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 3346 edges, step by step analysis is shown below.
Estimate vertex centrality measures
Estimate centrality measures with values added as vertex attributes.
BioNAR supports centrality measures as following: * DEG - degree, * BET - betweenness, * CC - clustering coefficient, * SL - semilocal centrality, * mnSP - mean shortest path, * PR - page rank, * sdSP - standard deviation of the shortest path. These are saved as vertex atrtributes.
gg <- calcCentrality(gg)
summary(gg)
#> IGRAPH 0a8c340 UN-- 2275 9190 --
#> + attr: name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c), DEG (v/c), BET (v/c), CC (v/c), SL (v/c),
#> | mnSP (v/c), PR (v/c), sdSP (v/c)
Get vertex centralities as a matrix.
Instead of saving entrality centrality values on the graph, e.g. to provide different names for the vertex centrality attributes, they can be obtained in a matrix form:
Get the centrality measures for random graph
Sometimes one needs to compare the graph properties of the the properties of an the observed network to randomised networks of a similar size. The BioNAR command below provides three ways of generating randomization, randomised networks given an observed network including: G(n,p) Erdos-Renyi model, Barabasi-Albert model and new random graph from a given graph by randomly adding/removing edges.
{r}
ggrm <- getRandomGraphCentrality(sgg, type = c("cgnp"))
head(ggrm)
Power law fit
To examine a network’s underlying structure (i.e. not random), one can test a network’s degree distribution for evidence of scale-free structure and compare this against randomised network models. For this we used the R “PoweRlaw” package (version 0.50.0) (Gillespie, 2015). For the case study, i.e. our presynaptic PPI network, we found evidence for disassortative mixing (Newman, 2002), i.e. a preference for high-degree genes to attach to low-degree gene(presynaptic: -0.16).
Get entropy rate
Evidence for scale-free structure can also be tested by performing a perturbation analysis of each of the network’s vertices. In this analysis each protein is being perturbed through over-expression (red) and under-expression (green), with the global graph entropy rate (SR) after each proteins perturbation being plotted against the log of the proteins degree, as shown at the plot below. In our case study of the presynaptic PPI network we observe a bi-modal response, between gene over-expression and degree, and opposing bi-phasic response relative to over/under-expression between global entropy rate and degree. This type of bi-modal, bi-phasic behaviour has been observed only in networks with scale-free or approximate scale-free topology (Teschendorff et al, 2014).
Get modularity. Normalised modularity.
Normalised modularity (Qm) allows the comparison of networks with varying structure. Qm based on the previous studies by Parter et al., 2007, Takemoto, 2012, Takemoto, 2013, Takemoto and Borjigin, 2011, which was defined as:
\[Qm = \frac{Q_{real}-Q_{rand}}{Q_{max}-Q_{rand}}\]
Where \(Q_{real}\) is the network modularity of a real-world signaling network and, \(Q_{rand}\) is the average network modularity value obtained from 10,000 randomized networks constructed from its real-world network. \(Q_{max}\) was estimated as: \[Q_{max}=1 − \frac{1}{M}\], where \(M\) is the number of modules in the real network.
Randomized networks were generated from a real-world network using the edge-rewiring algorithm (Maslov and Sneppen, 2002).
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)
| 273 |
1 |
| 6455 |
1 |
| 1759 |
1 |
| 1785 |
1 |
| 26052 |
1 |
| 1837 |
2 |
Due to internal random initialisation consecutive invocation of the same algorithm could produce slightly different community structures:
| 5 |
26052 |
1 |
26052 |
2 |
| 6 |
1837 |
2 |
1837 |
3 |
| 7 |
1821 |
2 |
1821 |
3 |
| 8 |
1605 |
2 |
1605 |
3 |
| 9 |
2923 |
3 |
2923 |
4 |
| 10 |
26986 |
4 |
26986 |
5 |
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 0a8c340 UN-- 2275 9190 --
#> + attr: louvain (g/n), name (v/c), GeneName (v/c), TopOnto_OVG (v/c),
#> | TopOnto_OVG_HDO_ID (v/c), DEG (v/c), BET (v/c), CC (v/c), SL (v/c),
#> | mnSP (v/c), PR (v/c), sdSP (v/c), louvain (v/c)
Comminity membership data could be obtained from the graph vertex attribute:
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.
