Introduction

Proteomic studies typically generate a massive list of proteins being identified within a specific tissue, compartment or cell type, often accompanied by additional qualitative and/or quantitative information. Conversion of these data into meaningful biological insight requires processing in several stages to identify possible structural and/or functional dependencies.

One of the most popular ways of representing proteomic data is a protein-protein interaction network, which allows to study its topology and how it correlates with functional annotation mapped onto the network.

Many existing packages support different steps of the network building and analysis process, but few packages combine network analysis methodology into a single coherent pipeline.

We designed BioNAR to support a range of network analysis functionality, complementing existing R packages and filling the methodological gaps necessary to interrogate biomedical networks with respect to functional and disease domains. For that purpose, we do not implement network reconstruction directly (unless for synaptic networks), as other tools such as Cytoscape and Network Analyst do this already. Rathher, we provide a detailed topologically-based network analysis package, enabling the researcher to load networks generated from the lab’s own meta-data, thus making the tool as widely applicable and flexible as possible. We also provide a synaptic proteome network of our own for validation.

Overview of capabilities

The BioNAR’s pipeline starts with importing the graph of interest (typically built from nodes/proteins and edges/PPI interactions), and annotating its vertices with available metadata [annotate_vertex].

This is followed by the analysis of general network properties, such as estimating a network’s “scale-free” property. For this we used the R “PoweRlaw” package (version 0.50.0) (Gillespie, 2015) [FitDegree] and a network entropy analysis (Teschendorff et al, 2014) [getEntopy].

The package allows estimation of the main network vertex centrality measures: degree, betweenness centrality, clustering coefficient, semilocal centrality, mean shortest path, page rank, and standard deviation of the shortest path. Values for centrality values measures can be added as vertex attributes [calcCentrality] or returned as an R matrix [getCentralityMatrix], depending on user’s preferences. Any other vertex meta-data, which can be represented in matrix form, can also be stored as a vertex attribute.

To compare observed networks vertex centrality values against those of equivalently sized but randomised graphs, we support three varying randomisation models including G(n,p) Erdos-Renyi model , Barabasi-Albert model, and new random graph from a given graph by randomly adding/removing edges [getRandomGraphCentrality].

Additionally, to allow comparison of networks with different structures, we implemented normalized modularity measure (Parter et al., 2007, Takemoto, 2012, Takemoto, 2013, Takemoto and Borjigin, 2011)[normModularity].

BioNAR then proceeds to analyse the network’s community structure, which can be performed via nine different clustering algorithms, simultaneously [calcAllClustering] or with a chosen algorithm [calcClustering], community membership being stored as a vertex attribute. In situations where the network is dense and clusters are large and barely tractable, reclustering can be applied [calcReclusterMatrix]. The obtained community structure can be visualized with [layoutByCluster], and communiities further tested for robustness [getRobustness] by comparing against randomised networks. As a result, a consensus matrix can be estimated [makeConsensusMatrix], which is needed for the next step -identifying the “influential” or “bridging” proteins (Nepusz et al., 2008).

For this, we enabled a function for calculating the “bridgeness” [getBridgeness] metric, which takes into account the probability a vertex to belongs to different communities [getBridgeness], such that a vertex can be ranked under assumption the higher its community membership the more influence it has to the network topology and signaling (Han et al., 2004). “Bridgeness” can be plotted against any other centrality measure, e.g. semi-local centrality (plot is implemented), to enable useful indication of vertex (protein) importance within the network topology.

To provide a perspective of the molecular signature of multiple diseases (or biological functions) and how they might interact or overap at the network level, we implemented a disease-disease overlap analysis by measuring the mean shortest distance for each disease (⟨d⟩), using the shortest distance between each gene-disease association (GDA) to its next nearest GDA neighbor (Menche et al., 2015) [calcDiseasePairs], [runPermDisease] to be used for obtaining significance values. In the case example of the presynaptic network we found a set of neurological disorders to overlap with a high significance, e.g. AD-PD, SCH-BP, ASD-ID, and, indeed, their comorbidity was confirmed by the literature. Note that while developed for disease-disease correlation, the analysis can be performed using any in-house vertex meta-data, including biological function terms.

To study the distribution of the specific annotation(s) over a clustered graph (typically disease of biologial process/function), we enabled overrepresentation analysis [clusterORA], which helps identify the network communities enriched for specific function or disease, or any other annotation.

