Multi-omics pathway enrichment analysis
Introduction
ActivePathways is a tool for multivariate pathway enrichment analysis that identifies gene sets, such as pathways or Gene Ontology terms, that are over-represented in a list or matrix of genes. ActivePathways uses a data fusion method to combine multiple omics datasets, prioritizes genes based on the significance and direction of signals from the omics datasets, and performs pathway enrichment analysis of these prioritized genes. We can find pathways and genes supported by single or multiple omics datasets, as well as additional genes and pathways that are only apparent through data integration and remain undetected in any single dataset alone.
The new version of ActivePathways is described in our recent publication in Nature Communications (2024).
Mykhaylo Slobodyanyuk^, Alexander T. Bahcheli^, Zoe P. Klein, Masroor Bayati, Lisa J. Strug, Jüri Reimand. Directional integration and pathway enrichment analysis for multi-omics data. Nature Communications (2024) (^ - co-first authors) https://www.nature.com/articles/s41467-024-49986-4 https://pubmed.ncbi.nlm.nih.gov/38971800/
The first version of ActivePathways was published in Nature Communications with the PCAWG Pan-Cancer project.
Marta Paczkowska^, Jonathan Barenboim^, Nardnisa Sintupisut, Natalie S. Fox, Helen Zhu, Diala Abd-Rabbo, Miles W. Mee, Paul C. Boutros, PCAWG Drivers and Functional Interpretation Working Group, PCAWG Consortium, Juri Reimand. Integrative pathway enrichment analysis of multivariate omics data. Nature Communications 11 735 (2020) (^ - co-first authors) https://www.nature.com/articles/s41467-019-13983-9 https://pubmed.ncbi.nlm.nih.gov/32024846/
Pathway enrichment analysis using the ranked hypergeometric test
From a matrix of p-values, ActivePathways creates a
ranked gene list where genes are prioritised based on their combined
significance. The combined significance of each gene is determined by
performing statistical data fusion on a series of omics datasets
provided in the input matrix. The ranked gene list includes the most
significant genes first. ActivePathways then performs a
ranked hypergeometric test to determine if a pathway (i.e., a gene set
with a common functional annotation) is enriched in the ranked gene
list, by performing a series of hypergeometric tests (also known as
Fisher’s exact tests). In each such test, a larger set of genes from the
top of the ranked gene list is considered. At the end of the series, the
ranked hypergeometric test returns the top, most significant p-value
from the series, corresponding to the point in the ranked gene list
where the pathway enrichment reached the greatest significance of
enrichment. This approach is useful when the genes in our ranked gene
list have varying signals of biological importance in the input omics
datasets, as the test identifies the top subset of genes that are the
most relevant to the enrichment of the pathway.
Using the package
A basic example of using ActivePathways is shown below.
We will analyse cancer driver gene predictions for a collection of cancer genomes. Each dataset (i.e., column in the matrix) contains a statistical significance score (P-value) where genes with small P-values are considered stronger candidates of cancer drivers based on the distribution of mutations in the genes. For each gene (i.e., row in the matrix), we have several predictions representing genomic elements of the gene, such as coding sequences (CDS), untranslated regions (UTR), and core promoters (promCore).
To analyse these driver genes using existing knowledge of gene function, we will use gene sets corresponding to known molecular pathways from the Reactome database. These gene sets are commonly distributed in text files in the GMT format (Gene Matrix Transposed) file.
Let’s start by reading the data from the files embedded in the R
package. For the p-value matrix, ActivePathways expects an
object of the matrix class so the table has to be cast to the correct
class after reading the file.
scores <- read.table(
system.file('extdata', 'Adenocarcinoma_scores_subset.tsv', package = 'ActivePathways'),
header = TRUE, sep = '\t', row.names = 'Gene')
scores <- as.matrix(scores)
scores## X3UTR X5UTR CDS promCore
## A2M NA 3.339676e-01 9.051708e-01 4.499201e-01
## AAAS NA 4.250601e-01 7.047723e-01 7.257641e-01
## ABAT 0.9664125635 4.202735e-02 7.600985e-01 1.903789e-01
## ABCC1 0.9383431571 4.599443e-01 2.599319e-01 2.980455e-01
## ABCC5 0.8021028187 4.478902e-01 4.788846e-01 8.447995e-01
## ABCC8 NA 4.699356e-01 6.890250e-01 9.226617e-01
## ABHD6 0.4019418029 4.488881e-01 7.587176e-01 3.062514e-01
## ABI1 0.2894847305 1.977600e-01 4.815032e-01 3.486056e-01
## [ reached getOption("max.print") -- omitted 2406 rows ]ActivePathways does not allow missing (NA) values in the
matrix of P-values and these need to be removed. One conservative option
is to re-assign all missing values as ones, indicating our confidence
that the missing values are not indicative of cancer drivers.
Alternatively, one may consider removing genes with NA values.
Basic use
The basic use of ActivePathways requires only two input
parameters, the matrix of P-values with genes in rows and datasets in
columns, as prepared above, and the path to the GMT file in the file
system. Importantly, the gene IDs (symbols, accession numbers, etc) in
the P-value matrix need to match those in the GMT file.
