Author: Anstasiia Gainullina, Mariia Emelianova, Alexey Sergushichev

# Using gatom package

This tutorial describes an R-package for finding active metabolic modules based on high throughput data. The pipeline takes as input transcriptional and/or metabolic data and finds a metabolic subnetwork (module) most regulated between the two conditions of interest.

The package relies on the active module analysis framework developed in BioNet package, but extends it to work with metabolic reaction networks. Further, it illustrates the usage of mwcsr package which provides a number of solvers for Maximum Weight Connected Subgraph problem and its variants.

Example of using the pipeline include:

- studying metabolic differences between pro- and anti-inflammatory macrophage activation (Jha et al, 2015);
- studying metabolic rewiring associated with glucose-independent tumor growth (Vinent at al, 2015);
- identification of deregulation of energy metabolism in Trem2-deficient macrophages (Ulland et al, 2017);
- identification of inositol-triphosphate metabolism activation in monocytes in fasting mice (Jordan et al, 2019).

More details on the pipeline are available in Sergushichev et al, 2016 and Emelianova et al, 2022.

# Installation

You can install gatom via `BiocManager`:

    # if (!require("BiocManager", quietly = TRUE))
    #     install.packages("BiocManager")
    #
    # BiocManager::install("gatom")

# Example workfow

In this example we will find an active metabolic module based on macrophage activation gene expression and metabolomics data (Jha et al, 2015). For improved performance here we will consider a simplified version of the data. See Example on full data and full network section for the real-scale analysis.

    library(gatom)
    library(data.table)
    library(igraph)
    library(mwcsr)

First let’s load the example tables with input differential gene expression and metabolite abundance data for LPS-IFNg stimulated macrophages compared to controls:

    data("gene.de.rawEx")
    print(head(gene.de.rawEx))

    ## # A tibble: 6 × 4
    ##   ID               pval log2FC baseMean
    ##   <chr>           <dbl>  <dbl>    <dbl>
    ## 1 NM_008392    8.83e-16  10.3   16589.
    ## 2 NM_001110517 1.12e-12   5.97    153.
    ## 3 NM_001253809 3.22e-11  -5.87     43.6
    ## 4 NM_013693    1.88e-10   4.92    326.
    ## 5 NM_009114    8.59e-10  -3.21    473.
    ## 6 NM_021491    2.36e- 9  -6.69     50.9

    data("met.de.rawEx")
    print(head(met.de.rawEx))

    ## # A tibble: 6 × 4
    ##   ID            pval log2FC baseMean
    ##   <chr>        <dbl>  <dbl>    <dbl>
    ## 1 HMDB02092 8.83e-34  3.12      17.1
    ## 2 HMDB00749 8.83e-34  3.12      17.1
    ## 3 HMDB00263 3.16e-19  1.41      12.8
    ## 4 HMDB01316 2.88e-13 -1.23      13.2
    ## 5 HMDB00191 4.39e-13  0.735     16.4
    ## 6 HMDB01112 6.60e-13  0.653     15.2

Next we will load example network related objects: global reaction network (`networkEx` object), metabolite annotations (`met.kegg.dbEx`), and organism-specific enzyme annotations for mouse (`org.Mm.eg.gatom.annoEx`).

    data("networkEx")
    data("met.kegg.dbEx")
    data("org.Mm.eg.gatom.annoEx")

Here `networkEx` object contain information about 204 KEGG reactions, their atom mappings and relation to enzymes:

    str(networkEx, max.level=1, give.attr = FALSE)

    ## List of 5
    ##  $ reactions      :Classes 'data.table' and 'data.frame':    204 obs. of  4 variables:
    ##  $ enzyme2reaction:Classes 'data.table' and 'data.frame':    243 obs. of  2 variables:
    ##  $ reaction2align :Classes 'data.table' and 'data.frame':    3919 obs. of  3 variables:
    ##  $ atoms          :Classes 'data.table' and 'data.frame':    1689 obs. of  3 variables:
    ##  $ metabolite2atom:Classes 'data.table' and 'data.frame':    1689 obs. of  2 variables:

Object `met.kegg.dbEx` contains information about 138 KEGG metabolites, including mappings from HMDB and ChEBI:

    str(met.kegg.dbEx, max.level=2, give.attr = FALSE)

    ## List of 4
    ##  $ baseId     : chr "KEGG"
    ##  $ metabolites:Classes 'data.table' and 'data.frame':    138 obs. of  3 variables:
    ##   ..$ metabolite     : chr [1:138] "C00002" "C00003" "C00004" "C00005" ...
    ##   ..$ metabolite_name: chr [1:138] "ATP" "NAD+" "NADH" "NADPH" ...
    ##   ..$ metabolite_url : chr [1:138] "http://www.kegg.jp/entry/C00002" "http://www.kegg.jp/entry/C00003" "http://www.kegg.jp/entry/C00004" "http://www.kegg.jp/entry/C00005" ...
    ##  $ anomers    :List of 2
    ##   ..$ metabolite2base_metabolite:Classes 'data.table' and 'data.frame':  238 obs. of  2 variables:
    ##   ..$ base_metabolite2metabolite:Classes 'data.table' and 'data.frame':  238 obs. of  2 variables:
    ##  $ mapFrom    :List of 2
    ##   ..$ HMDB :Classes 'data.table' and 'data.frame':   212 obs. of  2 variables:
    ##   ..$ ChEBI:Classes 'data.table' and 'data.frame':   161 obs. of  2 variables:

