSample)
htSample
sapply(htSample,nrow)
@ 
\normalsize

\texttt{htSample} is a \texttt{RangedDataList} object storing the chromosome, start and end
positions for reads mapped to the first 500kb of the drosophila melanogaster chromosome 2L.
\texttt{htSample} contains 2 immuno-precipitated and 2 control input samples
obtained in two separate Illumina sequencing runs, which we named Batch1 and Batch2.
The standard Illumina pipeline was used for pre-processing the data.
Following the Bowtie defaults,
only uniquely mapping reads with at most 2 mismatches in the first 28 bases were kept.
We do not give any further details about the experiment, as the results
have not yet been published.

\section{Quality control}
\label{sec:quality_control}

\subsection{A PCA analogue for sequencing data}
\label{ssec:mds}

PCA is a commonly used technique to assess overall quality and identify problematic
samples in high-throughput experiments.
PCA requires to define a common set of entities (e.g. genes)
for all samples and obtain some numerical measurement for each entity
in each sample (e.g. gene expression).
Therefore, unfortunately PCA is not directly applicable to sequencing data.
One option is to pre-process the data so that PCA
can be applied, e.g. computing the number of reads falling in some
pre-defined genomic regions.
The inconvenient of this approach is its lack of generality, since
different kinds of sequencing data generally require different pre-processing.
For instance, while in RNA-Seq we can obtain a PCA based on RPKM expression
measures \citep{mortazavi:2008},
this same strategy is not adequate for ChIP-Seq data
where many reads may be mapped to promoter or inter-genic regions.

Instead, we propose 
comparing the read coverage across samples and
using Multi-Dimensional Scaling (MDS) to obtain a low-dimensional
visual representation.
Read coverage is a universal measure which can be computed
efficiently for any type of sequencing data.
We measure similarity between samples $i$ and $j$ with $\rho_{ij}$,
the Pearson correlation between their log-coverages,
and define their distance as $d_{ij}= 0.5 (1-\rho_{ij})$.
We compute correlations in the log-scale to take into
account that the coverage distribution is typically highly asymmetric.
MDS is then used to plot the samples in a low-dimensional space,
in a way such that the Euclidean distance between two points is closest
to the Pearson distances.
Our approach is implemented in a \texttt{cmds} method for \texttt{RangedDataList} objects.
We illustrate its use by obtaining a two-dimensional MDS
for our sample data.

\footnotesize

<<getmds>>=
cmds1 <- cmds(htSample,k=2)
cmds1
@ 

\normalsize

The R$^2$ coefficient between the original distances and their approximation in the
plot 
can be seen as an analogue to the percentage of explained variability in a PCA analysis.
For our sample data R$^2$=1 (up to rounding), 
which indicates a perfect fit and that therefore a 3-dimensional plot is not necessary.

\footnotesize

<<label=figmds>>=
plot(cmds1)
@ 

\normalsize

Figure \ref{fig:mds} shows the resulting plot.
The IP samples from both runs group nicely, indicating that they
have similar coverage profiles. The control samples also group
reasonably well, although they present more differences than the IP samples.
This is to be expected, since the IP samples focus on a relatively small genomic regions.
The MDS plot also reveals a minor batch effect, as samples from the same batch appear slightly
closer in the map.

\setkeys{Gin}{width=0.7\textwidth} 
\begin{figure}
\begin{center}
<<label=figmds,fig=TRUE,echo=FALSE>>=
<<figmds>>
@
\end{center}
\caption{2-dimensional MDS plot. Samples with similar coverage appear close-by}
\label{fig:mds}
\end{figure}

\subsection{Exploring coverage uniformity}
\label{ssec:coverunif}

In some next-generation sequencing experiments we expect some samples to exhibit
large accumulations of reads in certain genomic regions,
whereas other samples should present a more uniform coverage
along the genome.
For instance, in ChIP-seq one should observe higher peaks for immuno-precipitated (IP) samples 
than in the controls.
That is, IP samples should present coverage rich and coverage poor regions,
whereas differences in coverage in the controls should be smaller.

