DEsubs

Table of Contents

  1. Package setup
  2. User input
  3. Pathway network construction
  4. Pathway network processing
  5. Subpathway extraction
  6. Subpathway enrichment analysis
  7. Visualization

1. Package Setup

DEsubs is a network-based systems biology R package that extracts disease-perturbed subpathways within a pathway network as recorded by RNA-seq experiments. It contains an extensive and customizable framework with a broad range of operation modes at all stages of the subpathway analysis, enabling a case-specific approach. The operation modes refer to the pathway network construction and processing, the subpathway extraction, visualization and enrichment analysis with regard to various biological and pharmacological features. It’s capabilities render it a valuable tool for both the modeler and experimentalist searching for the identification of more robust systems-level drug targets and biomarkers for complex diseases.

Before loading the package, please specify a user-accessible home directory using the following commands, which currently reflect the default directories for each architecture:

if (.Platform[['OS.type']] == 'unix') 
{ 
    options('DEsubs_CACHE'=file.path(path.expand("~"), 'DEsubs') ) 
}
if (.Platform[['OS.type']] == 'windows') 
{ 
    options('DEsubs_CACHE'=file.path(
            gsub("\\\\", "/", Sys.getenv("USERPROFILE")), "AppData/DEsubs"))
}

Now the package, as well as the toy-data can be loaded as follows:

library('DEsubs')

load(system.file('extdata', 'data.RData', package='DEsubs'))

2. User Input

DEsubs accepts RNA-seq expression paired case-control profile data. The following example in Table 1 shows the right structure for RNA-seq expression data input.

Example of user input format
Gene Case 1 Case 2 Case 3 Case 4 Control 1 Control 2 Control 3 Control 4
Gene 1 1879 2734 2369 2636 2188 9743 9932 10099
Gene 2 97 124 146 114 126 33 19 31
Gene 3 485 485 469 428 475 128 135 103
… … … … … … … … …
Gene N-1 84 25 67 62 61 277 246 297
Gene N 120 312 78 514 210 324 95 102

3. Pathway network construction

KEGG signaling pathway maps have been downloaded and converted to pathway networks using CHRONOS package. Pathway networks for the seven supported organisms are included in the package itself (see Table 2).

Supported KEGG organisms
Supported Organisms R command
Homo sapiens ‘hsa’
Mus musculus ‘mmu’
Drosophila melanogaster ‘dme’
Saccharomyces cerevisiae ‘sce’
Arabidopsis thaliana ‘ath’
Rattus norvegicus ‘rno’
Danio rerio ‘dre’

DEsubs operates with Entrez ID labels, however twelve other label systems are supported after converting to Entrez IDs via a lexicon included in the package itself (see Table 3).

Supported gene labels
Supported Labels R command
Entrez ‘entrezgene’
Ensemble ‘ensembl_gene_id’, ‘ensembl_transcript_id’
‘ensembl_peptide_id’
HGNC ‘hgnc_id’, ‘hgnc_symbol’, ‘hgnc_transcript_name’
Refseq ‘refseq_mrna’, ‘refseq_peptide’

4. Pathway network processing

Next, the RNA-seq data are mapped onto the nodes and edges of the pathway network and two the pruning rules are applied to isolate interactions of interest among statistically significant differentially expressed genes (DEGs). DEGs are identified using the differential expression analysis tools in Table 5 by considering the FDR-adjusted P-value of each gene (Q-value). Instead of selecting one tools in Table 5, the user can import a custom ranked list of genes accompanied by their Q-values (argument rankedList).

Based on this information, the NodeRule prunes the nodes of the original network G=(V,E), where Q-threshold (argument DEpar) defaults to 0.05:

Qvalue(i) < Q.threshold, i ∈ V

Next, the interactions among the selected genes are pruned based on both prior biological knowledge and the expression profiles of neighbouring genes, , where C-threshold defaults to 0.6 (argument CORpar):

cor(i, j) * reg(i, j) > C.threshold,,i, j ∈ V

If genes i,j are connected with an edge with an activation type, then reg is set to 1, while if it the activation type is inhibitory, it is set to -1. The correlation between the profiles of the two genes i, j is calculated using the measures in Table 4 (argument CORtool).

