• Introduction
• Installation
• Usage
  • Importing the Ontology
  • The Differential Expression Dataset to Analyse
  • The Unordered Set-Based Overrepresentation Analysis (ORA)
  • Gene Set Enrichment Analysis (GSEA)
  • Formatting the Results of a Differential Expression Analysis
• Session Info
• How to Cite the mulea Package?
• References

The mulea R package (Turek et al. 2024) is a comprehensive tool for functional enrichment analysis. It provides two different approaches:

1. For unranked sets of elements, such as significantly up- or down-regulated genes, mulea employs the set-based overrepresentation analysis (ORA).

2. Alternatively, if the data consists of ranked elements, for instance, genes ordered by p-value or log fold-change calculated by the differential expression analysis, mulea offers the gene set enrichment (GSEA) approach.

For the overrepresentation analysis, mulea employs a progressive empirical false discovery rate (eFDR) method, specifically designed for interconnected biological data, to accurately identify significant terms within diverse ontologies.

mulea expands beyond traditional tools by incorporating a wide range of ontologies, encompassing Gene Ontology, pathways, regulatory elements, genomic locations, and protein domains for 27 model organisms, covering 22 ontology types from 16 databases and various identifiers resulting in 879 files available at the ELTEbioinformatics/GMT_files_for_mulea GitHub repository and through the muleaData ExperimentData Bioconductor package.

Install the dependency fgsea BioConductor package:

# Installing the BiocManager package if needed
if (!require("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
# Installing the fgsea package with the BiocManager
BiocManager::install("fgsea")

To install mulea from CRAN:

install.packages("mulea")

To install the development version of mulea from GitHub:

# Installing the devtools package if needed
if (!require("devtools", quietly = TRUE))
    install.packages("devtools")

# Installing the mulea package from GitHub
devtools::install_github("https://github.com/ELTEbioinformatics/mulea")

First, load the mulea and dplyr libraries. The dplyr library is not essential but is used here to facilitate data manipulation and inspection.

library(mulea)
library(tidyverse)

This section demonstrates how to import the desired ontology, such as transcription factors and their target genes downloaded from the database, into a data frame suitable for enrichment analysis. We present multiple methods for importing the ontology. Ensure that the identifier type (e.g., UniProt protein ID, Entrez ID, Gene Symbol, Ensembl gene ID) matches between the ontology and the elements you wish to investigate.

The GMT (Gene Matrix Transposed) format contains collections of genes or proteins associated with specific ontology terms in a tab-delimited text file. The GMT file can be read into R as a data frame using the read_gmt function from the mulea package. Each term is represented by a single row in both the GMT file and the data frame. Each row includes three types of elements:

1. Ontology identifier (“ontology_id”): This uniquely identifies each term within the file or data frame.

2. Ontology name or description (“ontology_name”): This provides a user-friendly label or textual description for each term.

3. Associated gene or protein identifiers: These are listed in the “list_of_values” column, with identifiers separated by spaces, and belong to each term.¹

Alongside with the mulea package we provide ontologies collected from 16 publicly available databases, in a standardised GMT format for 27 model organisms, from Bacteria to human. These files are available at the ELTEbioinformatics/GMT_files_for_mulea GitHub repository.

To read a downloaded GMT file locally:

# Reading the mulea GMT file locally
tf_ontology <- read_gmt("Transcription_factor_RegulonDB_Escherichia_coli_GeneSymbol.gmt")

Alternatively, one can read it directly from the GitHub repository:

# Reading the GMT file from the GitHub repository
tf_ontology <- read_gmt("https://raw.githubusercontent.com/ELTEbioinformatics/GMT_files_for_mulea/main/GMT_files/Escherichia_coli_83333/Transcription_factor_RegulonDB_Escherichia_coli_GeneSymbol.gmt")

mulea is compatible with GMT files provided with the Enricher R package (Kuleshov et al. 2016). Download and read such a GMT file (e. g. TRRUST_Transcription_Factors_2019.txt) locally. Note that this ontology is not suitable for analyzing the Escherichia coli differential expression data described in the section The Differential Expression Dataset to Analyse.

