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\newcommand{\groHMM}{\Rpackage{groHMM}}

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\begin{document}
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\title{\Rpackage{groHMM} Tutorial}
\author{Minho Chae\textsuperscript{1,2} \and Charles G. Danko\textsuperscript{3}
\and W. Lee Kraus\textsuperscript{1,2}\footnote{Correspondence: lee.kraus@utsouthwestern.edu}
\and \\\textsuperscript{1}Laboratory of Signaling and Gene Regulation \\ Cecil H. \& Ida Green Center for Reproductive Biology Science\\
\textsuperscript{2}Division of Basic Sciences, Department of Obstetrics and Gynecology
\\UT Southwestern Medical Center, Dallas, Texas, 75390-8511 \\
\\\textsuperscript{3} Baker Institute for Animal Health, College of Veterinary Medicine \\
Cornell University, Ithaca, NY 14853
}
\date{\today}

\maketitle

\tableofcontents

\section{Introduction}
\underline{G}lobal Nuclear \underline{R}un \underline{O}n and Sequencing
(GRO-seq) was developed for comprehensively map transcriptional activity in
cells \cite{Core2008,Hah2011}.  GRO-seq, which provides a genome wide `map'
of the position and orientation of all transcriptionally active RNA
polymerases, has become increasingly widely used in recent years because it
has numerous advantages compared to alternative methods of
transcriptome profiling, such as expression microarrays and RNA-seq.
Among these, GRO-seq provides information on instantaneous transactional
responses because it detects primary transcription, as opposed to mature,
processed mRNA.  In addition, because it is independent of RNA polyadenylation,
processing, and stability, GRO-seq provides extensive information on the
non-coding transcriptome, including primary miRNAs, lincRNAs, enhancer RNAs,
and potentially additional, yet undiscovered classes of transcription
occurring in cells \cite{Hah2011,Hah2013,Luo2014}.
Thus, GRO-seq data provides a complete and instantaneous picture of
transcription, and has extensive applications in deciphering the mechanisms
of transcriptional regulation.

We have recently developed several important analytical approaches which make
use of GRO-seq data to address new biological questions.
Our pipleline has been packaged and documented, resulting in
the \Rpackage{groHMM} package for Bioconductor.
Among the more advanced features, \Rpackage{groHMM} predicts the boundaries of
transcriptional activity across the genome \emph{de novo} using a two-state
hidden Markov model (HMM).
Our model essentially divides the genome into ``transcribed'' and
``non-transcribed'' regions in a strand specific manner \cite{Hah2011}.
We also use HMMs to identify the leading edge of Pol II at genes activated by a
stimulus in GRO-seq time course data.  This approach allows the genome-wide
interrogation of transcription rates in cells \cite{Danko2013}.

In addition to these advanced features, \Rpackage{groHMM} provides wrapper
functions for counting raw reads \cite{PagesGRanges}, generating wiggle
files for visualization \cite{Michael2009}, and creating metagene
(averaging) plots.  \Rpackage{groHMM} takes over all aspects of
analysis after reads have been aligned to a reference genome with
short-read alignment tools.  Although \Rpackage{groHMM} is tailored
towards GRO-seq data, the same functions and analytical methodologies
can, in principal, be applied to a wide variety of other short read data
sets since the package includes a number of easily usable and extensible
functions for general short read data analysis.
This guide focuses on the most common application of the package.


\section{Preparation}
The \Rpackage{groHMM} package is available in the Bioconductor and can be
downloaded as follows:
<<install groHMM, eval=FALSE>>=
source("http://bioconductor.org/biocLite.R")
biocLite("groHMM")
@

The following packages are not required to use \Rpackage{groHMM}, but they
are used to download annotations and evaluate transcripts, and should be
installed for this tutorial.
<<install packages, eval=FALSE>>=
biocLite("GenomicFeatures")
biocLite("org.Hs.eg.db")
biocLite("edgeR")
biocLite("TxDb.Hsapiens.UCSC.hg19.knownGene")
@

\section{\Rpackage{groHMM} Workflow}
\subsection{Read GRO-seq Data Files}
In this tutorial we will use example data from Hah et al. [2011] (GEO
accession GSE27463).   This experiment was designed to assess transcriptional
changes following treatment of MCF-7 cells with 17$\beta$ estradiol (E2).
The data include a time course of GRO-seq data following treatment with E2
(\emph{i.e.}, 0, 10, 40 and 160 min.).  Two biological replicates are
available for each time point.  Bed files were obtained from GEO and lifted
over to hg19 using the UCSC \Rpackage{liftOver} tool.
In order to make the package size more manageable, we have included
data from chromosome 7 only in 0 and 10 min. conditions.  
\Rpackage{groHMM} supports parallel processing and the number of cores to 
use can be set using \Rcode{mc.cores} option.