Edge Rule options
Type R command
Pearson product-moment correlation coefficient ‘pearson’
Spearman rank correlation coefficient ‘spearman’
Kendall rank correlation coefficient ‘kedhall’
Node Rule options
Supported Labels R command
(Robinson, McCarthy, and Smyth 2010) ‘edgeR’
(Anders and Huber 2010) ‘DESeq2’
(Leng et al. 2013) ‘EBSeq’
(Smyth 2004) ‘vst2+limma’
(Anders and Huber 2010); (Smyth 2004) ‘voom+limma’
(Di et al. 2011) ‘NBPSeq’
(Auer and Doerge 2011) ‘TSPM’

5. Subpathway Extraction

5.1. Main Categories

Subpathway extraction is based on five main categories, (i) components, (ii) communities, (iii) streams, (iv) neighborhoods, (v) cascades. Each one sketches different topological aspect within the network. Indicative examples and a short description of DEsubs five main subpathway categories can be found in Figure 1.

Stream, neighborhood and cascade types build each subpathway (blue nodes) by starting from a gene of interest (red nodes). Components and communities are densely linked group of genes with the difference that the genes sharing common properties are maintained within the graph (green nodes).

Stream, neighborhood and cascade types build each subpathway (blue nodes) by starting from a gene of interest (red nodes). Components and communities are densely linked group of genes with the difference that the genes sharing common properties are maintained within the graph (green nodes).

The component category extracts strongly connected group of genes indicating dense local areas within the network. The community category extracts linked genes sharing a common property within the network. Thus the user can observe local gene sub-areas with a specific role within the network. Cascade, stream and neighborhood categories are generated starting from a gene of interest (GOI) in order to view the local perturbations within the network from different points of interest. The generation is performed by traversing either the forward or the backward propagation that stems from the GOI and is illustrated via three different topological schemes, gene sequences (‘cascade’ category), gene streams (‘stream’ category) and gene direct neighbors (‘neighborhood’ category).

5.2. Gene of interest (GOI)

Genes having crucial topological or functional roles within the network are considered as GOIs (see Table 6). The topological roles are portrayed using various topological measures from igraph package (Csardi and Nepusz 2006) capturing the local as well as global aspects of the network. Genes with crucial functional roles are considered as key genes for several biological and pharmacological features through fscore, a measure which estimates how a gene acts as a bridge among specific functional terms. In more detail, fscore is the number of condition-based functional terms in which a gene participates. For a functional condition fc with n terms and pij = 1 or 0 if gene(i) participates or not in term(j), the fscore of gene(i) is as follows: $$ fscore(i)=\sum_{j=1}^{n}p_i^j $$

A high value of fscore(i) for a condition j indicates that gene i participates to several functional terms of condition j (for e.g. terms for diseases), hence it operates as a bridge for the terms of condition j within the graph. As functional conditions we considered various biological and pharmacological features related with pathways, gene ontologies, diseases, drugs, microRNAs and transcription factors. External references are used to imprint gene associations by each feature separately. The references based on the approach of (Barneh, Jafari, and Mirzaie 2015); (Chen et al. 2013); (X. Li et al. 2011); (Vrahatis et al. 2016). Details are shown in Table 6.

Summarizing, a user-defined threshold (namely top) is used for the selection of GOIs. After the calculation of topological measures and functional measures by each condition (through fscore), the genes with the top best values are considered as GOIs. The parameter top is user-defined with default value top = 30. In GOIs with crucial functional role we add and those having the lowest Q-value by each user-defined experimental dataset. Thus, the user is allowed to generate subpathways starting from the most statistical significant DEGs of his own experiment. A short description for all GOI types along with the corresponding parameters are shown in Table 6.