Table continues below
| lec |
0.2029 |
2 |
0 |
2 |
0.2163 |
552 |
818.2 |
| wt |
0.3602 |
231 |
116 |
4 |
0.4874 |
1 |
1 |
| fc |
0.4382 |
26 |
0 |
5 |
0.3682 |
3 |
3.25 |
| infomap |
0.4179 |
159 |
0 |
2 |
0.5449 |
2 |
5 |
| louvain |
0.4656 |
15 |
0 |
9 |
0.4313 |
22 |
77.5 |
| sgG1 |
0.4755 |
34 |
0 |
7 |
0.4017 |
2 |
4 |
| sgG2 |
0.4596 |
44 |
0 |
6 |
0.4948 |
3 |
16.25 |
| sgG5 |
0.392 |
97 |
0 |
0 |
0.5909 |
2 |
13 |
| lec |
1084 |
1084 |
1351 |
1617 |
| wt |
1 |
9.39 |
3 |
594 |
| fc |
8 |
83.42 |
31 |
475 |
| infomap |
9 |
13.64 |
13 |
181 |
| louvain |
152 |
144.6 |
205.5 |
290 |
| sgG1 |
7.5 |
63.79 |
73.75 |
361 |
| sgG2 |
44 |
49.3 |
69.25 |
163 |
| sgG5 |
20 |
22.36 |
28 |
82 |
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:
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:
Reclustering
Reclustering a clustered graph using the same, or different, clustering algorithm:
And we can apply second order clustering layout:
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)
Consensus matrix
To assess the robustness of obtained clusters, a randomization study can be performed, which applies the same clustering algorithm to N perturbed networks. The clustering results are returned as a consensus matrix where each matrix elements is assigned the frequency with which a pair of nodes vertices is found in the same cluster.
Where ‘alg’ gives the name of the clustering algorithm, ‘type’ the sampling scheme (1 sample edges, and 2 sample verices) used, ‘mask’ the percentage of edges or vertices to mask, and ‘reclust’ whether reclustering should be performed on the community set found, ‘Cnmin’ minimum cluster size and ‘Cnmax’ the maximum cluster size above which reclustering will be preformed (if reClust=TRUE).
For the sake of timing we use only five randomisation rounds, for the real analysis you should use at least 500.
##Consensus matrix value distribution
Consensus matrix values can be visualised in the following way:
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))
Cluster robustness
Cluster robustness assesses the robustness of obtained clusters and can help evaluate the “goodness” of a chosen clustering algorithm.
| louvain |
1 |
261 |
0.09042 |
0.5721 |
| louvain |
2 |
308 |
0.0887 |
0.4977 |
| louvain |
3 |
295 |
0.0875 |
0.4463 |
| louvain |
4 |
251 |
0.08325 |
0.2631 |
| louvain |
5 |
130 |
0.08605 |
0.3839 |
| louvain |
6 |
74 |
0.0822 |
0.2181 |
| louvain |
7 |
66 |
0.1004 |
1 |
| louvain |
8 |
181 |
0.08264 |
0.2371 |
| louvain |
9 |
164 |
0.08354 |
0.2754 |
| louvain |
10 |
245 |
0.09244 |
0.6589 |
| louvain |
11 |
93 |
0.08852 |
0.4902 |
| louvain |
12 |
38 |
0.08656 |
0.4056 |
| louvain |
13 |
146 |
0.08842 |
0.4859 |
| louvain |
14 |
23 |
0.07714 |
0 |
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.
| 273 |
AMPH |
0.3566 |
| 6455 |
SH3GL1 |
0.5501 |
| 1759 |
DNM1 |
1.11e-16 |
| 1785 |
DNM2 |
0.3267 |
| 26052 |
DNM3 |
0.1443 |
| 1837 |
DTNA |
0.3672 |
Bridgeness plot
Semi-local centrality measure (Chen et al., 2011) also lies between 0 and 1 indicating whether protein is important globally or locally. By plotting Bridgeness against semi-local centrality we can categorises the influence each protein found in our network has on the overall network structure: * Region 1, proteins having a ‘global’ rather than ‘local’ influence in the network (also been called bottle-neck bridges, connector or kinless hubs (0<Sl<0.5; 0.5<Br<1). * Region 2, proteins having ‘global’ and ‘local’ influence (0.5<Sl<1, 0.5<Br<1). * Region 3, proteins centred within the community they belong to, but also communicating with a few other specific communities (0<Sl<0.5; 0.1<Br<0.5). * Region 4, proteins with ‘local’ impact , primarily within one or two communities (local or party hubs, 0.5<Sl<1, 0<Br<0.5).
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
#Interactive view of bridgeness plot
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.
| DOID:10652 |
0 |
-0.03963 |
| DOID:3312 |
NA |
0 |
Table continues below
| DOID:10652 |
310 |
DOID:10652 |
310 |
0 |
. |
. |
0 |
| DOID:10652 |
310 |
DOID:3312 |
153 |
-0.2763 |
. |
YES |
-3.221 |
| DOID:3312 |
153 |
DOID:3312 |
153 |
0 |
. |
. |
0 |
| 1 |
larger |
. |
1 |
1 |
| 0.001278 |
Smaller |
** |
0.007027 |
0.003833 |
| 1 |
larger |
. |
1 |
1 |
Cluster overrepresentation
To identify the clusters with overrepresented function or disease we introduced the function which calculates the overrepesentation (enrichment for specified annotation). Based on R package fgsea.