<<use groHMM, eval=TRUE>>=
library(groHMM)
options(mc.cores=getCores(4))
@

\Rpackage{groHMM} uses the \Rpackage{GRanges} class from the
\Rpackage{GenomicRanges} packages to represent a collection of genomic
features, allowing synergy with other useful packages in Bioconductor.
Most of the functions in the package take at least two arguments: `reads'
and `features'.  Reads represent the genomic coordinates of a
set of mapped short reads.   Features represent a set of genomic coordinates
of interest such as genes, exons, or transcripts.

The example data included in this package can be loaded into \software{R}
using the following commands.

<<load data, eval=TRUE>>=
S0mR1 <- as(readGAlignments(system.file("extdata", "S0mR1.bam",
        package="groHMM")), "GRanges")
S0mR2 <- as(readGAlignments(system.file("extdata", "S0mR1.bam",
        package="groHMM")), "GRanges") # Use R1 as R2
S40mR1 <- as(readGAlignments(system.file("extdata", "S40mR1.bam",
        package="groHMM")), "GRanges")
S40mR2 <- as(readGAlignments(system.file("extdata", "S40mR1.bam",
        package="groHMM")), "GRanges") # Use R1 as R2
@


\subsection{Create a Wiggle File}
Wiggle files are created for each strand after replicates are combined in
order to visualize GRO-seq data in the UCSC genome browser.
Wiggle files can be also normalized by the sequencing depth, \emph{i.e.},
average number of reads in the dataset. \Rcode{writeWiggle} function is a
wrapper of \Rcode{export} in \Rpackage{rtracklayer} for generation of
wiggle/bigWig type of files.

<<combine replicates, eval=TRUE>>=
# Combine replicates
S0m <- c(S0mR1, S0mR2)
S40m <- c(S40mR1, S40mR2)
@

<<write wiggle files, eval=FALSE>>=
writeWiggle(reads=S0m, file="S0m_Plus.wig", fileType="wig", strand="+",
        reverse=FALSE)
writeWiggle(reads=S0m, file="S0m_Minus.wig", fileType="wig", strand="-",
        reverse=TRUE)

# For BigWig file:
# library(BSgenome.Hsapiens.UCSC.hg19)
# si <- seqinfo(BSgenome.Hsapiens.UCSC.hg19)
# writeWiggle(reads=S0m, file="S0m_Plus.wig", fileType="BigWig", strand="+",#
#               reverse=FALSE, seqinfo=si)

# Normalized wiggle files
expCounts <- mean(c(NROW(S0m), NROW(S40m)))
writeWiggle(reads=S0m, file="S0m_Plus_Norm.wig", fileType="wig", strand="+",
           normCounts=expCounts/NROW(S0m), reverse=FALSE)
@

The resulting wiggle files can be uploaded as `custom tracks' in the UCSC
genome browser, or your visualization software of choice.



\subsection{Transcript Calling}

\begin{figure}[h]
    \centering
    \subfloat[GRO-seq with called transcripts]{\label{FigGROseq}
    \includegraphics[width=.55\textwidth]{GROseqData.png}}
    \qquad
    \subfloat[2-state HMM]{\label{FigHMM}
    \includegraphics[width=.35\textwidth]{GROseqHMM.png}}
    \caption{HMM calling of GRO-seq data}
\end{figure}

In \Rpackage{groHMM}, transcribed regions are detected \emph{de novo} using
a two-state hidden Markov model (HMM).
The model takes GRO-seq read counts as input across the
genome and divides the genome into ``transcribed'' and ``non-transcribed''
state as shown in Figure 1.  First, a single read set is generated by
combining all samples for each time point.  This combined approach improves
sensitivity for transcripts with low expression levels.
Combined reads are used to train the model parameters using the
Baum-Welch Expectation Maximization (EM) algorithm.  Each strand is modeled
separately dividing the genome into non-overlapping 50 bp windows classified
as either state.


