pathfindR: An R Package for Comprehensive Identification of Enriched Pathways in Omics Data Through Active Subnetworks

1High-throughput technologies revolutionized biomedical research by enabling comprehensive characterization of biological systems. One of the most common use cases of these technologies is to perform experiments comparing two groups of samples (typically disease versus control) and identify a list of altered genes. However, this list alone often falls short of providing mechanistic insights into the underlying biology of the disease being studied. Therefore, researchers face a challenge posed by high-throughput experiments: extracting relevant information that allows them to understand the underlying mechanisms from a long list of genes.

2One approach that reduces the complexity of analysis while simultaneously providing great explanatory power is identifying groups of genes that function in the same pathways, i.e., pathway analysis. Pathway analysis has been successfully and repeatedly applied to gene expression, proteomics, and DNA methylation data.

3Most commonly used pathway analysis methods are overrepresentation analysis (ORA) and functional class scoring (FCS). For each pathway, ORA statistically evaluates the proportion of altered genes among the pathway genes against the proportion among a set of background genes. In FCS, a gene-level statistic is calculated using the measurements from the experiment. These gene-level statistics are then aggregated into a pathway-level statistic for each pathway. Finally, the significance of each pathway-level statistic is assessed, and significant pathways are determined.

4While they are widely used, there are drawbacks to conventional pathway analysis methods. The statistics used by ORA approaches usually consider the number of genes in a list alone. ORA methods are also independent of the values associated with these genes, such as fold changes or p values. Most importantly, both ORA and FCS methods lack in incorporating interaction information. We propose that directly performing pathway analysis on a gene set is not completely informative because this approach reduces gene-phenotype association evidence by ignoring information on interactions of genes.

5We propose a pathway analysis method, which we named pathfindR, that first identifies active subnetworks and then performs enrichment analysis using the identified active subnetworks. For a given list of significantly altered genes, an active subnetwork is defined as a group of interconnected genes in a protein-protein interaction network (PIN) that predominantly consists of significantly altered genes. In other words, active subnetworks define distinct disease-associated sets of interacting genes.

6The idea of utilizing PIN information to enhance pathway enrichment results was sought and successfully implemented in numerous studies. Gene Network Enrichment Analysis (GNEA) analyzes gene expression data. The mRNA expression of every gene is mapped onto a PIN, and a significantly transcriptionally affected subnetwork is identified via jActiveModules. To determine the gene set enrichment, each gene set is then tested for overrepresentation in the subnetwork. In EnrichNet, input genes and pathway genes are mapped on a PIN. Using the random walk with restart (RWR) algorithm, distances between input genes and pathway genes are calculated. Enrichment results are obtained by comparing these distances to a background model. In both NetPEA and NetPEA′, initially, the RWR algorithm is used to measure distances between pathways and input gene sets. The significances of pathways are then calculated by comparing against a background model created with two different approaches: a) randomizing input genes (NetPEA) and b) randomizing input genes and the PIN (NetPEA′).

7With pathfindR, our aim was likewise to exploit interaction information to extract the most relevant pathways. We aimed to combine together active subnetwork search and pathway enrichment analysis. By implementing this original active-subnetwork-oriented pathway analysis approach as an R package, our intention was to provide the research community with a set of utilities (in addition to pathway analysis, clustering of pathways, scoring of pathways, and visualization utilities) that will be effective, beneficial, and straightforward to utilize for pathway enrichment analysis exploiting interaction information.

8The active-subnetwork-oriented pathway enrichment paradigm of pathfindR can be summarized as follows: Mapping the statistical significance of each gene onto a PIN, active subnetworks, i.e., subnetworks in the PIN that contain an optimal number of significant nodes maximizing the overall significance of the subnetwork, either in direct contact or in indirect contact via an insignificant (non-input) node, are identified. Following a subnetwork filtering step, enrichment analyses are then performed on these active subnetworks. Similar to the above-mentioned PIN-aided enrichment approaches, utilization of active subnetworks allows for efficient exploitation of interaction information and enhances enrichment analysis.

9For the identification of active subnetworks, various algorithms have been proposed, such as greedy algorithms, simulated annealing, genetic algorithms, and mathematical programming-based methods. In pathfindR, we provide implementations for a greedy algorithm, a simulated annealing algorithm, and a genetic algorithm.

10In summary, pathfindR integrates information from three main resources to enhance determination of the mechanisms underlying a phenotype: (i) differential expression/methylation information obtained through omics analyses, (ii) interaction information through a PIN via active subnetwork identification, and (iii) pathway/gene set annotations from sources such as Kyoto Encyclopedia of Genes and Genomes (KEGG), Reactome, BioCarta, and Gene Ontology (GO).

11The pathfindR R (https://www.R-project.org/) package was developed based on a previous approach developed by our group for genome-wide association studies (GWASes): Pathway and Network-Oriented GWAS Analysis (PANOGA). PANOGA was successfully applied to uncover the underlying mechanisms in GWASes of various diseases, such as intracranial aneurysm, epilepsy, and Behcet’s disease. With pathfindR, we aimed to extend the approach of PANOGA to omics analyses and provide novel functionality.