Object `org.Mm.eg.gatom.annoEx` contains mouse-specific mapping between enzyme classes and genes, as well as mapping between different types of gene identifiers:

    str(org.Mm.eg.gatom.annoEx, max.level=2, give.attr = FALSE)

    ## List of 4
    ##  $ baseId     : chr "Entrez"
    ##  $ gene2enzyme:Classes 'data.table' and 'data.frame':    150 obs. of  2 variables:
    ##   ..$ gene  : chr [1:150] "100042025" "100198" "100198" "100678" ...
    ##   ..$ enzyme: chr [1:150] "1.2.1.12" "3.1.1.31" "1.1.1.47" "3.1.3.3" ...
    ##  $ genes      :Classes 'data.table' and 'data.frame':    135 obs. of  2 variables:
    ##   ..$ gene  : chr [1:135] "100042025" "100198" "100678" "100705" ...
    ##   ..$ symbol: chr [1:135] "Gapdh-ps15" "H6pd" "Psph" "Acacb" ...
    ##  $ mapFrom    :List of 3
    ##   ..$ RefSeq :Classes 'data.table' and 'data.frame': 724 obs. of  2 variables:
    ##   ..$ Ensembl:Classes 'data.table' and 'data.frame': 135 obs. of  2 variables:
    ##   ..$ Symbol :Classes 'data.table' and 'data.frame': 135 obs. of  2 variables:

Then we create a metabolic graph with atom topology from the loaded data. Depending on `topology` parameter, the graph vertices can correspond either to `atoms` or `metabolites`. For metabolite topology, see Using metabolite-level network section.

    g <- makeMetabolicGraph(network=networkEx,
                            topology="atoms",
                            org.gatom.anno=org.Mm.eg.gatom.annoEx,
                            gene.de=gene.de.rawEx,
                            met.db=met.kegg.dbEx,
                            met.de=met.de.rawEx)

    ## Found DE table for genes with RefSeq IDs

    ## Found DE table for metabolites with HMDB IDs

    print(g)

    ## IGRAPH 494b620 UN-- 176 190 --
    ## + attr: name (v/c), metabolite (v/c), element (v/c), label (v/c), url
    ## | (v/c), pval (v/n), origin (v/n), HMDB (v/c), log2FC (v/n), baseMean
    ## | (v/n), logPval (v/n), signal (v/c), label (e/c), pval (e/n), origin
    ## | (e/n), RefSeq (e/c), gene (e/c), enzyme (e/c), reaction_name (e/c),
    ## | reaction_equation (e/c), url (e/c), reaction (e/c), log2FC (e/n),
    ## | baseMean (e/n), logPval (e/n), signal (e/c), signalRank (e/n)
    ## + edges from 494b620 (vertex names):
    ## [1] C00025_-0.3248_2.8125 --C00026_-0.3248_2.8125
    ## [2] C00025_-1.6238_3.5625 --C00026_-1.6238_3.5625
    ## [3] C00025_-2.9228_2.8125 --C00026_-2.9228_2.8125
    ## + ... omitted several edges

After creating the metabolic graph, we then score it, obtaining an instance of Signal Generalized Maximum Weight Subgraph (SGMWCS) problem.

The size of the module can be controlled by changing scoring parameters `k.gene` and `k.met`. The higher the values of scoring parameters are, the bigger the module is going to be.

    gs <- scoreGraph(g, k.gene = 25, k.met = 25)

Then we initialize an SMGWCS solver. Here, we use a heuristic relax-and-cut solver `rnc_solver` for simplicity.

See `mwcsr` package documentation for more solver options, or Using exact solver section for the recommended way.

    solver <- rnc_solver()

Then we find an active metabolic module with chosen solver and scored graph:

    set.seed(42)
    res <- solve_mwcsp(solver, gs)
    m <- res$graph

The result module is an `igraph` object that captures the most regulated reactions:

    print(m)

    ## IGRAPH ad680a6 UN-- 33 32 --
    ## + attr: signals (g/n), name (v/c), metabolite (v/c), element (v/c),
    ## | label (v/c), url (v/c), pval (v/n), origin (v/n), HMDB (v/c), log2FC
    ## | (v/n), baseMean (v/n), logPval (v/n), signal (v/c), score (v/n),
    ## | label (e/c), pval (e/n), origin (e/n), RefSeq (e/c), gene (e/c),
    ## | enzyme (e/c), reaction_name (e/c), reaction_equation (e/c), url
    ## | (e/c), reaction (e/c), log2FC (e/n), baseMean (e/n), logPval (e/n),
    ## | signal (e/c), signalRank (e/n), score (e/n)
    ## + edges from ad680a6 (vertex names):
    ## [1] C00025_-1.6238_3.5625--C00026_-1.6238_3.5625
    ## [2] C00022_-1.299_2.25   --C00041_-1.299_2.25
    ## + ... omitted several edges

    head(E(m)$label)