# Reading the Enrichr GMT file locally
tf_enrichr_ontology <- read_gmt("TRRUST_Transcription_Factors_2019.txt")

# The ontology_name is empty, therefore we need to fill it with the ontology_id
tf_enrichr_ontology$ontology_name <- tf_enrichr_ontology$ontology_id

mulea is compatible with the MsigDB (Subramanian et al. 2005) GMT files. Download and read such a GMT file (e. g. c3.tft.v2023.2.Hs.symbols.gmt) locally. Note that this ontology is not suitable for analyzing the Escherichia coli differential expression data described in the section The Differential Expression Dataset to Analyse.

# Reading the MsigDB GMT file locally
tf_msigdb_ontology <- read_gmt("c3.tft.v2023.2.Hs.symbols.gmt")

Alternatively, you can retrieve the ontology using the muleaData ExperimentData Bioconductor package:

# Installing the ExperimentHub package from Bioconductor
BiocManager::install("ExperimentHub")

# Calling the ExperimentHub library.
library(ExperimentHub)

# Downloading the metadata from ExperimentHub.
eh <- ExperimentHub()

# Creating the muleaData variable.
muleaData <- query(eh, "muleaData")

# Looking for the ExperimentalHub ID of the ontology.
EHID <- mcols(muleaData) %>% 
  as.data.frame() %>% 
  dplyr::filter(title == "Transcription_factor_RegulonDB_Escherichia_coli_GeneSymbol.rds") %>% 
  rownames()

# Reading the ontology from the muleaData package.
tf_ontology <- muleaData[[EHID]]

# Change the header
tf_ontology <- tf_ontology %>% 
  rename(ontology_id = "ontologyId",
         ontology_name = "ontologyName",
         list_of_values = "listOfValues")

Enrichment analysis results can sometimes be skewed by overly specific or broad entries. mulea allows you to customise the size of ontology entries – the number of genes or proteins belonging to a term – ensuring your analysis aligns with your desired scope.

Let’s exclude ontology entries with less than 3 or more than 400 gene symbols.

# Filtering the ontology
tf_ontology_filtered <- filter_ontology(gmt = tf_ontology,
                                        min_nr_of_elements = 3,
                                        max_nr_of_elements = 400)

You can save the ontology as a GMT file using the write_gmt function.

# Saving the ontology to GMT file
write_gmt(gmt = tf_ontology_filtered, 
          file = "Filtered.gmt")

The mulea package provides the list_to_gmt function to convert a list of gene sets into an ontology data frame. The following example demonstrates how to use this function:

# Creating a list of gene sets
ontology_list <- list(gene_set1 = c("gene1", "gene2", "gene3"),
                      gene_set2 = c("gene4", "gene5", "gene6"))

# Converting the list to a ontology (GMT) object
new_ontology_df <- list_to_gmt(ontology_list)

For further steps we will analyse a dataset from a microarray experiment (GSE55662) in the NCBI Gene Expression Omnibus . The study by Méhi et al. (2014) investigated antibiotic resistance evolution in Escherichia coli. Gene expression changes were compared between ciprofloxacin antibiotic-treated Escherichia coli bacteria and non-treated controls.

The expression levels of these groups were compared with the GEO2R tool:

• Non-treated control samples (2 replicates): WT_noCPR_1, WT_noCPR_2
• Ciprofloxacin-treated samples (2 replicates): WT_CPR_1, WT_CPR_2

To see how the dataset were prepared go to the Formatting the Results of a Differential Expression Analysis section.