In these cases we propose to measure the unevennes in the coverage using either the
coverage standard deviation or Gini's coefficient \citep{gini:1912},
which is a classical econometrics measure to assess unevennes of wealth distribution.
Comparing these statistical dispersion measures between samples can reveal
samples with innefficient immuno-precipitation (e.g. due to an inadequate antibody).
Both measures can be easily obtained
 with the functions \texttt{ssdCoverage} and \texttt{giniCoverage}.
Simple algebra shows that the expected value of the coverage standard deviation is
proportional to $\sqrt{n}$, where $n$ is the number of reads.
Therefore \texttt{ssdCoverage} reports $\mbox{SD}_n=\mbox{SD}/\sqrt{n}$
as a measure that can be compared across samples with different number of reads.
Similarly, simulations show that the expected Gini also depends on $n$.
Since no closed-form expression is available,
we estimate its expected value by generating $n$ reads uniformly distributed along the genome
and computing the Gini coefficient.
The adjusted Gini ($G_n$) is the difference between the observed Gini ($G$) minus 
its estimated expected value $\hat{\mbox{E}}(G|n)$.


\footnotesize

<<qcontrol1>>=
ssdCoverage(htSample)
giniCoverage(htSample,mc.cores=1)
@ 

\normalsize

The coverage exhibits higher  dispersion in the IP samples
than in the controls, which indicates there were no substantial problems
in the immuno-precipitation.
The function \texttt{giniCoverage} allows to graphically assess
the non-uniformity in the coverage distribution 
by plotting the probability and cumulative probability function.
The top panels in Figure \ref{fig:gini} show the log probability mass function
of the coverage, and the bottom panels show the Lorenz curve
(\cite{gastwirth:1972}, see \texttt{Lc} from package \texttt{ineq} for details).
We observe a more pronounced non-uniformity in the IP sample.

\footnotesize

<<label=figgini1,include=FALSE,results=hide>>=
giniCoverage(htSample[['ctrlBatch2']],mc.cores=1,mk.plot=TRUE)
@

<<label=figgini2,include=FALSE,results=hide>>=
giniCoverage(htSample[['ipBatch2']],mc.cores=1,mk.plot=TRUE)
@

\normalsize

\setkeys{Gin}{width=0.5\textwidth} 
\begin{figure}
\begin{center}
\begin{tabular}{cc}
<<label=figgini1,fig=TRUE,echo=FALSE,results=hide>>=
<<figgini1>>
@ &
<<label=figgini2,fig=TRUE,echo=FALSE,results=hide>>=
<<figgini2>>
@
\end{tabular}
\end{center}
\caption{Lorenz curves to assess coverage uniformity. Left: control; Right: immuno-precipitated sample}
\label{fig:gini}
\end{figure}

\subsection{Detecting over-amplification artifacts}
\label{ssec:overamp}

High-throughput sequencing requires a PCR amplification step to enrich for adapter-ligated
fragments. This step can induce biases as some DNA regions amplify more efficiently than
others (e.g. depending on GC content).
These PCR artifacts, caused by over-amplification or primer dimers,
affect the accuracy of the coverage and can create biases in the downstream analyses.
The function \texttt{filterDupReads} aims to automatically detect and remove
these artifacts.
The basic rationale is that, by counting the number of times that each read is repeated,
we can detect the reads repeating an unusually large number of times.
The argument \texttt{maxRepeats} can be used to eliminate all reads appearing more
than this user-specified threshold.
However, notice that ideally this threshold 
should be determined for each sample separately,
as the expected number of naturally occurring repeats depends on the sequencing depth,
and may also depend on the characteristics of each sample.
For instance, sequences from
IP samples focus on a relatively small 
genomic region while those from controls are distributed along most of the genome,
and therefore we expect a higher number of repeats in IP samples.
When specifying the argument \texttt{fdrOverAmp},
\texttt{filterDuplReads} determines the threshold in a data-adaptive manner.

Although this filtering can be performed with a single call to \texttt{filterDuplReads},
we now illustrate its inner workings in a step-by-step fashion. 
We add 200 repeats of an artificial sequence to sample \texttt{"ctrlBatch1"},
and count the number of times that each sequence appears with 
the function \texttt{tabDuplReads}.

