pathfindR is a tool for enrichment analysis via active subnetworks. The package also offers functionalities to cluster the enriched terms and identify representative terms in each cluster, to score the enriched terms per sample and to visualize analysis results.

The functionalities of pathfindR is described in detail in Ulgen E, Ozisik O, Sezerman OU. 2019. pathfindR: An R Package for Comprehensive Identification of Enriched Pathways in Omics Data Through Active Subnetworks. Front. Genet.


The observation that motivated us to develop pathfindR was that direct enrichment analysis of differential RNA/protein expression or DNA methylation results may not provide the researcher with the full picture. That is to say: enrichment analysis of only a list of significant genes alone may not be informative enough to explain the underlying disease mechanisms. Therefore, we considered leveraging interaction information from a protein-protein interaction network (PIN) to identify distinct active subnetworks and then perform enrichment analyses on these subnetworks.

An active subnetwork can be defined as a group of interconnected genes in a PIN that predominantly consists of significantly altered genes. In other words, active subnetworks define distinct disease-associated sets of interacting genes, whether discovered through the original analysis or discovered because of being in interaction with a significant gene.

The active-subnetwork-oriented enrichment analysis approach of pathfindR can be summarized as follows: Mapping the input genes with the associated p values onto the PIN (after processing the input), active subnetwork search is performed. The resulting active subnetworks are then filtered based on their scores and the number of significant genes they contain. This filtered list of active subnetworks are then used for enrichment analyses, i.e. using the genes in each of the active subnetworks, the significantly enriched terms (pathways/gene sets) are identified. Enriched terms with adjusted p values larger than the given threshold are discarded and the lowest adjusted p value (over all active subnetworks) for each term is kept. This process of active subnetwork search + enrichment analyses is repeated for a selected number of iterations, performed in parallel. Over all iterations, the lowest and the highest adjusted-p values, as well as number of occurrences over all iterations are reported for each significantly enriched term in the resulting data frame. An HTML report containing the results is also provided containing links to the visualizations of the enriched terms. This active-subnetwork-oriented enrichment approach is demonstrated in the section Active-subnetwork-oriented Enrichment Analysis of this vignette.

The enrichment analysis usually yields a great number of enriched terms whose biological functions are related. Therefore, we implemented two clustering approaches using a pairwise distance matrix based on the kappa statistics between the enriched terms (as proposed by Huang et al. 1). Based on this distance metric, the user can perform either hierarchical (default) or fuzzy clustering of the enriched terms. Details of clustering and partitioning of enriched terms are presented in the Clustering Enriched Terms section of this vignette.

Other functionalities of pathfindR including:

  • agglomerated score calculation per each term (to investigate how a gene set is altered in a given sample)
  • visualization of terms and term-related genes as a graph (to determine the degree of overlap between the enriched terms by identifying shared and/or distinct significant genes) and
  • pathfindR analysis with custom gene sets are also briefly described.

Active-subnetwork-oriented Enrichment Analysis

For convenience, we provide the wrapper function run_pathfindR() to be used for the active-subnetwork-oriented enrichment analysis. The input for this function must be a data frame consisting of the columns containing: Gene Symbols, Change Values (optional) and p values. The example data frame used in this vignette (input_df) is the dataset containing the differentially-expressed genes for the GEO dataset GSE15573 comparing 18 rheumatoid arthritis (RA) patients versus 15 healthy subjects.

The first 6 rows of the example input data frame are displayed below:

Gene.symbol logFC adj.P.Val
FAM110A -0.6939359 0.0000034
RNASE2 1.3535040 0.0000101
S100A8 1.5448338 0.0000347
S100A9 1.0280904 0.0002263
TEX261 -0.3235994 0.0002263
ARHGAP17 -0.6919330 0.0002708

For a detailed step-by-step explanation and an unwrapped demonstration of the active-subnetwork-oriented enrichment analysis, see the vignette Step-by-Step Execution of the pathfindR Enrichment Workflow

Executing the workflow is straightforward (but does typically take several minutes):

output_df <- run_pathfindR(input_df)

Useful arguments

This subsection demonstrates some (selected) useful arguments of run_pathfindR(). For a full list of arguments, see ?run_pathfindR or visit our GitHub wiki.

