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\title{Random Walk with Restart on Multiplex and Heterogeneous Network}
\author[1, 2]
{Alberto Valdeolivas Urbelz\thanks{\email{alvaldeolivas@gmail.com}}}
\affil[1]{MMG, Marseille Medical Genetics U 1251, Faculte de Medecine, France}
\affil[2]{ProGeLife, 8 Rue Sainte Barbe 13001, Marseille, France}

\begin{document}
\SweaveOpts{concordance=TRUE}
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\maketitle

\begin{abstract}
This vignette describes how to use the \Biocpkg{RandomWalkRestartMH} package
to run Random Walk with Restart algorithms on monoplex, multiplex, 
heterogeneous and multiplex-heterogeneous networks.
It is based on the work we presented on the following article:

\url{https://www.biorxiv.org/content/early/2017/08/30/134734}

\end{abstract}

\packageVersion{\Sexpr{BiocStyle::pkg_ver("RandomWalkRestartMH")}}

Report issues to \email{alvaldeolivas@gmail.com}

\newpage

\tableofcontents

\newpage

\section{Introduction}

\Biocpkg{RandomWalkRestartMH} (Random Walk with Restart on Multiplex and
Heterogeneous Networks) is an R package built to provide easy access to the
Random Walk with Restart (RWR) algorithm on different types of networks:
i) Monoplex networks, ii) Multiplex networks, iii) Heterogeneous networks and 
iv) Multiplex-Heterogeneous networks. It is based on the work we presented in 
the article: \url{https://www.biorxiv.org/content/early/2017/08/30/134734}.

RWR simulates an imaginary particle that starts on a seed(s) node(s) and
follows randomly the edges of a network. At each step, there is a restart
probability, r, meaning that the particle can come back to the seed(s)
\cite{Pan2004}. This imaginary particle can explore the following types
of networks:

\begin{itemize}
\item A monoplex or single network, which contains solely nodes of the same
nature. In addition, all the edges belong to the same category.

\item A multiplex network, defined as a collection of monoplex networks 
considered as layers of the multiplex network. In a multiplex network, the 
different layers share the same set of nodes, but the edges represent 
relationships of different nature \cite{Battiston2014}. In this case, the RWR 
particle can jump from one node to its counterparts on different layers.

\item A heterogeneous network, which is composed of two monoplex networks
containing nodes of different nature. These different kind of nodes can be
connected thanks to bipartite edges, allowing the RWR particle to jump between
the two networks.

\item A multiplex and heterogeneous network, which is built by linking the nodes
in every layer of a multiplex network to nodes of different nature thanks to
bipartite edges. The RWR particle can now explore the full 
multiplex-heterogeneous network.
\end{itemize}

The user can introduce up to six single networks (monoplex networks) to create
a multiplex network. The multiplex network can also be integrated, thanks to
bipartite relationships, with a network containing nodes of different nature.
Proceeding this way, a network both multiplex and heterogeneous will be
generated.

Please note that this first version of the package deals only with undirected 
and unweighted networks. New functionalities will be included in future updated 
versions of \Biocpkg{RandomWalkRestartMH}.

\section{Installation of the \Biocpkg{RandomWalkRestartMH} package}
First of all, you need a current version of \R{}~\url{(www.r-project.org)}.
\Biocpkg{RandomWalkRestartMH} is a freely available package deposited on
\url{http://bioconductor.org/}. You can install it by running the following
commands on an \R{}~console:

<<installation,eval=FALSE>>=
source("http://bioconductor.org/biocLite.R")
biocLite("RandomWalkRestartMH")
@

\section{A Detailed Workflow}
In the following paragraphs, we describe how to use the
\Biocpkg{RandomWalkRestartMH} package to perform RWR on different types
of biological networks. Concretely, we use a protein-protein interaction (PPI)
network, a pathway network, a disease-disease similarity network and
combinations thereof. These networks are obtained as detailed in
\cite{Valdeolivas2017}. The PPI and the Pathway network were reduced by only
considering genes/proteins expressed in the adipose tissue, in order to reduce
the computation time of this vignette.

The goal in the example presented here is, as described in 
\cite{Valdeolivas2017}, to find candidate genes potentially associated with 
diseases by a guilt-by-association approach. This is based on the fact that 
genes/proteins with similar functions or similar phenotypes tend to 
lie closer in biological networks. Therefore, the larger the RWR score of a 
gene, the more likely it is to be functionally related with the seeds. 