<<transcript calling, eval=TRUE, keep.source=TRUE, results=hide>>=
Sall <- sort(c(S0m, S40m))
# hmmResult <- detectTranscripts(Sall, LtProbB=-200, UTS=5,
#                   threshold=1)
# Load hmmResult from the saved previous run 
load(system.file("extdata", "Vignette.RData", package="groHMM"))
txHMM <- hmmResult$transcripts
@
<<called transcripts, eval=TRUE, keep.source=TRUE>>=
head(txHMM)
@

The \Rfunction{detectTranscripts} function also uses two hold-out parameters.
These parameters, specified by the arguments \Rfunarg{LtProbB} and
\Rfunarg{UTS}, represents the log-transformed transition probability of
switching from transcribed state to non-transcribed state and variance of the
emission probability for reads in the non-transcribed state, respectively.
Holdout parameters are used to optimize the performance of HMM predictions
on known genes.


ubsection{Evaluation of Transcript Calling}
Predicted transcripts are evaluated by comparison to known annotations, making
the assumption that GRO-seq transcripts should largely be in agreement with
available annotations.  Two types of error may occur, as described
below.  The HMM parameters are evaluated by the sum of the error rates.
The procedure involves collecting a set of high-confidence reference
transcripts.  An annotation dataset can be constructed by downloading
from the UCSC database or alternatively, pre-made TranscriptDb objects can be
used if they are available in the Bioconductor.  We will use the UCSC knownGene
track and retrieve transcript annotations with
\Rpackage{GenomicFeatures} \cite{CarsonGFeatures} package.

<<use ucsc genes, eval=TRUE>>=
library(TxDb.Hsapiens.UCSC.hg19.knownGene)
kgdb <- TxDb.Hsapiens.UCSC.hg19.knownGene

library(GenomicFeatures)
# For refseq annotations:
# rgdb <- makeTranscriptDbFromUCSC(genome="hg19", tablename="refGene")
# saveDb(hg19RGdb, file="hg19RefGene.sqlite")
# rgdb <- loadDb("hg19RefGene.sqlite")
kgChr7 <- transcripts(kgdb, vals=list(tx_chrom = "chr7"),
                      columns=c("gene_id", "tx_id", "tx_name"))
seqlevels(kgChr7) <- seqlevelsInUse(kgChr7)
@

Because annotations do not provide precise cell type-specific expression
information, overlapping transcripts must be merged into a single set,
in which each annotation represents the 5$'$- and 3$'$-most boundaries of
genes.  Different isoforms of each gene are collapsed into one using the
ENTREZID.  These consensus annotations are used for the evaluation of HMM
calling.

<<make consensus annotations, eval=TRUE, keep.source=TRUE, results=hide>>=
# Collapse overlapping annotations
kgConsensus <- makeConsensusAnnotations(kgChr7, keytype="gene_id",
        mc.cores=getOption("mc.cores"))
library(org.Hs.eg.db)
map <- select(org.Hs.eg.db,
    keys=unlist(mcols(kgConsensus)$gene_id),
        columns=c("SYMBOL"), keytype=c("ENTREZID"))
mcols(kgConsensus)$symbol <- map$SYMBOL
mcols(kgConsensus)$type <- "gene"
@

There are two types of error that can be evaluated when comparing predicted
transcripts with annotations.  (1) The number of transcripts
overlapping two or more annotations, (\emph{i.e.}, these transcripts `merged annotations 
together') and (2) the number of annotations that overlap two or more
transcripts on the same strand (\emph{i.e.}, we say that these transcript
calls `dissociated a single annotation') must be determined.   The optimal tuning
parameters can be found by minimizing the sum of the two errors.
This approach allows identification of the model that best fits
the existing annotations and should more precisely predict transcripts
in non-annotated parts of the genome.
<<evaluation of transcript calling, eval=TRUE>>=
e <- evaluateHMMInAnnotations(txHMM, kgConsensus)
e$eval
@

\subsection{HMM Tuning}
Here we demonstrate how the optimal value for each tuning parameters can be
obtained by running HMM multiple times over a certain range of the parameters.
Among the nine test cases, both the sum of errors and error rate per called transcript 
show minimal at case \#7, as shown below.  The variation of errors should be
greater if whole chromosomes are used.
Also, a larger set of the parameters might be used in practice.  This tunning
step takes long time, so you may skip it for quick review of the package.