Filtering Input Genes

By default, run_pathfindR() uses the input genes with p-values < 0.05. To change this threshold, use p_val_threshold:

output_df <- run_pathfindR(input_df, p_val_threshold = 0.01)

Output Directory

By default, run_pathfindR() creates a directory named "pathfindR_Results" under the current working directory for writing the output files. To change the output directory, use output_dir:

output_df <- run_pathfindR(input_df, output_dir = "this_is_my_output_directory")

This creates "this_is_my_output_directory" under the current working directory.

In essence, this argument is treated as a path so it can be used to create the output directory anywhere. For example, to create the directory "my_dir" under "~/Desktop" and run the analysis there, you may run:

output_df <- run_pathfindR(input_df, output_dir = "~/Desktop/my_dir")

Note: If the output directory (e.g. "my_dir") already exists, run_pathfindR() creates and works under "my_dir(1)". If that exists also exists, it creates "my_dir(2)" and so on. This was intentionally implemented so that any previous pathfindR results are not overwritten.

Gene Sets for Enrichment

The active-subnetwork-oriented enrichment analyses can be performed on any gene sets (biological pathways, gene ontology terms, transcription factor target genes, miRNA target genes etc.). The available gene sets in pathfindR are “KEGG”, “Reactome”, “BioCarta”, “GO-All”, “GO-BP”, “GO-CC” and “GO-MF” (all for Homo sapiens). For changing the default gene sets for enrichment analysis (hsa KEGG pathways), use the argument gene_sets

output_df <- run_pathfindR(input_df, gene_sets = "GO-MF")

By default, run_pathfindR() filters the gene sets by including only the terms containing at least 10 and at most 300 genes. To change the default behavior, you may change min_gset_size and max_gset_size:

## Including more terms for enrichment analysis
output_df <- run_pathfindR(input_df, 
                           gene_sets = "GO-MF",
                           min_gset_size = 5,
                           max_gset_size = 500)

Note that increasing the number of terms for enrichment analysis may result in significantly longer run time.

If the user prefers to use another gene set source, the gene_sets argument should be set to "Custom" and the custom gene sets (list) and the custom gene set descriptions (named vector) should be supplied via the arguments custom_genes and custom_descriptions, respectively. See ?fetch_gene_set for more details and Analysis with Custom Gene Sets for a simple demonstration.

For details on obtaining organism-specific Gene Sets and PIN data, see the vignette Obtaining PIN and Gene Sets Data.

Filtering Enriched Terms by Adjusted-p Values

By default, run_pathfindR() adjusts the enrichment p values via the “bonferroni” method and filters the enriched terms by adjusted-p value < 0.05. To change this adjustment method and the threshold, set adj_method and enrichment_threshold, respectively:

output_df <- run_pathfindR(input_df, 
                           adj_method = "fdr",
                           enrichment_threshold = 0.01)

Protein-protein Interaction Network

For the active subnetwork search process, a protein-protein interaction network (PIN) is used. run_pathfindR() maps the input genes onto this PIN and identifies active subnetworks which are then be used for enrichment analyses. To change the default PIN (“Biogrid”), use the pin_name_path argument:

output_df <- run_pathfindR(input_df, pin_name_path = "IntAct")

The pin_name_path argument can be one of “Biogrid”, “STRING”, “GeneMania”, “IntAct”, “KEGG”, “mmu_STRING” or it can be the path to a custom PIN file provided by the user.

# to use an external PIN of your choice
output_df <- run_pathfindR(input_df, pin_name_path = "/path/to/myPIN.sif")

NOTE: the PIN is also used for generating the background genes (in this case, all unique genes in the PIN) during hypergeometric-distribution-based tests in enrichment analyses. Therefore, a large PIN will generally result in better results.

Active Subnetwork Search Method

Currently, there are three algorithms implemented in pathfindR for active subnetwork search: Greedy Algorithm (default, based on Ideker et al. 2), Simulated Annealing Algorithm (based on Ideker et al. 3) and Genetic Algorithm (based on Ozisik et al. 4). For a detailed discussion on which algorithm to use see this wiki entry

# for simulated annealing:
output_df <- run_pathfindR(input_df, search_method = "SA")
# for genetic algorithm:
output_df <- run_pathfindR(input_df, search_method = "GA")

Other Arguments

Because the active subnetwork search algorithms are stochastic, run_pathfindR() may be set to iterate the active subnetwork identification and enrichment steps multiple times (by default 1 time). To change this number, set iterations:

output_df <- run_pathfindR(input_df, iterations = 25) 

run_pathfindR() uses a parallel loop (using the package foreach) for performing these iterations in parallel. By default, the number of processes to be used is determined automatically. To override, change n_processes:

# if not set, n_processes defaults to (number of detected cores - 1)
output_df <- run_pathfindR(input_df, iterations = 5, n_processes = 2)


Enriched Terms Data Frame

run_pathfindR() returns a data frame of enriched terms. Columns are:

  • ID: ID of the enriched term
  • Term_Description: Description of the enriched term
  • Fold_Enrichment: Fold enrichment value for the enriched term (Calculated using ONLY the input genes)
  • occurrence: The number of iterations that the given term was found to enriched over all iterations
  • lowest_p: the lowest adjusted-p value of the given term over all iterations
  • highest_p: the highest adjusted-p value of the given term over all iterations
  • non_Signif_Snw_Genes (OPTIONAL): the non-significant active subnetwork genes, comma-separated (controlled by list_active_snw_genes, default is FALSE)
  • Up_regulated: the up-regulated genes (as determined by change value > 0, if the change column was provided) in the input involved in the given term’s gene set, comma-separated. If change column was not provided, all affected input genes are listed here.
  • Down_regulated: the down-regulated genes (as determined by change value < 0, if the change column was provided) in the input involved in the given term’s gene set, comma-separated

The first 2 rows of the output data frame of the example analysis on the rheumatoid arthritis gene-level differential expression input data (RA_input) is shown below:

knitr::kable(head(RA_output, 2))
ID Term_Description Fold_Enrichment occurrence support lowest_p highest_p Up_regulated Down_regulated
hsa04714 Thermogenesis 2.503010 1 0.0322581 1e-07 1e-07 NDUFA1, NDUFB3, UQCRQ, COX6A1, COX7A2, COX7C ADCY7, CREB1, KDM1A, SMARCA4, ACTG1, ACTB, ARID1A, MTOR
hsa04130 SNARE interactions in vesicular transport 4.529257 1 0.0241935 1e-07 1e-07 STX6 STX2, BET1L, SNAP23

By default, run_pathfindR() also produces a graphical summary of enrichment results for top 10 enriched terms, which can also be later produced by enrichment_chart():

You may also disable plotting this chart by setting plot_enrichment_chart=FALSE and later produce this plot via the function enrichment_chart():

# change number of top terms plotted (default = 10)
enrichment_chart(result_df = RA_output, 
                 top_terms = 15)

HTML Report

The function also creates an HTML report results.html that is saved in the output directory. This report contains links to two other HTML files:

1. enriched_terms.html

This document contains the table of the active subnetwork-oriented enrichment results (same as the returned data frame). By default, each enriched term description is linked to the visualization of the term, with the gene nodes colored according to their change values. If you choose not to create the visualization files, set visualize_enriched_terms = FALSE.

2. conversion_table.html

This document contains the table of converted gene symbols. Columns are:

  • Old Symbol: the original gene symbol
  • Converted Symbol: the alias symbol that was found in the PIN
  • Change: the provided change value
  • p-value: the provided adjusted p value

During input processing, gene symbols that are not in the PIN are identified and excluded. For human genes, if aliases of these missing gene symbols are found in the PIN, these symbols are converted to the corresponding aliases (controlled by the argument convert2alias). This step is performed to best map the input data onto the PIN.

The document contains a second table of genes for which no interactions were identified after checking for alias symbols (so these could not be used during the analysis).

Clustering Enriched Terms

The wrapper function cluster_enriched_terms() can be used to perform clustering of enriched terms and partitioning the terms into biologically-relevant groups. Clustering can be performed either via hierarchical or fuzzy method using the pairwise kappa statistics (a chance-corrected measure of co-occurrence between two sets of categorized data) matrix between all enriched terms.

Hierarchical Clustering

By default, cluster_enriched_terms() performs hierarchical clustering of the terms (using \(1 - \kappa\) as the distance metric). Iterating over \(2,3,...n\) clusters (where \(n\) is the number of terms), cluster_enriched_terms() determines the optimal number of clusters by maximizing the average silhouette width, partitions the data into this optimal number of clusters and returns a data frame with cluster assignments.