12In this article, we present an overview of pathfindR, example applications on three gene expression data sets, and comparison of the results of pathfindR with those obtained using three tools widely used for enrichment analyses: The Database for Annotation, Visualization and Integrated Discovery (DAVID), Signaling Pathway Impact Analysis (SPIA), and Gene Set Enrichment Analysis (GSEA).

13PIN data available in pathfindR by default are KEGG, Biogrid, GeneMania, and IntAct. The default PIN is Biogrid. Besides these four default PINs, the researcher can also use any other PIN of their choice on the condition that they provide the PIN file in simple interaction file (SIF) format.

14The KEGG Homo sapiens PIN was created by an in-house script using the KEGG pathways. In KEGG, pathways are represented in XML files that contain genes and gene groups, such as protein complexes as entries and interactions as entry pairs. The KEGG pathway XML files were obtained using the official KEGG Application Programming Interface (API) which is a REST-style interface to the KEGG database resource. Using the in-house script, the XML files were parsed; the interactions were added as undirected pairs, while interaction types were disregarded. In cases of an entry in an interacting pair containing multiple genes, interactions from all of these genes to the other entry were built.

15For Biogrid, Homo sapiens PIN data in tab-delimited text format from release 3.4.156 (BIOGRID-ORGANISM-Homo_sapiens-3.4.156.tab.txt) was obtained from the Biogrid Download File Repository (https://downloads.thebiogrid.org/BioGRID).

16For IntAct, the PIN data in Proteomics Standards Initiative – Molecular Interactions tab-delimited (PSI-MI TAB) (MITAB) format (intact.txt) were obtained from the IntAct Molecular Interaction Database FTP site (ftp://ftp.ebi.ac.uk/pub/databases/intact/current) in January 2018.

17For GeneMania, Homo sapiens PIN data in tab-delimited text format from the latest release (COMBINED.DEFAULT_NETWORKS.BP_COMBINING.txt) was obtained from the official data repository (http://genemania.org/data/current/Homo_sapiens.COMBINED/). For this PIN only, only interactions with GeneMania weights ≥0.0006 were kept, allowing only strong interactions.

18No filtration for interaction types were performed for any PIN (i.e., all types of interactions were kept). The processing steps performed for all the PINs were (1.) if the HUGO Gene Nomenclature Committee (HGNC) symbols for interacting genes were not provided, conversion of provided gene identifiers to HGNC symbols using biomaRt was performed; (2.) duplicate interactions and self-interactions (if any) were removed; and (3.) all PINs were formatted as SIFs.

19Gene sets available in pathfindR are KEGG, Reactome, BioCarta, GO-Biological Process (GO-BP), GO-Cellular Component (GO-CC), GO-Molecular Function (GO-MF) and GO-All (GO-BP, GO-CC, and GO-MF combined).

20KEGG gene sets were obtained using the R package KEGGREST. Reactome gene sets in Gene Matrix Transposed (GMT) file format were obtained from the Reactome website (https://reactome.org/download/current/). BioCarta gene sets in GMT format were retrieved from the Molecular Signatures Database (MSigDB) website (http://software.broadinstitute.org/gsea/msigdb). All “High-quality” GO gene sets were obtained from GO2MSIG web interface (http://www.go2msig.org/cgi-bin/prebuilt.cgi?taxid=9606) in GMT format. All of the datasets were processed using R to obtain (1) a list containing the genes involved in each given gene set/pathway (hence, each element of the list is named by the gene set ID and is a vector of gene symbols located in the given gene set/pathway) and (2) a list containing the descriptions for each gene set/pathway (i.e., a list linking gene set IDs to description).

21All of the gene sets in pathfindR are for Homo sapiens, and the default gene set is KEGG. The researcher can also use a gene set of their choice following the instructions on pathfindR wiki.

22All of the default data for PINs and gene sets are planned to be updated annually.

23In pathfindR, we followed the scoring scheme that was proposed by ). The p value of each gene is converted to a z score using equation (1), and the score of a subnetwork is calculated using equation (2). In equation (1) Φ–1 is the inverse normal cumulative distribution function. In equation (2), A is the set of genes in the subnetwork and k is its cardinality.

24In the same scoring scheme, a Monte Carlo approach is used for the calibration of the scores of subnetworks against a background distribution. Using randomly selected genes, 2,000 subnetworks of each possible size are constructed, and for each possible size, the mean and standard deviation of the score is calculated. These values are used to calibrate the subnetwork score using equation (3).

25Currently, there are three algorithms implemented in the pathfindR package for active subnetwork search, described below.