Gene of interest (GOI) types
Type Description R command
Topological
Degree Number of adjacent interactions of the gene ‘degree’
Betweenness Number of shortest paths from all vertices to all ‘betweenness’
others that pass through that node
Closeness Inverse of farness, which is the sum of distances ‘closeness’
to all other nodes
Hub score Kleinbergs hub centrality score ‘hub_score’
Eccentricity Shortest path distance from the farthest ‘eccentricity’
node in the graph
Page rank Google Page Rank ‘page_rank’
Start Nodes Nodes without any incoming links ‘start_nodes’
Functional
DEG Genes highly differentially expressed ‘deg’
according to the experimental data
Pathways Genes acting as bridges among KEGG pathways ‘KEGG’
Biological Process Genes acting as bridges among ‘GO_bp’
Gene Ontology Biological Process terms
Cellular Component Genes acting as bridges among ‘GO_cc’
Gene Ontology Cellular Component terms
Molecular Function Genes acting as bridges among ‘GO_mf’
Gene Ontology Molecular Function terms
Disease Genes acting as bridges for OMIM targets ‘Disease_OMIM’
Disease Genes acting as bridges for GAD targets ‘Disease_GAD’
Drug Genes acting as bridges for DrugBank targets ‘Drug_DrugBank’
microRNA Genes acting as bridges for microRNA targets ‘miRNA’
Transcription Factors Genes acting as bridges for TF targets ‘TF’

5.3. All subpathway options

Cascade, stream and neighborhood subpathway types can start from seventeen (17) different GOI types and their generation is performed either with forward or backward propagation. Thus, thirty-four (34) different types are created for each of the three types. Also, the component-based types are sixteen and the community-based types are six based on igraph package. DEsubs therefore supports 124 subpathway types as described in Tables 7-11.

