Contents

1 Introduction

FELLA is an R package that brings a new concept for metabolomics data interpretation. The starting point of this data enrichment is a list of affected metabolites, which can stem from a contrast between experimental groups. This list, that may vary in size, encompasses key role players from different biological pathways that generate a biological perturbation.

The classical way to analyse this list is the over representation analysis. Each metabolic pathway has a statistic, the number of affected metabolites in it, that yields a p-value. After correcting for multiple testing, a list of prioritised pathways helps performing a quality check on the data and suggesting novel biological mechanisms related to the data. Subsequent generations of pathway analysis methods attempt to include quantitative and/or topological data in the statistics in order to improve power for subtle signals, but the interpretation of a prioritised pathway list remains a challenge.

Package FELLA, on the other hand, introduces a comprehensive output that encompasses other biological entities that coherently relate the top ranked pathways. The priorisation of the pathways and other entiteis stems from a diffusion process on a holistic graph representation of the KEGG database. FELLA needs:

  1. The KEGG graph and other complementary data files. This is stored in a unique FELLA.DATA S4 object.
  2. A list of affected metabolites (KEGG compounds). This is stored in a unique FELLA.USER S4 object, along with user analyses.

2 Loading the KEGG data

This vignette makes use of sample data that contains small subgraph of FELLA’s KEGG graph (mid 2017 KEGG release). All the necessary contextual data is stored in an S4 data structure with class FELLA.DATA. Several functions need access to the contextual data, passed as an argument called data, being the enrichment itself among them.

library(FELLA)

data("FELLA.sample")
class(FELLA.sample)
## [1] "FELLA.DATA"
## attr(,"package")
## [1] "FELLA"
show(FELLA.sample)
## General data:
## - KEGG graph:
##   * Nodes:  670 
##   * Edges:  1677 
##   * Density:  0.003741383 
##   * Categories:
##     + pathway [2]
##     + module [6]
##     + enzyme [58]
##     + reaction [279]
##     + compound [325]
##   * Size:  366.9 Kb 
## - KEGG names are ready.
## -----------------------------
## Hypergeometric test:
## - Matrix is ready
##   * Dim:  325 x 2 
##   * Size:  25 Kb
## -----------------------------
## Heat diffusion:
## - Matrix not loaded.
## - RowSums are ready.
## -----------------------------
## PageRank:
## - Matrix not loaded.
## - RowSums are ready.

Keep in mind that FELLA.DATA objects need to be constructed only once by using buildGraphFromKEGGREST and buildDataFromGraph, in that precise order. This will store them in a local path and they should be loaded through loadKEGGdata. The user is disadvised from manually modifying the database internal files and the FELLA.DATA object slots not to corrupt the database.

3 Loading the metabolomics summary data

The second block of necessary data is a list of affected metabolites, which shoud be specified as KEGG compound IDs. Provided is a list of hypothetical affected metabolites belonging to the graph, to which some decoys that do not map to the graph are added.

data("input.sample")
input.full <- c(input.sample, paste0("intruder", 1:10))

show(input.full)
##  [1] "C00143"     "C00546"     "C04225"     "C16328"     "C00091"    
##  [6] "C15979"     "C16333"     "C05264"     "C05258"     "C00011"    
## [11] "C00083"     "C00044"     "C05266"     "C00479"     "C05280"    
## [16] "C01352"     "C05268"     "C16329"     "C00334"     "C05275"    
## [21] "C14145"     "C00081"     "C04253"     "C00027"     "C00111"    
## [26] "C00332"     "C00003"     "C00288"     "C05467"     "C00164"    
## [31] "intruder1"  "intruder2"  "intruder3"  "intruder4"  "intruder5" 
## [36] "intruder6"  "intruder7"  "intruder8"  "intruder9"  "intruder10"

Compounds are introduced through the defineCompounds function and provide the first FELLA.USER user data object containing the mapped compounds and empty analyses slots. The user should always build FELLA.USER objects through defineCompounds instead of manipulating the slots of the object manually - this might skip quality checks.

myAnalysis <- defineCompounds(
    compounds = input.full, 
    data = FELLA.sample)
## No background compounds specified. Default background will be used.
## Warning in defineCompounds(compounds = input.full, data = FELLA.sample):
## Some compounds were introduced as affected but they do not belong to
## the background. These compounds will be excluded from the analysis. Use
## 'getExcluded' to see them.