    ## [1] "Psat1" "Gpt2"  "Got2"  "Shmt1" "Pkm"   "Tpi1"

    head(V(m)$label)

    ## [1] "Pyruvate"       "L-Glutamate"    "2-Oxoglutarate" "Oxaloacetate"
    ## [5] "Glycine"        "L-Alanine"

The module can be plotted in R Viewer with `createShinyCyJSWidget()`. Here, red color corresponds to up-regulation (positive log-2 fold change) and green to down-regulation (negative log-2 fold change). Blue nodes and edges come from data with absent log-2 fold change values. Bigger size of nodes and width of edges reflect lower p-values.

    createShinyCyJSWidget(m)

# Saving modules

We can save the module to graphml format with `write_graph()` function from `igraph`:

    write_graph(m, file = file.path(tempdir(), "M0.vs.M1.graphml"), format = "graphml")

Or it can be saved to an interactive html widget:

    saveModuleToHtml(module = m, file = file.path(tempdir(), "M0.vs.M1.html"),
                     name="M0.vs.M1")

We can also save the module to dot format:

    saveModuleToDot(m, file = file.path(tempdir(), "M0.vs.M1.dot"), name = "M0.vs.M1")

Such dot file can be further used to generate svg file using `neato` tool from graphviz suite if it is installed on the system:

    system(paste0("neato -Tsvg ", file.path(tempdir(), "M0.vs.M1.dot"),
                  " > ", file.path(tempdir(), "M0.vs.M1.svg")),
           ignore.stderr=TRUE)

Alternatively, the module can be saved to pdf format with a nice layout.

You may vary the meaning of repel force and the number of iterations of repel algorithm for label layout. Note, that the larger your graph is the softer force you should use.

You may also set different seed for different variants of edge layout with `set.seed()`.

    set.seed(42)
    saveModuleToPdf(m, file = file.path(tempdir(), "M0.vs.M1.pdf"), name = "M0.vs.M1",
                    n_iter=100, force=1e-5)

# Example on full data and full network

Let’s now look at how the analysis will work with the full dataset and the full network. For this case we will be using the combined network instead of KEGG network (see Networks for details on the network types).

    library(R.utils)
    library(data.table)

The full macrophage LPS+IFNG-activation dataset can be downloaded from http://artyomovlab.wustl.edu/publications/supp_materials/GAM/:

    met.de.raw <- fread("http://artyomovlab.wustl.edu/publications/supp_materials/GAM/Ctrl.vs.MandLPSandIFNg.met.de.tsv.gz")
    gene.de.raw <- fread("http://artyomovlab.wustl.edu/publications/supp_materials/GAM/Ctrl.vs.MandLPSandIFNg.gene.de.tsv.gz")

Full pre-generated combined network, corresponding metabolite annotation, and enzyme annotation can be downloaded from http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/:

    network.combined <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/network.combined.rds"))
    met.combined.db <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/met.combined.db.rds"))

    org.Mm.eg.gatom.anno <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/org.Mm.eg.gatom.anno.rds"))

For better work of the combined network we highly recommend using additional supplementary gene files (see Supplementary Genes).

    gene2reaction.extra <- fread("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/gene2reaction.combined.mmu.eg.tsv", colClasses="character")

Running `gatom` on the combined network and the full dataset:

    cg <- makeMetabolicGraph(network=network.combined,
                             topology="atoms",
                             org.gatom.anno=org.Mm.eg.gatom.anno,
                             gene.de=gene.de.raw,
                             met.db=met.combined.db,
                             met.de=met.de.raw,
                             gene2reaction.extra=gene2reaction.extra)

    ## Found DE table for genes with RefSeq IDs

    ## Found DE table for metabolites with HMDB IDs

    cgs <- scoreGraph(cg, k.gene = 50, k.met = 50)

    ## Metabolite p-value threshold: 0.038971

    ## Metabolite BU alpha: 0.078854

    ## FDR for metabolites: 0.054345

    ## Gene p-value threshold: 0.001204

    ## Gene BU alpha: 0.153709

    ## FDR for genes: 0.006234

    solver <- rnc_solver()
    set.seed(42)
    sol <- solve_mwcsp(solver, cgs)
    cm <- sol$graph
    cm

