FGGA: Factor Graph GO Annotation
2023-12-31
Abstract
We present a tutorial to use FGGA, a hierarchical ensemble method that exploits the ability of factor graphs for modeling logical and statistical constraints over system variables. The FGGA model is built in two main steps. In the first step, a core Factor Graph (FG) modeling hidden GO-term predictions and relationships is created. In the second step, the FG is enriched with nodes modeling observable GO-term predictions issued by binary SVM classifiers. In addition, probabilistic constraints modeling learning gaps between hidden and observable GO-term predictions are introduced. These gaps are assumed to be independent among GO-terms, locally additive with respect to observed predictions, and zero-mean Gaussian. FGGA predictions are issued by the native iterative message passing algorithm of factor graphs.Package
fgga 1.10.2
Contents
1 Automated Gene Ontology (GO) annotation methods
As volume of genomic data grows, computational methods become essential for providing a first glimpse onto gene annotations. Automated Gene Ontology (GO) annotation methods based on hierarchical ensemble classification techniques are particularly interesting when interpretability of annotation results is a main concern. In these methods, raw GO-term predictions computed by base binary classifiers are leveraged by checking the consistency of predefined GO relationships. FGGA is a factor graph approach to the hierarchical ensemble formulation of the automated GO annotation problem. In this formal method, a core factor graph is first built based on the GO structure and then enriched to take into account the noisy nature of GO-term predictions. Hence, starting from raw GO-term predictions, an iterative message passing algorithm between nodes of the factor graph is used to compute marginal probabilities of target GO-terms.
The method is detailed in the original publications [1, 2], but this brief vignette explains how to use FGGA to predict a set of GO-terms (GO node labels) from gene-product sequences of a given organism. The aim is to improve the quality of existing electronic annotations and provide a new annotation for those unknown sequences that can not be classified by traditional methods such as Blast.
Thus, FGGA is a tool to the automated annotation of protein sequences, however, the annotation of other types of striking functional gene products is also possible, e.g., long non-coding RNAs. FGGA may bring an opportunity for improving the annotation of long non-coding RNA sequences through boosting the confidence of base binary classifiers by the characterization of their structures primary, secondary and tertiary. Along the vignette, we used protein coding genes data from Cannis familiaris organism obtained with UniProt.
Fig. 1 - Workflow of FGGA algorithm.
2 Installation
The fgga R source package can be downloaded from Bioconductor repository or GitHub repository. This R package contains a experimental dataset as example, one pre-run R object and all functions needed to run FGGA.
## From Bioconductor repository
if (!requireNamespace("BiocManager", quietly = TRUE)) {
install.packages("BiocManager")
}
BiocManager::install("fgga")
## Or from GitHub repository using devtools
BiocManager::install("devtools")
devtools::install_github("fspetale/fgga")After the package is installed, it can be loaded into R workspace by
library(fgga)3 Input data
At present, the method directly supports data characterized from gene product sequences. This characterization can be generated according to the expert’s criteria. For example, possible characterizations can be: PFAM motifs, physico-chemical properties, signal peptides, among others. The admitted values can be of the numeric, boolean or character type. However, for greater efficiency of the binary classification algorithm it is recommended that the use of normalized numerical values. These datasets must have at least 50 annotations per GO-term to train the FGGA model.
4 An example of the usage of FGGA for the automated GO annotation
In this section, we apply FGGA to predict the biological functions, GO-terms, of Canis lupus familiaris proteins. We download 6962 Canis lupus familiaris, Cf, protein sequences with their GO annotations from UniProt and then were characterized through physico-chemical properties from R package Peptides.