Note that a warning message informs the user that some compounds did not map to the KEGG compound collection. Compounds that successfully mapped can be obtained through getInput,

getInput(myAnalysis)
##  [1] "C00003" "C00011" "C00027" "C00044" "C00081" "C00083" "C00091" "C00111"
##  [9] "C00143" "C00164" "C00288" "C00332" "C00334" "C00479" "C00546" "C01352"
## [17] "C04225" "C04253" "C05258" "C05264" "C05266" "C05268" "C05275" "C05280"
## [25] "C05467" "C14145" "C15979" "C16328" "C16329" "C16333"

while compounds that were excluded because of mismatch can be accessed through getExcluded:

getExcluded(myAnalysis)
##  [1] "intruder1"  "intruder2"  "intruder3"  "intruder4"  "intruder5" 
##  [6] "intruder6"  "intruder7"  "intruder8"  "intruder9"  "intruder10"

Keep in mind that exact matching is sought, so be extremely careful with whitespaces, tabs or similar characters that might create mismatches. For example:

input.fail <- paste0(" ", input.full)
defineCompounds(
    compounds = input.fail, 
    data = FELLA.sample)
## Error in defineCompounds(compounds = input.fail, data = FELLA.sample): None of the specified compounds appear in the available KEGG data.

4 Enriching the data

Once the FELLA.DATA and the FELLA.USER with the affected metabolites are ready, the data can be easily enriched.

4.1 Enrichment methods

There are three methods to enrich:

  1. Hypergeometric test (method = "hypergeom"): it performs the metabolite-sampling hypergeometric test using the connections in FELLA’s KEGG graph. This is included for completeness and does not include the contextual novelty of the diffusive methods.
  2. Diffusion (method = "diffusion"): it performs sub-network analysis on the KEGG graph to extract a meaningful subgraph. This subgraph can be plotted an interpreted
  3. PageRank (method = "pagerank"): analogous to "diffusion" but using the directed diffusion, which matches the PageRank algorithm for web ranking.

4.2 Statistical approximations

For methods "diffusion" and "pagerank", two statistical approximations are proposed:

  1. Normal approximation (approx = "normality"): scores are computed through z-scores based on analytical expected value and covariance matrix of the null model for diffusion. This approximation is deterministic and fast.
  2. Monte Carlo trials (approx = "simulation"): scores are computed through Monte Carlo trials of the random variables. This approximation requires computing the random trials, governed by the ntrials argument.

4.3 Enrichment: methods, approximations and wrapper function

The function enrich wraps the functions defineCompounds, runHypergeom, runDiffusion and runPagerank in an easily usable manner, returning a FELLA.USER object with complete analyses.

myAnalysis <- enrich(
    compounds = input.full, 
    method = "diffusion", 
    approx = "normality", 
    data = FELLA.sample)
## No background compounds specified. Default background will be used.
## Warning in defineCompounds(compounds = compounds, compoundsBackground =
## compoundsBackground, : Some compounds were introduced as affected but they
## do not belong to the background. These compounds will be excluded from the
## analysis. Use 'getExcluded' to see them.
## Running diffusion...
## Computing p-scores through the specified distribution.
## Done.