    ## IGRAPH 8a77f79 UN-- 75 77 --
    ## + attr: signals (g/n), name (v/c), metabolite (v/c), element (v/c),
    ## | label (v/c), url (v/c), pval (v/n), origin (v/n), HMDB (v/c), log2FC
    ## | (v/n), baseMean (v/n), logPval (v/n), signal (v/c), score (v/n),
    ## | label (e/c), pval (e/n), origin (e/n), RefSeq (e/c), gene (e/c),
    ## | enzyme (e/c), reaction_name (e/c), reaction_equation (e/c), url
    ## | (e/c), reaction (e/c), log2FC (e/n), baseMean (e/n), logPval (e/n),
    ## | signal (e/c), signalRank (e/n), score (e/n)
    ## + edges from 8a77f79 (vertex names):
    ## [1] C00025_1.299_0.75--C00025_1.299_0.75  C00022_1.299_0.75--C00026_-1.299_0.75
    ## [3] C00025_1.299_0.75--C00026_-1.299_0.75 C00025_0_0       --C00026_1.299_0.75
    ## + ... omitted several edges

The result module for combined network:

    createShinyCyJSWidget(cm)

# Networks

We provide four types of networks that can be used for analysis:

1. KEGG network
2. Rhea network
3. Combined network
4. Rhea lipid subnetwork

## KEGG

KEGG network consists of `network.kegg.rds` & `met.kegg.db.rds` files and is based on KEGG database.

Both metabolites and reactions in KEGG network have KEGG IDs.

This network was generated with the pipeline available here. For extra details on KEGG network you can also reference shinyGatom and GAM articles.

    network <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/network.kegg.rds"))
    met.db <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/met.kegg.db.rds"))

Running `gatom` with KEGG network on full dataset:

    kg <- makeMetabolicGraph(network=network,
                            topology="atoms",
                            org.gatom.anno=org.Mm.eg.gatom.anno,
                            gene.de=gene.de.raw,
                            met.db=met.db,
                            met.de=met.de.raw)

    ## Found DE table for genes with RefSeq IDs

    ## Found DE table for metabolites with HMDB IDs

    kgs <- scoreGraph(kg, k.gene = 50, k.met = 50)

    ## Metabolite p-value threshold: 0.055133

    ## Metabolite BU alpha: 0.087937

    ## FDR for metabolites: 0.070765

    ## Gene p-value threshold: 0.002471

    ## Gene BU alpha: 0.164266

    ## FDR for genes: 0.010231

    solver <- rnc_solver()
    set.seed(42)
    sol <- solve_mwcsp(solver, kgs)
    km <- sol$graph
    km

    ## IGRAPH 7494ef5 UN-- 67 67 --
    ## + attr: signals (g/n), name (v/c), metabolite (v/c), element (v/c),
    ## | label (v/c), url (v/c), pval (v/n), origin (v/n), HMDB (v/c), log2FC
    ## | (v/n), baseMean (v/n), logPval (v/n), signal (v/c), score (v/n),
    ## | label (e/c), pval (e/n), origin (e/n), RefSeq (e/c), gene (e/c),
    ## | enzyme (e/c), reaction_name (e/c), reaction_equation (e/c), url
    ## | (e/c), reaction (e/c), log2FC (e/n), baseMean (e/n), logPval (e/n),
    ## | signal (e/c), signalRank (e/n), score (e/n)
    ## + edges from 7494ef5 (vertex names):
    ## [1] C00025_-4.2219_3.5625--C00026_-4.2219_3.5625
    ## [2] C00025_0.9743_3.5625 --C00026_-4.2219_3.5625
    ## + ... omitted several edges

    createShinyCyJSWidget(km)

## Rhea

Rhea network consists of `network.rhea.rds` & `met.rhea.db.rds` files and is based on Rhea database.

Reactions in Rhea have their own IDs, but unlike KEGG, metabolite IDs come from a separate database – ChEBI database.

This network was generated with the pipeline available here. For extra details on Rhea network you can also reference shinyGatom article.

To use Rhea network download the following files:

    network.rhea <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/network.rhea.rds"))
    met.rhea.db <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/met.rhea.db.rds"))

For proper work of the Rhea network we also need a corresponding supplementary gene file (ref. Supplementary Genes).

    gene2reaction.extra <- fread("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/gene2reaction.rhea.mmu.eg.tsv", colClasses="character")

And run `gatom` on Rhea network:

    rg <- makeMetabolicGraph(network=network.rhea,
                             topology="atoms",
                             org.gatom.anno=org.Mm.eg.gatom.anno,
                             gene.de=gene.de.raw,
                             met.db=met.rhea.db,
                             met.de=met.de.raw,
                             gene2reaction.extra=gene2reaction.extra)

    ## Found DE table for genes with RefSeq IDs

    ## Found DE table for metabolites with HMDB IDs

    rgs <- scoreGraph(rg, k.gene = 50, k.met = 50)

    ## Metabolite p-value threshold: 0.046206

    ## Metabolite BU alpha: 0.082053

    ## FDR for metabolites: 0.092911

    ## Gene p-value threshold: 0.000695

    ## Gene BU alpha: 0.161730

    ## FDR for genes: 0.004909

    solver <- rnc_solver()
    set.seed(42)
    sol <- solve_mwcsp(solver, rgs)
    rm <- sol$graph
    rm