\footnotesize

<<qcontrol2>>=
contamSample <- RangedData(IRanges(rep(1,200),rep(36,200)),space=rep('chr2L',200),strand='+')
contamSample <- rbind(htSample[['ctrlBatch1']],contamSample)
nrepeats <- tabDuplReads(contamSample)
nrepeats
@ 

\normalsize

There are 11812 sequences appearing only once, 10112 appearing twice etc.
The function \texttt{fdrEnrichedCounts} (called by \texttt{filterDuplReads})
determines the over-amplification threshold in a data-adaptive manner.
Basically, it assumes that only large number of repeats are artifacts
and models the reads with few repeats with a truncated negative binomial mixture
(fit via Maximum Likelihood),
which we observed to fit experimental data reasonably well.
The number of components to be used is chosen in parameter
\texttt{components}.
If this parameter has value 0 the optimal number of components is
selected using the Bayesian information criterion (BIC).
Here we used one component for computational speed.
An empirical Bayes approach similar to that in \cite{efron:2001}
is then used to estimate the FDR
associated with a given cutoff
(see \texttt{help(fdrEnrichedCounts)} for details).

\footnotesize

<<qcontrol3>>=
q <- which(cumsum(nrepeats/sum(nrepeats))>.999)[1]
q
fdrest <- fdrEnrichedCounts(nrepeats, use=1:q, components=1)
numRepeArtif <- rownames(fdrest[fdrest$fdrEnriched<0.01,])[1]
numRepeArtif
@ 

\normalsize

Here we assumed that less than 1/1000 reads are artifacts
and fit a negative binomial truncated at
$\left[ 1,14 \right]$.
Notice that, although here we used \texttt{fdrEnrichedCounts} to detect over-amplification,
it can also be used in any other setup when one whishes to detect large counts.
In Figure \ref{fig:filterDuplReads} we produce a plot showing the estimated FDR for a series of cutoffs.
The argument \texttt{fdrOverAmp} to \texttt{filterDuplReads}
indicates the FDR cutoff to determine over-amplification.
We also show the distribution of the observed number of repeats
(blue)
and its truncated negative binomial approximation in $\left[ 1,14 \right]$ (red).
Notice that any sequence repeating over 25 times
(including our artificial sequence repeating 200 times)
is regarded
as an artifact.

\footnotesize

<<label=figrepeats1,include=FALSE>>=
plot(fdrest$fdrEnriched,type='l',ylab='',xlab='Number of repeats (r)')
lines(fdrest$pdfOverall,col=4)
lines(fdrest$pdfH0,col=2,lty=2)
legend('topright',c('FDR','P(r | no artifact)','P(r)'),lty=c(1,2,1),col=c(1,2,4))
@ 

\normalsize

\setkeys{Gin}{width=0.5\textwidth} 
\begin{figure}
\begin{center}
<<label=figrepeats1,fig=TRUE,echo=FALSE>>=
<<figrepeats1>>
@ 
\end{center}
\caption{Black line: 
  estimated FDR for each number of repeats cutoff.
Red line: distribution of the number of repeats
as estimated by a truncated negative binomial with 2 components
(representing not over-amplified reads).
Blue line: distribution of the number of repeats in the observed data.}
\label{fig:filterDuplReads}
\end{figure}


\section{Data pre-processing}
\label{sec:preprocess}

We discuss several tools which can be useful for ChIP-seq data preprocessing.
In these studies there typically is a strand-specific bias:
reads coming from the + strand pile up to the left of reads from the - strand.
Removing this bias is important, as it provides a highly increased accuraccy
for peak detection.
\texttt{alignPeaks} implements a procedure to correct this bias,
which is fairly similar to the MACS procedure \citep{zhang:2008}.
A nice alternative is provided in function \texttt{estimate.mean.fraglen}
from package \texttt{chipseq}.
To illustrate the need for the adjustment
we plot the coverage in a certain genomic region before the adjustment
(displayed in Figure \ref{fig:preprocess1}, left panel).