Here we use a GMT file provided with the package. This GMT file is heavily filtered and outdated; thus users must provide their own GMT file when using the package. These GMT files can be acquired from multiple sources such as Gene Ontology, Reactome and others. For better accuracy and statistical power these pathway databases should be combined. Acquiring an up-to-date GMT file is essential to avoid using unreliable outdated annotations (see this paper).
library(ActivePathways)
gmt_file <- system.file('extdata', 'hsapiens_REAC_subset.gmt', package = 'ActivePathways')
ActivePathways(scores, gmt_file)## term_id term_name adjusted_p_val term_size
## <char> <char> <num> <int>
## 1: REAC:2424491 DAP12 signaling 4.491268e-05 358
## 2: REAC:422475 Axon guidance 4.625918e-04 555
## overlap evidence
## <list> <list>
## 1: TP53,PIK3CA,KRAS,PTEN,BRAF,NRAS,... CDS
## 2: PIK3CA,KRAS,BRAF,NRAS,CALM2,RPS6KA3,... X3UTR,promCore
## Genes_X3UTR Genes_X5UTR
## <list> <list>
## 1: NA NA
## 2: CALM2,ARPC2,RHOA,NUMB,CALM1,ACTB,... NA
## Genes_CDS
## <list>
## 1: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,...
## 2: NA
## Genes_promCore
## <list>
## 1: NA
## 2: EFNA1,IQGAP1,COL4A1,SCN2B,RPS6KA3,CALM2,...
## [ reached getOption("max.print") -- omitted 32 rows ]ActivePathways 2.0 Directional integration of multi-omics data
ActivePathways 2.0 extends our integrative pathway analysis framework significantly. Users can now provide directional assumptions of input omics datasets for more accurate analyses. This allows us to prioritise genes and pathways where certain directional assumptions are met and penalise those where the assumptions are violated.
For example, fold-change in protein expression would be expected to associate positively with mRNA fold-change of the corresponding gene, while negative associations would be unexpected and indicate more-complex situations or potential false positives. We can instruct the pathway analysis to prioritise positively-associated protein/mRNA pairs and penalise negative associations (or vice versa).
Two additional inputs are included in ActivePathways that allow diverse multi-omics analyses. These inputs are optional.
The scores_direction and constraints_vector parameters are provided in the merge_p_values() and ActivePathways() functions to incorporate this directional penalty into the data fusion and pathway enrichment analyses.
The parameter constraints_vector is a vector that allows the user to represent the expected relationship between the input omics datasets. The vector size is n_datasets. Values include +1, -1, and 0.
The parameter scores_direction is a matrix that reflects the directions that the genes/transcripts/protein show in the data. The matrix size is n_genes * n_datasets, that is the same size as the P-value matrix. This is a numeric matrix, but only the signs of the values are accounted for.
Directional data integration at the gene level
Load a dataset of P-values and fold-changes for mRNA and protein levels. This dataset is embedded in the package. Examine a few example genes.
fname_data_matrix <- system.file('extdata',
'Differential_expression_rna_protein.tsv',
package = 'ActivePathways')
pvals_FCs <- read.table(fname_data_matrix, header = TRUE, sep = '\t')
example_genes <- c('ACTN4','PIK3R4','PPIL1','NELFE','LUZP1','ITGB2')
pvals_FCs[pvals_FCs$gene %in% example_genes,]## gene rna_pval rna_log2fc protein_pval protein_log2fc
## 73 PIK3R4 1.266285e-03 1.1557077 2.791135e-03 -0.8344799
## 74 PPIL1 1.276838e-03 -1.1694221 1.199303e-04 -1.1193605
## 606 NELFE 1.447553e-02 -0.9120687 1.615592e-05 -1.2630114
## 4048 LUZP1 3.253382e-05 1.5830796 4.129125e-02 0.5791377
## 4050 ITGB2 4.584450e-05 1.6472117 1.327997e-01 0.4221579
## 4052 ACTN4 5.725503e-05 1.5531533 8.238317e-07 1.4279158Create a matrix of gene/protein P-values. Where the columns are different omics datasets (mRNA, protein) and the rows are genes. Examine a few genes in the P-value matrix, and convert missing values to P = 1.
pval_matrix <- data.frame(
row.names = pvals_FCs$gene,
rna = pvals_FCs$rna_pval,
protein = pvals_FCs$protein_pval)
pval_matrix <- as.matrix(pval_matrix)
pval_matrix[is.na(pval_matrix)] <- 1
pval_matrix[example_genes,]## rna protein
## ACTN4 5.725503e-05 8.238317e-07
## PIK3R4 1.266285e-03 2.791135e-03
## PPIL1 1.276838e-03 1.199303e-04
## NELFE 1.447553e-02 1.615592e-05
## LUZP1 3.253382e-05 4.129125e-02
## ITGB2 4.584450e-05 1.327997e-01Create a matrix of gene/protein directions similarly to the P-value matrix (i.e., scores_direction). ActivePathways only uses the signs of the direction values (ie +1 or -1). If directions are missing (NA), we recommend setting the values to zero. Lets examine a few genes in the direction matrix.
dir_matrix <- data.frame(
row.names = pvals_FCs$gene,
rna = pvals_FCs$rna_log2fc,
protein = pvals_FCs$protein_log2fc)
dir_matrix <- as.matrix(dir_matrix)
dir_matrix <- sign(dir_matrix)
dir_matrix[is.na(dir_matrix)] <- 0
dir_matrix[example_genes,]## rna protein
## ACTN4 1 1
## PIK3R4 1 -1
## PPIL1 -1 -1
## NELFE -1 -1
## LUZP1 1 1
## ITGB2 1 1This matrix has to be accompanied by a vector that provides the expected relationship between the different datasets. Here, mRNA levels and protein levels are expected to have consistent directions: either both positive or both negative (eg log fold-change). Alternatively, we can use another vector to prioritise genes/proteins where the directions are the opposite.