    ## IGRAPH c670d3c UN-- 46 46 --
    ## + attr: signals (g/n), name (v/c), metabolite (v/c), element (v/c),
    ## | label (v/c), url (v/c), pval (v/n), origin (v/n), HMDB (v/c), log2FC
    ## | (v/n), baseMean (v/n), logPval (v/n), signal (v/c), score (v/n),
    ## | label (e/c), pval (e/n), origin (e/n), RefSeq (e/c), gene (e/c),
    ## | enzyme (e/c), url (e/c), reaction (e/c), log2FC (e/n), baseMean
    ## | (e/n), logPval (e/n), signal (e/c), signalRank (e/n), score (e/n)
    ## + edges from c670d3c (vertex names):
    ## [1] CHEBI:15562_-2.9228_2.8125--CHEBI:16383_-0.3248_2.8125
    ## [2] CHEBI:15361_-1.299_3.75   --CHEBI:16452_-1.9486_3.375
    ## [3] CHEBI:15562_-2.9228_2.8125--CHEBI:16810_-0.3248_2.8125
    ## + ... omitted several edges

Result Rhea network module:

    createShinyCyJSWidget(rm)

## Combined network

Combined network comprises not only KEGG and Rhea reactions, but also transport reactions from BIGG database.

This means that reactions in such network have either KEGG or Rhea or BIGG IDs, and metabolite IDs are KEGGs and ChEBIs.

## Rhea lipid subnetwork

Rhea lipid subnetwork is subset of Rhea reactions that involve lipids, and it consists of `network.rhea.lipids.rds` & `met.rhea.lipids.db.rds` files.

This network was generated with the pipeline available here. For extra details on Rhea lipid subnetwork you can also reference shinyGatom article.

    network.lipids <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/network.rhea.lipids.rds"))
    met.lipids.db <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/met.lipids.db.rds"))

For proper work of the lipid network we will also need a corresponding supplementary gene file (ref. Supplementary Genes)

    gene2reaction.extra <- fread("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/gene2reaction.rhea.mmu.eg.tsv", colClasses="character")

To test lipid network we will use example lipidomics data for WT mice control vs high fat diet comparison from ST001289 dataset.

    met.de.lipids <- fread("https://artyomovlab.wustl.edu/publications/supp_materials/GATOM/Ctrl.vs.HighFat.lipid.de.csv")

For lipid network we recommend setting topology to `metabolites` (ref. Using metabolite-level network):

    lg <- makeMetabolicGraph(network=network.lipids,
                             topology="metabolites",
                             org.gatom.anno=org.Mm.eg.gatom.anno,
                             gene.de=NULL,
                             met.db=met.lipids.db,
                             met.de=met.de.lipids,
                             gene2reaction.extra=gene2reaction.extra)

    ## Found DE table for metabolites with Species IDs

    lgs <- scoreGraph(lg, k.gene = NULL, k.met = 50)

    ## Metabolite p-value threshold: 0.009204

    ## Metabolite BU alpha: 0.145591

    ## FDR for metabolites: 0.006065

    solver <- rnc_solver()
    set.seed(42)
    sol <- solve_mwcsp(solver, lgs)
    lm <- sol$graph
    lm

    ## IGRAPH 0d4d99e UN-- 47 46 --
    ## + attr: signals (g/n), name (v/c), metabolite (v/c), element (v/c),
    ## | label (v/c), url (v/c), LipidMaps_ID (v/c), SwissLipids_ID (v/c),
    ## | Class_LipidMaps (v/c), Abbreviation_LipidMaps (v/c),
    ## | Synonyms_LipidMaps (v/c), Class_SwissLipids (v/c),
    ## | Abbreviation_SwissLipids (v/c), pval (v/n), origin (v/n), Species
    ## | (v/c), Mean(ctrl) (v/n), Mean(exp) (v/n), FC (v/n), log2FC (v/n),
    ## | -Log10(p-value) (v/n), -Log10(padj) (v/n), adj.P.Val (v/n),
    ## | Significance(padj) (v/c), Significance(p-value) (v/c), logPval (v/n),
    ## | signal (v/c), score (v/n), label (e/c), pval (e/l), gene (e/c),
    ## | enzyme (e/c), url (e/c), reaction (e/c), score (e/n), signal (e/c)
    ## + edges from 0d4d99e (vertex names):

Result lipid subnetwork module:

    createShinyCyJSWidget(lm)

If IDs for metabolite differential abundance data are of type `Species` we can process metabolite labels into more readable ones:

    lm1 <- abbreviateLabels(lm, orig.names = TRUE, abbrev.names = TRUE)

    createShinyCyJSWidget(lm1)

# Misc

## Supplementary gene files

For combined, Rhea and lipid networks we provide supplementary files with genes that either come from proteome or are not linked to a specific enzyme. These files are organism-specific and are also available at http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/.