The output is quite informative and aggregates all the warnings. Let’s compare an empty FELLA.USER object

show(new("FELLA.USER"))
## Compounds in the input: empty
## Background compounds: all available compounds (default)
## -----------------------------
## Hypergeometric test: not performed
## -----------------------------
## Heat diffusion: not performed
## -----------------------------
## PageRank: not performed

to the output of a processed one:

show(myAnalysis)
## Compounds in the input: 30
##  [1] "C00003" "C00011" "C00027" "C00044" "C00081" "C00083" "C00091" "C00111"
##  [9] "C00143" "C00164" "C00288" "C00332" "C00334" "C00479" "C00546" "C01352"
## [17] "C04225" "C04253" "C05258" "C05264" "C05266" "C05268" "C05275" "C05280"
## [25] "C05467" "C14145" "C15979" "C16328" "C16329" "C16333"
## Background compounds: all available compounds (default)
## -----------------------------
## Hypergeometric test: not performed
## -----------------------------
## Heat diffusion: ready.
## P-scores under 0.05:  86
## -----------------------------
## PageRank: not performed

The wrapper function enrich can run the three analysis at once with the option method = listMethods(), or only the desired ones providing them as a character vector:

myAnalysis <- enrich(
    compounds = input.full, 
    method = listMethods(), 
    approx = "normality", 
    data = FELLA.sample)

show(myAnalysis)
## Compounds in the input: 30
##  [1] "C00003" "C00011" "C00027" "C00044" "C00081" "C00083" "C00091" "C00111"
##  [9] "C00143" "C00164" "C00288" "C00332" "C00334" "C00479" "C00546" "C01352"
## [17] "C04225" "C04253" "C05258" "C05264" "C05266" "C05268" "C05275" "C05280"
## [25] "C05467" "C14145" "C15979" "C16328" "C16329" "C16333"
## Background compounds: all available compounds (default)
## -----------------------------
## Hypergeometric test: ready.
## Top 2 p-values:
##     hsa00640     hsa00010 
## 8.540386e-09 9.999888e-01 
## 
## -----------------------------
## Heat diffusion: ready.
## P-scores under 0.05:  86
## -----------------------------
## PageRank: ready.
## P-scores under 0.05:  70

The wrapped functions work in a similar way, here is an example with runDiffusion:

myAnalysis_bis <- runDiffusion(
    object = myAnalysis, 
    approx = "normality", 
    data = FELLA.sample)
## Running diffusion...
## Computing p-scores through the specified distribution.
## Done.
show(myAnalysis_bis)
## Compounds in the input: 30
##  [1] "C00003" "C00011" "C00027" "C00044" "C00081" "C00083" "C00091" "C00111"
##  [9] "C00143" "C00164" "C00288" "C00332" "C00334" "C00479" "C00546" "C01352"
## [17] "C04225" "C04253" "C05258" "C05264" "C05266" "C05268" "C05275" "C05280"
## [25] "C05467" "C14145" "C15979" "C16328" "C16329" "C16333"
## Background compounds: all available compounds (default)
## -----------------------------
## Hypergeometric test: ready.
## Top 2 p-values:
##     hsa00640     hsa00010 
## 8.540386e-09 9.999888e-01 
## 
## -----------------------------
## Heat diffusion: ready.
## P-scores under 0.05:  86
## -----------------------------
## PageRank: ready.
## P-scores under 0.05:  70

5 Visualising the results

The method plot for data from the package FELLA allows a friendly visualisation of the relevant part of the KEGG graph.

5.1 Hypergeom

In the case method = "hypergeom" the plot encompasses a bipartite graph that contains top pathways and affected compounds. In that case, threshold = 1 allows the visualisation of both pathways; otherwise a plot with only one pathway would be quite uninformative.

plot(
    x = myAnalysis, 
    method = "hypergeom", 
    main = "My first enrichment using the hypergeometric test in FELLA", 
    threshold = 1, 
    data = FELLA.sample)

5.2 Diffusion

For method = "diffusion" the graph contains a richer representations involving modules, enzymes and reactions that link affected pathways and compounds.

plot(
    x = myAnalysis, 
    method = "diffusion", 
    main = "My first enrichment using the diffusion analysis in FELLA", 
    threshold = 0.1, 
    data = FELLA.sample)

5.3 PageRank

For method = "pagerank" the concept is analogous to diffusion:

plot(
    x = myAnalysis, 
    method = "pagerank", 
    main = "My first enrichment using the PageRank analysis in FELLA", 
    threshold = 0.1, 
    data = FELLA.sample)

6 Exporting the results

FELLA offers several exporting alternatives, both for the R environment and for external software.