We focus on a real biological example: the SHORT syndrome
(MIM code: 269880) and its causative gene \textit{PIK3R1} as described in
\cite{Valdeolivas2017}. We will see throughout the following paragraphs how the
RWR results evolve due to the the integration and exploration of additional 
networks.

\subsection{Random Walk with Restart on a Monoplex Network}
RWR has usually been applied within the framework of single
PPI networks in bioinformatics\cite{Kohler2008}. A gene or a set of genes,
so-called seed(s), known to be implicated in a concrete function or in a 
specific disease, are chosen as the starting point(s) of the algorithm. The 
RWR particle explores the neighbourhood of the seeds and the algorithm computes 
a score for all the nodes of the network. The larger it is the score of a node, 
the closer it is to the seed(s).

Let us generate an object of the class \Rclass{Multiplex}, even if it is a 
monoplex network, with our PPI network.

<<>>=
library(RandomWalkRestartMH)
library(igraph)
data(PPI_Network) # We load the PPI_Network

## We create a Multiplex object composed of 1 layer (It's a Monoplex Network) 
## and we display how it looks like
PPI_MultiplexObject <- create.multiplex(PPI_Network,Layers_Name=c("PPI"))
PPI_MultiplexObject
@

To apply the RWR on a monoplex network, we need to compute the adjacency matrix
of the network and normalize it by column \cite{Kohler2008}, as follows:

<<>>=
AdjMatrix_PPI <- compute.adjacency.matrix(PPI_MultiplexObject)
AdjMatrixNorm_PPI <- normalize.multiplex.adjacency(AdjMatrix_PPI)
@

Then, we need to define the seed(s) before running the RWR algorithm on this PPI 
network. As commented above, we are focusing on the example of the SHORT 
syndrome. Therefore, we take the \textit{PIK3R1} gene as seed, and we execute
RWR.

<<>>=
SeedGene <- c("PIK3R1")
## We launch the algorithm with the default parameters (See details on manual)
RWR_PPI_Results <- Random.Walk.Restart.Multiplex(AdjMatrixNorm_PPI,
                        PPI_MultiplexObject,SeedGene)
# We display the results
RWR_PPI_Results
@

Finally, we can create a network (an \Rclass{igraph} object) with the top
scored genes. Visualize the top results within their interaction network is 
always a good idea in order to prioritize genes, since we can have a global view 
of all the potential candidates. The results are presented in 
Figure~\ref{fig:1}.

<<>>=
## In this case we selected to induce a network with the Top 15 genes.
TopResults_PPI <-
    create.multiplexNetwork.topResults(RWR_PPI_Results,PPI_MultiplexObject,
                                       k=15)
@

<<fig1, echo=TRUE, fig=TRUE, include=FALSE, width=10, height=5>>=
par(mar=c(0.1,0.1,0.1,0.1))
plot(TopResults_PPI, vertex.label.color="black",vertex.frame.color="#ffffff",
    vertex.size= 20, edge.curved=.2,
    vertex.color = ifelse(igraph::V(TopResults_PPI)$name == "PIK3R1","yellow",
    "#00CCFF"), edge.color="blue",edge.width=0.8)
@

\begin{figure*}
\includegraphics{\jobname-fig1}
\caption{\label{fig:1} RWR on a monoplex PPI Network.
Network representation of the top 15 ranked genes when the RWR algorithm is
executed using the \textit{PIK3R1} gene as seed (yellow node). Blue edges
represent PPI interactions.
}
\end{figure*}

\subsection{Random Walk with Restart on a Heterogeneous Network}
A RWR on a heterogeneous (RWR-H) biological network was described by
\cite{Li2010}. They connected a PPI network with a disease-disease similarity
network using known gene-disease associations. In this case, genes and/or
diseases can be used as seed nodes for the algorithm. In the following example,
we also use a heterogeneous network integrating a PPI and a disease-disease
similarity network. However, the procedure to obtain these networks is different
to the one proposed in \cite{Li2010}, and the details are described in our
article \cite{Valdeolivas2017}.