4.1 Data Loading
Let us import the toy dataset in the workspace:
# Loading Canis lupus familiaris dataset and example R objects
data(CfData)# To see the summarized experiment object
summary(CfData)
#> Length Class Mode
#> dxCf 501264 -none- numeric
#> graphCfGO 1296 -none- numeric
#> indexGO 2 -none- list
#> tableCfGO 250632 -none- numeric
#> nodesGO 36 -none- character
#> varianceGOs 36 -none- numeric
# To see the information of characterized data
dim(CfData$dxCf)
#> [1] 6962 72
colnames(CfData$dxCf)[1:20]
#> [1] "Numb_Amino" "A" "C" "D" "E" "F" "G"
#> [8] "H" "I" "K" "L" "M" "N" "P"
#> [15] "Q" "R" "S" "T" "V" "W"
rownames(CfData$dxCf)[1:10]
#> [1] "E2QTB2" "F1PQ93" "E2RQU4" "E2RN67" "E2RGI4" "E2RFJ5" "J9P0Z9" "E2RL61" "F1PAF1" "J9P1G2"
head.matrix(CfData$dxCf[, 51:61], n = 10)
#> pK.C Surrounding.hydrop Mol.weight pI Pos_charged_res2 Pos_changed_res3
#> E2QTB2 -0.0790 0.0474 58225.55 4.9492 0.1175 0.1368
#> F1PQ93 -0.0953 0.0494 27833.13 4.6956 0.1250 0.1371
#> E2RQU4 -0.0117 0.1234 83933.57 9.0031 0.1344 0.1694
#> E2RN67 0.0185 0.0424 73821.11 7.9705 0.0848 0.1161
#> E2RGI4 0.0715 0.0368 28713.98 5.3223 0.1304 0.1423
#> E2RFJ5 -0.0194 0.0066 30101.85 4.6895 0.1049 0.1199
#> J9P0Z9 0.0010 0.0619 67510.79 6.3768 0.1267 0.1467
#> E2RL61 -0.0559 0.0226 163422.56 5.6757 0.1291 0.1463
#> F1PAF1 -0.0407 -0.0550 107808.45 5.4839 0.0932 0.1087
#> J9P1G2 -0.1119 0.0330 26295.98 9.1588 0.1040 0.1200
#> Neg_changed_res Carbon Hydrogen Nitrogen Oxygen
#> E2QTB2 0.1676 2518 3935 739 816
#> F1PQ93 0.1976 1209 1922 330 402
#> E2RQU4 0.1183 3779 5963 1033 1083
#> E2RN67 0.0818 3374 5180 910 914
#> E2RGI4 0.1542 1289 2035 331 387
#> E2RFJ5 0.1723 1327 2072 348 426
#> J9P0Z9 0.1333 3003 4694 808 908
#> E2RL61 0.1470 7269 11378 2012 2209
#> F1PAF1 0.1118 4755 7406 1294 1451
#> J9P1G2 0.0800 1166 1842 328 347
# to see the information of GO data
dim(CfData$tableCfGO)
#> [1] 6962 36
colnames(CfData$tableCfGO)[1:10]
#> [1] "GO:0000166" "GO:0003674" "GO:0003676" "GO:0003677" "GO:0003824" "GO:0004888" "GO:0005102"
#> [8] "GO:0005215" "GO:0005488" "GO:0005515"
rownames(CfData$tableCfGO)[1:10]
#> [1] "E2QTB2" "F1PQ93" "E2RQU4" "E2RN67" "E2RGI4" "E2RFJ5" "J9P0Z9" "E2RL61" "F1PAF1" "J9P1G2"
head(CfData$tableCfGO)[, 1:8]
#> GO:0000166 GO:0003674 GO:0003676 GO:0003677 GO:0003824 GO:0004888 GO:0005102 GO:0005215
#> E2QTB2 0 1 1 0 0 0 0 0
#> F1PQ93 0 1 0 0 0 0 0 0
#> E2RQU4 1 1 0 0 1 0 0 0
#> E2RN67 0 1 0 0 1 0 0 0
#> E2RGI4 0 1 0 0 0 0 0 1
#> E2RFJ5 0 1 1 0 0 0 0 0tableCfGO is a binary matrix whose \((i, j)_{th}\) component is 1 if protein \(i\) is annotated with \(GO-term_j\), 0 otherwise. Note that the row names of both dxCf and tableCfGO are identical. Our binary classifiers require at least 50 annotations per GO-terms. Therefore, this condition is checked and those GO-terms that do not comply are eliminated.