6.1 Exporting inside R

The appropriate functions to export the results inside R are generateResultsTable for a data.frame object:

myTable <- generateResultsTable(
    object = myAnalysis, 
    method = "diffusion", 
    threshold = 0.1, 
    data = FELLA.sample)
## Writing diffusion results...
## Done.
knitr::kable(head(myTable, 20))
KEGG.id Entry.type KEGG.name p.score
hsa00640 pathway Propanoate metabolism - Homo sapiens (human) 0.0036894
M00013 module Malonate semialdehyde pathway, propanoyl-CoA … 0.0044683
1.1.1.211 enzyme long-chain-3-hydroxyacyl-CoA dehydrogenase 0.0371099
1.1.1.35 enzyme 3-hydroxyacyl-CoA dehydrogenase 0.0392511
1.2.1.18 enzyme malonate-semialdehyde dehydrogenase (acetylat… 0.0069255
1.2.1.27 enzyme methylmalonate-semialdehyde dehydrogenase (Co… 0.0165439
2.3.1.9 enzyme acetyl-CoA C-acetyltransferase 0.0085923
3.1.2.4 enzyme 3-hydroxyisobutyryl-CoA hydrolase 0.0786804
4.1.1.32 enzyme phosphoenolpyruvate carboxykinase (GTP) 0.0700429
4.1.1.41 enzyme (S)-methylmalonyl-CoA decarboxylase 0.0223899
4.1.1.9 enzyme malonyl-CoA decarboxylase 0.0002538
4.2.1.17 enzyme enoyl-CoA hydratase 0.0015731
5.3.3.8 enzyme dodecenoyl-CoA isomerase 0.0164255
6.2.1.4 enzyme succinate—CoA ligase (GDP-forming) 0.0019142
6.2.1.5 enzyme succinate—CoA ligase (ADP-forming) 0.0125330
R00209 reaction pyruvate:NAD+ 2-oxidoreductase (CoA-acetylati… 0.0885938
R00233 reaction malonyl-CoA carboxy-lyase (acetyl-CoA-forming… 0.0000698
R00238 reaction Acetyl-CoA:acetyl-CoA C-acetyltransferase 0.0001037
R00353 reaction malonyl-CoA:pyruvate carboxytransferase 0.0065794
R00405 reaction Succinate:CoA ligase (ADP-forming) 0.0468613

…and generateResultsGraph for a graph in igraph format:

myGraph <- generateResultsGraph(
    object = myAnalysis, 
    method = "diffusion", 
    threshold = 0.1, 
    data = FELLA.sample)

show(myGraph)
## IGRAPH 5159c25 UNW- 102 166 -- 
## + attr: name (v/c), com (v/n), NAME (v/x), entrez (v/x), label
## | (v/c), input (v/l), weight (e/n)
## + edges from 5159c25 (vertex names):
##  [1] hsa00640--M00013    M00013  --1.1.1.211 M00013  --1.1.1.35 
##  [4] M00013  --1.2.1.18  M00013  --1.2.1.27  hsa00640--2.3.1.9  
##  [7] M00013  --3.1.2.4   hsa00640--4.1.1.41  hsa00640--4.1.1.9  
## [10] M00013  --4.2.1.17  M00013  --5.3.3.8   hsa00640--6.2.1.4  
## [13] hsa00640--6.2.1.5   4.1.1.9 --R00233    2.3.1.9 --R00238   
## [16] hsa00640--R00353    6.2.1.5 --R00405    4.1.1.32--R00431   
## [19] 6.2.1.4 --R00432    1.2.1.18--R00705    1.2.1.27--R00705   
## + ... omitted several edges