26Greedy algorithm is the problem-solving/optimization concept that chooses locally the best option in each stage with the expectation of reaching the global optimum. In active subnetwork search, this is generally applied by starting with a significant seed node and considering addition of a neighbor in each step to maximize the subnetwork score. In pathfindR, we used the approach described by. This algorithm considers addition of a node within a specified distance d to the current subnetwork. In our method, the maximum depth from the seed can also be set. With the default parameters, our greedy method considers addition of direct neighbors (d = 1) and forms a subnetwork with a maximum depth of 1 for each seed. Because the expansion process runs for each significant seed node, several overlapping subnetworks emerge. Overlapping subnetworks are handled by discarding a subnetwork that overlaps with a higher scoring subnetwork more than a given threshold, which is set to 0.5 by default.

27Simulated annealing is an optimization algorithm inspired by annealing in metallurgy. In the annealing process, the material is heated above its recrystallization temperature and cooled slowly, allowing atoms to diffuse within the material and decrease dislocations. Analogous to this process, simulated annealing algorithm starts with a “high temperature” in which there is a high probability of accepting a solution that is worse than the current one as the solution space is explored. The acceptability of worse solutions allows a global search and escaping from local optima. The equation connecting temperature and probability of accepting a new solution is given in equation (4). In this equation, P(Acceptance) is the probability of accepting the new solution. In scorenew and scorecurrent are the scores of the new and the current solutions, respectively. Finally, temperature is the current temperature.

28A less worse solution and higher temperature are the conditions that increase the chance of acceptation of a new solution. The probability of accepting a non-optimal action decreases in each iteration, as the temperature decreases in each step.

29Simulated annealing provides improved performance over the greedy search by accepting non-optimal actions to increase exploration in the search space. In the active subnetwork search context, the search begins with a set of randomly chosen genes (the chosen genes are referred to as genes in “on” state and the not chosen genes are referred to as genes in “off” state). Connected components in this candidate solution are found, and the scores are calculated. In each iteration, the state of a random node is changed from on to off and vice versa. Connected components are found in the new solution, and their scores are calculated. If the score improves, the change is accepted. If the score decreases, the change is accepted with a probability proportional to the temperature parameter that decreases in each step.

30Genetic algorithm is a bio-inspired algorithm that mimics evolution by implementing natural selection, chromosomal crossover, and mutation. The main phases of the genetic algorithm are “the selection phase” and “the crossover phase.”

31In the selection phase, parents from the existing population are selected through a fitness-based process to breed a new generation. Common selection methods are (i) roulette wheel selection in which a solution’s selection probability is proportional to its fitness score, (ii) rank selection in which a solution’s selection probability is proportional to its rank, thus preventing the domination of a high fitness solution to the rest, and (iii) tournament selection in which parents are selected among the members of randomly selected groups of solutions, thus giving more chance to small fitness solutions that would have little chance in other selection methods.

32In the crossover phase, encoded solution parameters of the parents are exchanged analogous to chromosomal crossover. The common crossover operators are (i) single-point crossover in which the segment next to a randomly chosen point in the solution representation is substituted between parents, (ii) two-point crossover in which the segment between two randomly chosen points is substituted, and (iii) uniform crossover in which each parameter is randomly selected from either of the parents. Mutation is the process of randomly changing parameters in the offspring solutions in order to maintain genetic diversity and explore search space.

33In our genetic algorithm implementation, candidate solutions represent the on/off state of each gene. In the implementation, we used rank selection and uniform crossover. In each iteration, the fittest solution of the previous population is preserved if the highest score of the current population is less than the previous population’s score. In every 10 iterations, the worst scoring 10% of the population is replaced with random solutions. Because uniform cross-over and addition of random solutions make adequate contribution to the exploration of the search space, mutation is not performed under the default settings.

34The default search method in pathfindR is greedy algorithm with a search depth of 1 and maximum depth of 1. This method stands out with its simplicity and speed. This is also the “local subnetwork approach” used in the Local Enrichment Analysis (LEAN) method. As mentioned in the LEAN study, the number of subnetworks to be identified typically increases exponentially with increasing number of genes in the PIN, and the “local subnetwork approach” enables iterating over each local subnetwork and determining phenotype-related clusters. Greedy algorithm with search depth and maximum depth equal to 2 or more lets the search algorithm look further in the network for another significant gene to add to the cluster, but this may result in a slower runtime and a loss in interpretability.

35Simulated annealing and genetic algorithms are heuristic methods that do not make any assumptions on the active subnetwork model. They can let insignificant genes between two clusters of significant genes to create a single connected active subnetwork. Thus, these algorithms may result in a large highest scoring active subnetwork, while the remaining subnetworks identified become small and therefore uninformative. This tendency towards large subnetworks was attributed to a statistical bias prevalent in many tools.

36The default active search method (greedy algorithm with a search depth of 1 and maximum depth of 1) in pathfindR was preferred because multiple active subnetworks are used for enrichment analyses. If the researcher decides to use the single highest scoring active subnetwork for the enrichment process, they are encouraged to consider greedy algorithm with greater depth, simulated annealing, or genetic algorithm.

37The overview of the active-subnetwork-oriented pathway enrichment approach is presented in Figure 1A.