## [1] 1 1Now we merge the P-values of the two datasets using directional assumptions and compare these with the plain non-directional merging. The top 5 scoring genes differ if we penalise genes where this directional logic is violated: While 4 of 5 genes retain significance, the gene PIK3R4 is penalised. Interestingly, as a consequence of penalizing PIK3R4, other genes such as ITGB2 move up in rank.
directional_merged_pvals <- merge_p_values(pval_matrix,
method = "DPM", dir_matrix, constraints_vector)
merged_pvals <- merge_p_values(pval_matrix, method = "Brown")
sort(merged_pvals)[1:5]## ACTN4 PPIL1 NELFE LUZP1 PIK3R4
## 1.168708e-09 2.556067e-06 3.804646e-06 1.950607e-05 4.790125e-05## ACTN4 PPIL1 NELFE LUZP1 ITGB2
## 1.168708e-09 2.556067e-06 3.804646e-06 1.950607e-05 7.920157e-05PIK3R4 is penalised because the fold-changes of its mRNA and protein levels are significant and have the opposite signs:
## gene rna_pval rna_log2fc protein_pval protein_log2fc
## 73 PIK3R4 0.001266285 1.155708 0.002791135 -0.8344799## rna protein
## 0.001266285 0.002791135## rna protein
## 1 -1## PIK3R4
## 4.790125e-05## PIK3R4
## 0.8122527To assess the impact of the directional penalty on gene merged P-value signals we create a plot showing directional results on the y axis and non-directional results on the x. Blue dots are prioritised hits, red dots are penalised.
lineplot_df <- data.frame(original = -log10(merged_pvals),
modified = -log10(directional_merged_pvals))
ggplot(lineplot_df) +
geom_point(size = 2.4, shape = 19,
aes(original, modified,
color = ifelse(original <= -log10(0.05),"gray",
ifelse(modified > -log10(0.05),"#1F449C","#F05039")))) +
labs(title = "",
x ="Merged -log10(P)",
y = "Directional Merged -log10(P)") +
geom_hline(yintercept = 1.301, linetype = "dashed",
col = 'black', size = 0.5) +
geom_vline(xintercept = 1.301, linetype = "dashed",
col = "black", size = 0.5) +
geom_abline(size = 0.5, slope = 1,intercept = 0) +
scale_color_identity()
Constraints vector intuition
The constraints_vector parameter is provided in the merge_p_values() and ActivePathways() functions to incorporate directional penalty into the data fusion and pathway enrichment analyses. The constraints_vector parameter is a vector of size n_datasets that allows the user to represent the expected relationship between the input omics datasets, and includes the values +1, -1, and 0.
The constraints_vector should reflect the expected relative directional relationship between datasets. For example, the two constraints_vector values shown below are functionally identical.
We use different constraints_vector values depending on the type of data we are analyzing and the specific question we are asking. The simplest directional use case and the default for the ActivePathways package is to assume that the datasets have no directional constraints. This is useful when merging datasets where the relative impact of gene perturbations is not clear. For example, gene-level mutational burden and chromatin-immunoprecipitation sequencing (ChIP-seq) experiments can provide gene-level information, however, we cannot know from these datatypes whether gene function is increased or decreased. Therefore, we would set the constraints_vector for gene mutational burden and ChIP-seq datatypes to 0.
When combining datasets that have directional information, we provide the expected relative directions between datasets in the constraints_vector. This is useful when measuring different data types or different conditions.
To investigate the transcriptomic differences following gene knockdown or overexpression, we would provide constraints_vector values that reflect the expected opposing relationship between gene knockdown and gene overexpression.
The constraints_vector is also useful when merging different data types such as gene and protein expression, promoter methylation, and chromatin accessibility. Importantly, the expected relative direction between each datatype must be closely considered given the experimental conditions. For example, when combining gene expression, protein expression, and promoter methylation data measured in the same biological condition, we would provide a constraints_vector to reflect the expected agreement between gene and protein expression and disagreement with promoter methylation.
The intuition for merging these datasets is that direction of change in gene expression and protein expression tend to associate with each other according to the central dogma of biology while the direction of change of promoter methylation has the opposite effect as methylation insulates genes from transcription.
Pathway-level insight
To explore how changes on the individual gene level impact biological pathways, we can compare results before and after incorporating a directional penalty.
Use the example GMT file embedded in the package.
First perform integrative pathway enrichment analysis with no directionality. Then perform directional integration and pathway enrichment analysis. For this analysis the directional coefficients and constraints_vector are from the gene-based analysis described above.
enriched_pathways <- ActivePathways(
pval_matrix, gmt = fname_GMT2, cytoscape_file_tag = "Original_")
constraints_vector <- c(1,1)
constraints_vector## [1] 1 1## rna protein
## ACTN4 1 1
## PIK3R4 1 -1
## PPIL1 -1 -1
## NELFE -1 -1
## LUZP1 1 1
## ITGB2 1 1enriched_pathways_directional <- ActivePathways(
pval_matrix, gmt = fname_GMT2, cytoscape_file_tag = "Directional_", merge_method = "DPM",
scores_direction = dir_matrix, constraints_vector = constraints_vector)Examine the pathways that are lost when directional information is incorporated in the data integration.