Subpathway Options - STREAM
Description R parameter
Topological
Forward and backward streams starting from ‘fwd.stream.topological.degree’
genes/nodes with crucial topological roles ‘fwd.stream.topological.betweenness’
within the network ‘fwd.stream.topological.closeness’
‘fwd.stream.topological.hub_score’
‘fwd.stream.topological.eccentricity’
‘fwd.stream.topological.page_rank’
‘fwd.stream.topological.start_nodes’
‘bwd.stream.topological.degree’
‘bwd.stream.topological.betweenness’
‘bwd.stream.topological.closeness’
‘bwd.stream.topological.hub_score’
‘bwd.stream.topological.eccentricity’
‘bwd.stream.topological.page_rank’
‘bwd.stream.topological.start_nodes’
Functional
Forward and backward streams starting from ‘fwd.stream.functional.GO_bp’
genes/nodes with crucial functional roles ‘fwd.stream.functional.GO_cc’
within the network ‘fwd.stream.functional.GO_mf’
‘fwd.stream.functional.Disease_OMIM’
‘fwd.stream.functional.Disease_GAD’
‘fwd.stream.functional.Drug_DrugBank’
‘fwd.stream.functional.miRNA’
‘fwd.stream.functional.TF’
‘fwd.stream.functional.KEGG’
‘fwd.stream.functional.DEG’
‘bwd.stream.functional.GO_bp’
‘bwd.stream.functional.GO_cc’
‘bwd.stream.functional.GO_mf’
‘bwd.stream.functional.Disease_OMIM’
‘bwd.stream.functional.Disease_GAD’
‘bwd.stream.functional.Drug_DrugBank’
‘bwd.stream.functional.miRNA’
‘bwd.stream.functional.TF’
‘bwd.stream.functional.KEGG’
‘bwd.stream.functional.DEG’
Subpathway Options - NEIGHBOURHOOD
Description R parameter
Topological
Forward and backward neighbourhoods starting ‘fwd.neighbourhood.topological.degree’
from genes/nodes with crucial topological ‘fwd.neighbourhood.topological.betweenness’
roles within the network ‘fwd.neighbourhood.topological.closeness’
‘fwd.neighbourhood.topological.hub_score’
‘fwd.neighbourhood.topological.eccentricity’
‘fwd.neighbourhood.topological.page_rank’
‘fwd.neighbourhood.topological.start_nodes’
‘bwd.neighbourhood.topological.degree’
‘bwd.neighbourhood.topological.betweenness’
‘bwd.neighbourhood.topological.closeness’
‘bwd.neighbourhood.topological.hub_score’
‘bwd.neighbourhood.topological.eccentricity’
‘bwd.neighbourhood.topological.page_rank’
‘bwd.neighbourhood.topological.start_nodes’
Functional
Forward and backward neighbourhoods starting ‘fwd.neighbourhood.functional.GO_bp’
from genes/nodes with crucial topological ‘fwd.neighbourhood.functional.GO_cc’
roles within the network ‘fwd.neighbourhood.functional.GO_mf’
‘fwd.neighbourhood.functional.Disease_OMIM’
‘fwd.neighbourhood.functional.Disease_GAD’
‘fwd.neighbourhood.functional.Drug_DrugBank’
‘fwd.neighbourhood.functional.miRNA’
‘fwd.neighbourhood.functional.TF’
‘fwd.neighbourhood.functional.KEGG’
‘fwd.neighbourhood.functional.DEG’
‘bwd.neighbourhood.functional.GO_bp’
‘bwd.neighbourhood.functional.GO_cc’
‘bwd.neighbourhood.functional.GO_mf’
‘bwd.neighbourhood.functional.Disease_OMIM’
‘bwd.neighbourhood.functional.Disease_GAD’
‘bwd.neighbourhood.functional.Drug_DrugBank’
‘bwd.neighbourhood.functional.miRNA’
‘bwd.neighbourhood.functional.TF’
‘bwd.neighbourhood.functional.KEGG’
‘bwd.neighbourhood.functional.DEG’
Subpathway Options - CASCADE
Description R parameter
Topological
Forward and backward cascades starting ‘fwd.cascade.topological.degree’
from genes/nodes with crucial topological ‘fwd.cascade.topological.betweenness’
roles within the network ‘fwd.cascade.topological.closeness’
‘fwd.cascade.topological.hub_score’
‘fwd.cascade.topological.eccentricity’
‘fwd.cascade.topological.page_rank’
‘fwd.cascade.topological.start_nodes’
‘bwd.cascade.topological.degree’
‘bwd.cascade.topological.betweenness’
‘bwd.cascade.topological.closeness’
‘bwd.cascade.topological.hub_score’
‘bwd.cascade.topological.eccentricity’
‘bwd.cascade.topological.page_rank’
‘bwd.cascade.topological.start_nodes’
Functional
Forward and backward cascades starting ‘fwd.cascade.functional.GO_bp’
from genes/nodes with crucial topological ‘fwd.cascade.functional.GO_cc’
roles within the network ‘fwd.cascade.functional.GO_mf’
‘fwd.cascade.functional.Disease_OMIM’
‘fwd.cascade.functional.Disease_GAD’
‘fwd.cascade.functional.Drug_DrugBank’
‘fwd.cascade.functional.miRNA’
‘fwd.cascade.functional.TF’
‘fwd.cascade.functional.KEGG’
‘fwd.cascade.functional.DEG’
‘bwd.cascade.functional.GO_bp’
‘bwd.cascade.functional.GO_cc’
‘bwd.cascade.functional.GO_mf’
‘bwd.cascade.functional.Disease_OMIM’
‘bwd.cascade.functional.Disease_GAD’
‘bwd.cascade.functional.Drug_DrugBank’
‘bwd.cascade.functional.miRNA’
‘bwd.cascade.functional.TF’
‘bwd.cascade.functional.KEGG’
‘bwd.cascade.functional.DEG’
Subpathway Options - COMMUNITY
Type Description R parameter
Random Walk Community structures that minimize ‘community.infomap’
the expected description length of
a random walker trajectory
Modular Community structures via a modularity ‘community.louvain’
measure and a hierarchical approach
Walktraps Densely connected subgraphs via ‘community.walktrap’
random walks
Leading eigen Densely connected subgraphs based ‘community.leading_eigen’
on the leading non-negative eigen-
vector of the modularity matrix
Betweeneess Community structures detection ‘community.edge_betweenness’
via edge betweenness
Greedy Community structures via greedy ‘community.fast_greedy’
optimization of modularity
Subpathway Options - COMPONENT
Type Description R parameter
Cliques A subgraph where every two distinct ‘component.3-cliques’
vertices in the clique are adjacent …
‘component.9-cliques’
K-core A maximal subgraph in which each ‘component.3-coreness’
vertex has at least degree k …
‘component.9-coreness’
Max cliques Largest of maximal cliques ‘component.max_cliques’
Components All single components ‘component.decompose’

An example follows where community.walktrap is selected as the subpathway type.