    network.combined <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/network.combined.rds"))
    met.combined.db <- readRDS(url("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/met.combined.db.rds"))
    gene2reaction.extra <- fread("http://artyomovlab.wustl.edu/publications/supp_materials/GATOM/gene2reaction.combined.mmu.eg.tsv", colClasses="character")

    gg <- makeMetabolicGraph(network=network.combined,
                             topology="atoms",
                             org.gatom.anno=org.Mm.eg.gatom.anno,
                             gene.de=gene.de.raw,
                             met.db=met.combined.db,
                             met.de=met.de.raw,
                             gene2reaction.extra=gene2reaction.extra)

    ## Found DE table for genes with RefSeq IDs

    ## Found DE table for metabolites with HMDB IDs

    gg

    ## IGRAPH c49898d UN-- 5047 6374 --
    ## + attr: name (v/c), metabolite (v/c), element (v/c), label (v/c), url
    ## | (v/c), pval (v/n), origin (v/n), HMDB (v/c), log2FC (v/n), baseMean
    ## | (v/n), logPval (v/n), signal (v/c), label (e/c), pval (e/n), origin
    ## | (e/n), RefSeq (e/c), gene (e/c), enzyme (e/c), reaction_name (e/c),
    ## | reaction_equation (e/c), url (e/c), reaction (e/c), log2FC (e/n),
    ## | baseMean (e/n), logPval (e/n), signal (e/c), signalRank (e/n)
    ## + edges from c49898d (vertex names):
    ## [1] C00019_-0.75_-1.299--C00019_-0.75_-1.299
    ## [2] C00019_-1.5_0      --C00019_-1.5_0
    ## [3] C00019_0.75_-1.299 --C00019_0.75_-1.299
    ## + ... omitted several edges

## Non-enzymatic reactions

Optionally, we can also preserve non-enzymatic reactions that are found in the network. This can be done by setting `keepReactionsWithoutEnzymes` to `TRUE`:

    ge <- makeMetabolicGraph(network=network.combined,
                             topology="atoms",
                             org.gatom.anno=org.Mm.eg.gatom.anno,
                             gene.de=gene.de.raw,
                             met.db=met.combined.db,
                             met.de=met.de.raw,
                             gene2reaction.extra=gene2reaction.extra,
                             keepReactionsWithoutEnzymes=TRUE)

    ## Found DE table for genes with RefSeq IDs

    ## Found DE table for metabolites with HMDB IDs

    ge

    ## IGRAPH eb9958f UN-- 5171 6519 --
    ## + attr: name (v/c), metabolite (v/c), element (v/c), label (v/c), url
    ## | (v/c), pval (v/n), origin (v/n), HMDB (v/c), log2FC (v/n), baseMean
    ## | (v/n), logPval (v/n), signal (v/c), label (e/c), pval (e/n), origin
    ## | (e/n), RefSeq (e/c), gene (e/c), enzyme (e/c), reaction_name (e/c),
    ## | reaction_equation (e/c), url (e/c), reaction (e/c), log2FC (e/n),
    ## | baseMean (e/n), logPval (e/n), signal (e/c), signalRank (e/n)
    ## + edges from eb9958f (vertex names):
    ## [1] C00019_-0.75_-1.299--C00019_-0.75_-1.299
    ## [2] C00019_-1.5_0      --C00019_-1.5_0
    ## [3] C00019_0.75_-1.299 --C00019_0.75_-1.299
    ## + ... omitted several edges

## Using exact solver

For proper analysis quality we recommend to use exact SGMWCS solver `virgo_solver()`, which requires Java (version >= 11) and CPLEX (version >= 12.7) to be installed. If the requirements are met you can then find a module as following:

    vsolver <- virgo_solver(cplex_dir=Sys.getenv("CPLEX_HOME"),
                            threads=4, penalty=0.001, log=1)
    sol <- solve_mwcsp(vsolver, gs)
    m <- sol$graph

Edge penalty option there is used to remove excessive redundancy in genes.

## Running with no metabolite data

If there is no metabolite data in your experiment assign `met.de` and `k.met` to `NULL`:

    g <- makeMetabolicGraph(network=networkEx,
                            topology="atoms",
                            org.gatom.anno=org.Mm.eg.gatom.annoEx,
                            gene.de=gene.de.rawEx,
                            met.db=met.kegg.dbEx,
                            met.de=NULL)

    ## Found DE table for genes with RefSeq IDs

    gs <- scoreGraph(g, k.gene = 50, k.met = NULL)

    ## Warning in bumOptim(x = x, starts): One or both parameters are on the limit of
    ## the defined parameter space

    ## Gene p-value threshold: 0.130626

    ## Gene BU alpha: 0.364527

    ## FDR for genes: 0.100000

## Running with no gene data

If there is no gene data in your experiment assign `gene.de` and `k.gene` to `NULL`:

    g <- makeMetabolicGraph(network=networkEx,
                            topology="atoms",
                            org.gatom.anno=org.Mm.eg.gatom.annoEx,
                            gene.de=NULL,
                            met.db=met.kegg.dbEx,
                            met.de=met.de.rawEx)