To generate a PPI-disease heterogeneous network object, we load the
disease-disease network, and combine it with our previously defined 
\Rclass{Multiplex} object containing the PPI network, thanks to the 
gene-diseases associations obtained from OMIM \cite{Hamosh2005}. 
A \Rclass{MultiplexHet} object will be created, even if we are dealing with 
a monoplex-heterogeneous network.

<<>>=
data(Disease_Network) # We load our disease Network

## We load a data frame containing the gene-disease associations.
## See ?create.multiplexHet for details about its format
data(GeneDiseaseRelations)

## We keep gene-diseases associations where genes are present in the PPI
## network
GeneDiseaseRelations_PPI <-
    GeneDiseaseRelations[which(GeneDiseaseRelations$hgnc_symbol %in%
    PPI_MultiplexObject$Pool_of_Nodes),]

## We create the MultiplexHet object.
PPI_Disease_Net <- create.multiplexHet(PPI_MultiplexObject,
    Disease_Network, GeneDiseaseRelations_PPI, c("Disease"))

## The results look like that
PPI_Disease_Net
@

To apply the RWR-H on a heterogeneous network, we need to compute a matrix that
accounts for all the possible transitions of the RWR particle within that 
network \cite{Li2010}.

<<>>=
PPIHetTranMatrix <- compute.transition.matrix(PPI_Disease_Net)
@

Before running RWR-H on this PPI-disease heterogeneous network, we need to
define the seed(s). As in the previous paragraph, we take \textit{PIK3R1} as a
seed gene. In addition, we can now set the SHORT syndrome itself as a seed
disease.
<<>>=
SeedDisease <- c("269880")

## We launch the algorithm with the default parameters (See details on manual)
RWRH_PPI_Disease_Results <-
    Random.Walk.Restart.MultiplexHet(PPIHetTranMatrix,
    PPI_Disease_Net,SeedGene,SeedDisease)

# We display the results
RWRH_PPI_Disease_Results
@

Finally, we can create a heterogeneous network (an \Rclass{igraph} object) with
the top scored genes and the top scored diseases. The results are presented in
Figure~\ref{fig:2}.

<<>>=
## In this case we select to induce a network with the Top 10 genes
## and the Top 10 diseases.
TopResults_PPI_Disease <-
    create.multiplexHetNetwork.topResults(RWRH_PPI_Disease_Results,
    PPI_Disease_Net, GeneDiseaseRelations_PPI, k=10)
@

<<fig2, echo=TRUE, fig=TRUE, include=FALSE, width=10, height=5>>=
par(mar=c(0.1,0.1,0.1,0.1))
plot(TopResults_PPI_Disease, vertex.label.color="black",
    vertex.frame.color="#ffffff",
    vertex.size= 20, edge.curved=.2,
    vertex.color = ifelse(V(TopResults_PPI_Disease)$name == "PIK3R1"
    | V(TopResults_PPI_Disease)$name == "269880","yellow",
    ifelse(V(TopResults_PPI_Disease)$name %in% PPI_Disease_Net$Pool_of_Nodes,
    "#00CCFF","Grey75")),
    edge.color=ifelse(E(TopResults_PPI_Disease)$type == "PPI","blue",
        ifelse(E(TopResults_PPI_Disease)$type == "Disease","black","grey50")),
    edge.width=0.8,
    edge.lty=ifelse(E(TopResults_PPI_Disease)$type == "bipartiteRelations",
        2,1),
    vertex.shape= ifelse(V(TopResults_PPI_Disease)$name %in%
        PPI_Disease_Net$Pool_of_Nodes,"circle","rectangle"))
@

\begin{figure*}
\includegraphics{\jobname-fig2}
\caption{\label{fig:2} RWR-H on a heterogeneous PPI-Disease Network.
Network representation of the top 10 ranked genes and the top 10 ranked diseases
when the RWR-H algorithm is executed using the \textit{PIK3R1} gene and
the SHORT syndrome disease (MIM code: 269880) as seeds (yellow nodes).
Circular nodes represent genes and rectangular nodes show diseases.
Blue edges are PPI interactions and black edges are similarity links between
diseases. Dashed edges are the bipartite gene-disease associations.
}
\end{figure*}

\subsection{Random Walk with Restart on a Multiplex Network}

Some limitations can arise when single networks are used to represent and
describe systems whose entities can interact through more than one type of
connections \cite{Battiston2014}. This is the case of social interactions,
transportation networks or biological systems, among others. The Multiplex
framework provides an appealing approach to describe these systems, since they
are able to integrate this diversity of data while keeping track of the
original features and topologies of the different sources.