DEsubs.run <- DEsubs(
                    org='hsa', 
                    mRNAexpr=mRNAexpr, 
                    mRNAnomenclature='entrezgene', 
                    pathways='All', 
                    DEtool=NULL, DEpar=0.05, 
                    CORtool='pearson', CORpar=0.7,
                    subpathwayType='community.walktrap',
                    rankedList=rankedList, 
                    verbose=FALSE)
Subpathway extraction options consist of five main categories. The three of them (cascade, neighborhood, stream) are sub-categorized according to features (topological or functional) and the direction of propagation (forward or backward) of the gene of interest where each subpathway is starting. The other two (component, community) are sub-categorized according to various topological properties.

Subpathway extraction options consist of five main categories. The three of them (cascade, neighborhood, stream) are sub-categorized according to features (topological or functional) and the direction of propagation (forward or backward) of the gene of interest where each subpathway is starting. The other two (component, community) are sub-categorized according to various topological properties.

6. Subpathway enrichment analysis

Eight different datasets with external resources are stored locally for further enrichment analysis of resulting subpathways. Each dataset is formed with a list of terms related to biological and pharmacological features and the respective associated genes for each term. A detailed description is shown in Table 12. Additionally, the user can supply a custom gene-set in the form of an .RData file storing a matrix, named targetsPerClass. The matrix should store the terms as rownames and the targets of each term at each row. Since some rows are bound to havemore elements that others, empty cells should be filled with ‘0’ characters. Once the file is stored in a directory DEsubs/Data, it will be permanently availiable along with the other eight resources, using the filename (without the .RData suffix) as the new functional feature type along with the any of the default eight features.

The enrichment analysis is performed based on the cumulative hypergeometric distribution, where G is the number of genes in the user input list, l the number of those genes included in the subpathway, D the number of associated genes for a term and d the number of genes included in the subpathway (C. Li et al. 2013). Terms with P < 0.05 are regarded as terms with significant association with the respective subpathway.

$$ P = 1 - \sum_{x=0}^{d}\frac{\binom{D}{x}\binom{G-D}{l-x}}{\binom{G}{l}} $$

List of external databases
Type Description (# of terms) Source
Pathway Term KEGG pathway maps (179) (Chen et al. 2013)
GO Biological Process Genes sharing a common (Chen et al. 2013)
biological process (5.192)
GO Cellular Component Genes sharing a common (Chen et al. 2013)
cellular component (641)
GO Molecular Function Genes sharing a common (Chen et al. 2013)
molecular level (1.136)
OMIM Disease Disease related genes (90) (Chen et al. 2013)
GAD Disease Disease related genes (412) (X. Li et al. 2011)
DrugBank Drug Gene targets of drugs (1.488) (Barneh, Jafari, and Mirzaie 2015)
Transcription Factor Gene targetsof transcription (Chen et al. 2013)
factors (290)
Example of custom gene set
Term Target 1 Target 2 Target 3 Target 4 Target 5 Target 6 Target 7
Term 1 ACAD9 ACAD8 SH3GLB1 ESCO2 ESCO1 ADH1C ‘0’
Term 2 ADH1C ADH1B ADHFE1 ADH1A ADH6 ADH7 ADH4
… … … … … … … …
Term N PTPN1 RHOA ACTN4 ACTN3 ACTN2 ‘0’ ‘0’

7. Visualization

DEsubs visualizes its results at a gene, subpathway and organism level through various schemes such as bar plots, heat maps, directed weighted graphs, circular diagrams (Gu et al. 2014) and dot plots. Indicative examples are illustrated in figures 2-8 based on DEsubs executions using the human pathway network and a synthetic dataset. Bar plots show the genes with the best Q-value from the user-selected DE analysis tool (the user defines the desired gene number). The figures are exported in the directory Output within the user specified location. Heat maps show the genes with the highest values either in our topological or functional measures (see Table 6).