# Checking the amount of annotations by GO-term
apply(CfData$tableCfGO, MARGIN=2, sum)
#> GO:0000166 GO:0003674 GO:0003676 GO:0003677 GO:0003824 GO:0004888 GO:0005102 GO:0005215 GO:0005488
#> 995 6962 1558 857 2679 516 520 565 5183
#> GO:0005515 GO:0005524 GO:0008144 GO:0016740 GO:0016787 GO:0017076 GO:0019899 GO:0030554 GO:0032553
#> 2738 682 764 1040 1097 878 870 707 882
#> GO:0032555 GO:0032559 GO:0035639 GO:0036094 GO:0038023 GO:0042802 GO:0043167 GO:0043168 GO:0043169
#> 871 702 847 1147 593 656 2273 1232 1307
#> GO:0046872 GO:0060089 GO:0097159 GO:0097367 GO:0098772 GO:0140096 GO:0140110 GO:1901265 GO:1901363
#> 1274 610 2523 992 650 978 615 995 24984.2 GO subgraph building
If we want to predict GO-terms in a single subdomain, BP, MF or CC , we must build the GO-DAG associated with these GO-terms.
library(GO.db)
library(GOstats)
mygraph <- GOGraph(CfData$nodesGO, GOMFPARENTS)
# Delete root node called all
mygraph <- subGraph(CfData$nodesGO, mygraph)
# We adapt the graph to the format used by FGGA
mygraph <- t(as(mygraph, "matrix"))
mygraphGO <- as(mygraph, "graphNEL")
# We search the root GO-term
rootGO <- leaves(mygraphGO, "in")
rootGO
#> [1] "GO:0003674" "GO:0008144"
plot(mygraphGO)
On the other hand, if you want to predict in two or three subdomains you should use the preCoreFG function. This function builds a graph respecting the GO constraints of inference and also links the GO-terms of the selected subdomains.
# We add GO-terms corresponding to Cellular Component subdomain
myGOs <- c(CfData[['nodesGO']], "GO:1902494", "GO:0032991", "GO:1990234",
"GO:0005575")
# We build a graph respecting the GO constraints of inference to MF, CC and BP subdomains
mygraphGO <- preCoreFG(myGOs, domains="GOMF")
plot(mygraphGO)
Fig. 3 - GO-Plus subgraph.
4.3 Matching a GO-DAG to a Factor Graph
Let’s a GO subgraph, GO-terms GO:i are mapped to binary-valued variable nodes \(x_i\) of a factor graph while relationships between GO-terms are mapped to logical factor nodes \(f_k\) describing valid GO:i configurations under the True Path Graph constraint.
modelFGGA <- fgga2bipartite(mygraphGO)4.4 Flat prediction with FGGA clasiffier
Now, let’s use the MF subgraph to build our model of binary SVM classifiers with a training set of the Cf data.