The case study illustrates the package functionality for the protein-protein interaction network for the presynaptic compartment of the synapse generated from Synaptic proteome database (Sorokina et al., 2021) with Synaptome.db package. The network has 1073 vertices and 6620 edges, step by step analysis is shown below.

Build the network

BioNAR allows building a network from a data frame, where the rows correspond to the edges of the graph; alternatively for our synaptic proteome exemple, a list of vertices (genes) is needed, for which the information will be retrieved from SynaptomeDB package.

file <- system.file("extdata", "PPI_Presynaptic.csv", package = "BioNAR")
tbl <- read.csv(file, sep="\t")
head(tbl)
#>   entA  entB We
#> 1  273  1759  1
#> 2  273  1785  1
#> 3  273 26052  1
#> 4  273   824  1
#> 5  273   161  1
#> 6  273  1020  1
gg <- buildNetwork(tbl)
summary(gg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: name (v/c)

file <- system.file("extdata", "PPI_Presynaptic.gml", package = "BioNAR")
gg1 <- igraph::read_graph(file,format="gml")
summary(gg1)
#> IGRAPH 31dd0b0 UN-- 2169 8673 -- 
#> + attr: id (v/n), name (v/c), GeneName (v/c), UniProt (v/c), louvain
#> | (v/n), TopOntoOVG (v/c), TopOntoOVGHDOID (v/c)

Annotate the nodes with node attributes

As soon as the graph is loaded it can be annotated with any relevant annotations, such as protein names [annotateGeneNames], functionality [annotateGOont], disease associations [annotateTopOntoOVG], or any customized annotation set [annotate_vertex {BioNAR}]. We also provide two functional annotations for synaptic graphs based on published synaptic functional studies ([annotateSCHanno], and [annotatePresynaptic].

gg<-annotateGeneNames(gg)
summary(gg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: name (v/c), GeneName (v/c)
head(V(gg))
#> + 6/1780 vertices, named, from 8edb44d:
#> [1] 273   6455  1759  1785  26052 2923
head(V(gg)$GeneName)
#> [1] "AMPH"   "SH3GL1" "DNM1"   "DNM2"   "DNM3"   "PDIA3"

any(is.na(V(gg)$GeneName))
#> [1] FALSE

idx <- which(V(gg)$name == '80273')
V(gg)$GeneName[idx]<-'GRPEL1'

afile<-system.file("extdata", "flatfile_human_gene2HDO.csv", package = "BioNAR")
dis <- read.table(afile,sep="\t",skip=1,header=FALSE,strip.white=TRUE,quote="")
gg <- annotateTopOntoOVG(gg, dis)
summary(gg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c)

sfile<-system.file("extdata", "SCH_flatfile.csv", package = "BioNAR")
shan<- read.table(sfile,sep="\t",skip=1,header=FALSE,strip.white=TRUE,quote="")
sgg<-annotateSCHanno(gg,shan)
summary(sgg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c), Schanno (v/c)

sfile<-system.file("extdata", "PresynAn.csv", package = "BioNAR")
pres <- read.csv(sfile,skip=1,header=FALSE,strip.white=TRUE,quote="")
sgg <- annotatePresynaptic(gg, pres)
summary(sgg)

ggGO <- annotateGOont(gg)

#however, functionality from GO: BP, MF,CC can be added

sfile<-system.file("extdata", "flatfile.go.BP.csv", package = "BioNAR")
goBP <- read.table(sfile,sep="\t",skip=1,header=FALSE,strip.white=TRUE,quote="")
sgg <- annotateGoBP(gg, goBP)
summary(sgg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c), GO_BP_ID (v/c), GO_BP (v/c)

sfile<-system.file("extdata", "flatfile.go.MF.csv", package = "BioNAR")
goMF <- read.table(sfile,sep="\t",skip=1,header=FALSE,strip.white=TRUE,quote="")
sgg <- annotateGoMF(gg, goMF)
summary(sgg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c), GO_MF_ID (v/c), GO_MF (v/c)

sfile<-system.file("extdata", "flatfile.go.CC.csv", package = "BioNAR")
goCC <- read.table(sfile,sep="\t",skip=1,header=FALSE,strip.white=TRUE,quote="")
sgg <- annotateGoCC(gg, goCC)
summary(sgg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c), GO_CC_ID (v/c), GO_CC (v/c)