Bar plots show the genes with the best Q-value from the user-selected DE analysis tool (the user defines the desired gene number). Heat maps show the genes with the highest values either in our topological or functional measures (see Table 6). Each extracted subpathway is illustrated though a directed graph by imprinting the degree of DE and correlation among the respective gene members. Subpathway enrichment in association with biological and pharmacological features (such as pathway terms, gene ontologies, regulators, diseases and drug targets) is depicted through circular diagrams. The total picture of the enriched subpathways is performed with dot plots.

Bar plots show the genes with the best Q-value from the user-selected DE analysis tool (the user defines the desired gene number). Heat maps show the genes with the highest values either in our topological or functional measures (see Table 6). Each extracted subpathway is illustrated though a directed graph by imprinting the degree of DE and correlation among the respective gene members. Subpathway enrichment in association with biological and pharmacological features (such as pathway terms, gene ontologies, regulators, diseases and drug targets) is depicted through circular diagrams. The total picture of the enriched subpathways is performed with dot plots.

7.1 Gene Level Visualization

res <- geneVisualization(  
            DEsubs.out=DEsubs.out, top=10, 
            measures.topological=c( 'degree', 'betweenness', 'closeness',
                                    'eccentricity', 'page_rank'),
            measures.functional=c(  'KEGG', 'GO_bp','GO_cc', 'GO_mf', 
                                    'Disease_OMIM', 'Disease_GAD', 
                                    'Drug_DrugBank','miRNA', 'TF'),
            size.topological=c(5,4), 
            size.functional=c(7,4), 
            size.barplot=c(5,6),
            export='plot', verbose=FALSE)
Bars illustrate the genes with the highest Q-values.

Bars illustrate the genes with the highest Q-values.

Heat map represents the twelve genes with the highest values of functional measures. The values are scaled and the red graduation indicates the value degree.

Heat map represents the twelve genes with the highest values of functional measures. The values are scaled and the red graduation indicates the value degree.

Heat map represents the twelve genes with the highest values of topological measures. The values are scaled and the red graduation indicates the value degree.

Heat map represents the twelve genes with the highest values of topological measures. The values are scaled and the red graduation indicates the value degree.

7.2. Subpathway Level Visualization

Each extracted subpathway is illustrated though a directed graph by imprinting the degree of differential expression and correlation among the respective gene members. Additionally, it can be extracted in a variety of formats so that it can be used by external software, such as .txt, .json, .gml, .ncol, .lgl, .graphml and .dot formats.

res <- subpathwayToGraph(
                    DEsubs.out=DEsubs.out, 
                    submethod='community.walktrap', 
                    subname='sub6', verbose=FALSE,
                    export='plot' )
Graph illustrates the links of a subpathway. Red graduation in nodes indicate the Q-value degree, the edge width indicates the correlation degree between the respective genes. Green or red color in edges indicates the positive or negative correlation respectively

Graph illustrates the links of a subpathway. Red graduation in nodes indicate the Q-value degree, the edge width indicates the correlation degree between the respective genes. Green or red color in edges indicates the positive or negative correlation respectively

Subpathway enrichment in association with biological and pharmacological features (such as pathway terms, gene ontologies, regulators, diseases and drug targets) is depicted through circular diagrams.

res <- subpathwayVisualization( 
                    DEsubs.out=DEsubs.out,  
                    references=c('GO', 'TF'), 
                    submethod='community.walktrap', 
                    subname='sub1', 
                    scale=c(1, 1), 
                    export='plot', 
                    verbose=FALSE)
Circular Diagram shows the associations among genes including in a subpathway and Gene Ontology terms where are enriched

Circular Diagram shows the associations among genes including in a subpathway and Gene Ontology terms where are enriched

Circular Diagram shows the associations among genes included in a subpathway and enriched Transcription Factors.