38The required input is a two- or three-column table: Gene symbols, change values as log-fold change (optional) and adjusted p values associated with the differential expression/methylation data.

39Initially, the input is filtered so that all p values are less than or equal to the given threshold (default is 0.05). Next, gene symbols that are not in the PIN are identified. If aliases of these gene symbols are found in the PIN, these symbols are converted to the corresponding aliases.

40The processed data are then used for active subnetwork search. The identified active subnetworks are filtered via the following criteria: (i) has a score larger than the given quantile threshold (default is 0.80) and (ii) contains at least a specified number of input genes (default is 10).

41For each filtered active subnetwork, using the genes contained in each of these subnetworks, separate pathway enrichment analyses are performed via one-sided hypergeometric testing. The enrichment tests use the genes in the PIN as the gene pool (i.e., background genes). Using the genes in the PIN instead of the whole genome is more appropriate and provides more statistical strength because active subnetworks are identified using only the genes in the PIN. Next, the p values obtained from the enrichment tests are adjusted (default is by Bonferroni method. However, the researcher may choose another method they prefer). Pathways with adjusted p values larger than the given threshold (default is 0.05) are discarded. These significantly enriched pathways per all filtered subnetworks are then aggregated by keeping only the lowest adjusted p value for each pathway if a pathway was found to be significantly enriched in the enrichment analysis of more than one subnetwork.

42This process of active subnetwork search and enrichment analysis (active subnetwork search, filtering of subnetworks, enrichment analysis on each filtered subnetwork, and aggregation of enrichment results over all subnetworks) is repeated for a selected number of iterations (default is 10 iterations for greedy and simulated annealing algorithms, 1 for genetic algorithm).

43Finally, the lowest and the highest adjusted p values, the number of occurrences over all iterations, and up-regulated and down-regulated genes in each enriched pathway are returned as a table. Additionally, a Hypertext Markup Language (HTML) format report with the pathfindR enrichment results is created. Pathways are linked to the visualizations of the pathways if KEGG gene sets are chosen. The KEGG pathway diagrams are created using the R package pathview. By default, these diagrams display the involved genes colored by change values, normalized between −1 and 1, on a KEGG pathway graph. If a gene set other than KEGG is chosen and visualization is required, graphs of interactions of genes involved in the enriched pathways in the chosen PIN are visualized via the R package igraph.

44Enrichment analysis usually yields a large number of related pathways. In order to establish representative pathways among similar groups of pathways, we propose that clustering can be performed either via hierarchical clustering (default) or via a fuzzy clustering method as described by. These clustering approaches are visually outlined in Figure 1B and described below:

45Firstly, using the input genes in each pathway, a kappa statistics matrix containing the pairwise kappa statistics, a chance-corrected measure of co-occurrence between two sets of categorized data, between the pathways is calculated.

46By default, the wrapper function for pathway clustering, cluster_pathways, performs agglomerative hierarchical clustering (defining the distance as 1 − kappa statistic), automatically determines the optimal number of clusters by maximizing the average silhouette width, and returns a table of pathways with cluster assignments.

47Alternatively, the fuzzy clustering method, previously proposed and described in detail by, can be used to obtain fuzzy cluster assignments. Hence, this fuzzy approach allows a pathway to be a member of multiple clusters.

48Finally, the representative pathway for each cluster is assigned as the pathway with the lowest adjusted p value.

49The researcher can get an overview of the alterations of genes in a pathway via the KEGG pathway graph. To provide even more insight into the activation/repression statuses of pathways per each sample, we devised a simple scoring scheme that aggregates gene-level values to pathway scores, described below.

50For an experiment values matrix (e.g., gene expression values matrix), EM, where columns indicate samples and rows indicate genes, the gene score GS of a gene g in a sample s is calculated as:

51Here, is the mean value for gene g across all samples, and sd g is the standard deviation for gene g across all samples.

52For a set P i, the set of k genes in pathway i, and a sample j, the i th row and j th column of the pathway score matrix PS is calculated as follows:

53The pathway score of a sample for a given pathway is therefore the average value of the scores of the genes in the pathway for the given sample.

54After calculation of the pathway score matrix, a heat map of these scores is plotted. Via this heat map, the researcher can examine the activity of a pathway in individual samples as well as compare the overall activity of the pathway between cases and controls.

55To analyze the performance of pathfindR, we used three gene expression datasets. All datasets were obtained via the Gene Expression Omnibus (GEO). The first dataset (GSE15573) aimed to characterize and compare gene expression profiles in the peripheral blood mononuclear cells of 18 rheumatoid arthritis (RA) patients versus 15 healthy subjects using the Illumina human-6 v2.0 expression bead chip platform. This dataset will be referred to as RA. The second dataset (GSE4107) compared the gene expression profiles of the colonic mucosa of 12 early onset colorectal cancer patients and 10 healthy controls using the Affymetrix Human Genome U133 Plus 2.0 Array platform. The second dataset will be referred to as CRC. The third dataset (GSE55945) compared the expression profiles of prostate tissue from 13 prostate cancer patients versus 8 controls using the Affymetrix Human Genome U133 Plus 2.0 Array platform. This dataset will be referred to as PCa.