Estimate vertex centrality measures

gg <- calcCentrality(gg)
summary(gg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c), DEG (v/n), BET (v/n), CC (v/n), SL (v/n),
#> | mnSP (v/n), PR (v/n), sdSP (v/c)

mc <- getCentralityMatrix(gg)
head(mc)
#>      ID DEG        BET         CC     SL  mnSP           PR  sdSP
#> 1   273  12   833.2335 0.10606061  44656 3.424 0.0007855514 0.707
#> 2  6455  22  5444.7102 0.08225108 170211 2.955 0.0013374528 0.683
#> 3  1759  16  1744.9317 0.21666667 150771 3.062 0.0009619764 0.687
#> 4  1785  27 10994.5087 0.07122507 218717 2.890 0.0016436995 0.701
#> 5 26052   6   291.1377 0.13333333  55060 3.503 0.0004051298 0.743
#> 6  2923   7  1225.7092 0.09523810  55104 3.391 0.0005312439 0.758

{r}
ggrm <- getRandomGraphCentrality(sgg, type = c("cgnp"))
head(ggrm)

pFit <- fitDegree( as.vector(igraph::degree(graph=gg)),threads=1,Nsim=5,
                    plot=TRUE,WIDTH=2480, HEIGHT=2480)

ent <- getEntropyRate(gg)
ent
#> $maxSr
#> [1] 3.822764
#> 
#> $SRo
#> [1] 2.639026
SRprime <- getEntropy(gg, maxSr = NULL)
head(SRprime)
#>   ENTREZ.ID GENE.NAME DEGREE        UP      DOWN
#> 1       273      AMPH     12 0.6877989 0.6903153
#> 2      6455    SH3GL1     22 0.6884665 0.6899068
#> 3      1759      DNM1     16 0.6892206 0.6899577
#> 4      1785      DNM2     27 0.6896328 0.6895775
#> 5     26052      DNM3      6 0.6891432 0.6902969
#> 6      2923     PDIA3      7 0.6888827 0.6903132
plotEntropy(SRprime, subTIT = "Entropy", SRo = ent$SRo, maxSr = ent$maxSr)

nm<-normModularity(gg,alg='louvain')
nm
#> [1] 0.01387291

Clustering

Clustering, or community detection, in networks has been well studied in the field of statistical physics with particular attention to methods developed for social science networks. The underlying assumption(s) of what makes a community in social science, translates remarkably well to what we think of as a community (sub-complex, module or cluster) in PPI networks. The possible algorithms of choice implemented in BioNAR are: * “lec”(‘Leading-Eigenvector, Newman, 2006), * “wt”(Walktrap, Pons & Latapy, 2006), * “fc”(Fast-Greedy Community’ algorithm, Clauset et al., 2004), * “infomap” (InfoMAP, Rosvall et al., 2007; Rosvall et al., 2010), * “louvain” (Louvain, Blondel et al., 2008), * “sgG1”, “sgG2”, “sgG5”(SpinGlass, Reichardt & Bornholdt). For each algorithm of interest the community membership can be obtained with'calcMembership command. All algorithm implementations, apart from Spectral were performed using the publicly available R package igraph (Csardi & Nepusz, 2006) (R version 3.4.2, igraph version 1.1.2). Parameters used in the fc, lec, sg, wt and lourvain algorithms were chosen as to maximise the measure Modularity (Newman & Girvan, 2004); infomap seeks the optimal community structure in the data by maximising the objective function called the Minimum Description Length (Rissanen, 1978; Grwald et al., 2005)

# choose one algorithm from the list
alg = "louvain"
mem <- calcMembership(gg, alg)
pander(head(mem))

Due to internal random initialisation consecutive invocation of the same algorithm could produce slightly different community structures:

mem2 <- calcMembership(gg, alg)
idx<-match(mem$names,mem2$names)
idnx<-which(mem$membership!=mem2$membership[idx])
pander(head(cbind(mem[idnx,],mem2[idx[idnx],])))

To avoid inconsistency in downstream analysis we provide two additional functions calcClustering and calcAllClustering that use calcMembership to calculate community memberships and store them within the graph vertices attributes named after the algorithm. They also calculate modularity values and store them as graph vertex attributes named after the clustering algorithm. The difference between calcClustering and calcAllClustering is that calcAllClusteringallows to calculate memberships for all clustering algorithms simultaneously (may take time), and store them as graph vertices attributes, while calcClusteringcommand will work for a specific algorithm.