pathways_lost_in_directional_integration =
setdiff(enriched_pathways$term_id, enriched_pathways_directional$term_id)
pathways_lost_in_directional_integration## [1] "REAC:R-HSA-3858494" "REAC:R-HSA-69206" "REAC:R-HSA-69242"
## [4] "REAC:R-HSA-9013149"## term_id term_name adjusted_p_val
## <char> <char> <num>
## 1: REAC:R-HSA-3858494 Beta-catenin independent WNT signaling 0.013437464
## 2: REAC:R-HSA-69206 G1/S Transition 0.026263457
## 3: REAC:R-HSA-69242 S Phase 0.009478766
## term_size overlap evidence
## <int> <list> <list>
## 1: 143 PSMA5,PSMB4,PSMC5,PSMD11,PSMA8,GNG13,... rna,protein
## 2: 130 PSMA5,PSMB4,CDK4,PSMC5,PSMD11,CCNB1,... protein
## 3: 162 PSMA5,PSMB4,RFC3,CDK4,PSMC5,PSMD11,... combined
## Genes_rna
## <list>
## 1: GNG13,PSMC1,PSMA5,PSMB4,ITPR3,DVL1,...
## 2: NA
## 3: NA
## Genes_protein
## <list>
## 1: PSMA8,PSMD11,PSMA5,PRKG1,PSMD10,PSMB4,...
## 2: PSMD11,PSMA5,PSMD10,PSMB4,CDK7,ORC2,...
## 3: NA
## [ reached getOption("max.print") -- omitted 1 row ]An example of a lost pathway is Beta-catenin independent WNT signaling. Out of the 32 genes that contribute to this pathway enrichment, 10 genes are in directional conflict. The enrichment is no longer identified when these genes are penalised due to the conflicting log2 fold-change directions.
wnt_pathway_id <- "REAC:R-HSA-3858494"
enriched_pathway_genes <- unlist(
enriched_pathways[enriched_pathways$term_id == wnt_pathway_id,]$overlap)
enriched_pathway_genes## [1] "PSMA5" "PSMB4" "PSMC5" "PSMD11" "PSMA8" "GNG13" "SMURF1" "PSMC1"
## [9] "PSMA4" "PLCB2" "PRKG1" "PSMD4" "PSMD1" "PSMD10" "PSMA6" "PSMA2"
## [17] "PSMA1" "PRKCA" "PSMC6" "RHOA" "PSMB3" "PSMB1" "PSME3" "ITPR3"
## [25] "AGO4" "DVL3" "PSMA3" "PPP3R1" "DVL1" "CLTA" "PSME2" "CALM1"
## [33] "PSMD6" "PSMB6"Examine the pathway genes that have directional disagreement and contribute to the lack of pathway enrichment in the directional analysis
pathway_gene_pvals = pval_matrix[enriched_pathway_genes,]
pathway_gene_directions = dir_matrix[enriched_pathway_genes,]
directional_conflict_genes = names(which(
pathway_gene_directions[,1] != pathway_gene_directions[,2] &
pathway_gene_directions[,1] != 0 & pathway_gene_directions[,2] != 0))
pathway_gene_pvals[directional_conflict_genes,]## rna protein
## PSMD11 0.34121101 0.002094310
## PSMA8 0.55510836 0.001415197
## SMURF1 0.03353629 0.042995333
## PSMD1 0.04650877 0.100178048
## RHOA 0.01786687 0.474628084
## PSME3 0.07148904 0.130184883
## ITPR3 0.01660850 0.589929787
## DVL3 0.46381447 0.022535743
## PSME2 0.03274707 0.514351089
## PSMB6 0.02863259 0.677224905## rna protein
## PSMD11 1 -1
## PSMA8 1 -1
## SMURF1 1 -1
## PSMD1 1 -1
## RHOA -1 1
## PSME3 1 -1
## ITPR3 1 -1
## DVL3 1 -1
## PSME2 -1 1
## PSMB6 -1 1## [1] 10To visualise differences in biological pathways between ActivePathways analyses with or without a directional penalty, we combine both outputs into a single enrichment map for plotting.
Significance threshold and returning all results
A pathway is considered to be significantly enriched if it has
adjusted_p_val <= significant. The parameter
significant represents the maximum adjusted P-value for a
resulting pathway to be considered statistically significant. Only the
significant pathways are returned. P-values from pathway enrichment
analysis are adjusted for multiple testing correction to provide a more
conservative analysis (see below).
## [1] 33## [1] 36GMT objects
In the most common use case, a GMT file is downloaded from a database
and provided directly to ActivePathways as a location in
the file system. In some cases, it may be useful to load a GMT file
separately for preprocessing. The ActivePathways package includes an
interface for working with GMT objects. The GMT object can be read from
a file using the read.GMT function. The GMT is structured
as a list of terms (e.g., molecular pathways, biological processes,
etc.). In the GMT object, each term is a list containing an id, a name,
and the list of genes associated with this term.