    ## Found DE table for metabolites with HMDB IDs

    gs <- scoreGraph(g, k.gene = NULL, k.met = 50)

    ## Metabolite p-value threshold: 0.260385

    ## Metabolite BU alpha: 0.080774

    ## FDR for metabolites: 0.100000

## Using metabolite-level network

Sometimes it could make sense to work with metabolite-metabolite topology of the network, not atom-atom one. Such network is less structured, but contains more genes.

    gm <- makeMetabolicGraph(network=network,
                            topology="metabolite",
                            org.gatom.anno=org.Mm.eg.gatom.anno,
                            gene.de=gene.de.raw,
                            met.db=met.db,
                            met.de=met.de.raw)

    ## Found DE table for genes with RefSeq IDs

    ## Found DE table for metabolites with HMDB IDs

    gms <- scoreGraph(gm, k.gene = 50, k.met = 50)

    ## Metabolite p-value threshold: 0.037216

    ## Metabolite BU alpha: 0.078983

    ## FDR for metabolites: 0.062353

    ## Gene p-value threshold: 0.001241

    ## Gene BU alpha: 0.163383

    ## FDR for genes: 0.006075

    solver <- rnc_solver()
    set.seed(42)
    sol <- solve_mwcsp(solver, gms)
    mm <- sol$graph
    mm

    ## IGRAPH 6fcb7f8 UN-- 63 63 --
    ## + attr: signals (g/n), name (v/c), metabolite (v/c), element (v/c),
    ## | label (v/c), url (v/c), pval (v/n), origin (v/n), HMDB (v/c), log2FC
    ## | (v/n), baseMean (v/n), logPval (v/n), signal (v/c), score (v/n),
    ## | label (e/c), pval (e/n), origin (e/n), RefSeq (e/c), gene (e/c),
    ## | enzyme (e/c), reaction_name (e/c), reaction_equation (e/c), url
    ## | (e/c), reaction (e/c), log2FC (e/n), baseMean (e/n), logPval (e/n),
    ## | signal (e/c), signalRank (e/n), score (e/n)
    ## + edges from 6fcb7f8 (vertex names):
    ##  [1] C00219--C05956 C00062--C05933 C00327--C05933 C00417--C00490 C00062--C00086
    ##  [6] C00157--C00162 C00157--C00219 C00162--C00350 C00550--C00588 C00669--C01879
    ## + ... omitted several edges

## Pathway annotation

To get functional annotation of obtained modules by KEGG and Reactome metabolic pathways, we can use hypergeometric test with `fora()` function from `fgsea` package.

    foraRes <- fgsea::fora(pathways=org.Mm.eg.gatom.anno$pathways,
                           genes=E(km)$gene,
                           universe=unique(E(kg)$gene),
                           minSize=5)
    foraRes[padj < 0.05]

    ##                                                                  pathway
    ##                                                                   <char>
    ## 1:  mmu_M00002: Glycolysis, core module involving three-carbon compounds
    ## 2:              mmu_M00003: Gluconeogenesis, oxaloacetate => fructose-6P
    ## 3: mmu_M00001: Glycolysis (Embden-Meyerhof pathway), glucose => pyruvate
    ## 4:                                      mmu00565: Ether lipid metabolism
    ## 5:                                mmu00010: Glycolysis / Gluconeogenesis
    ## 6:                                   mmu00030: Pentose phosphate pathway
    ## 7:                                   mmu00020: Citrate cycle (TCA cycle)
    ## 8:                              mmu00564: Glycerophospholipid metabolism
    ## 9:       mmu_M00004: Pentose phosphate pathway (Pentose phosphate cycle)
    ##            pval        padj foldEnrichment overlap  size
    ##           <num>       <num>          <num>   <int> <int>
    ## 1: 5.046444e-05 0.003532511       7.017241       5     5
    ## 2: 2.695203e-04 0.005915625       5.847701       5     6
    ## 3: 3.925355e-04 0.005915625       4.678161       6     9
    ## 4: 3.925355e-04 0.005915625       4.678161       6     9
    ## 5: 4.225447e-04 0.005915625       3.050975      10    23
    ## 6: 2.154500e-03 0.025135833       3.274713       7    15
    ## 7: 3.034903e-03 0.026789277       3.508621       6    12
    ## 8: 3.061632e-03 0.026789277       2.631466       9    24
    ## 9: 3.996354e-03 0.031082754       3.898467       5     9
    ##                                     overlapGenes
    ##                                           <list>
    ## 1:                 21991,14433,18648,13806,18746
    ## 2:                 74551,13806,18648,14433,21991
    ## 3:          212032,21991,14433,18648,13806,18746
    ## 4:         18783,225845,270084,27226,67916,99712
    ## 5:   13806,14433,17330,18597,18648,18746,...[10]
    ## 6:  110208,110639,19895,21351,21881,66646,...[7]
    ## 7:          11428,15926,18597,20917,235339,74551
    ## 8: 14571,18783,225845,241274,270084,67916,...[9]
    ## 9:                110208,66646,19895,21881,21351