Consequently, algorithms able to exploit the information stored on multiplex
networks should improve the results provided by methods operating on
single networks. In this context, we extended the random walk with restart
algorithm to multiplex networks (RWR-M) \cite{Valdeolivas2017}.

In the following example, we create a multiplex network integrated by our PPI
network and a network derived from pathway databases \cite{Valdeolivas2017}.

<<>>=
data(Pathway_Network) # We load the Pathway Network

## We create a 2-layers Multiplex object
PPI_PATH_Multiplex <- create.multiplex(PPI_Network,Pathway_Network,
                        Layers_Name=c("PPI","PATH"))
PPI_PATH_Multiplex
@

Afterwards, as in the monoplex case, we have to compute and normalize the
adjacency matrix of the multiplex network.

<<>>=
AdjMatrix_PPI_PATH <- compute.adjacency.matrix(PPI_PATH_Multiplex)
AdjMatrixNorm_PPI_PATH <- normalize.multiplex.adjacency(AdjMatrix_PPI_PATH)
@

Then, we set again as seed the \textit{PIK3R1} gene and we perform RWR-M
on this new multiplex network.

<<>>=
## We launch the algorithm with the default parameters (See details on manual)
RWR_PPI_PATH_Results <- Random.Walk.Restart.Multiplex(AdjMatrixNorm_PPI_PATH,
                        PPI_PATH_Multiplex,SeedGene)
# We display the results
RWR_PPI_PATH_Results
@

Finally, we can create a multiplex network (an \Rclass{igraph} object) with the
top scored genes. The results are presented in Figure~\ref{fig:3}.

<<>>=
## In this case we select to induce a multiplex network with the Top 15 genes.
TopResults_PPI_PATH <-
    create.multiplexNetwork.topResults(RWR_PPI_PATH_Results,
                                        PPI_PATH_Multiplex, k=15)
@

<<fig3, echo=TRUE, fig=TRUE, include=FALSE, width=10, height=5>>=
par(mar=c(0.1,0.1,0.1,0.1))
plot(TopResults_PPI_PATH, vertex.label.color="black",
    vertex.frame.color="#ffffff", vertex.size= 20,
    edge.curved= ifelse(E(TopResults_PPI_PATH)$type == "PPI",
                    0.4,0),
    vertex.color = ifelse(igraph::V(TopResults_PPI_PATH)$name == "PIK3R1",
                    "yellow","#00CCFF"),edge.width=0.8,
    edge.color=ifelse(E(TopResults_PPI_PATH)$type == "PPI",
                      "blue","red"))
@

\begin{figure*}
\includegraphics{\jobname-fig3}
\caption{\label{fig:3} RWR-M on a multiplex PPI-Pathway Network.
Network representation of the top 15 ranked genes
when the RWR-M algorithm is executed using the \textit{PIK3R1} gene (yellow
node). Blue curved edges are PPI interactions and red straight edges are
Pathways links. All the interactions are aggregated into a monoplex network
only for visualization purposes.
}
\end{figure*}

\subsection{Random Walk with Restart on a Multiplex-Heterogeneous Network}
RWR-H and RWR-M remarkably improve the results obtained by classical RWR on
monoplex networks, as we demonstrated in the particular case of
retrieving known gene-disease associations \cite{Valdeolivas2017}.
Therefore, an algorithm able to execute a random walk with restart on both,
multiplex and heterogeneous networks, is expected to achieve an even better
performance. We extended our RWR-M approach to heterogeneous networks, defining
a random walk with restart on multiplex-heterogeneous networks (RWR-MH)
\cite{Valdeolivas2017}.

Let us integrate all the networks described previously (PPI, Pathways and
disease-disease similarity) into a multiplex and heterogeneous network. To
do so, we connect genes in both multiplex layers (PPI and Pathways) to the
disease network, if a bipartite gene-disease relation exists.