The mulea package implements a set-based enrichment analysis approach using the hypergeometric test, which is analogous to the one-tailed Fisher’s exact test. This method identifies statistically significant overrepresentation of elements from a target set (e.g., significantly up- or downregulated genes) within a background set (e.g., all genes that were investigated in the experiment). Therefore, a predefined threshold value, such as 0.05 for the corrected p-value or 2-fold change, should be used in the preceding analysis.

The overrepresentation analysis is implemented in the ora function which requires three inputs:

1. Ontology data frame: Fits the investigated taxa and the applied gene or protein identifier type, such as GO, pathway, transcription factor regulation, microRNA regulation, gene expression data, genomic location data, or protein domain content.

2. Target set: A vector of elements to investigate, containing genes or proteins of interest, such as significantly overexpressed genes in the experiment.

3. Background set: A vector of background elements representing the broader context, often including all genes investigated in the study.

Let’s read the text files containing the identifiers (gene symbols) of the target and the background gene set directly from the GitHub website. To see how these files were prepared, refer to the section on Formatting the Results of a Differential Expression Analysis.

# Taget set
target_set <- readLines("https://raw.githubusercontent.com/ELTEbioinformatics/mulea/master/inst/extdata/target_set.txt")

# Background set
background_set  <- readLines("https://raw.githubusercontent.com/ELTEbioinformatics/mulea/master/inst/extdata/background_set.txt")

To perform the analysis, we will first establish a model using the ora function. This model defines the parameters for the enrichment analysis. We then execute the test itself using the run_test function. It is important to note that for this example, we will employ 10,000 permutations for the empirical false discovery rate (eFDR), which is the recommended minimum, to ensure robust correction for multiple testing.

# Creating the ORA model using the GMT variable
ora_model <- ora(gmt = tf_ontology_filtered, 
                 # Test set variable
                 element_names = target_set, 
                 # Background set variable
                 background_element_names = background_set, 
                 # p-value adjustment method
                 p_value_adjustment_method = "eFDR", 
                 # Number of permutations
                 number_of_permutations = 10000,
                 # Number of processor threads to use
                 nthreads = 2, 
                 # Setting a random seed for reproducibility
                 random_seed = 1) 

# Running the ORA
ora_results <- run_test(ora_model)

The ora_results data frame summarises the enrichment analysis, listing enriched ontology entries – in our case transcription factors – alongside their associated p-values and eFDR values.

We can now determine the number of transcription factors classified as “enriched” based on these statistical measures (eFDR < 0.05).

ora_results %>%
  # Rows where the eFDR < 0.05
  filter(eFDR < 0.05) %>% 
  # Number of such rows
  nrow()
#> [1] 10

Inspect the significant results:

ora_results %>%
  # Arrange the rows by the eFDR values
  arrange(eFDR) %>% 
  # Rows where the eFDR < 0.05
  filter(eFDR < 0.05)

To gain a comprehensive understanding of the enriched transcription factors, mulea offers diverse visualisation tools, including lollipop charts, bar plots, networks, and heatmaps. These visualisations effectively reveal patterns and relationships among the enriched factors.

Initialising the visualisation with the reshape_results function:

# Reshapeing the ORA results for visualisation
ora_reshaped_results <- reshape_results(model = ora_model, 
                                        model_results = ora_results, 
                                        # Choosing which column to use for the
                                        #     indication of significance
                                        p_value_type_colname = "eFDR")

Visualising the Spread of eFDR Values: Lollipop Plot

Lollipop charts provide a graphical representation of the distribution of enriched transcription factors. The y-axis displays the transcription factors, while the x-axis represents their corresponding eFDR values. The dots are coloured based on their eFDR values. This visualisation helps us examine the spread of eFDRs and identify factors exceeding the commonly used significance threshold of 0.05.

plot_lollipop(reshaped_results = ora_reshaped_results,
              # Column containing the names we wish to plot
              ontology_id_colname = "ontology_id",
              # Upper threshold for the value indicating the significance
              p_value_max_threshold = 0.05,
              # Column that indicates the significance values
              p_value_type_colname = "eFDR")