56After preprocessing, which included log2 transformation and quantile normalization, differential expression testing via a moderated t test using limma was performed. Next, the resulting p values were corrected using false discovery rate (FDR) adjustment. The differentially expressed genes (DEGs) were defined as those with FDR < 0.05. Probes mapping to multiple genes and probes that do not map to any gene were excluded. If a gene was targeted by multiple probes, the lowest p value was kept. The results of differential expression analyses for RA, CRC, and PCa, prior to filtering (differential expression statistics for all probes) and after filtering (lists of DEGs), are provided in Supplementary Data Sheet 1.

57We chose to use these three datasets because these are well-studied diseases and the involved mechanisms are considerably well characterized. These different datasets also allowed us to test the capabilities of pathfindR on DEGs obtained from different platforms.

58We performed enrichment analysis with pathfindR, using the default settings. Greedy algorithm for active subnetwork search was used, and the analysis was carried out over 10 iterations. The enrichment significance cutoff value was set to 0.25 for each analysis (changing the argument enrichment_threshold of run_pathfindR function) as we later performed validation of the results using the three significance cutoff values of 0.05, 0.1, and 0.25

59To better evaluate the performance of pathfindR, we compared results on the three gene expression datasets by three widely used pathway analysis tools, namely, DAVID, SPIA, and GSEA. DAVID 6.8 was used for the analyses. SPIA was performed using the default settings. GSEA was also performed using the default settings (using phenotype permutations). Additionally, pre-ranked GSEA was performed (GSEAPreranked) using the default settings. The rank of the i th gene rank i was calculated as follows:

60The unfiltered results of enrichment analyses using the different methods on the three datasets are presented in Supplementary Data Sheet 2.

61For each analysis, the Bonferroni-corrected p values for pathfindR were used to filter the results. For all the other tools, as the Bonferroni method would be too strict and result in too few or no significant pathways, the FDR-corrected p values were used.

62Because there is no definitive answer to which pathways are involved in the pathogenesis of the conditions under study, we analyzed the results in light of the existing biological knowledge on the conditions and compared our results with other tools in this context. The significant pathways were assessed on the basis of how well they fitted with the existing knowledge. For this, two separate approaches were taken: (i) assessment of literature support for the significantly enriched pathways (using a significance threshold of 0.05), and (ii) assessment of the percentages of pathway genes that are also known disease genes (using the three significance thresholds of 0.05, 0.10, and 0.25). While both assessments could be separately used to determine the “disease-relatedness” of a pathway, we chose to use them both as these are complementary measures: the former is a more subjective but a comprehensive measure of association, and the latter is a limited but a more objective measure of association. For determining the percentages of known disease genes in each significantly enriched pathway, two curated lists were used. For the RA dataset, mapped genes in the curated list of SNPs associated with RA was obtained from the NHGRI-EBI Catalog of published genome-wide association studies (GWAS Catalog, retrieved on 19.12.2018). These genes will be referred to as “RA Genes.” For the CRC and PCa datasets, the “Cancer Gene Census” (CGC) genes from the Catalogue of Somatic Mutations in Cancer (COSMIC, http://cancer.sanger.ac.uk, retrieved on 19.12.2018) were used. These genes will be referred to as “CGC Genes.”

63We performed pathfindR analyses using real and permuted data with different sizes to assess the number of enriched pathways identified in the permuted data against the actual data. For this assessment, the RA data was used. The analyses were performed on data subsets taken as the top 200, 300, 400, and 500 most significant DEGs as well as the complete list of 572 DEGs. For each input size, 100 separate pathfindR analyses were performed on both the actual input data and permuted data. While the real input data were kept unchanged, for the permuted data, a random permutation of genes (using the set of all genes available on the microarray platform) was carried out at each iteration over 100 analyses. Analyses with pathfindR were performed using the default settings described above.

64The distributions of the number of enriched pathways for actual vs. permuted data were compared using Wilcoxon rank sum test.

65We performed ORA as implemented in pathfindR (as the “enrichment” function) to assess any effect of removing DEGs without any interactions on enrichment results. For this purpose, ORA were performed for (i) the full lists of DEGs for all datasets and (ii) the lists of DEGs that are found in the Biogrid PIN. As gene sets, KEGG pathways were used. As background genes, all of the genes in the Biogrid PIN were used for both analyses so that the results could be comparable. The enrichment p values were adjusted using the FDR method. Pathway enrichment was considered significant if FDR was <0.05.

66To analyze the effect of the chosen PIN on the enrichment results, we performed pathfindR analyses using the four PINs provided by default: the Biogrid, GeneMania, IntAct, and KEGGPINs. For these analyses, the default settings were used with the default active search algorithm (greedy) and the default gene sets (KEGG).