## [1] "id" "name" "genes"## REAC:1630316 - Glycosaminoglycan metabolism
## ST3GAL1, CHP1, B4GALT5, ST3GAL4, SLC9A1, CHST11, B3GAT3, SLC26A1, ARSB, ABCC5, LUM, PAPSS1, SDC4, NAGLU, AC022400.6, HYAL1, NDST3, SLC35B2, B3GAT1, CHST2, DCN, CEMIP, IDS, IDUA, HS3ST3B1, B3GNT7, CHST12, CHST14, BCAN, B4GALT3, HS3ST1, B4GALT1, CSPG4, CHPF2, HEXB, UST, XYLT1, NDST2, AL050331.3, NAT6, CHSY3, NCAN, FMOD, B3GNT2, HPSE, ACAN, LYVE1, GPC2, GPC1, B4GALT2, SLC35B3, KERA, GPC4, GUSB, HYAL3, HS6ST3, HAS3, CHPF, OMD, SDC2, B3GNT3, CSGALNACT2, CSPG5, BGN, CHST6, HS6ST2, SDC3, HS2ST1, CD44, AGRN, B3GALT6, PRELP, GLB1, GPC6, B3GNT4, PAPSS2, HS3ST4, CHST9, GNS, CHST1, CSGALNACT1, HS6ST1, CHST7, AL590542.1, HYAL2, HAS1, CHSY1, OGN, B4GAT1, B4GALT4, DSEL, EXT1, SDC1, SLC35D2, EXT2, ST3GAL2, ST3GAL6, CHST3, CHST5, HSPG2, SLC26A2, HEXA, XYLT2, HS3ST6, HS3ST5, GLCE, AC244197.3, B4GALT7, HAS2, NDST4, CHST15, B4GALT6, B3GAT2, STAB2, HMMR, ST3GAL3, VCAN, NDST1, HS3ST2, GPC5, HS3ST3A1, HPSE2, GLB1L, SGSH, GPC3, CHST13, DSE
##
## REAC:5633007 - Regulation of TP53 Activity
## PPP1R13L, RFC3, SGK1, HDAC1, SETD9, RPA3, CSNK2A2, EHMT1, PDPK1, CCNG1, TAF6, ING5, TP53INP1, BRCA1, TAF1, TAF9, EHMT2, RBBP8, CHD4, USP2, BRPF1, BANP, PPP2R5C, SSRP1, TAF4, TMEM55B, PPP1R13B, TAF10, PRR5, ATM, ZNF385A, MRE11, PIP4K2C, SMYD2, BARD1, MBD3, TP53BP2, AURKA, RPA1, KAT6A, CHD3, ATR, EXO1, PIN1, RMI2, PRKAB2, AKT2, PPP2CA, TAF13, RAD9B, PPP2CB, MDM4, POU4F1, TAF4B, MDM2, BRD1, CDK2, CSNK2B, PIP4K2A, RAD50, PML, AKT3, RAD1, USP7, PRDM1, RFC4, MTOR, POU4F2, RFC2, KMT5A, DNA2, NUAK1, PIP4K2B, MAPKAP1, PPP2R1A, RBBP7, MTA2, TP53RK, TAF1L, GATAD2B, JMY, TAF12, CDK5R1, RICTOR, PHF20, AC134772.2, STK11, TAF3, BLM, ATRIP, TAF7L, TP73, MAP2K6, RPA2, PRKAG1, TOPBP1, PRKAB1, TOP3A, CCNA1, RBBP4, PPP2R1B, DAXX, TTC5, CHEK2, CDK5, RMI1, TAF2, NOC2L, TP63, CSNK2A1, UBB, PRKAG2, ING2, RNF34, MLST8, HIPK2, TBP, L3MBTL1, EP300, MAPK11, BRIP1, PRMT5, PRKAG3, RFC5, NBN, TPX2, HDAC2, CDK1, MAPKAPK5, CHEK1, TAF5, BRPF3, RPS27A, AKT1, GATAD2A, RHNO1, CCNA2, HUS1, MEAF6, PRKAA1, CDKN2A, RAD17, KAT5, SUPT16H, TAF7, PLK3, UBA52, WRN, MAPK14, TAF9B, UBC, HIPK1, TP53, DYRK2, RFFL, TAF11, BRD7, RAD9A, AURKB, PRKAA2
##
## REAC:5358346 - Hedgehog ligand biogenesis
## PSMB11, PSMD8, PSMB6, PSMB8, PSMD13, PSMA2, PSMB3, PSMB7, PSME2, PSMD1, PSMA8, PSMA1, PSMD2, PSMD14, PSMC1, IHH, SEL1L, SCUBE2, PSMB10, PSMD10, PSMA5, PSMD3, PSMC2, PSMC6, PSME1, PSME4, PSMC4, AC010132.3, PSMD5, UBB, GPC5, PSMA7, PSMB2, PSMD9, SEM1, PSMA3, DISP2, PSMB9, PSMD6, OS9, PSMC3, PSMA6, RPS27A, ADAM17, PSMB1, DHH, PSMF1, HHAT, UBA52, UBC, DERL2, PSMD4, VCP, ERLEC1, PSME3, PSMB4, P4HB, PSMA4, PSMD7, PSMD11, PSMC5, NOTUM, PSMD12, PSMB5, SYVN1, SHH## [1] "ST3GAL1" "CHP1" "B4GALT5" "ST3GAL4" "SLC9A1"
## [6] "CHST11" "B3GAT3" "SLC26A1" "ARSB" "ABCC5"
## [11] "LUM" "PAPSS1" "SDC4" "NAGLU" "AC022400.6"
## [16] "HYAL1" "NDST3" "SLC35B2" "B3GAT1" "CHST2"
## [21] "DCN" "CEMIP" "IDS" "IDUA" "HS3ST3B1"
## [26] "B3GNT7" "CHST12" "CHST14" "BCAN" "B4GALT3"
## [31] "HS3ST1" "B4GALT1" "CSPG4" "CHPF2" "HEXB"
## [ reached getOption("max.print") -- omitted 92 entries ]## [1] "DAP12 signaling"The most common processing step for GMT files is the removal of gene sets that are too large or small. Here we remove pathways (gene sets) that have less than 10 or more than 500 annotated genes.
