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%\VignetteIndexEntry{Using flagme -- Fragment-level analysis of GC-MS-based metabolomics data}

\title{\texttt{flagme}: Fragment-level analysis of \\ GC-MS-based 
  metabolomics data}
\author{Mark Robinson \\ \texttt{mrobinson@wehi.edu.au} \\ Riccardo  
  Romoli \\ \texttt{riccardo.romoli@unifi.it}} 
\maketitle


\section{Introduction}
\noindent This document gives a brief introduction to the
\texttt{flagme} package, which is designed to process, visualise and
statistically analyze sets of GC-MS samples. The ideas discussed here
were originally designed with GC-MS-based metabolomics in mind, but
indeed some of the methods and visualizations could be useful for
LC-MS data sets. The {\em fragment-level analysis} though, takes
advantage of the rich fragmentation patterns observed from electron
interaction (EI) ionization. 

There are many aspects of data processing for GC-MS data. Generally,
algorithms are run separately on each sample to detect features, or
{\em peaks} (e.g. AMDIS). Due to retention time shifts from
run-to-run, an alignment algorithm is employed to allow the matching
of the same feature across multiple samples.  Alternatively, if known
standards are introduced to the samples, retention {\em indices} can
be computed for each peak and used for alignment. After peaks are
matched across all samples, further processing steps are employed to
create a matrix of abundances, leading into detecting differences in
abundance. 

Many of these data processing steps are prone to errors and they often
tend to be black boxes. But, with effective exploratory data
analysis, many of the pitfalls can be avoided and any problems can be
fixed before proceeding to the downstream statistical analysis. The
package provides various visualizations to ensure the methods applied
are not black boxes. 

The \texttt{flagme} package gives a complete suite of methods to go
through all common stages of data processing. In addition, R is
especially well suited to the downstream data analysis tasks since it
is very rich in analysis tools and has excellent visualization
capabilities. In addition, it is freely available
(\texttt{www.r-project.org}), extensible and there is a growing
community of users and developers. For routine analyses, graphical
user interfaces could be designed. 


\section{Reading and visualizing GC-MS data}
To run these examples, you must have the \texttt{gcspikelite} package
installed.  This data package contains several GC-MS samples from a
spike-in experiment we designed to interrogate data processing
methods.  So, first, we load the packages: 

<<libraries, echo=FALSE>>=
require(gcspikelite)
library(flagme)
@

To load the data and corresponding peak detection results, we simply
create vectors of the file-names and create a \texttt{peakDataset}
object. Note that we can speed up the import time by setting the
retention time range to a subset of the elution, as below: 

<<rawdata>>=
gcmsPath <- paste(find.package("gcspikelite"), "data", sep="/")
data(targets)
cdfFiles <- paste(gcmsPath, targets$FileName, sep="/")
eluFiles <- gsub("CDF", "ELU", cdfFiles)
pd <- peaksDataset(cdfFiles, mz=seq(50,550), rtrange=c(7.5,8.5))
pd <- addAMDISPeaks(pd, eluFiles)
pd
@

Here, we have added peaks from AMDIS, a well known and mature
algorithm for deconvolution of GC-MS data. For GC-TOF-MS data, we have
implemented a parser for the \texttt{ChromaTOF} output (see the
analogous \texttt{addChromaTOFPeaks} function). The
\texttt{addXCMSPeaks} allows to use all the XCMS peak-picking
algorithms; using this approach it is also possible to elaborate the
raw data file from within R instead of using an external software.
%% Support for XMCS or MzMine may be added in the future. Ask the author
%% if another detection result format is desired as the parsers are
%% generally easy to design.   
In particular the function reads the raw data using XCMS, group each extracted ion
according to their retention time using CAMERA and attaches them to an
already created \texttt{peaksDataset} object:

<<addXCMS>>=
pd.2 <- peaksDataset(cdfFiles[1:3], mz=seq(50,550), rtrange=c(7.5,8.5))
pd.2 <- addXCMSPeaks(cdfFiles[1:3], pd.2, peakPicking=c('mF'),
                     snthresh=3, fwhm=4, step=1, steps=2, mzdiff=0.5)
pd.2
@ 

The possibility to work using computer cluster will be added in the future. 