67The pathfindR package is freely available for use under MIT license: https://cran.r-project.org/package=pathfindR. The code of the pathfindR package is deposited in a GitHub repository (https://github.com/egeulgen/pathfindR) along with a detailed wiki, documenting the features of pathfindR in detail. Docker images for the latest stable version and the development version of pathfindR are deposited on Docker Hub (https://hub.docker.com/r/egeulgen/pathfindr)

68A total of 572 DEGs were identified for the RA dataset ( Supplementary Data Sheet 1 ). Filtered by adjusted p values (adjusted-p ≤ 0.05), pathfindR identified 78 significantly enriched KEGG pathways which were partitioned into 10 clusters ( Figures 2A, B ). The relevancy of 31 out of 78 (39.74%) pathways was supported by literature, briefly stated in Table 1.

69The summary of results obtained using the different tools and literature support for the identified pathways (where applicable) are presented in Table 1. For this dataset, SPIA identified two significant pathways, which were both also identified by pathfindR. No significant pathway was identified by the other tools.

70Clustering allowed us to obtain coherent groups of pathways and identify mechanisms relevant to RA, including autoimmune response to the spliceosome, mechanisms related with response to microbial infection, such as generation of neo-autoantigens and molecular mimicry, dysregulation of various signaling pathways, DNA damage repair, dysregulation of energy metabolism, and modulation of immune response and inflammation by the proteasome.

71The activity scores of the representative pathways for each subject indicated that most representative pathways were down-regulated in the majority of subjects ( Figure 2C ).

72For the CRC dataset, 1,356 DEGs were identified ( Supplementary Data Sheet 1 ). pathfindR identified 100 significantly enriched pathways (adjusted-p ≤ 0.05) which were partitioned into 14 coherent clusters ( Figures 3A, B ). Forty-eight (48%) of these enriched pathways were relevant to CRC biology, as supported by literature. Brief descriptions of how these are relevant are provided in Table 2.

73The results obtained using the different tools and literature support for the identified pathways (where applicable) are presented in Table 2. For this dataset, DAVID identified 20 significant pathways, 15 of which were also found by pathfindR (4 out of the remaining 5 were not supported by literature to be relevant to CRC). SPIA identified 13 significantly enriched pathways, 11 of which were also identified by pathfindR. Out of the remaining two enriched pathways, only “PPAR signaling pathway” was related to CRC biology. Neither GSEA nor GSEAPreranked yielded any significant pathways for the CRC dataset. The Colorectal cancer pathway was identified to be significantly enriched only by pathfindR.

74Upon clustering, 14 clusters were identified ( Figures 3A, B ). These clusters implied processes previously indicated in colorectal cancer, including but not limited to colorectal cancer and related signaling pathways, apoptosis, p53 signaling, dysregulation of metabolic functions, including glucose metabolism, fatty acid metabolism, and amino acid metabolism, and cell cycle. Brief descriptions of all pathways relevant to CRC are provided in Table 2.

75Representative pathways that were upregulated in the majority of subjects included important pathways related to cancer in general and colorectal cancer, such as the proteoglycans in cancer, adherens junction, gap junction, and Hippo signaling pathway. Representative pathways that were downregulated in the majority of subjects included other important pathways related to colorectal cancer, such as valine, leucine, and isoleucine degradation, mTOR signaling pathway, and cell cycle ( Figure 3C ).

76For the PCa dataset, 1,240 DEGs were identified ( Supplementary Data Sheet 1 ). pathfindR identified 92 significantly enriched pathways (adjusted-p ≤ 0.05) which were clustered into 14 coherent clusters ( Figures 4A, B ). Forty-six (50%) of these enriched pathways were relevant to PCa biology, as supported by literature. Brief descriptions of the relevancies are provided in Table 3.

77The results obtained using the different tools and literature support for the identified pathways (where applicable) are presented in Table 3. DAVID identified eight significant pathways, which were all also identified by pathfindR and only half of which were relevant to PCa. SPIA identified five significantly enriched pathways, all of which were also identified by pathfindR. GSEA identified no significant pathways, whereas GSEAPreranked identified one significant pathway, for which no association with PCa was provided by the literature. The prostate cancer pathway was identified to be significantly enriched only by pathfindR.

78The clusters identified by pathfindR pointed to several mechanisms previously shown to be important for prostate cancer. These mechanisms included but were not limited to the prostate cancer pathway and related signaling pathways, cancer immunity, Hippo signaling, cell cycle, autophagy, and insulin signaling.

79The majority of representative pathways relevant to PCa were down-regulated ( Figure 4C ).

80Because the CRC and PCa datasets were both cancers, they were expected to have common pathways identified by pathfindR. Indeed, 47 common significant pathways (adjusted-p ≤ 0.05) were identified ( Supplementary Table 1 ). These common pathways included general cancer-related pathways, such as pathways in cancer, proteoglycans in cancer, MAPK signaling pathway, Ras signaling pathway, Hippo signaling pathway, mTOR signaling pathway, Toll-like receptor signaling pathway, Wnt signaling pathway, and adherens junction.