gmt <- Filter(function(term) length(term$genes) >= 10, gmt)
gmt <- Filter(function(term) length(term$genes) <= 500, gmt)The new GMT object can now be used for analysis with
ActivePathways
## term_id term_name adjusted_p_val term_size
## <char> <char> <num> <int>
## 1: REAC:2424491 DAP12 signaling 0.0002890847 358
## 2: REAC:177929 Signaling by EGFR 0.0015162274 366
## overlap evidence
## <list> <list>
## 1: TP53,PIK3CA,KRAS,PTEN,BRAF,NRAS,... CDS
## 2: TP53,PIK3CA,KRAS,PTEN,BRAF,NRAS,... CDS
## Genes_X3UTR Genes_X5UTR
## <list> <list>
## 1: NA NA
## 2: NA NA
## Genes_CDS Genes_promCore
## <list> <list>
## 1: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,... NA
## 2: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,... NA
## [ reached getOption("max.print") -- omitted 29 rows ]This filtering can also be done automatically using the
geneset_filter option to the ActivePathways
function. By default, ActivePathways removes gene sets with
less than five or more than a thousand genes from the GMT prior to
analysis. In general, gene sets that are too large are likely not
specific and less useful in interpreting the data and may also cause
statistical inflation of enrichment scores in the analysis. Gene sets
that are too small are likely too specific for most analyses and make
the multiple testing corrections more stringent, potentially causing
deflation of results. A stricter filter can be applied by running
ActivePathways with the parameter
geneset_filter = c(10, 500).
## term_id term_name adjusted_p_val term_size
## <char> <char> <num> <int>
## 1: REAC:2424491 DAP12 signaling 3.660807e-05 358
## 2: REAC:177929 Signaling by EGFR 5.039994e-04 366
## overlap evidence
## <list> <list>
## 1: TP53,PIK3CA,KRAS,PTEN,BRAF,NRAS,... CDS
## 2: TP53,PIK3CA,KRAS,PTEN,BRAF,NRAS,... CDS
## Genes_X3UTR Genes_X5UTR
## <list> <list>
## 1: NA NA
## 2: NA NA
## Genes_CDS Genes_promCore
## <list> <list>
## 1: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,... NA
## 2: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,... NA
## [ reached getOption("max.print") -- omitted 29 rows ]This GMT object can be saved to a file
Background gene set for statistical analysis
To perform pathway enrichment analysis, a global set of genes needs to be defined as a statistical background set. This represents the universe of all genes in the organism that the analysis can potentially consider. By default, this background gene set includes every gene that is found in the GMT file in any of the biological processes and pathways. Another option is to provide the full set of all protein-coding genes, however, this may cause statistical inflation of the results since a sizable fraction of all protein-coding genes still lack any known function.
Sometimes the statistical background set needs to be considerably narrower than the GMT file or the full set of genes. Genes need to be excluded from the background if the analysis or experiment specifically excluded these genes initially. An example would be a targeted screen or sequencing panel that only considered a specific class of genes or proteins (e.g., kinases). In analysing such data, all non-kinase genes need to be excluded from the background set to avoid statistical inflation of all gene sets related to kinase signalling, phosphorylation and similar functions.
To alter the background gene set in ActivePathways, one
can provide a character vector of gene names that make up the
statistical background set. In this example, we start from the original
list of genes in the entire GMT and remove one gene, the tumor
suppressor TP53. The new background set is then used for the
ActivePathways analysis.
background <- makeBackground(gmt)
background <- background[background != 'TP53']
ActivePathways(scores, gmt_file, background = background)## term_id term_name adjusted_p_val term_size
## <char> <char> <num> <int>
## 1: REAC:2424491 DAP12 signaling 0.0022333168 358
## 2: REAC:422475 Axon guidance 0.0001161168 555
## overlap evidence
## <list> <list>
## 1: PIK3CA,KRAS,PTEN,BRAF,NRAS,B2M,... CDS
## 2: PIK3CA,KRAS,BRAF,NRAS,CALM2,RPS6KA3,... X3UTR
## Genes_X3UTR Genes_X5UTR
## <list> <list>
## 1: NA NA
## 2: CALM2,ARPC2,RHOA,NUMB,CALM1,ACTB,... NA
## Genes_CDS Genes_promCore
## <list> <list>
## 1: PTEN,KRAS,PIK3CA,BRAF,NRAS,CDKN1A,... NA
## 2: NA NA
## [ reached getOption("max.print") -- omitted 29 rows ]Note that only the genes found in the background set are used for
testing enrichment. Any genes in the input data that are not in the
background set will be automatically removed by
ActivePathways.
Merging p-values
A key feature of ActivePathways is the integration of
multiple complementary omics datasets to prioritise genes for the
pathway analysis. In this approach, genes with significant scores in
multiple datasets will get the highest priority, and certain genes with
weak scores in multiple datasets may be ranked higher, highlighting
functions that would be missed when only single datasets were analysed.