<<tuning HMM, eval=TRUE, results=hide>>=
tune <- data.frame(LtProbB=c(rep(-100,3), rep(-200,3), rep(-300,3)),
           UTS=rep(c(5,10,15), 3))

Fp <- windowAnalysis(Sall, strand="+", windowSize=50)
Fm <- windowAnalysis(Sall, strand="-", windowSize=50)

# evals <- mclapply(seq_len(9), function(x) {
#        hmm <- detectTranscripts(Fp=Fp, Fm=Fm, LtProbB=tune$LtProbB[x],
#                  UTS=tune$UTS[x])
#        e <- evaluateHMMInAnnotations(hmm$transcripts, kgConsensus)
#        e$eval
#        }, mc.cores=getOption("mc.cores"),  mc.silent=TRUE)
tune <- cbind(tune, do.call(rbind, evals))  # evals from the previous run
@

<<check tuning, eval=TRUE>>=
tune
which.min(tune$total)
which.min(tune$errorRate)
@

To robustly compare transcripts with known genes, densities representing the
frequency of transcripts can be calculated relative to their mapped gene
annotations.
Conceptually, the plot is divided into three distinct regions as shown in
Figure 2, including upstream of known gene annotations, inside genes,
and downstream of the annotated polyadenylation site.

Metrics to evaluate the degree of overlap with gene annotations focus on the
region upstream of gene annotations, which provides a measure of specificity,
and the region inside of genes, which provides a measure of sensitivity.
The region downstream of the polyadenylation site is known to contain residual
transcription \cite{Core2008} and consequently is not used to define quality.

The metrics are defined relative to an `ideal' transcript caller, which takes
the form of a step function (\emph{i.e.}, red line in the plot).
Our quality metrics represent the following
(see the plot below for a graphical representation):

\begin{enumerate}
  \item true transcript density (TTD)  =
    (gene annotation area under the curve) /(max area for matched transcripts),
  \item true non-transcript density  (TND) =  1 - TTD,
  \item false transcript density (FTD)  =
    (5$'$ overhang area under the curve) /(max area for matched transcripts),
  \item false non-transcript density (FND) =  1- FTD.
\end{enumerate}

Note that these quality metrics are conceptually very similar to true
positive, true negative, false positive and false negative, respectively.
During the comparison, only expressed annotations are used
and genes either too small or too large in size are excluded.
And also size of transcripts and annotations are
scaled to a smaller unit, \emph{i.e.}, 1K for a visual representation.
Here best overlapped annotations or transcripts
are used for either `merged annotations' or  `dissociated a single annotation'
type of error.  Final quality metrics are represented as an AUC number.

<<expressed genes, eval=TRUE>>=
getExpressedAnnotations <- function(features, reads) {
     fLimit <- limitToXkb(features)
     count <- countOverlaps(fLimit, reads)
     features <- features[count!=0,]
     return(features[(quantile(width(features), .05) < width(features))
    & (width(features) < quantile(width(features), .95)),])}
conExpressed <- getExpressedAnnotations(features=kgConsensus,reads=Sall)
@
<<fig2plot, eval=TRUE>>=
td <- getTxDensity(txHMM, conExpressed, mc.cores=getOption("mc.cores"))
u <- par("usr")
lines(c(u[1], 0, 0, 1000, 1000, u[2]), c(0,0,u[4]-.04,u[4]-.04,0,0),
      col="red")
legend("topright", lty=c(1,1), col=c(2,1), c("ideal", "groHMM"))
text(c(-500,500), c(.05,.5), c("FTD", "TTD"))
td
@


\begin{figure}
\begin{center}
<<label=fig2,fig=TRUE,echo=FALSE, results=hide>>=
<<fig2plot>>
@
\end{center}
\caption{Transcript Density Plot}
\label{Figure:2}
\end{figure}


\subsection{Repairing Transcript Calling with Annotations}
Prediction of transcripts by the HMM is not perfect.
Discrepancies with the annotations will occur even after the parameters
are optimally tuned.  Transcript calls can be `fixed' for known types
of error by (1) breaking transcripts that have merged annotations and
(2) combining transcripts that have dissociated a single annotation.  
The following method will generate a final set of transcripts for further analysis.