Regardless of platform and peak detection algorithm, a useful
visualization of a set of samples is the set of total ion currents
(TIC), or extracted ion currents (XICs). To view TICs, you can call:

<<plotexample1, fig=TRUE, width=9, height=7>>=
plot(pd, rtrange=c(7.5,8.5), plotPeaks=TRUE, plotPeakLabels=TRUE,
     max.near=8, how.near=0.5, col=rep(c("blue","red","black"), each=3))
@

Note here the little {\em hashes} represent the detected peaks and are
labelled with an integer index. One of the main challenges is to match
these peak detections across several samples, given that the appear at
slightly different times in different runs.

For XICs, you need to give the indices (of \texttt{pd@mz}, the grid of
mass-to-charge values) that you want to plot through the
\texttt{mzind} argument.  This could be a single ion
(e.g. \texttt{mzind=24}) or could be a range of indices if multiple
ions are of interest (e.g. \texttt{mzind=c(24,25,98,99)}). 

There are several other features within the \texttt{plot} command on
\texttt{peaksDataset} objects that can be useful. See \texttt{?plot}
(and select the flagme version) for full details. 

Another useful visualization, at least for individual samples, is a 2D
heatmap of intensity. Such plots can be enlightening, especially when
peak detection results are overlaid. For example (with detected
fragment peaks from AMDIS shown in white): 

<<plotexample2,fig=TRUE,width=9,height=7>>=
r <- 1
plotImage(pd, run=r, rtrange=c(7.5,8.5), main="")
v <- which(pd@peaksdata[[r]] > 0, arr.ind=TRUE) # find detected peaks
abline(v=pd@peaksrt[[r]])
points(pd@peaksrt[[r]][v[,2]], pd@mz[v[,1]], pch=19, cex=.6, col="white")
@


\section{Pairwise alignment with dynamic programming algorithm}
One of the first challenges of GC-MS data is the matching of detected
peaks (i.e. metabolites) across several samples. Although gas
chromatography is quite robust, there can be some drift in the elution
time of the same analyte from run to run. We have devised a strategy,
based on dynamic programming, that takes into account both the
similarity in spectrum (at the apex of the called peak) and the
similarity in retention time, without requiring the identity of each
peak; this matching uses the data alone. If each sample gives a `peak
list' of the detected peaks (such as that from AMDIS that we have
attached to our \texttt{peaksDataset} object), the challenge is to
introduce gaps into these lists such that they are best aligned. From
this a matrix of retention times or a matrix of peak abundances can be
extracted for further statistical analysis, visualization and
interpretation. For this matching, we created a procedure analogous to
a multiple {\em sequence} alignment. 

To highlight the dynamic programming-based alignment strategy, we
first illustrate a pairwise alignment of two peak lists. This example
also illustrates the selection of parameters necessary for the
alignment. From the data read in previously, let us consider the
alignment of two samples, denoted \texttt{0709\_468} and
\texttt{0709\_474}. First, a similarity matrix for two samples is
calculated. This is calculated based on a scoring function and takes
into account the similarity in retention time and in the similarity of
the apex spectra, according to: 
\[
S_{ij}(D) = \frac{\sum_{k=1}^K x_{ik} y_{jk}}{\sqrt{ \sum_{k=1}^K
    x_{ik}^2 \cdot \sum_{k=1}^K y_{jk}^2 } } \cdot \exp \left( -
  \frac{1}{2} \frac{(t_i-t_j)^2}{D^2} \right) 
\]
\noindent where $i$ is the index of the peak in the first sample and
$j$ is the index of the peak in the second sample, $\mathbf{x}_i$ and
$\mathbf{y}_j$ are the spectra vectors and $t_i$ and $t_j$ are their
respective retention times. As you can see, there are two components
to the similarity: spectra similarity (left term) and similarity in
retention time (right term). Of course, other metrics for spectra
similarity are feasible. Ask the author if you want to see other
metrices implemented. We have some non-optimized code for a few
alternative metrics. 

The peak alignment algorithm, much like sequence alignments, requires
a \texttt{gap} parameter to be set, here a number between 0 and 1.  A
high gap penalty discourages gaps when matching the two lists of peaks
and a low gap penalty allows gaps at a very low {\em cost}.  We find
that a gap penalty in the middle range (0.4-0.6) works well for GC-MS
peak matching.  Another parameter, \texttt{D}, modulates the impact of
the difference in retention time penalty. A large value for
\texttt{D} essentially eliminates the effect. Generally, we set this
parameter to be a bit larger than the average width of a peak,
allowing a little flexibility for retention time shifts between
samples. Keep in mind the \texttt{D} parameter should be set on the
scale (i.e. seconds or minutes) of the \texttt{peaksrt} slot of the
\texttt{peaksDataset} object. The next example shows the effect of
the \texttt{gap} and \texttt{D} penalty on the matching of a small
ranges of peaks. 