\footnotesize

<<label=figpreprocess1,include=FALSE>>=
covbefore <- coverage(htSample[['ipBatch2']])
covbefore <- seqselect(covbefore[['chr2L']],295108,297413)
plot(as.integer(covbefore),type='l',ylab='Coverage')
@

\normalsize

Now we perform the adjustment with \texttt{alignPeaks} and plot the resulting
coverage as the solid black line in Figure \ref{fig:preprocess1} (right panel).
In blue and red color we display the coverage computed separately from
reads on the + and - strands, respectively.
The blue and red lines present a similar profile, but they are shifted.
Exploring other peaks reveals similar patterns.
Removing this strand specific bias results in sharper peaks and prevents detecting
two separate peaks when there should actually be one,
as illustrated by the left-most peak in Figure \ref{fig:preprocess1}.

\footnotesize

<<preprocess1>>=
ip2Aligned <- alignPeaks(htSample[['ipBatch2']],strand='strand', npeaks=100)
covafter <- coverage(ip2Aligned)
covafter <- seqselect(covafter[['chr2L']],295108,297413)
covplus <- coverage(htSample[['ipBatch2']][htSample[['ipBatch2']][['strand']]=='+',])
covplus <- seqselect(covplus[['chr2L']],295108,297413)
covminus <- coverage(htSample[['ipBatch2']][htSample[['ipBatch2']][['strand']]=='-',])
covminus <- seqselect(covminus[['chr2L']],295108,297413)
@

<<label=figpreprocess2,include=FALSE>>=
plot(as.integer(covafter),type='l',ylab='Coverage')
lines(as.integer(covplus),col='blue',lty=2)
lines(as.integer(covminus),col='red',lty=2)
@

\normalsize

\setkeys{Gin}{width=0.5\textwidth} 
\begin{figure}
\begin{center}
\begin{tabular}{cc}
<<label=figpreprocess1,fig=TRUE,echo=FALSE>>=
<<figpreprocess1>>
@ &
<<label=figpreprocess2,fig=TRUE,echo=FALSE>>=
<<figpreprocess2>>
@ 
\end{tabular}
\end{center}
\caption{Coverage for gene p38b. Left: Before adjustment; Right: After adjustment.
Blue line: + strand; Red line: - strand; 
Black line: global estimate after peak alignment by \texttt{alignPeaks}.}
\label{fig:preprocess1}
\end{figure}

In ChIP-seq experiments, it is sometimes convenient to extend the reads to take into
account that we only sequenced the first few bases (typically 40-100 bp)
from a larger DNA fragment (typically around 300bp).
In practice, this achieves some smoothing of the read coverage.
\texttt{extendRanges} extends the reads up to a user-specified length.


\section{Basic data analysis}
\label{sec:analysis}

Finding genomic regions with large accumulation of reads is an important task
in many sequencing experiments, including ChIP-Seq and RNA-Seq.
\texttt{islandCounts} performs a
simple analysis using tools provided in the \texttt{IRanges} package.
We search for genomic regions with an overall coverage $\geq 10$ (i.e. across all samples),
and obtain the number of reads in each sample overlapping with these regions.

\footnotesize

<<islandCounts>>=
ip <- rbind(htSample[[2]],htSample[[4]])
ctrl <- rbind(htSample[[1]],htSample[[3]])
pool <- RangedDataList(ip=ip, ctrl=ctrl)
counts <- islandCounts(pool,minReads=10)
head(counts)
@ 

\normalsize

There are a number of analysis strategies to compare these counts between groups.
For instance for short RNA sequencing data we could compare expression levels
across groups using the tools in package \texttt{DEseq}.
Here we show a simple analysis based on likelihood-ratio tests
with the function \texttt{enrichedRegions}.

\footnotesize

<<enrichedRegions>>=
mappedreads <- c(ip=nrow(ip),ctrl=nrow(ctrl))
mappedreads
regions <- enrichedRegions(sample1=ip,sample2=ctrl,minReads=10,mappedreads=mappedreads,p.adjust.method='BY',pvalFilter=.05,twoTailed=FALSE)
head(regions)
nrow(regions)
@ 

\normalsize

The argument \texttt{twoTailed=FALSE} indicates that only regions 
with a significantly higher number of reads in \texttt{sample1} than in \texttt{sample2} are reported.
Regions with overall coverage $\geq$10 
are selected, and a likelihood-ratio test is used to compare the proportion of reads
in \texttt{sample1} falling in a given region with the proportion in \texttt{sample2}.
When setting \texttt{exact} to \texttt{TRUE}, a permutation-based Chi-square test is used
whenever the expected counts in any group is below 5.
Here we reported only regions with Benjamini-Yekutielli adjusted p-values below 0.05.