gg <- calcClustering(gg, alg)
summary(gg)
#> IGRAPH 8edb44d UN-- 1780 6620 -- 
#> + attr: louvain (g/n), name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c), DEG (v/n), BET (v/n), CC (v/n), SL (v/n),
#> | mnSP (v/n), PR (v/n), sdSP (v/c), louvain (v/c)

Comminity membership data could be obtained from the graph vertex attribute:

mem.df<-data.frame(names=V(gg)$name,membership=as.numeric(V(gg)$louvain))

To compare different clustering algorithms,a summary matrix can be calculated with the following properties: 1. maximum Modularity obtained (mod), 2. number of detected communities (C), 3. the number of communities with size (Cn1) equal to 1, 4. the number of communities >= 100 (Cn100), 5. the fraction of edges lying between communities (mu), 6. the size of the smallest community (Min. C), 7. the size of the largest community (Max. C), 8. the average ( Mean C), median (Median C), 9. first quartile (1st Qu. C), and 10. third quartile (3rd Qu. C) of the community size.

ggc <- calcAllClustering(gg)

m<-clusteringSummary(ggc,att=c('lec','wt','fc',
                                'infomap','louvain',
                                'sgG1','sgG2','sgG5'))
pander(m)

It is often useful to be able to visualize clusters of the graph. The simplest way to do this is to color each cluster uniquely and plot the graph:

palette <- distinctColorPalette(max(as.numeric(mem.df$membership)))
plot(gg,vertex.size=3,layout=layout_nicely,
        vertex.label=NA,
        vertex.color=palette[as.numeric(mem.df$membership)],
        edge.color='grey95')
legend('topright',legend=names(table(mem.df$membership)),
        col=palette,pch=19,ncol = 2)

On the plot we can see some distinctive clusters but most verices are indistinguishable within the central part of the plot. So we could layout graph clusterwise:

lay<-layoutByCluster(gg,mem.df,layout = layout_nicely)
plot(gg,vertex.size=3,layout=lay,
        vertex.label=NA,
        vertex.color=palette[as.numeric(mem.df$membership)],
        edge.color='grey95')
legend('topright',legend=names(table(mem.df$membership)),
        col=palette,pch=19,ncol = 2)

It is also possible to visualize the interaction between communities:

idx<-match(V(gg)$name,mem.df$names)
cgg<-getCommunityGraph(gg,mem.df$membership[idx])
D0 = unname(degree(cgg))
plot(cgg, vertex.size=sqrt(V(cgg)$size), vertex.cex = 0.8,
vertex.color=round(log(D0))+1,layout=layout_with_kk,margin=0)

remem<-calcReclusterMatrix(gg,mem.df,alg,10)
head(remem)
#>   names membership recluster
#> 1   273          1         1
#> 2  6455          1         2
#> 3  1759          1         2
#> 4  1785          1         2
#> 5 26052          2         9
#> 6  2923          3        18

lay<-layoutByRecluster(gg,remem,layout_nicely)
plot(gg,vertex.size=3,layout=lay,
        vertex.label=NA,
        vertex.color=palette[as.numeric(mem.df$membership)],
        edge.color='grey95')
legend('topright',legend=names(table(mem.df$membership)),
        col=palette,pch=19,ncol = 2)

#Build consensus matrix for louvain clustering
conmat <- makeConsensusMatrix(gg, N=5,
                                alg = alg, type = 2, 
                                mask = 10,reclust = FALSE, 
                                Cnmax = 10)

steps <- 100
Fn  <- ecdf(conmat[lower.tri(conmat)])
X<-seq(0,1,length.out=steps+1)
cdf<-Fn(X)
dt<-data.frame(cons=X,cdf=cdf)
ggplot(dt,aes(x=cons,y=cdf))+geom_line()+
        theme(            
        axis.title.x=element_text(face="bold",size=rel(2.5)),
        axis.title.y=element_text(face="bold",size=rel(2.5)),
        legend.title=element_text(face="bold",size=rel(1.5)),
        legend.text=element_text(face="bold",size=rel(1.5)),
        legend.key=element_blank())+
    theme(panel.grid.major = element_line(colour="grey40",size=0.2),
            panel.grid.minor = element_line(colour="grey40",size=0.1),
            panel.background = element_rect(fill="white"),
            panel.border = element_rect(linetype="solid",fill=NA))

clrob<-getRobustness(gg, alg = alg, conmat)
pander(clrob)

Bridgeness

Bridging proteins are known to interact with many neighbours simultaneously, organise function inside the communities they belong to, but also affect/influence other communities in the network (Nepusz et al., 2008). Bridgeness can be estimated from the consensus clustering matrix estimated above and vertex degree to calculate the vertex’s community membership, i.e.  the probability a specific vertex belongs to every community obtained by a given clustering algorithm.