81The percentages of disease-related genes for each pathway found to be enriched by any tool (adjusted-p ≤ 0.05) are presented in the corresponding columns of Tables 1, 2, and 3 (“% RA Genes” for the RA dataset and “% CGC Genes” for the CRC and PCa datasets). These percentages show great variability but support the literature search results in assessing the disease-relatedness of the enriched pathways.

82The distributions of disease-related gene percentages in pathways identified by each tool in the three different datasets, filtered by the adjusted-p value thresholds of 0.05, 0.1, and 0.25, are presented in Figure 5. As stated before, for the RA dataset, only pathfindR and SPIA identified significant pathways. The median percentages of RA-associated genes of the enriched pathways of pathfindR was higher than the median percentages of SPIA (2.43% vs. 0.96% for the 0.05 cutoff, 2.5% vs. 0.61% for the 0.1 cutoff, and 2.27% vs. 0.67% for the 0.25 cutoff). For CRC, pathfindR displayed the highest median percentage of CGC genes for all the cutoff values (17.84%, 17.72%, and 16.7% for 0.05, 0.1, and 0.25, respectively). For the PCa dataset, the median percentages of CGC genes of the enriched pathways of pathfindR were again the highest among all tools for all significance cutoff values (18.73%, 18.37%, and 17.93% for 0.05, 0.1, and 0.25, respectively).

83To assess the number of pathways identified to be enriched by pathfindR, we performed analyses using actual and permuted data of different sizes. Comparison of the distributions of actual vs. permuted data is presented in Figure 6. Wilcoxon rank sum tests revealed that the distributions of the numbers of enriched pathways obtained using actual and permuted input data were significantly different (all p < 0.001). The median number of enriched pathways was lower for permuted data in each case.

84It was observed that the ratio of the median number of pathways (permuted/actual) tended to increase as the number of input genes increased. This is most likely because as the input size gets larger, there is higher chance in finding highly connected subnetworks that in turn leads to identifying a higher number of enriched pathways.

85To gain further support for our proposal that directly performing enrichment analysis on a list of genes is not completely informative because this ignores the interaction information, we performed ORA (as implemented in pathfindR) on (i) all of the DEG lists (RA, CRC, and PCa) and (ii) the filtered list of DEGs for the same datasets so that they only contain DEGs found in the Biogrid PIN. This allowed us to assess any effect of eliminating DEGs with no interactions on the enrichment results.

86The numbers of DEGs found in the Biogrid PIN for each dataset was as follows: RA—481 (out of 572 total), CRC—989 (out of 1,356) and PCa—900 (out of 1,240). The ORA results are presented in Supplementary Data Sheet 3. The elimination of DEGs without any interaction clearly affected numbers of significantly enriched (FDR < 0.05) KEGG pathways ( Supplementary Table 2 ). For the RA dataset, no significantly enriched pathways were found using all DEGs, whereas elimination of non-interacting DEGs resulted in one significant pathway. For CRC and PCa, using only DEGs found in the PIN, the number of significantly enriched pathways were doubled compared to using all of the genes without taking into account any interaction information. We would like to note that these results partly explain why taking interaction information into account results in enhanced enrichment results.

87To assess any effect of the choice of PIN on pathfindR results, we first compared the default PINs in terms of the interactions they contain. The number of interactions in the PINs were as follows: 289,417 interactions in Biogrid, 79,741 interactions in GeneMania, 121,007 interactions in IntAct, and 53,047 interactions in KEGG. The numbers of common interactions between any pair of PINs and the overlap percentages of the interactions are presented in Supplementary Table 3. The results show that there is very little overlap between the PINs. Despite the fact that Biogrid has more than double the interactions of IntAct and 3 times the interactions of GeneMania, it remarkably does not contain half of the interactions they contain, implying this lack of overlap between PINs may affect pathfindR results.

88We then proceeded with analyzing any effect of the choice of PIN on active-subnetwork-oriented pathway enrichment analysis. Venn diagrams comparing enrichment results obtained through pathfindR analyses with all available PINs are presented in Supplementary Figure 1. This comparison revealed that there was no compelling overlap among the enriched pathways obtained by using different PINs. Overall, using Biogrid and KEGG resulted in the highest number of significantly enriched pathways for all datasets.

89As described in Materials and Methods, the results presented in this subsection were obtained using greedy search with search depth of 1 and maximum depth of 1, which results in multiple subnetworks structured as local subnetworks. Although it is not fully dependent on it, this method requires direct interactions between input genes. In the extreme case where there is no direct connection between any pair of two input genes, it is impossible to get any multi-node subnetworks with this method. Therefore, in order to gain a better understanding of the lack of overlap between the enrichment results presented above, we analyzed the numbers of direct interactions of input genes in each PIN. These results are presented as Venn diagrams in Supplementary Figure 2. It is striking that there are only nine common interactions of RA DEGs in all PINs (although there are 54 common interactions in PINs except KEGG). The findings are similar for the CRC and PCa datasets: there are 11 common CRC DEG interactions in all PINs (81 in PINs except KEGG), and 5 PCa DEG interactions (56 in PINs except KEGG).