Visualising the Spread of eFDR Values: Bar Plot

Bar charts offer a graphical representation similar to lollipop plots. The y-axis displays the enriched ontology categories (e.g., transcription factors), while the x-axis represents their corresponding eFDR values. The bars are coloured based on their eFDR values, aiding in examining the spread of eFDRs and identifying factors exceeding the significance threshold of 0.05.

plot_barplot(reshaped_results = ora_reshaped_results,
              # Column containing the names we wish to plot
              ontology_id_colname = "ontology_id",
              # Upper threshold for the value indicating the significance
              p_value_max_threshold = 0.05,
              # Column that indicates the significance values
              p_value_type_colname = "eFDR")

Visualising the Associations: Graph Plot

This function generates a network visualisation of the enriched ontology categories (e.g., transcription factors). Each node represents an eriched ontology category, coloured based on its eFDR value. An edge is drawn between two nodes if they share at least one common gene belonging to the target set, indicating co-regulation. The thickness of the edge reflects the number of shared genes.

plot_graph(reshaped_results = ora_reshaped_results,
           # Column containing the names we wish to plot
           ontology_id_colname = "ontology_id",
           # Upper threshold for the value indicating the significance
           p_value_max_threshold = 0.05,
           # Column that indicates the significance values
           p_value_type_colname = "eFDR")

Visualising the Associations: Heatmap

The heatmap displays the genes associated with the enriched ontology categories (e.g., transcription factors). Each row represents a category, coloured based on its eFDR value. Each column represents a gene from the target set belonging to the enriched ontology category, indicating potential regulation by one or more enriched transcription factors.

plot_heatmap(reshaped_results = ora_reshaped_results,
             # Column containing the names we wish to plot
             ontology_id_colname = "ontology_id",
             # Column that indicates the significance values
             p_value_type_colname = "eFDR")

The ora function allows you to choose between different methods for calculating the FDR and adjusting the p-values: eFDR, and all method options from the stats::p.adjust documentation (holm, hochberg, hommel, bonferroni, BH, BY, and fdr). The following code snippet demonstrates how to perform the analysis using the Benjamini-Hochberg and Bonferroni corrections:

# Creating the ORA model using the Benjamini-Hochberg p-value correction method
BH_ora_model <- ora(gmt = tf_ontology_filtered, 
                 # Test set variable
                 element_names = target_set, 
                 # Background set variable
                 background_element_names = background_set, 
                 # p-value adjustment method
                 p_value_adjustment_method = "BH") 

# Running the ORA
BH_results <- run_test(BH_ora_model)

# Creating the ORA model using the Bonferroni p-value correction method
Bonferroni_ora_model <- ora(gmt = tf_ontology_filtered, 
                            # Test set variable
                            element_names = target_set, 
                            # Background set variable
                            background_element_names = background_set, 
                            # p-value adjustment method
                            p_value_adjustment_method = "bonferroni") 

# Running the ORA
Bonferroni_results <- run_test(Bonferroni_ora_model)

To compare the significant results (using the conventional < 0.05 threshold) of the eFDR, Benjamini-Hochberg, and Bonferroni corrections, we can merge and filter the result tables:

# Merging the Benjamini-Hochberg and eFDR results
merged_results <- BH_results %>% 
  # Renaming the column
  rename(BH_adjusted_p_value = adjusted_p_value) %>% 
  # Selecting the necessary columns
  select(ontology_id, BH_adjusted_p_value) %>%
  # Joining with the eFDR results
  left_join(ora_results, ., by = "ontology_id") %>% 
  # Converting the data.frame to a tibble
  tibble()