<<repairing called transcripts, eval=TRUE>>=
bPlus <- breakTranscriptsOnGenes(txHMM, kgConsensus, strand="+")
bMinus <- breakTranscriptsOnGenes(txHMM, kgConsensus, strand="-")
txBroken <- c(bPlus, bMinus)
txFinal <- combineTranscripts(txBroken, kgConsensus)
@

<<plotTxDensity_final, eval=FALSE, keep.source=TRUE, results=hide>>=
tdFinal <- getTxDensity(txFinal, conExpressed, mc.cores=getOption("mc.cores"))
@

\subsection{Differential Analysis with \Rpackage{edgeR}}
There are several packages in Bioconductor for differential expression
analysis such as \Rpackage{DESeq}, \Rpackage{baySeq}, \Rpackage{DEGSeq},
or \Rpackage{edgeR}.
\Rpackage{edgeR} \cite{Robinson2010} is used for this demonstration.
Differential expression analysis can be done using either by called
transcripts or known annotations depending on the nature of your research
question.
The procedures are quite similar except reads are counted using the
genomic locations of either called transcript or known annotations.   For
longer transcripts or annotated genes, we use a window of +1 to +13 kb from
the transcription start site (TSS), which was chosen in order to exclude reads
from RNA polymerases engaged at the promoter and to allow enough time for the
elongation of newly initiated Pol II (See Hah et al., 2011).
However, variations can be used, including the entire length of the called or
annotated transcripts.

<<DE for trascripts, eval=TRUE, echo=TRUE>>=
# For called transcripts
library(edgeR)
txLimit <- limitToXkb(txFinal)
ctS0mR1 <- countOverlaps(txLimit, S0mR1)
ctS0mR2 <- countOverlaps(txLimit, S0mR2)
ctS40mR1 <- countOverlaps(txLimit, S40mR1)
ctS40mR2 <- countOverlaps(txLimit, S40mR2)

pcounts <- as.matrix(data.frame(ctS0mR1, ctS0mR2, ctS40mR1, ctS40mR2))
group <- factor(c("S0m", "S0m", "S40m", "S40m"))
lib.size <- c(NROW(S0mR1), NROW(S0mR2), NROW(S40mR1), NROW(S40mR2))
d <- DGEList(counts=pcounts, lib.size=lib.size, group=group)
d <- estimateCommonDisp(d)
et <- exactTest(d)
de <- decideTestsDGE(et, p=0.001, adjust="fdr")
detags <- seq_len(NROW(d))[as.logical(de)]
# Number of transcripts regulated at 40m
cat("up: ",sum(de==1), " down: ", sum(de==-1), "\n")
@

<<fig3plot, eval=TRUE, echo=TRUE, include=FALSE>>=
plotSmear(et, de.tags=detags)
# 2 fold up or down
abline(h = c(-1,1), col="blue")
@

\begin{figure}
\begin{center}
<<label=fig3,fig=TRUE,echo=FALSE>>=
<<fig3plot>>
@
\end{center}
\caption{Transcript MAplot}
\label{Figure:three}
\end{figure}


<<DE for annotated genes, eval=TRUE, echo=TRUE, include=FALSE>>=
# For ucsc knownGenes
kgChr7 <- transcripts(kgdb, vals <- list(tx_chrom = "chr7"),
                      columns=c("gene_id", "tx_id", "tx_name"))
map <- select(org.Hs.eg.db,
        keys=unique(unlist(mcols(kgChr7)$gene_id)),
        columns=c("SYMBOL"), keytype=c("ENTREZID"))
missing <- elementLengths(mcols(kgChr7)[,"gene_id"]) == 0
kgChr7 <- kgChr7[!missing,]

inx <- match(unlist(mcols(kgChr7)$gene_id), map$ENTREZID)
mcols(kgChr7)$symbol <- map[inx,"SYMBOL"]

kgLimit <- limitToXkb(kgChr7)
ctS0mR1 <- countOverlaps(kgLimit, S0mR1)
ctS0mR2 <- countOverlaps(kgLimit, S0mR2)
ctS40mR1 <- countOverlaps(kgLimit, S40mR1)
ctS40mR2 <- countOverlaps(kgLimit, S40mR2)