Circular Diagram shows the associations among genes included in a subpathway and enriched Transcription Factors.

7.3. Organism Level Visualization

The total picture of the enriched subpathways is performed with dot plots. The number of features represented are selected using topTerms argument.

res <- organismVisualization( 
                    DEsubs.out=DEsubs.out, 
                    references='KEGG', 
                    topSubs=10, 
                    topTerms=20, 
                    export='plot', 
                    verbose=FALSE)
Dot plot shows the enriched associations among experiment-specific extracted subpathways and pathwaysfrom KEGG database. Twenty pathways were selected as the desired number of terms.

Dot plot shows the enriched associations among experiment-specific extracted subpathways and pathwaysfrom KEGG database. Twenty pathways were selected as the desired number of terms.

References

Anders, Simon, and Wolfgang Huber. 2010. “Differential Expression Analysis for Sequence Count Data.” Genome Biology 11 (10): 1.
Auer, Paul L, and Rebecca W Doerge. 2011. “A Two-Stage Poisson Model for Testing RNA-Seq Data.” Statistical Applications in Genetics and Molecular Biology 10 (1).
Barneh, Farnaz, Mohieddin Jafari, and Mehdi Mirzaie. 2015. “Updates on Drug–Target Network; Facilitating Polypharmacology and Data Integration by Growth of DrugBank Database.” Briefings in Bioinformatics, bbv094.
Chen, Edward Y, Christopher M Tan, Yan Kou, Qiaonan Duan, Zichen Wang, Gabriela Vaz Meirelles, Neil R Clark, and Avi Ma’ayan. 2013. “Enrichr: Interactive and Collaborative HTML5 Gene List Enrichment Analysis Tool.” BMC Bioinformatics 14 (1): 1.
Csardi, Gabor, and Tamas Nepusz. 2006. “The Igraph Software Package for Complex Network Research.” InterJournal, Complex Systems 1695 (5): 1–9.
Di, Yanming, Daniel W Schafer, Jason S Cumbie, and Jeff H Chang. 2011. “The NBP Negative Binomial Model for Assessing Differential Gene Expression from RNA-Seq.” Statistical Applications in Genetics and Molecular Biology 10 (1).
Gu, Zuguang, Lei Gu, Roland Eils, Matthias Schlesner, and Benedikt Brors. 2014. “Circlize Implements and Enhances Circular Visualization in r.” Bioinformatics, btu393.
Leng, Ning, John A Dawson, James A Thomson, Victor Ruotti, Anna I Rissman, Bart MG Smits, Jill D Haag, Michael N Gould, Ron M Stewart, and Christina Kendziorski. 2013. “EBSeq: An Empirical Bayes Hierarchical Model for Inference in RNA-Seq Experiments.” Bioinformatics 29 (8): 1035–43.
Li, Chunquan, Junwei Han, Qianlan Yao, Chendan Zou, Yanjun Xu, Chunlong Zhang, Desi Shang, et al. 2013. “Subpathway-GM: Identification of Metabolic Subpathways via Joint Power of Interesting Genes and Metabolites and Their Topologies Within Pathways.” Nucleic Acids Research 41 (9): e101–1.
Li, Xia, Chunquan Li, Desi Shang, Jing Li, Junwei Han, Yingbo Miao, Yan Wang, et al. 2011. “The Implications of Relationships Between Human Diseases and Metabolic Subpathways.” PloS One 6 (6): e21131.
Robinson, Mark D, Davis J McCarthy, and Gordon K Smyth. 2010. “edgeR: A Bioconductor Package for Differential Expression Analysis of Digital Gene Expression Data.” Bioinformatics 26 (1): 139–40.
Smyth, G. K. 2004. “Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments.” Statistical Applications in Genetics and Molecular Biology 3 (1).
Vrahatis, Aristidis G, Konstantina Dimitrakopoulou, Panos Balomenos, Athanasios K Tsakalidis, and Anastasios Bezerianos. 2016. “CHRONOS: A Time-Varying Method for microRNA-Mediated Subpathway Enrichment Analysis.” Bioinformatics 32 (6): 884–92.