# Merging the Bonferroni results with the merged results
merged_results <- Bonferroni_results %>% 
  # Renaming the column
  rename(Bonferroni_adjusted_p_value = adjusted_p_value) %>% 
  # Selecting the necessary columns
  select(ontology_id, Bonferroni_adjusted_p_value) %>%
  # Joining with the eFDR results
  left_join(merged_results, ., by = "ontology_id") %>% 
  # Arranging by the p-value
  arrange(p_value)

# filter the p-value < 0.05 results
merged_results_filtered <- merged_results %>% 
  filter(p_value < 0.05) %>% 
  # remove the unnecessary columns
  select(-ontology_id, -nr_common_with_tested_elements, 
         -nr_common_with_background_elements)

A comparison of the significant results revealed that conventional p-value corrections (Benjamini-Hochberg and Bonferroni) tend to be overly conservative, leading to a reduction in the number of significant transcription factors compared to the eFDR. As illustrated in the below figure, by applying the eFDR we were able to identify 10 significant transcription factors, while with the Benjamini-Hochberg and Bonferroni corrections only 7 and 3, respectively. This suggests that the eFDR may be a more suitable approach for controlling false positives in this context.

To perform enrichment analysis using ranked lists, you need to provide an ordered list of elements, such as genes or proteins. This ranking is typically based on the results of your prior analysis, using metrics like p-values, z-scores, fold-changes, or others. Crucially, the ranked list should include all elements involved in your analysis. For example, in a differential expression study, it should encompass all genes that were measured.

mulea utilises the Kolmogorov-Smirnov approach with a permutation test (developed by Subramanian et al. (2005)) to calculate gene set enrichment analyses. This functionality is implemented through the integration of the fgsea Bioconductor package (created by Korotkevich et al. (2021)).

GSEA requires input data about the genes analysed in our experiment. This data can be formatted in two ways:

1. Data frame: This format should include all genes investigated and their respective log fold change values (or other values for ordering the genes) obtained from the differential expression analysis.

2. Two vectors: Alternatively, you can provide two separate vectors. One vector should contain the gene symbols (or IDs), and the other should hold the corresponding log fold change values (or other values for ordering the genes) for each gene.

Let’s read the TSV file containing the identifiers (gene symbols) and the log fold change values of the investigated set directly from the GitHub website. For details on how this file was prepared, please refer to the Formatting the Results of a Differential Expression Analysis section.

# Reading the tsv containing the ordered set
ordered_set <- read_tsv("https://raw.githubusercontent.com/ELTEbioinformatics/mulea/master/inst/extdata/ordered_set.tsv")

To perform the analysis, we will first establish a model using the gsea function. This model defines the parameters for the enrichment analysis. Subsequently, we will execute the test itself using the run_test function. We will employ 10,000 permutations for the false discovery rate, to ensure robust correction for multiple testing.

# Creating the GSEA model using the GMT variable
gsea_model <- gsea(gmt = tf_ontology_filtered,
                   # Names of elements to test
                   element_names = ordered_set$Gene.symbol,
                   # LogFC-s of elements to test
                   element_scores = ordered_set$logFC,
                   # Consider elements having positive logFC values only
                   element_score_type = "pos",
                   # Number of permutations
                   number_of_permutations = 10000)

# Running the GSEA
gsea_results <- run_test(gsea_model)

The gsea_results data frame summarises the enrichment analysis, listing enriched ontology entries – in our case transcription factors – alongside their associated p-values and adjusted p-value values.

We can now determine the number of transcription factors classified as “enriched” based on these statistical measures (adjusted p-value < 0.05).

gsea_results %>%
  # rows where the adjusted_p_value < 0.05
  filter(adjusted_p_value < 0.05) %>% 
  # the number of such rows
  nrow()
#> [1] 10

Inspect the significant results:

gsea_results %>%
  # arrange the rows by the adjusted_p_value values
  arrange(adjusted_p_value) %>% 
  # rows where the adjusted_p_value < 0.05
  filter(adjusted_p_value < 0.05)

Initializing the visualisation with the reshape_results function:

# Reshaping the GSEA results for visualisation
gsea_reshaped_results <- reshape_results(model = gsea_model, 
                                         model_results = gsea_results, 
                                         # choosing which column to use for the
                                         # indication of significance
                                         p_value_type_colname = "adjusted_p_value")

Visualising Relationships: Graph Plot

This function generates a network visualisation of the enriched ontology categories (e.g., transcription factors). Each node represents a category and is coloured based on its significance level. A connection (edge) is drawn between two nodes if they share at least one common gene belonging to the ranked list, meaning that both transcription factors regulate the expression of the same target gene. The thickness of the edge reflects the number of shared genes.

plot_graph(reshaped_results = gsea_reshaped_results,
           # the column containing the names we wish to plot
           ontology_id_colname = "ontology_id",
           # upper threshold for the value indicating the significance
           p_value_max_threshold = 0.05,
           # column that indicates the significance values
           p_value_type_colname = "adjusted_p_value")

Other plot types such as lollipop plots, bar plots, and heatmaps can also be used to investigate the GSEA results.

This section aims to elucidate the structure and essential components of the provided DE results table. It offers guidance to users on interpreting the data effectively for subsequent analysis with mulea.

Let’s read the differential expression result file named GSE55662.table_wt_non_vs_cipro.tsv located in the inst/extdata/ folder directly from the GitHub website.

# Importing necessary libraries and reading the DE results table
geo2r_result_tab <- read_tsv("https://raw.githubusercontent.com/ELTEbioinformatics/mulea/master/inst/extdata/GSE55662.table_wt_non_vs_cipro.tsv")

Let’s delve into the geo2r_result_tab data frame by examining its initial rows:

# Printing the first few rows of the data frame
geo2r_result_tab %>%  
  head(3)

Preparing the data frame appropriately for enrichment analysis is crucial. This involves specific steps tailored to the microarray experiment type. Here, we undertake the following transformations:

• Gene Symbol Extraction: We isolate the primary gene symbol from the Gene.symbol column, eliminating any extraneous information.

• Handling Missing Values: Rows with missing gene symbols (NA) are excluded.

• Sorting by Fold Change: The data frame is sorted by log-fold change (logFC) in descending order, prioritizing genes with the most significant expression alterations.

# Formatting the data frame
geo2r_result_tab <- geo2r_result_tab %>% 
  # Extracting the primary gene symbol and removing extraneous information
  mutate(Gene.symbol = str_remove(string = Gene.symbol,
                                  pattern = "\\/.*")) %>% 
  # Filtering out rows with NA gene symbols
  filter(!is.na(Gene.symbol)) %>% 
  # Sorting by logFC
  arrange(desc(logFC))

Before proceeding with enrichment analysis, let’s examine the initial rows of the formatted geo2r_result_tab data frame:

# Printing the first few rows of the formatted data frame
geo2r_result_tab %>%  
  head(3)

Following these formatting steps, the data frame is primed for further analysis.

A vector containing the gene symbols of significantly overexpressed (adjusted p-value < 0.05) genes with greater than 2 fold-change (logFC > 1).

target_set <- geo2r_result_tab %>% 
  # Filtering for adjusted p-value < 0.05 and logFC > 1
  filter(adj.P.Val < 0.05 & logFC > 1) %>% 
  # Selecting the Gene.symbol column
  select(Gene.symbol) %>% 
  # Converting the tibble to a vector
  pull() %>% 
  # Removing duplicates
  unique()

The first 10 elements of the target set:

target_set %>% 
  head(10)
#>  [1] "gnsB"    "sulA"    "recN"    "c4435"   "dinI"    "c2757"   "c1431"  
#>  [8] "gabP"    "recA"    "ECs5456"

The number of genes in the target set:

target_set %>% 
  length()
#> [1] 241

A vector containing the gene symbols of all genes were included in the differential expression analysis.