ActivePathways accomplishes this by merging the series of
p-values in the columns of the scores matrix for each gene into a single
combined P-value. The four methods to merge P-values are Fisher’s method
(the default), Brown’s method (extension of Fisher’s), Stouffer’s method
and Strube’s method (extension of Stouffer’s). Each of these methods
have been extended to account for the directional activity of genes
across multi-omics datasets with Fisher_directional, DPM,
Stouffer_directional, and Strube_directional methods. The Brown’s and
Strube’s methods are more conservative in the case when the input
datasets show some large-scale similarities (i.e., covariation), since
they will take that into account when prioritising genes across similar
datasets. The Brown’s or Strube’s method are recommended for most cases
since omics datasets are often not statistically independent of each
other and genes with high scores in one dataset are more likely to have
high scores in another dataset just by chance.
The following example compares the merged P-values of the first few genes between the four methods. Fisher’s and Stouffer’s method are two alternative strategies to merge p-values and as a result the top scoring genes and p-values may differ. The genes with the top scores for Brown’s method are the same as Fisher’s, but their P-values are more conservative. This is the case for Strube’s method as well, in which the top scoring genes are the same as Stouffer’s method, but the P-values are more conservative.
## TP53 VHL PIK3CA KRAS PTEN
## 2.275933e-32 4.677780e-31 9.878802e-30 5.169163e-29 5.813021e-29## TP53 VHL PIK3CA KRAS PTEN
## 2.850936e-21 1.933490e-20 1.334809e-19 3.808817e-19 4.102937e-19## TP53 VHL PIK3CA KRAS PTEN
## 5.889756e-18 1.228308e-15 3.067765e-15 1.396875e-13 2.275649e-13## TP53 VHL PIK3CA KRAS PTEN
## 1.170932e-11 3.249661e-10 5.746455e-10 6.206504e-09 8.414282e-09This function can be used to combine some of the data before the
analysis for any follow-up analysis or visualisation. For example, we
can merge the columns X5UTR, X3UTR, and
promCore into a single non_coding column
(these correspond to predictions of driver mutations in 5’UTRs, 3’UTRs,
and core promoters of genes, respectively). This will consider the three
non-coding regions as a single column, rather than giving them all equal
weight to the CDS column.
scores2 <- cbind(scores[, 'CDS'], merge_p_values(scores[, c('X3UTR', 'X5UTR', 'promCore')], 'Brown'))
colnames(scores2) <- c('CDS', 'non_coding')
scores[c(2179, 1760),]## X3UTR X5UTR CDS promCore
## TP53 0.8331532 0.005613463 1.842404e-33 0.0254239
## PTEN 0.1627596 0.310132725 2.180301e-32 0.6867016## CDS non_coding
## TP53 1.842404e-33 0.0189964
## PTEN 2.180301e-32 0.3437851## term_id term_name adjusted_p_val term_size
## <char> <char> <num> <int>
## 1: REAC:2424491 DAP12 signaling 4.491268e-05 358
## 2: REAC:422475 Axon guidance 4.625918e-04 555
## overlap evidence
## <list> <list>
## 1: TP53,PIK3CA,KRAS,PTEN,BRAF,NRAS,... CDS
## 2: PIK3CA,KRAS,BRAF,NRAS,CALM2,RPS6KA3,... X3UTR,promCore
## Genes_X3UTR Genes_X5UTR
## <list> <list>
## 1: NA NA
## 2: CALM2,ARPC2,RHOA,NUMB,CALM1,ACTB,... NA
## Genes_CDS
## <list>
## 1: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,...
## 2: NA
## Genes_promCore
## <list>
## 1: NA
## 2: EFNA1,IQGAP1,COL4A1,SCN2B,RPS6KA3,CALM2,...
## [ reached getOption("max.print") -- omitted 32 rows ]## term_id term_name adjusted_p_val term_size
## <char> <char> <num> <int>
## 1: REAC:2424491 DAP12 signaling 0.0003694968 358
## 2: REAC:422475 Axon guidance 0.0051873493 555
## 3: REAC:177929 Signaling by EGFR 0.0014545468 366
## overlap evidence
## <list> <list>
## 1: TP53,PIK3CA,PTEN,KRAS,BRAF,NRAS,... CDS
## 2: PIK3CA,KRAS,BRAF,NRAS,RPS6KA3,CALM2,... combined
## 3: TP53,PIK3CA,PTEN,KRAS,BRAF,NRAS,... CDS
## Genes_CDS Genes_non_coding
## <list> <list>
## 1: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,... NA
## 2: NA NA
## 3: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,... NA
## [ reached getOption("max.print") -- omitted 27 rows ]Cutoff for filtering the ranked gene list for pathway enrichment analysis
To perform pathway enrichment of the ranked gene list of merged
P-values, ActivePathways defines a P-value cutoff to filter
genes that have little or no significance in the series of omics
datasets. This threshold represents the maximum p-value for a gene to be
considered of interest in our analysis. The threshold is
0.1 by default but can be changed using the
cutoff option. The default option considers raw P-values
that have not been adjusted for multiple-testing correction. Therefore,
the default option provides a relatively lenient approach to filtering
the input data. This is useful for finding additional genes with weaker
signals that associate with well-annotated and strongly significant
genes in the pathway and functional context.
## [1] 33## [1] 18Adjusting P-values using multiple testing correction
Multiple testing correction is essential in the analysis of omics
data since each analysis routinely considers thousands of hypotheses and
apparently significant P-values will occur by chance alone.
ActivePathways uses multiple testing correction at the
level of pathways as P-values from the ranked hypergeometric test are
adjusted for multiple testing (note that the ranked gene list provided
to the ranked hypergeometric test remain unadjusted for multiple testing
by design).