<<pairwisealignexample, fig=TRUE, width=7, height=7>>=
Ds <- c(0.1, 10, 0.1, 0.1)
gaps <- c(0.5, 0.5, 0.1, 0.9)
par(mfrow=c(2,2), mai=c(0.8466,0.4806,0.4806,0.1486))
for(i in 1:4){
  pa <- peaksAlignment(pd@peaksdata[[1]], pd@peaksdata[[2]],
                       pd@peaksrt[[1]], pd@peaksrt[[2]], D=Ds[i],
                       gap=gaps[i]) 
  plot(pa, xlim=c(0, 17), ylim=c(0, 16), matchCol="yellow",
       main=paste("D=", Ds[i], " gap=", gaps[i], sep=""))
}
@

You might ask: is the flagme package useful without peak detection
results? Possibly. There have been some developments in alignment
(generally on LC-MS proteomics experiments) without peak/feature
detection, such as Prince et al. 2006, where a very similar dynamic
programming is used for a pairwise alignment. We have experimented
with alignments without using the peaks, but do not have any
convincing results. It does introduce a new set of challenges in terms
of highlighting differentially abundant metabolites. However, in the
\texttt{peaksAlignment} routine above (and those mentioned below), you
can set \texttt{usePeaks=FALSE} in order to do {\em scan}-based
alignments instead of {\em peak}-based alignments. In addition, the
\texttt{flagme} package may be useful simply for its bare-bones
dynamic programming algorithm. 


\subsection{Normalizing retention time score to drift estimates}
In what is mentioned above for pairwise alignments, we are penalizing
for differences in retention times that are non-zero. But, as you can
see from the TICs, some differences in retention time are
consistent. For example, all of the peaks from sample
\texttt{0709\_485} elute at later times than peaks from sample
\texttt{0709\_496}. We should be able to estimate this drift and
normalize the time penalty to that estimate, instead of penalizing to
zero. That is, we should replace $t_i-t_j$ with $t_i-t_j-\hat{d}_{ij}$
where $\hat{d}_{ij}$ is the expected drift between peak $i$ of the
first sample and peak $j$ of the second sample. 

More details coming soon.


\subsection{Imputing location of undetected peaks}
One goal of the alignment leading into downstream data analyses is the
generation of a table of abundances for each metabolite across all
samples. As you can see from the TICs above, there are some low
intensity peaks that fall below detection in some but not all
samples. Our view is that instead of inserting arbitrary low constants
(such as 0 or half the detection limit) or imputing the intensities
post-hoc or having missing data in the data matrices, it is best to
return to the area of the where the peak should be and give some kind
of abundance. The alignments themselves are rich in information with
respect to the location of undetected peaks. We feel this is a more
conservative and statistically valid approach than introducing
arbitrary values. 

More details coming soon.


\section{Multiple alignment of several experimental groups}
Next, we discuss the multiple alignment of peaks across many
samples. With replicates, we typically do an alignment within
replicates, then combine these together into a summarized form. This
cuts down on the computational cost. For example, consider 2 sets of
samples, each with 5 replicates. Aligning first within replicates
requires 10+10+1 total alignments whereas an all-pairwise alignment
requires 45 pairwise alignments. In addition, this allows some
flexibility in setting different gap and distance penalty parameters
for the {\em within} alignment and {\em between} alignment. An
example follows. 

<<multiplealignment>>=
print(targets)
ma <- multipleAlignment(pd, group=targets$Group, wn.gap=0.5, wn.D=.05,
                        bw.gap=.6, bw.D=0.05, usePeaks=TRUE,
                        filterMin=2, df=50, verbose=FALSE)
ma
@

If you set \texttt{verbose=TRUE}, many nitty-gritty details of the
alignment procedure are given.  Next, we can take the alignment
results and overlay it onto the TICs, allowing a visual inspection. 