# We take a subset of Cf data to train our model
idsTrain <- CfData$indexGO[["indexTrain"]][1:750]
# We build our model of binary SVM classifiers
modelSVMs <- lapply(CfData[["nodesGO"]], FUN = svmTrain,
tableOntoTerms = CfData[["tableCfGO"]][idsTrain, ],
dxCharacterized = CfData[["dxCf"]][idsTrain, ],
graphOnto = mygraphGO, kernelSVM = "radial")# We calculate the reliability of each GO-term
varianceGOs <- varianceOnto(tableOntoTerms = CfData[["tableCfGO"]][idsTrain, ],
dxCharacterized = CfData[["dxCf"]][idsTrain, ],
kFold = 5, graphOnto = mygraphGO, rootNode = rootGO,
kernelSVM = "radial")
varianceGOs#> GO:0000166 GO:0003674 GO:0003676 GO:0003677 GO:0003824 GO:0004888 GO:0005102 GO:0005215 GO:0005488
#> 1.401 0.001 2.591 1.545 3.344 1.434 1.476 1.785 3.896
#> GO:0005515 GO:0005524 GO:0008144 GO:0016740 GO:0016787 GO:0017076 GO:0019899 GO:0030554 GO:0032553
#> 3.153 0.911 1.039 2.026 2.428 1.128 2.171 0.891 0.960
#> GO:0032555 GO:0032559 GO:0035639 GO:0036094 GO:0038023 GO:0042802 GO:0043167 GO:0043168 GO:0043169
#> 1.014 0.949 0.975 1.243 1.770 1.383 2.982 1.654 2.973
#> GO:0046872 GO:0060089 GO:0097159 GO:0097367 GO:0098772 GO:0140096 GO:0140110 GO:1901265 GO:1901363
#> 3.070 1.548 3.112 1.431 1.839 2.205 1.745 1.429 3.135Next, we predict each GO-terms from a test set using our model of binary SVM classifiers.
dxTestCharacterized <- CfData[["dxCf"]][CfData$indexGO[["indexTest"]][1:50], ]
matrixGOTest <- svmOnto(svmMoldel = modelSVMs,
dxCharacterized = dxTestCharacterized,
rootNode = rootGO,
varianceSVM = varianceGOs)
head(matrixGOTest)[,1:8]
#> GO:0000166 GO:0003674 GO:0003676 GO:0003677 GO:0003824 GO:0004888 GO:0005102 GO:0005215
#> J9P8X1 0.62272713 0.9999 0.5673337 0.31559790 0.3213095 0.4095285 0.22925060 0.4412909
#> F1PVD9 0.22071344 0.9999 0.6810226 0.76938069 0.1875907 0.1584329 0.80021086 0.2024100
#> F1PTQ9 0.06022098 0.9999 0.5674606 0.56304596 0.3993549 0.1888531 0.35036334 0.3557600
#> E2R8P1 0.73115427 0.9999 0.2439744 0.09241107 0.5969643 0.2650171 0.35972801 0.1832719
#> F6UWV4 0.05171393 0.9999 0.1485072 0.06781999 0.5342228 0.2971163 0.39328570 0.4708444
#> E2RQR5 0.78087757 0.9999 0.1871167 0.03004135 0.5083126 0.1945202 0.08638426 0.56603024.5 Compute marginal probabilities of GO-terms by each protein
Once a factor graph model FG for the automated GO annotation problem has been defined, an iterative message passing algorithm between nodes of FG can be used to compute maximum a posteriori (MAP) estimates of variable nodes \(x_i\) modeling actual GO:i annotations.
The function msgFGGA returns a matrix with k rows and m columns corresponding to the Cf proteins and MF GO-terms respectively.