The package uses the p.adjust function of base R to run
multiple testing corrections and all methods in this function are
available. By default, ‘holm’ correction is used. The option
correction_method = 'none' can be used to override P-value
adjustment (not recommended in most cases).
## [1] 33## [1] 88The results table of ActivePathways
Consider the results object from the basic use case of
ActivePathways
## term_id term_name adjusted_p_val term_size
## <char> <char> <num> <int>
## 1: REAC:2424491 DAP12 signaling 4.491268e-05 358
## 2: REAC:422475 Axon guidance 4.625918e-04 555
## overlap evidence
## <list> <list>
## 1: TP53,PIK3CA,KRAS,PTEN,BRAF,NRAS,... CDS
## 2: PIK3CA,KRAS,BRAF,NRAS,CALM2,RPS6KA3,... X3UTR,promCore
## Genes_X3UTR Genes_X5UTR
## <list> <list>
## 1: NA NA
## 2: CALM2,ARPC2,RHOA,NUMB,CALM1,ACTB,... NA
## Genes_CDS
## <list>
## 1: TP53,PTEN,KRAS,PIK3CA,BRAF,NRAS,...
## 2: NA
## Genes_promCore
## <list>
## 1: NA
## 2: EFNA1,IQGAP1,COL4A1,SCN2B,RPS6KA3,CALM2,...
## [ reached getOption("max.print") -- omitted 32 rows ]The columns term_id, term_name, and
term_size give information about each pathway detected in
the enrichment analysis. The adjusted_p_val column with the
adjusted P-value indicates the confidence that the pathway is enriched
after multiple testing correction.
The overlap column provides the set of genes from the
integrated gene list that occur in the given enriched gene set (i.e.,
molecular pathway or biological process). These genes were quantified
across multiple input omics datasets and prioritized based on their
joint significance in the input data. Note that the genes with the
strongest scores across the multiple datasets are listed first.
## [[1]]
## [1] "TP53" "PIK3CA" "KRAS" "PTEN" "BRAF" "NRAS" "B2M" "CALM2"
## [9] "CDKN1A" "CDKN1B"
##
## [[2]]
## [1] "PIK3CA" "KRAS" "BRAF" "NRAS" "CALM2" "RPS6KA3" "ACTB"
## [8] "EFNA1" "SCN2B" "EPHA2" "GAP43" "COL4A1" "RASAL2" "CLTC"
## [15] "IQGAP1" "NF1" "FGF9" "ADAM10" "PTPRC" "ITGA10" "PDGFB"
## [22] "COL4A2" "RGMB" "RASA1" "FGF6" "CALM1" "PSMB7" "PPP2R5D"
## [29] "PPP2R1A" "RAP1A" "CNTNAP1" "GRIN2B" "GRB2" "DLG1" "MET"
## [ reached getOption("max.print") -- omitted 6 entries ]
##
## [[3]]
## [1] "TP53" "PIK3CA" "KRAS" "PTEN" "BRAF" "NRAS" "CALM2" "CDKN1A"
## [9] "CDKN1B"This column is useful for further data analysis, allowing the researcher to go from the space of enriched pathways back to the space of individual genes and proteins involved in pathways and their input omics datasets.
The evidence column provides insights to which of the
input omics datasets (i.e., columns in the scores matrix) contributed to
the discovery of this pathway or process in the integrated enrichment
analysis. To achieve this level of detail, ActivePathways
also analyses the gene lists ranked by the individual columns of the
input matrix to detect enriched pathways. The evidence
column lists the name of a given column of the input matrix if the given
pathway is detected both in the integrated analysis and the analysis of
the individual column. For example, in this analysis the majority of the
detected pathways have only ‘CDS’ as their evidence, since these
pathways were found to be enriched in data fusion through P-value
merging and also by analysing the gene scores in the column
CDS (for reference, CDS corresponds to protein-coding
sequence where the majority of known driver mutations have been found).
As a counter-example, the record for the pathway
REAC:422475 in our results lists as evidence
list('X3UTR', 'promCore'), meaning that the pathway was
found to be enriched when considering either the X3UTR
column, the promCore column, or the combined omics
datasets.
## evidence1 evidence2
## "X3UTR" "promCore"Finally, if a pathway is found to be enriched only with the combined data and not in any individual column, ‘combined’ will be listed as the evidence. This subset of results may be particularly interesting since it highlights complementary aspects of the analysis that would remain hidden in the analysis of any input omics dataset separately.
The following columns named as Genes_{column} help
interpret how each pathway was detected in the multi-omics data
integration, as listed in the column evidence. These
columns show the genes present in the pathway and any of the input omics
datasets. If the given pathway was not identified using the scores of
the given column of the input scores matrix, an NA value is
shown. Again, the genes are ranked by the significance of their scores
in the input data, to facilitate identification of the most relevant
genes in the analysis.
Writing results to a CSV file
The results are returned as a data.table object due to
some additional data structures needed to store lists of gene IDs and
supporting evidence. The usual R functions write.table and
write.csv will struggle with exporting the data unless the
gene and evidence lists are manually transformed as strings.
Fortunately, the fwrite function of data.table
can be used to write the file directly and the ActivePathways package
includes the function export_as_CSV as a shortcut that uses
the vertical bar symbol to concatenate gene lists.
result_file <- paste('ActivePathways_results.csv', sep = '/')
export_as_CSV (res, result_file) # remove comment to run
read.csv(result_file, stringsAsFactors = F)[1:3,]The fwrite can be called directly for customised
output.