RA_clustered <- cluster_enriched_terms(RA_output, plot_dend = FALSE, plot_clusters_graph = FALSE)
## First 2 rows of clustered data frame
knitr::kable(head(RA_clustered, 2))
ID Term_Description Fold_Enrichment occurrence support lowest_p highest_p Up_regulated Down_regulated Cluster Status
1 hsa04714 Thermogenesis 2.503010 1 0.0322581 1e-07 1e-07 NDUFA1, NDUFB3, UQCRQ, COX6A1, COX7A2, COX7C ADCY7, CREB1, KDM1A, SMARCA4, ACTG1, ACTB, ARID1A, MTOR 1 Representative
3 hsa00190 Oxidative phosphorylation 2.976083 1 0.0241935 1e-07 1e-07 NDUFA1, NDUFB3, UQCRQ, COX6A1, COX7A2, COX7C, ATP6V1D, ATP6V0E1 ATP6V0E2 1 Member
## The representative terms
knitr::kable(RA_clustered[RA_clustered$Status == "Representative", ])
ID Term_Description Fold_Enrichment occurrence support lowest_p highest_p Up_regulated Down_regulated Cluster Status
1 hsa04714 Thermogenesis 2.503010 1 0.0322581 0.0000001 0.0000001 NDUFA1, NDUFB3, UQCRQ, COX6A1, COX7A2, COX7C ADCY7, CREB1, KDM1A, SMARCA4, ACTG1, ACTB, ARID1A, MTOR 1 Representative
2 hsa04130 SNARE interactions in vesicular transport 4.529257 1 0.0241935 0.0000001 0.0000001 STX6 STX2, BET1L, SNAP23 2 Representative
4 hsa04064 NF-kappa B signaling pathway 2.930696 1 0.0564516 0.0000001 0.0000001 LY96 PRKCQ, CARD11, TICAM1, IKBKB, PARP1, UBE2I, CSNK2A2 3 Representative
10 hsa03013 RNA transport 2.576991 1 0.0241935 0.0000034 0.0000034 NUP214 NUP62, NUP93, RANGAP1, UBE2I, SUMO3, GEMIN4, EIF2S3, EIF2B1, EIF4A3, RNPS1, SRRM1 4 Representative
11 hsa04722 Neurotrophin signaling pathway 2.849978 1 0.0564516 0.0000066 0.0000066 SH2B3, CRKL, FASLG, CALM3, CALM1, ABL1, MAGED1, IRAK2, IKBKB 5 Representative
12 hsa03040 Spliceosome 3.607788 1 0.0645161 0.0000077 0.0000077 SF3B6, LSM3, BUD31 SNRPB, SF3B2, U2AF2, PUF60, SNU13, DDX23, EIF4A3, HNRNPA1, PCBP1, SRSF8, SRSF5 6 Representative
17 hsa05230 Central carbon metabolism in cancer 2.166167 1 0.0241935 0.0000312 0.0000312 HK3 PDHA1, PDHB, MTOR 7 Representative
20 hsa05130 Pathogenic Escherichia coli infection 2.372468 1 0.0483871 0.0001086 0.0001086 TLR5, GAPDH, CLDN9 ARF1, ACTG1, ACTB, SLC9A3R1, TUBB, ABL1, ITGB1, IKBKB, FASLG 8 Representative
26 hsa04110 Cell cycle 1.506709 1 0.0241935 0.0002381 0.0002381 RBL2, ABL1, HDAC1, CDKN1C, ANAPC1 9 Representative
30 hsa03010 Ribosome 1.720820 1 0.0080645 0.0007479 0.0007479 MRPS18C, RPS24, MRPL33, RPL26, RPL31, RPL39 RPLP2 10 Representative
31 hsa03050 Proteasome 1.660728 1 0.0322581 0.0007802 0.0007802 PSMD7, PSMB10 11 Representative
38 hsa03420 Nucleotide excision repair 4.061562 1 0.0080645 0.0013233 0.0013233 GTF2H5, POLE4 XPC, RPA1, POLD2 12 Representative
51 hsa05202 Transcriptional misregulation in cancer 2.185168 1 0.0161290 0.0035608 0.0035608 MMP9, DDIT3 HDAC1, SIN3A, BCL11B, SLC45A3, EWSR1, IL2RB, TAF15, ASPSCR1 13 Representative
79 hsa04120 Ubiquitin mediated proteolysis 1.636483 1 0.0161290 0.0223077 0.0223077 TRIP12 UBE2G1, UBE2I, HERC1, PIAS3, ANAPC1 14 Representative
92 hsa04650 Natural killer cell mediated cytotoxicity 0.593117 1 0.0080645 0.0406276 0.0406276 LCP2, FASLG 15 Representative

After clustering, you may again plot the summary enrichment chart and display the enriched terms by clusters:

# plotting only selected clusters for better visualization
RA_selected <- subset(RA_clustered, Cluster %in% 5:7)
enrichment_chart(RA_selected, plot_by_cluster = TRUE)

For details, see ?hierarchical_term_clustering

Heuristic Fuzzy Multiple-linkage Partitioning

Alternatively, the fuzzy clustering method (as described by Huang et al.5) can be used:

RA_clustered_fuzzy <- cluster_enriched_terms(RA_output, method = "fuzzy")

For details, see ?fuzzy_term_clustering

Term-Gene Heatmap

The function term_gene_heatmap() can be used to visualize the heatmap of genes that are involved in the enriched terms. This heatmap allows visual identification of the input genes involved in the enriched terms, as well as the common or distinct genes between different terms. If the input data frame (same as in run_pathfindR()) is supplied, the tile colors indicate the change values.

term_gene_heatmap(result_df = RA_output, genes_df = RA_input)

See the vignette Visualization of pathfindR Enrichment Results for more details.

Term-Gene Graph

The visualization function term_gene_graph() (adapted from the “Gene-Concept network visualization” by the R package enrichplot) can be utilized to visualize which genes are involved in the enriched terms. The function creates a term-gene graph which shows the connections between genes and biological terms (enriched pathways or gene sets). This allows for the investigation of multiple terms to which significant genes are related. This graph also enables visual determination of the degree of overlap between the enriched terms by identifying shared and/or distinct significant genes.

term_gene_graph(result_df = RA_output, use_description = TRUE)

See the vignette Visualization of pathfindR Enrichment Results for more details.

UpSet Plot

UpSet plots are plots of the intersections of sets as a matrix. This function creates a ggplot object of an UpSet plot where the x-axis is the UpSet plot of intersections of enriched terms. By default (i.e., method = "heatmap"), the main plot is a heatmap of genes at the corresponding intersections, colored by up/down regulation (if genes_df is provided, colored by change values). If method = "barplot", the main plot is bar plots of the number of genes at the corresponding intersections. Finally, if method = "boxplot" and genes_df is provided, then the main plot displays the boxplots of change values of the genes at the corresponding intersections.

UpSet_plot(result_df = RA_output, genes_df = RA_input)

See the vignette Visualization of pathfindR Enrichment Results for more details.

Aggregated Term Scores per Sample

The function score_terms() can be used to calculate the agglomerated z score of each enriched term per sample. This allows the user to individually examine the scores and infer how a term is overall altered (activated or repressed) in a given sample or a group of samples.

## Vector of "Case" IDs
cases <- c("GSM389703", "GSM389704", "GSM389706", "GSM389708", 
           "GSM389711", "GSM389714", "GSM389716", "GSM389717", 
           "GSM389719", "GSM389721", "GSM389722", "GSM389724", 
           "GSM389726", "GSM389727", "GSM389730", "GSM389731", 
           "GSM389733", "GSM389735")

## Calculate scores for representative terms 
## and plot heat map using term descriptions
score_matrix <- score_terms(enrichment_table = RA_clustered[RA_clustered$Status == "Representative", ],
                            exp_mat = RA_exp_mat,
                            cases = cases,
                            use_description = TRUE, # default FALSE
                            label_samples = FALSE, # default = TRUE
                            case_title = "RA",  # default = "Case"
                            control_title = "Healthy", # default = "Control"
                            low = "#f7797d", # default = "green"
                            mid = "#fffde4", # default = "black"
                            high = "#1f4037") # default = "red"

Comparison of 2 pathfindR Results

The function combine_pathfindR_results() allows combination of two pathfindR active-subnetwork-oriented enrichment analysis results for investigating common and distinct terms between the groups. Below is an example for comparing results using two different rheumatoid arthritis-related data sets(RA_output and RA_comparison_output).

combined_df <- combine_pathfindR_results(result_A = RA_output, 
                                         result_B = RA_comparison_output, 
                                         plot_common = FALSE)
#> You may run `combined_results_graph()` to create visualizations of combined term-gene graphs of selected terms

For more details, see the vignette Comparing Two pathfindR Results

Analysis with Custom Gene Sets

As of v1.5, pathfindR offers utility functions for obtaining organism-specific PIN data and organism-specific gene sets data via get_pin_file() and get_gene_sets_list(), respectively. See the vignette Obtaining PIN and Gene Sets Data for detailed information on how to gather PIN and gene sets data (for any organism of your choice) for use with pathfindR.