The Bridgeness measure lies between 0 - implying a vertex clearly belongs in a single community, and 1 - implying a vertex forms a ‘global bridge’ across every community with the same strength.

br<-getBridgeness(gg,alg = alg,conmat)
pander(head(br))

gg<-calcBridgeness(gg,alg = alg,conmat)
vertex_attr_names(gg)
#>  [1] "name"               "GeneName"           "TopOnto_OVG"       
#>  [4] "TopOnto_OVG_HDO_ID" "DEG"                "BET"               
#>  [7] "CC"                 "SL"                 "mnSP"              
#> [10] "PR"                 "sdSP"               "louvain"           
#> [13] "BRIDGENESS.louvain"

g<-plotBridgeness(gg,alg = alg,
               VIPs=c('8495','22999','8927','8573',
                      '26059','8497','27445','8499'),
               Xatt='SL',
               Xlab = "Semilocal Centrality (SL)",
               Ylab = "Bridgeness (B)",
               bsize = 3,
               spsize =7,
               MainDivSize = 0.8,
               xmin = 0,
               xmax = 1,
               ymin = 0,
               ymax = 1,
               baseColor="royalblue2",
               SPColor="royalblue2")
g

library(plotly)
g<-plotBridgeness(gg,alg = alg,
               VIPs=c('8495','22999','8927','8573',
                      '26059','8497','27445','8499'),
               Xatt='SL',
               Xlab = "Semilocal Centrality (SL)",
               Ylab = "Bridgeness (B)",
               bsize = 1,
               spsize =2,
               MainDivSize = 0.8,
               xmin = 0,
               xmax = 1,
               ymin = 0,
               ymax = 1,
               baseColor="royalblue2",
               SPColor="royalblue2")
ggplotly(g)

Disease/annotation pairs

Given that Disease associated genes are connected within the graph, the common question is to check whether the networks for two different diseases are overlapping, which may indicate the common molecular mechanisms. Same is valid for any pair of annotations, e.g. one would ask if two different biological functions are related.

To address this question, we utilise the algorithm from Menche et al, which estimates the minimal shortest paths between two distinct annotations and compares this to the randomly annotated graph.

Below example shows the estimation of disease separation for the following diseases: DOID:10652 (Alzheimer’s_disease), (bipolar_disorder), DOID:12849 (autistic_disorder), DOID:1826 (epilepsy). Command calcDiseasePairs quickly estimates the two annotation separation on the graph and compares it with one randomly reannotated graph. This could be used for initial guess of the relationships between the annotations.

To assess the significance of the obtained separation values the command runPermDisease should be used, where the user can specify the number of permutations. TExecuting this command, which will take time depending of the number of permutations, returns table with of p-values, adjusted p-values, q-values and Bonferroni test for each disease-disease pair.

p <- calcDiseasePairs(
    gg,
    name = "TopOnto_OVG_HDO_ID",
    diseases = c("DOID:10652","DOID:3312"),
    permute = "r"
)
pander(p$disease_separation)

r <- runPermDisease(
    gg,
    name = "TopOnto_OVG_HDO_ID",
    diseases = c("DOID:10652","DOID:3312"),
    Nperm = 100,
    alpha = c(0.05, 0.01, 0.001)
)

pander(r$Disease_overlap_sig)

ora <- clusterORA(gg, alg, name = 'TopOnto_OVG_HDO_ID', vid = "name",
                  alpha = 0.1, col = COLLAPSE)

Session Info

Platform

• version: R version 4.4.1 (2024-06-14)
• os: Ubuntu 24.04.1 LTS
• system: x86_64, linux-gnu
• ui: X11
• language: (EN)
• collate: C
• ctype: en_US.UTF-8
• tz: Etc/UTC
• date: 2024-10-30
• pandoc: 3.2.1 @ /usr/local/bin/ (via rmarkdown)

Packages