counts <- as.matrix(data.frame(ctS0mR1, ctS0mR2, ctS40mR1, ctS40mR2))
group <- factor(c("S0m", "S0m", "S40m", "S40m"))
lib.size <- c(NROW(S0mR1), NROW(S0mR2), NROW(S40mR1), NROW(S40mR2))
d <- DGEList(counts=counts, lib.size=lib.size, group=group)

d <- estimateCommonDisp(d)
et <- exactTest(d)
de <- decideTestsDGE(et, p=0.001, adjust="fdr")
detags <- seq_len(NROW(d))[as.logical(de)]
symbols <- mcols(kgChr7)$symbol
# Number of unique genes regulated at 40m
cat("up: ", NROW(unique(symbols[de==1])), "\n")
cat("down: ", NROW(unique(symbols[de==-1])), "\n")
plotSmear(et, de.tags=detags)
abline(h = c(-1,1), col="blue")
@
\subsection{Metagene Analysis}
Metagenes show the distribution of reads near TSS of a set of regulated
genes (or some other alignable genomic features of interest).
It can be thought as a smoothed average of read density weighted
by expression over the set of TSS.  The \Rfunction{runMetaGene}
function has option for sampling.  If \Rcode{TRUE}, 10\% of the
transcription units are sampled with replacement 1,000 times and median value
at each position in the transcription unit over the samples is used for final
metagene result.  Using subsampling results in an image is more robust to
outliers, especially when the size of sample is relatively small.

<<metagene analysis, eval=TRUE, keep.source=TRUE, results=hide>>=
upGenes <- kgChr7[de==1,]
expReads <- mean(c(NROW(S0m), NROW(S40m)))
# Metagene around TSS
mg0m <- runMetaGene(features=upGenes, reads=S0m, size=100,
                       normCounts=expReads/NROW(S0m), sampling=FALSE,
               mc.cores=getOption("mc.cores"))
mg40m <- runMetaGene(features=upGenes, reads=S40m, size=100,
                        normCounts=expReads/NROW(S40m), sampling=FALSE,
                mc.cores=getOption("mc.cores"))
@

<<plot metagene, eval=TRUE, keep.source=TRUE, results=hide>>=
plotMetaGene <- function(POS=c(-10000:+9999), mg, MIN, MAX){
    plot(POS, mg$sense, col="red", type="h", xlim=c(-5000, 5000),
        ylim=c(floor(MIN),ceiling(MAX)), ylab="Read Density",
        xlab="Position (relative to TSS)")
     points(POS, (-1*rev(mg$antisense)), col="blue", type="h")
     abline(mean(mg$sense[5000:8000]), 0, lty="dotted")
}

MAX <- max(c(mg0m$sense, mg40m$sense))
MIN <- -1*max(c(mg0m$antisense, mg40m$antisense))
plotMetaGene(mg=mg0m, MIN=MIN, MAX=MAX)
plotMetaGene(mg=mg40m, MIN=MIN, MAX=MAX)
@

<<metagene figures, eval=TRUE, echo=FALSE, results=hide>>=
png(filename="metagene0m.png")
plotMetaGene(mg=mg0m, MIN=MIN, MAX=MAX)
dev.off()
png(filename="metagene40m.png", width=480, height=480)
plotMetaGene(mg=mg40m, MIN=MIN, MAX=MAX)
dev.off()
@

<<save data for vignette, eval=FALSE, echo=FALSE, results=hide>>=
save(hmmResult, evals, file="Vignette.RData")
@

\begin{figure}
    \begin{center}
    \subfloat[0 min.]{\label{fig:a}
    \includegraphics[width=.45\textwidth]{metagene0m.png}}
    \qquad
    \subfloat[40 min.]{\label{fig:b}
    \includegraphics[width=.45\textwidth]{metagene40m.png}}
    \caption{Metagenes}
    \end{center}
\end{figure}


\section{Session Info}
<<sessionInfo, results=tex, print=TRUE, eval=TRUE>>=
toLatex(sessionInfo())
@

<<eval=TRUE,echo=FALSE,results=hide>>=
setwd(savewd)
@
\bibliography{groHMM}

\end{document}