<<multiplealignmentfig,fig=TRUE,width=9,height=7>>=
plot(pd, rtrange=c(7.5,8.5), runs=ma@betweenAlignment@runs,
     mind=ma@betweenAlignment@ind, plotPeaks=TRUE,
     plotPeakLabels=TRUE, max.near=8, how.near=.5,
     col=rep(c("blue","red","black"), each=3))
@


\section{Correlation Alignment algorithm}
Another approach, represented by the \texttt{correlationAlignment}
function, is to use a modified form of the Pearson correlation
algorithm. After the correlation between two samples is calculated, a
penalization coefficient, based on the retention time differences, is
applied to the result. It is also possible to set a retention time
range in which the penalization is 0, this because in gas
chromatography we can have a little deviation in the retention time of
the metabolite so, based on the experimental data, we can choose the
retention time window for the penalization coefficient being applied.

<<correlationAlignment>>=
mp <- correlationAlignment(object=pd.2, thr=0.85, D=20, penality=0.2,
                           normalize=TRUE, minFilter=1)
mp
@ 

\noindent where \texttt{thr} represent correlation threshold from 0
(min) to 1 (max); \texttt{D} represent the retention time window in
seconds; \texttt{penality} represent the penality inflicted to a match
between two peaks when the retention time difference exceed the
parameter \texttt{D}; \texttt{normalize} is about the peak
normalization-to-100 before the correlation is calculated;
\texttt{minFilter} give the opportunity to exclude from the resulting
correlation matrix each feature that in represented in our samples
less time than this value. The value of minFilter must be smaller than
the number of samples. 

The correlation-based peak alignment for multiple GC-MS
peak lists uses a center-star technique to the alignment of the
peaks. The combination of the \texttt{D} and \texttt{penality} parameters
allow the users to force the algorithm to match the peaks close to the
reference. The \texttt{thr} parameter control the matching factor.


\subsection{Gathering results}
The alignment results can be extracted from the \texttt{multipleAlignment} object as:
<<multiplealignmentres>>=
ma@betweenAlignment@runs
ma@betweenAlignment@ind
@

\noindent This table would suggest that matched peak \texttt{8} (see
numbers below the TICs in the figure above) corresponds to detected
peaks \texttt{9, 12, 11} in runs \texttt{4, 5, 6} and so on, same as
shown in the above plot. 

In addition, you can gather a list of all the merged peaks with the
\texttt{gatherInfo} function, giving elements for the retention times,
the detected fragment ions and their intensities.  The example below
also shows the how to construct a table of retention times of the
matched peaks (No attempt is made here to adjust retention times onto
a common scale.  Instead, the peaks are matched to each other on their
original scale).  For example: 

<<alignmentres>>=
outList <- gatherInfo(pd,ma)
outList[[8]]
rtmat <- matrix(unlist(lapply(outList,.subset,"rt"), use.names=FALSE),
                nr=length(outList), byrow=TRUE)
colnames(rtmat) <- names(outList[[1]]$rt); rownames(rtmat) <- 1:nrow(rtmat)
round(rtmat, 3)
@


\section{Future improvements and extension}
There are many procedures that we have implemented in our
investigation of GC-MS data, but have not made part of the package just
yet. Some of the most useful procedures will be released, such as: 

\begin{enumerate}

\item Parsers for other peak detection algorithms (e.g. XCMS, MzMine)
  and parsers for other alignment procedures (e.g. SpectConnect) and
  perhaps retention indices procedures. 

\item More convenient access to the alignment information and abundance table.

\item Statistical analysis of differential metabolite abundance.

\item Fragment-level analysis, an alternative method to summarize
  abundance across all detected fragments of a metabolite peak. 

\end{enumerate}

\section{References}

See the following for further details:

\begin{enumerate}

\item Robinson MD. {\em Methods for the analysis of gas chromatography
    - mass spectrometry data.} {\bf Ph.D. Thesis}. October 2008.
  Department of Medical Biology (Walter and Eliza Hall Institute of
  Medical Research), University of Melbourne. 

\item Robinson MD, De Souza DP, Keen WW, Saunders EC, McConville MJ,
  Speed TP, Liki\'{c} VA. (2007) {\em A dynamic programming approach
    for the alignment of signal peaks in multiple gas
    chromatography-mass spectrometry experiments.} {\bf BMC
    Bioinformatics}. 8:419. 

\item Prince JT, Marcotte EM (2006) {\em Chromatographic alignment of
    ESI-LC-MS proteomics data sets by ordered bijective interpolated
    warping}. {\bf Anal Chem}. 78(17):6140-52. 

\end{enumerate}

\section{This vignette was built with/at ...}

<<session>>=
sessionInfo()
date()
@

\end{document}