\texttt{enrichedRegions} can also be used with no control sample,
in which case it looks for islands with a significant accumulation of reads
with an exact Binomial test.
The null hypothesis assumes that a read is equally likely to come
from any of the selected regions.

A related function is \texttt{enrichedPeaks},
which can be used to find peaks within the enriched regions.
Peaks are defined as enriched regions where the difference in coverage 
between \texttt{sample1} and \texttt{sample2} is above a user-specified threshold.
In this example we use \texttt{minHeight=100}.

\footnotesize

<<enrichedPeaks>>=
peaks <- enrichedPeaks(regions, sample1=ip, sample2=ctrl, minHeight=100)
peaks
@

\normalsize

It is possible to merge nearby regions, e.g. say no more than 300bp apart, into a single
region with the function \texttt{mergeRegions}.
\texttt{mergeRegions} allows to combine a numerical score across regions with any user-defined
function, e.g. the mean or median.
In the following example we merge regions less than 300bp apart and compute their median
\texttt{'height'}.

\footnotesize

<<mergeRegions>>=
mergeRegions(peaks, maxDist=300, score='height', aggregateFUN='median')
@

\normalsize

A common task is to 
identify genomic features close to the identified regions/peaks,
e.g. finding the closest gene. This can be performed with the function \texttt{annotatePeakInBatch}
from package \texttt{ChIPpeakAnno}, for instance.
Sometimes it is of interest to compare the list of genes which had a nearby peak with
the genes found in another experiment.
The function \texttt{listOverlap} quantifies the overlap and tests for its statistical significance.

Another analysis which may be of interest is locating hot chromosomal regions,
i.e., regions in the chromosome with a large number of peaks.
The function \texttt{enrichedChrRegions} can be used for this purpose.
First we need to define a named vector indicating the chromosome lengths.
Since our example data only contains reads aligning to the first 500,000 bases of 
chr2L, we manually its length.
More generally, one can determine the chromosome lengths from Bioconductor packages
(e.g. for drosophila melanogaster load \texttt{BSgenome.Dmelanogaster.UCSC.dm3} 
and evaluate \texttt{seqlengths(Dmelanogaster)}, and similarly for other organisms).
We run the function setting a window size of 9999 base pairs
and a 0.05 false discovery rate level. 
For computational speed here we only use \texttt{nSims=1} simulations to estimate the FDR.

\footnotesize

<<analysis2>>=
chrLength <- 500000
names(chrLength) <- c('chr2L')
chrregions <- enrichedChrRegions(peaks, chrLength=chrLength, windowSize=10^4-1, fdr=0.05, nSims=1)
chrregions[['chr2L']]
@ 

\normalsize

\texttt{enrichedChrRegions} returns a \texttt{RangedData} 
which for our sample data is empty, suggesting that there is no region with
an unusually high density of enriched regions.
Two related functions are \texttt{countHitsWindow} which computes the moving average of the
number of hits, and \texttt{plotChrRegions} to visualize the results.
For illustrative purposes we make up two regions with high density of enriched peaks
and plot them.

\footnotesize

<<label=figanalysis2,include=FALSE>>=
chrregions <- RangedData(ranges=IRanges(start=c(100000,200000),end=c(100100,210000)),space=c('chr2L','chr2R'))
plotChrRegions(regions=chrregions, chrLength=c(chr2L=500000,chr2R=500000))
@ 

\normalsize

\setkeys{Gin}{width=0.5\textwidth} 
\begin{figure}
\begin{center}
<<label=figanalysis2,fig=TRUE,echo=FALSE>>=
<<figanalysis2>>
@
\end{center}
\caption{Chromosomal regions with a large number of hits. Red marks indicate regions with high concentration of peaks.}
\label{fig:analysis2}
\end{figure}