6.2 Exporting outside R

Results can be saved as permanent files. The data.frame data format can be saved as a .csv file:

myTempDir <- tempdir()
myExp_csv <- paste0(myTempDir, "/table.csv")
exportResults(
    format = "csv", 
    file = myExp_csv, 
    method = "pagerank", 
    threshold = 0.1, 
    object = myAnalysis, 
    data = FELLA.sample)
## Exporting to a csv file...
## Writing pagerank results...
## Done.
## Done
test <- read.csv(file = myExp_csv)
knitr::kable(head(test))
KEGG.id Entry.type KEGG.name p.score
hsa00640 pathway Propanoate metabolism - Homo sapiens (human) 0.0000085
M00013 module Malonate semialdehyde pathway, propanoyl-CoA … 0.0010330
1.1.1.35 enzyme 3-hydroxyacyl-CoA dehydrogenase 0.0422528
4.1.1.32 enzyme phosphoenolpyruvate carboxykinase (GTP) 0.0088747
4.1.1.9 enzyme malonyl-CoA decarboxylase 0.0005280
4.2.1.17 enzyme enoyl-CoA hydratase 0.0003343

In the same line, the graph can be saved in RData:

myExp_graph <- paste0(myTempDir, "/graph.RData")
exportResults(
    format = "igraph", 
    file = myExp_graph, 
    method = "pagerank", 
    threshold = 0.1, 
    object = myAnalysis, 
    data = FELLA.sample)
## Exporting to a RData file using 'igraph' object...
## Done
stopifnot("graph.RData" %in% list.files(myTempDir))

Other formats exported by igraph are also available, internally using their function igraph::write.graph. Check the format argument of ?igraph::write.graph for a list of the supported formats. For example, using "pajek" format:

myExp_pajek <- paste0(myTempDir, "/graph.pajek")
exportResults(
    format = "pajek", 
    file = myExp_pajek, 
    method = "diffusion", 
    threshold = 0.1, 
    object = myAnalysis, 
    data = FELLA.sample)
## Exporting to the format pajek using igraph...
## Done
stopifnot("graph.pajek" %in% list.files(myTempDir))

This option is toggled if the format does not match any other predefined export option.

7 Session info

For reproducibility purposes, below is the sessionInfo() output:

sessionInfo()
## R version 3.5.1 RC (2018-06-24 r74929)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 16.04.4 LTS
## 
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.7-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.7-bioc/R/lib/libRlapack.so
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=C              
##  [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       
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] FELLA_1.0.1     BiocStyle_2.8.2
## 
## loaded via a namespace (and not attached):
##  [1] igraph_1.2.1        Rcpp_0.12.17        knitr_1.20         
##  [4] XVector_0.20.0      magrittr_1.5        zlibbioc_1.26.0    
##  [7] BiocGenerics_0.26.0 IRanges_2.14.10     lattice_0.20-35    
## [10] R6_2.2.2            highr_0.7           plyr_1.8.4         
## [13] stringr_1.3.1       httr_1.3.1          tools_3.5.1        
## [16] grid_3.5.1          parallel_3.5.1      xfun_0.3           
## [19] png_0.1-7           htmltools_0.3.6     yaml_2.1.19        
## [22] rprojroot_1.3-2     digest_0.6.15       bookdown_0.7       
## [25] Matrix_1.2-14       S4Vectors_0.18.3    KEGGREST_1.20.1    
## [28] evaluate_0.10.1     rmarkdown_1.10      stringi_1.2.3      
## [31] compiler_3.5.1      backports_1.1.2     Biostrings_2.48.0  
## [34] stats4_3.5.1        pkgconfig_2.0.1