matrixFGGATest <- t(apply(matrixGOTest, MARGIN = 1, FUN = msgFGGA,
matrixFGGA = modelFGGA, graphOnto = mygraphGO,
tmax = 50, epsilon = 0.001))
head(matrixFGGATest)[,1:8]
#> GO:0000166 GO:0003674 GO:0003676 GO:0003677 GO:0003824 GO:0004888 GO:0005102 GO:0005215
#> J9P8X1 5.868469e-01 1 0.55779358 0.1759273994 0.5203987 0.289269084 0.19467525 0.4412909
#> F1PVD9 2.499645e-02 1 0.82063609 0.6312197111 0.3556457 0.005939983 0.77284729 0.2024100
#> F1PTQ9 1.147813e-03 1 0.52260324 0.2942266273 0.8120869 0.048144948 0.29367784 0.3557600
#> E2R8P1 9.999998e-01 1 0.26229996 0.0242394207 0.9457162 0.018176862 0.24925253 0.1832719
#> F6UWV4 4.162882e-06 1 0.00394109 0.0002670268 0.9761948 0.010136951 0.16323066 0.4708444
#> E2RQR5 9.530343e-01 1 0.18507613 0.0055527269 0.9372415 0.002118380 0.07485599 0.56603025 FGGA Performance
We now evaluate the performance of FGGA in terms of hierarchical F-score. The hierarchical classification performance metrics like the hierarchical precision (HP), the hierarchical recall (HR), and the hierarchical F-score (HF) measures publications [3] properly recognize partially correct classifications and correspondingly penalize more distant or more superficial errors. The formulas of the hierarchical metrics are shown below:
\[ HP(s) = \frac{1}{\mid l(P_{G}(s)) \mid} \hspace{1.25mm} \sum_{q \hspace{0.5mm} \in \hspace{0.5mm} l(P_{G}(s))} \hspace{1.5mm} \max_{c \hspace{0.5mm} \in \hspace{0.5mm} l(C_{G}(s))} \frac{\mid \uparrow c \hspace{1mm} \cap \uparrow q \mid}{\uparrow q} \]
\[ HR(s) = \frac{1}{\mid l(C_{G}(s)) \mid} \hspace{1.25mm} \sum_{c \hspace{0.5mm} \in \hspace{0.5mm} (C_{G}(s))} \hspace{1.5mm} \max_{q \hspace{0.5mm} \in \hspace{0.5mm} l(P_{G}(s))} \frac{\mid \uparrow c \hspace{1mm} \cap \uparrow q \mid}{\uparrow c} \]
\[ HF(s) = \frac{2 \cdot HP \cdot HR}{HP + HR} \]
fHierarchicalMeasures(CfData$tableCfGO[rownames(matrixFGGATest), ],
matrixFGGATest, mygraphGO)
#> $HP
#> [1] 0.6803588
#>
#> $HR
#> [1] 0.8320968
#>
#> $HF
#> [1] 0.734725
#>
#> $nSample
#> [1] 50
#>
#> $noEvalSample
#> logical(0)Finally, we evaluate the performance of FGGA in terms of Area under the ROC Curve (AUC) and in terms of Precision x Recall (PxR). We use the R package pROC, which provides functions to compute the performance measures we need.
# Computing F-score
Fs <- fMeasures(CfData$tableCfGO[rownames(matrixFGGATest), ], matrixFGGATest)
# Average F-score
Fs$perfByTerms[4]
library(pROC)
# Computing ROC curve to the first term
rocGO <- roc(CfData$tableCfGO[rownames(matrixFGGATest), 1], matrixFGGATest[, 1])
# Average AUC the first term
auc(roc)
# Computing precision at different recall levels to the first term
rocGO <- roc(CfData$tableCfGO[rownames(matrixFGGATest), 1],
matrixFGGATest[, 1], percent=TRUE)
PXR <- coords(rocGO, "all", ret = c("recall", "precision"), transpose = FALSE)
# Average PxR to the first term
apply(as.matrix(PXR$precision[!is.na(PXR$precision)]), MARGIN = 2, mean#> R version 4.3.2 Patched (2023-11-13 r85521)
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#> [1] GOstats_2.68.0 Category_2.68.0 Matrix_1.6-4 GO.db_3.18.0
#> [5] AnnotationDbi_1.64.1 IRanges_2.36.0 S4Vectors_0.40.2 Biobase_2.62.0
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#> [73] xfun_0.41 MatrixGenerics_1.14.0 pkgconfig_2.0.36 References
Appendix
1: Spetale F.E., Tapia E., Krsticevic F., Roda F. and Bulacio P. “A Factor Graph Approach to Automated GO Annotation”. PLoS ONE 11(1): e0146986, 2016.
2: Spetale Flavio E., Arce D., Krsticevic F., Bulacio P. and Tapia E. “Consistent prediction of GO protein localization”. Scientific Report 7787(8), 2018
3: Verspoor K., Cohn J., Mnizewski S., Joslyn C. “A categorization approach to automated ontological function annotation”. Protein Science. 2006;15:1544–1549