\section{Plots}
\label{sec:plots}

\texttt{stdPeakLocation} and \texttt{PeakLocation} produce a plot useful for exploring overall patterns in ChIP-chip or ChIP-seq
experiments. Basically, it creates a density plot indicating where the peaks were located with respect to
the closest gene/genomic feature. 
\texttt{stdPeakLocation} indicates the location in standardized coordinates, 
i.e. relative to each gene/features's length,
which in some situations can help making genes/features comparable.
\texttt{PeakLocation} produces the same plot in base pairs (i.e. non-standardized coordinates),
which is useful as distances have a direct physical interpretation, 
e.g. to relate the peak location with nucleosome positioning.
As mentioned earlier, function \texttt{annotatePeakInBatch}
from package \texttt{ChIPpeakAnno} can be used to find the gene closest to each
region.
For illustrative purposes here we assign a fake gene to each region.
The fake genes start, end, strand and distance from the start to the region
by default are assumed to be stored in 
\texttt{'start\_position'}, \texttt{'end\_position'}, \texttt{'strand'}
and \texttt{'distance'}, respectively
(although different names can be given as arguments to \texttt{PeakLocation}
and \texttt{stdPeakLocation}). 

\footnotesize

<<label=figplots1,include=FALSE>>=
set.seed(1)
peaksanno <- peaks
peaksanno[['start_position']] <- start(peaksanno) + runif(nrow(peaksanno),-500,1000)
peaksanno[['end_position']] <- peaksanno[['start_position']] + 500
peaksanno[['distance']] <- peaksanno[['start_position']] - start(peaksanno)
peaksanno[['strand']] <- sample(c('+','-'),nrow(peaksanno),replace=TRUE)
PeakLocation(peaksanno,peakDistance=1000)
@ 

\normalsize

Figure \ref{fig:plots1} shows the resulting plot.
We see that most of the peaks occur right around the transcription start site.

\setkeys{Gin}{width=0.5\textwidth} 
\begin{figure}
\begin{center}
<<label=figplots1,fig=TRUE,echo=FALSE>>=
<<figplots1>>
@ 
\end{center}
\caption{Distribution of peaks around the closest gene}
\label{fig:plots1}
\end{figure}

Two related functions are \texttt{regionsCoverage} and \texttt{gridCoverage}, which evaluate the
coverage on user-specified genomic regions. 
We illustrate their use by obtaining the coverage for the regions
which we found to be enriched (as previously described).
\texttt{regionsCoverage} computes the coverage in the specified regions.
As each region has a different length it may be hard to compare coverages across regions,
e.g. to cluster regions with similar coverage profiles.
\texttt{gridCoverage} simplifies this task by evaluating the coverage on a regular grid
of 500 equally spaced points between the region start and end.
The result is stored in an object of class \texttt{gridCover}. The object contains the 
coverage, which can be accesed with the method \texttt{getViewsInfo}.


\footnotesize

<<regionscov>>=
cover <- coverage(ip)
rcov <- regionsCoverage(space(regions),start(regions),end(regions),cover=cover)
names(rcov)
rcov[['views']]
gridcov <- gridCoverage(rcov)
dim(getCover(gridcov))
getViewsInfo(gridcov)
@ 


\normalsize

We plot the coverage for the selected regions and see that they present different profiles Figure \ref{fig:plots2},
which suggests the use of some clustering technique to find subgroups of regions behaving similarly.

\footnotesize

<<label=figregCoverage,include=FALSE>>=
ylim <- c(0,max(getViewsInfo(gridcov)[['maxCov']]))
plot(gridcov, ylim=ylim,lwd=2)
for (i in 1:nrow(regions)) lines(getCover(gridcov)[i,], col='gray', lty=2)
@ 

\normalsize

\setkeys{Gin}{width=0.5\textwidth} 
\begin{figure}
\begin{center}
<<label=figregCoverage,fig=TRUE,echo=FALSE>>=
<<figregCoverage>>
@ 
\end{center}
\caption{Coverage for some selected regions}
\label{fig:plots2}
\end{figure}

\bibliographystyle{plainnat}
\bibliography{references} 

\end{document}