<<>>=
## We keep gene-diseases associations where genes are present in the PPI
## or in the pathway network
GeneDiseaseRelations_PPI_PATH <-
    GeneDiseaseRelations[which(GeneDiseaseRelations$hgnc_symbol %in%
    PPI_PATH_Multiplex$Pool_of_Nodes),]

## We create the MultiplexHet object.
PPI_PATH_Disease_Net <- create.multiplexHet(PPI_PATH_Multiplex,
    Disease_Network, GeneDiseaseRelations_PPI_PATH, c("Disease"))

## The results look like that
PPI_PATH_Disease_Net
@

To apply the RWR-MH on a multiplex and heterogeneous network, we need to
compute a matrix that accounts for all the possible transitions of the RWR 
particle within this network \cite{Valdeolivas2017}.

<<>>=
PPI_PATH_HetTranMatrix <- compute.transition.matrix(PPI_PATH_Disease_Net)
@

As in the RWR-H situation, we can take as seeds both, the \textit{PIK3R1} gene
and the the SHORT syndrome disease.

<<>>=
## We launch the algorithm with the default parameters (See details on manual)
RWRH_PPI_PATH_Disease_Results <-
    Random.Walk.Restart.MultiplexHet(PPI_PATH_HetTranMatrix,
    PPI_PATH_Disease_Net,SeedGene,SeedDisease)

# We display the results
RWRH_PPI_PATH_Disease_Results
@

Finally, we can create a multiplex and heterogeneous network (an \Rclass{igraph}
object) with the top scored genes and the top scored diseases. The results are
presented in Figure~\ref{fig:4}.

<<>>=
## In this case we select to induce a network with the Top 10 genes.
## and the Top 10 diseases.
TopResults_PPI_PATH_Disease <-
    create.multiplexHetNetwork.topResults(RWRH_PPI_PATH_Disease_Results,
    PPI_PATH_Disease_Net, GeneDiseaseRelations_PPI_PATH, k=10)
@


<<fig4, echo=TRUE, fig=TRUE, include=FALSE, width=10, height=5>>=
par(mar=c(0.1,0.1,0.1,0.1))
plot(TopResults_PPI_PATH_Disease, vertex.label.color="black",
    vertex.frame.color="#ffffff",
    vertex.size= 20,
    edge.curved=ifelse(E(TopResults_PPI_PATH_Disease)$type == "PATH",
                    0,0.3),
    vertex.color = ifelse(V(TopResults_PPI_PATH_Disease)$name == "PIK3R1"
    | V(TopResults_PPI_Disease)$name == "269880","yellow",
    ifelse(V(TopResults_PPI_PATH_Disease)$name %in%
               PPI_PATH_Disease_Net$Pool_of_Nodes,
    "#00CCFF","Grey75")),
    edge.color=ifelse(E(TopResults_PPI_PATH_Disease)$type == "PPI","blue",
    ifelse(E(TopResults_PPI_PATH_Disease)$type == "PATH","red",
    ifelse(E(TopResults_PPI_PATH_Disease)$type == "Disease","black","grey50"))),
    edge.width=0.8,
    edge.lty=ifelse(E(TopResults_PPI_PATH_Disease)$type ==
        "bipartiteRelations", 2,1),
    vertex.shape= ifelse(V(TopResults_PPI_PATH_Disease)$name %in%
        PPI_PATH_Disease_Net$Pool_of_Nodes,"circle","rectangle"))
@

\begin{figure*}
\includegraphics{\jobname-fig4}
\caption{\label{fig:4} RWR-MH on a multiplex and heterogeneous network
(PPI-Pathway-Disease).
Network representation of the top 10 ranked genes
and the top 10 ranked diseases when the RWR-H algorithm is executed using the
\textit{PIK3R1} gene and the SHORT syndrome disease (MIM code: 269880) as seeds
(yellow nodes). Circular nodes represent genes and rectangular nodes show
diseases. Blue curved edges are PPI interactions and red straight edges are
Pathways links. Black edges are similarity links between diseases.
Dashed edges are the bipartite gene-disease associations.
Multiplex interactions are aggregated into a monoplex network
only for visualization purposes.
}
\end{figure*}

\newpage

\bibliography{Bioc}

\newpage

\appendix


%---------------------------------------------------------
\section{Session info}
%---------------------------------------------------------

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toLatex(sessionInfo())
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\end{document}