It is possible to use run_pathfindR() with custom gene sets (including gene sets for non-Homo-sapiens species). Here, we provide an example application of active-subnetwork-oriented enrichment analysis of the target genes of two transcription factors.

We first load and prepare the gene sets:

## CREB target genes
CREB_target_genes <- normalizePath(system.file("extdata/CREB.txt", package = "pathfindR"))
CREB_target_genes <- readLines(CREB_target_genes)[-c(1, 2)] # skip the first two lines

## MYC target genes
MYC_target_genes <- normalizePath(system.file("extdata/MYC.txt", package = "pathfindR"))
MYC_target_genes <- readLines(MYC_target_genes)[-c(1, 2)] # skip the first two lines

## Prep for use
custom_genes <- list(TF1 = CREB_target_genes, TF2 = MYC_target_genes)
custom_descriptions <- c(TF1 = "CREB target genes", TF2 = "MYC target genes")

We next prepare the example input data frame. Because of the way we choose genes, we expect significant enrichment for MYC targets (40 MYC target genes + 10 CREB target genes). Because this is only an example, we also assign each genes random p-values between 0.001 and 0.05.


## Select 40 random genes from MYC gene sets and 10 from CREB gene sets
selected_genes <- sample(MYC_target_genes, 40)
selected_genes <- c(selected_genes, 
                    sample(CREB_target_genes, 10))

## Assign random p value between 0.001 and 0.05 for each selected gene
rand_p_vals <- sample(seq(0.001, 0.05, length.out = 5),
                      size = length(selected_genes),
                      replace = TRUE)

input_df <- data.frame(Gene_symbol = selected_genes,
                       p_val = rand_p_vals)
Gene_symbol p_val
HNRNPD 0.01325
IL1RAPL1 0.00100
CD3EAP 0.00100
LTBR 0.02550
CGREF1 0.00100
TPM2 0.05000

Finally, we perform active-subnetwork-oriented enrichment analysis via run_pathfindR() using the custom genes as the gene sets:

custom_result <- run_pathfindR(input_df,
                               gene_sets = "Custom",
                               custom_genes = custom_genes,
                               custom_descriptions = custom_descriptions,
                               max_gset_size = Inf, # DO NOT LIMIT GENE SET SIZE
                               output_dir = "misc/v1.4/CREB_MYC")

ID Term_Description Fold_Enrichment occurrence lowest_p highest_p Up_regulated Down_regulated
TF2 MYC target genes 17.82888 1 0.0000000 0.0000000 AGRP, ATP6V1C1, C19orf54, CD3EAP, CGREF1, CNPY3, EPB41, FOXD3, FXR1, GLA, HNRNPD, HOXA7, IL1RAPL1, KDM6A, LONP1, LTBR, MDN1, MICU1, NET1, NEUROD6, NMNAT2, NOL6, NUDC, PEPD, PKN1, PSMB3, RPS19, RPS28, RRS1, SLC9A5, SMC3, STC2, TESK2, TNPO2, TOPORS, TPM2, TSSK3, WBP2, ZBTB8OS, ZFYVE26, ZHX2
TF1 CREB target genes 19.94835 1 0.0008582 0.0008582 BRAF, DIO2, ELAVL1, EPB41, FAM65A, FOXD3, NEUROD6, NOC4L, NUPL2, PPP1R15A, SYNGR3, TIPRL

It is also possible to run pathfindR using non-human organism annotation. See the vignette pathfindR Analysis for non-Homo-sapiens organisms

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  2. Ideker T, Ozier O, Schwikowski B, Siegel AF. Discovering regulatory and signalling circuits in molecular interaction networks. Bioinformatics. 2002;18 Suppl 1:S233-40.↩︎

  3. Ideker T, Ozier O, Schwikowski B, Siegel AF. Discovering regulatory and signalling circuits in molecular interaction networks. Bioinformatics. 2002;18 Suppl 1:S233-40.↩︎

  4. Ozisik O, Bakir-Gungor B, Diri B, Sezerman OU. Active Subnetwork GA: A Two Stage Genetic Algorithm Approach to Active Subnetwork Search. Current Bioinformatics. 2017; 12(4):320-8. 10.2174/1574893611666160527100444↩︎

  5. Huang DW, Sherman BT, Tan Q, et al. The DAVID Gene Functional Classification Tool: a novel biological module-centric algorithm to functionally analyze large gene lists. Genome Biol. 2007;8(9):R183.↩︎