Optionally, redundancy in pathways can be decreased with `collapsePathwaysORA()` function:

    mainPathways <- fgsea::collapsePathwaysORA(
      foraRes[padj < 0.05],
      pathways=org.Mm.eg.gatom.anno$pathways,
      genes=E(km)$gene,
      universe=unique(E(kg)$gene))
    foraRes[pathway %in% mainPathways$mainPathways]

    ##                                                                 pathway
    ##                                                                  <char>
    ## 1: mmu_M00002: Glycolysis, core module involving three-carbon compounds
    ## 2:                                     mmu00565: Ether lipid metabolism
    ## 3:                                  mmu00030: Pentose phosphate pathway
    ## 4:                                  mmu00020: Citrate cycle (TCA cycle)
    ##            pval        padj foldEnrichment overlap  size
    ##           <num>       <num>          <num>   <int> <int>
    ## 1: 5.046444e-05 0.003532511       7.017241       5     5
    ## 2: 3.925355e-04 0.005915625       4.678161       6     9
    ## 3: 2.154500e-03 0.025135833       3.274713       7    15
    ## 4: 3.034903e-03 0.026789277       3.508621       6    12
    ##                                    overlapGenes
    ##                                          <list>
    ## 1:                21991,14433,18648,13806,18746
    ## 2:        18783,225845,270084,27226,67916,99712
    ## 3: 110208,110639,19895,21351,21881,66646,...[7]
    ## 4:         11428,15926,18597,20917,235339,74551

    sessionInfo()

    ## R version 4.6.0 (2026-04-24)
    ## Platform: x86_64-pc-linux-gnu
    ## Running under: Ubuntu 24.04.4 LTS
    ##
    ## Matrix products: default
    ## BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
    ## LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
    ##
    ## locale:
    ##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
    ##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8
    ##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8
    ##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C
    ##  [9] LC_ADDRESS=C               LC_TELEPHONE=C
    ## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
    ##
    ## time zone: Etc/UTC
    ## tzcode source: system (glibc)
    ##
    ## attached base packages:
    ## [1] stats     graphics  grDevices utils     datasets  methods   base
    ##
    ## other attached packages:
    ## [1] R.utils_2.13.0      R.oo_1.27.1         R.methodsS3_1.8.2
    ## [4] mwcsr_0.1.10        igraph_2.3.0        data.table_1.18.2.1
    ## [7] gatom_1.10.0        BiocStyle_2.40.0
    ##
    ## loaded via a namespace (and not attached):
    ##  [1] fastmatch_1.1-8       KEGGREST_1.52.0       gtable_0.3.6
    ##  [4] xfun_0.57             bslib_0.10.0          ggplot2_4.0.3
    ##  [7] htmlwidgets_1.6.4     Biobase_2.72.0        lattice_0.22-9
    ## [10] vctrs_0.7.3           tools_4.6.0           generics_0.1.4
    ## [13] parallel_4.6.0        stats4_4.6.0          tibble_3.3.1
    ## [16] AnnotationDbi_1.74.0  RSQLite_2.4.6         blob_1.3.0
    ## [19] pkgconfig_2.0.3       Matrix_1.7-5          RColorBrewer_1.1-3
    ## [22] S7_0.2.2              S4Vectors_0.50.0      lifecycle_1.0.5
    ## [25] compiler_4.6.0        farver_2.1.2          Biostrings_2.80.0
    ## [28] fgsea_1.38.0          codetools_0.2-20      Seqinfo_1.2.0
    ## [31] htmltools_0.5.9       sys_3.4.3             buildtools_1.0.0
    ## [34] sass_0.4.10           yaml_2.3.12           pillar_1.11.1
    ## [37] crayon_1.5.3          jquerylib_0.1.4       BiocParallel_1.46.0
    ## [40] cachem_1.1.0          BioNet_1.72.0         shinyCyJS_1.0.0
    ## [43] network_1.20.0        digest_0.6.39         labeling_0.4.3
    ## [46] maketools_1.3.2       cowplot_1.2.0         fastmap_1.2.0
    ## [49] grid_4.6.0            cli_3.6.6             magrittr_2.0.5
    ## [52] utf8_1.2.6            XML_3.99-0.23         withr_3.0.2
    ## [55] scales_1.4.0          ggnetwork_0.5.14      bit64_4.8.0
    ## [58] rmarkdown_2.31        XVector_0.52.0        httr_1.4.8
    ## [61] bit_4.6.0             png_0.1-9             sna_2.8
    ## [64] memoise_2.0.1         coda_0.19-4.1         evaluate_1.0.5
    ## [67] knitr_1.51            IRanges_2.46.0        rlang_1.2.0
    ## [70] Rcpp_1.1.1-1.1        glue_1.8.1            DBI_1.3.0
    ## [73] BiocManager_1.30.27   BiocGenerics_0.58.0   intergraph_2.0-4
    ## [76] jsonlite_2.0.0        plyr_1.8.9            R6_2.6.1
    ## [79] statnet.common_4.13.0