background_set <- geo2r_result_tab %>% 
  # Selecting the Gene.symbol column
  select(Gene.symbol) %>% 
  # Converting the tibble to a vector
  pull() %>% 
  # Removing duplicates
  unique()

The number of genes in the background set:

background_set %>% 
  length()
#> [1] 7381

Save the target and the background set vectors to text file:

# Save taget set to text file
target_set %>% 
  writeLines("target_set.txt")

# Save background set to text file
background_set %>% 
  writeLines("inst/extdata/background_set.txt")

# If there are duplicated Gene.symbols keep the first one only
ordered_set <- geo2r_result_tab %>% 
  # Grouping by Gene.symbol to be able to filter
  group_by(Gene.symbol) %>%
  # Keeping the first row for each Gene.symbol from rows with the same 
  #     Gene.symbol
  filter(row_number()==1) %>% 
  # Ungrouping
  ungroup() %>% 
  # Arranging by logFC in descending order
  arrange(desc(logFC)) %>%
  select(Gene.symbol, logFC)

The number of gene symbols in the ordered_set vector:

ordered_set %>% 
  nrow()
#> [1] 7381

Save the ordered set data frame to tab delimited file:

# Save ordered set to text file
ordered_set %>% 
  write_tsv("ordered_set.tsv")

sessionInfo()
#> R version 4.4.2 (2024-10-31)
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#> [1] stats     graphics  grDevices utils     datasets  methods   base     
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#> other attached packages:
#>  [1] lubridate_1.9.3 forcats_1.0.0   stringr_1.5.1   dplyr_1.1.4    
#>  [5] purrr_1.0.2     readr_2.1.5     tidyr_1.3.1     tibble_3.2.1   
#>  [9] ggplot2_3.5.1   tidyverse_2.0.0 mulea_1.0.2    
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#>  [4] ggrepel_0.9.6       lattice_0.22-6      tzdb_0.4.0         
#>  [7] vctrs_0.6.5         tools_4.4.2         generics_0.1.3     
#> [10] curl_5.2.2          parallel_4.4.2      fansi_1.0.6        
#> [13] highr_0.11          pkgconfig_2.0.3     Matrix_1.7-0       
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#> [19] farver_2.1.2        munsell_0.5.1       ggforce_0.4.2      
#> [22] fgsea_1.30.0        graphlayouts_1.2.0  codetools_0.2-20   
#> [25] htmltools_0.5.8.1   yaml_2.3.10         crayon_1.5.3       
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#> [34] digest_0.6.37       stringi_1.8.4       labeling_0.4.3     
#> [37] cowplot_1.1.3       polyclip_1.10-7     fastmap_1.2.0      
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#> [43] magrittr_2.0.3      ggraph_2.2.1        tidygraph_1.3.1    
#> [46] utf8_1.2.4          withr_3.0.1         scales_1.3.0       
#> [49] bit64_4.0.5         timechange_0.3.0    rmarkdown_2.28     
#> [52] bit_4.0.5           igraph_2.0.3        gridExtra_2.3      
#> [55] hms_1.1.3           memoise_2.0.1       evaluate_0.24.0    
#> [58] knitr_1.48          viridisLite_0.4.2   rlang_1.1.4        
#> [61] Rcpp_1.0.13         glue_1.7.0          tweenr_2.0.3       
#> [64] vroom_1.6.5         rstudioapi_0.16.0   R6_2.5.1           
#> [67] plyr_1.8.9

To cite package mulea in publications use:

Turek, Cezary, Márton Ölbei, Tamás Stirling, Gergely Fekete, Ervin Tasnádi, Leila Gul, Balázs Bohár, Balázs Papp, Wiktor Jurkowski, and Eszter Ari. 2024. “mulea: An R Package for Enrichment Analysis Using Multiple Ontologies and Empirical False Discovery Rate.” BMC Bioinformatics 25 (1): 334. https://doi.org/10.1186/s12859-024-08638-7.