90In case of utilizing KEGG PIN and KEGG pathways, the same interactions for both subnetwork interaction and enrichment analysis are considered. This approach does not introduce any extra information to the analysis, and it is clear that interacting gene groups in the KEGG PIN will be enriched in KEGG pathways. This explains the high number of pathways obtained using the KEGG PIN. Moreover, it is known that pathways in pathway databases may be strongly biased by some classes of genes or phenotypes that are popular targets, such as cancer signaling. Therefore, the PIN obtained through KEGG pathway interactions are biased. Biogrid has the highest coverage for direct interactions among DEGs as seen in Supplementary Figure 2. It is unbiased in terms of phenotypes, and using Biogrid to extract KEGG pathways combines the two sources of information.

91Considering all of the above-mentioned findings, we conclude that utilizing the Biogrid PIN can provide the researcher with the most extensive enrichment results.

92PathfindR is an R package that enables active subnetwork-oriented pathway analysis, complementing the gene-phenotype associations identified through differential expression/methylation analysis.

93In most gene set enrichment approaches, relational information captured in the graph structure of a PIN is overlooked. Hence, during these analyses, genes in the network neighborhood of significant genes are not taken into account. The approach we considered for exploiting interaction information to enhance pathway enrichment analysis was active subnetwork search. In a nutshell, active subnetwork search enables inclusion of genes that are not significant genes themselves but connect significant genes. This results in the identification of phenotype-associated connected significant subnetworks. Initially identifying active subnetworks in a list of significant genes and then performing pathway enrichment analysis of these active subnetworks efficiently exploits interaction information between the genes. This, in turn, helps uncover relevant phenotype-related mechanisms underlying the disease, as demonstrated in the example applications.

94Through pathfindR, numerous relevant pathways were identified in each example. The literature-supported disease-related pathways mostly ranked higher in the pathfindR results. The majority of additional pathways identified through pathfindR were relevant to the pathogenesis of the diseases under study, as supported by literature. A separate confirmation of disease-relatedness was provided by analysis of the distributions of the percentage of disease genes in the identified pathways. This analysis revealed that pathfindR pathways contained the highest median percentages of disease-related genes in each dataset regardless of significance cutoff value, implying that the pathways identified by pathfindR are indeed associated with the given disease. Together, these two assessments of disease-relatedness of pathways indicate that pathfindR produces pathway enrichment results at least as relevant as the other tools widely used for enrichment analysis.

95We propose that pathfindR performed better than the analyzed pathway analysis tools because, for enrichment analysis, it included disease-related genes that were not in the DEG list but that were known to interact with the DEGs, which most enrichment tools disregard. By performing enrichment analyses on distinct sets of interacting genes (i.e., active subnetworks), pathfindR also eliminated “false positive” genes that lacked any strong interaction. The above findings indicate that incorporating interaction information prior to enrichment analysis results in better identification of disease-related mechanisms.

96This package extends the use of the active-subnetwork-oriented pathway analysis approach to omics data. Additionally, it provides numerous improvements and useful new features. The package provides three active subnetwork search algorithms. The researcher is therefore able to choose between the different algorithms to obtain the optimal results. For the greedy and simulated annealing active subnetwork search algorithms, the search and enrichment processes are executed several times. By summarizing results over the iterations and identifying consistently enriched pathways, the stochasticity of these algorithms is overcome. Additionally, the researcher is able to choose from several built-in PINs and can use their own custom PIN by providing the path to the SIF file. The researcher is also able to choose from numerous built-in gene sets, listed above, and can also provide a custom gene set resource. pathfindR also allows for clustering of related pathways. This allows for combining relevant pathways together, uncovering coherent “meta-pathways” and reducing complexity for easier interpretation of findings. This clustering functionality also aids in eliminating falsely enriched pathways that are initially found because of their similarity to the actual pathway of interest. The package also allows for scoring of pathways in individual subjects, denoting the pathway activity. Finally, pathfindR is built as a stand-alone package, but it can easily be integrated with other tools, such as differential expression/methylation analysis tools, for building fully automated pipelines.

97To the best of our knowledge, pathfindR is the first and, so far, the only R package for active-subnetwork-oriented pathway enrichment analysis. It also offers functionality for pathway clustering, scoring, and visualization. All features in pathfindR work together to enable identification and further investigation of dysregulated pathways that potentially reflect the underlying pathological mechanisms. We hope that this approach will allow researchers to better answer their research questions and discover mechanisms underlying the phenotype being studied.

98OS, OO, and EU conceived the pathway analysis approach. OO and EU implemented the R package. EU performed the analyses presented in this article. OUS, OO, and EU interpreted the results. All authors were involved in the writing of the manuscript and read and approved the version being submitted.

99The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.