Real-time and interactive rendering of GO terms

Retrieving and mapping parental GO terms on the GO hierarchy for query GO terms is implemented as a basic functionality. In the GO Parents page, NaviGO retrieves parental terms for a query and visualizes those GO terms in the DAG interactively (Fig. 2). Users can investigate the relationship of multiple GO terms by looking for their common parent and relative position in the hierarchy. This function is useful for better understanding gene annotations. For example, in UniProt, a number of GO terms are listed as function annotation for a gene, but it is often difficult to understand which terms are closely related and which are not. In such case, visualizing GO annotations on NaviGO can provide clear picture of the annotation.

In the visualization, query GO terms will be circled with bold black in the hierarchy and parental terms for the input GO terms will be listed in the text area so that users can copy and paste them for further use or for writing a document. Branches of the GO DAG can be expanded interactively by clicking a node. Hovering any node in the GO visualization will update the node information on the upper right corner of the frame. To boost the rendering speed, an option is provided that avoids newly expanded nodes from checking and updating parental relationship with the whole set of existing nodes.

Quantification of GO term association

The tool from the next tab “GO Set” computes pairwise GO association scores for a list of input GO terms and outputs them in three formats: a similarity graph (Fig. 3), a bubble chart (Fig. 4), and a score table (Fig. 5). From the result page, users can choose the three different output formats. For each type of GO scoring schemes described in Methods, four cutoff thresholds are provided, which were computed from the overall distribution of GO pair scores under each scheme (top 1%, 5%, 10%, and 20%) and shown in the color-scale (red to pink for high to low) in the table format (Fig. 5). The last column in the table contains common parents between GO pairs and a link to the interactive visualization with GO Visualizer (Fig. 2). The result table can be downloaded in a CSV format file.

The last three examples illustrate cases where IAS can identify related GO terms across GO categories. The first example is a pair of BP GO term GO:0000279 M phase and CC GO term GO:0071065 alpha9-beta integrin-vascular cell adhesion molecule-1 complex. The SS score of these two terms is not calculated since these terms are from different categories, and SS is only defined for pairs from the same GO category. However, the pair has a very high IAS score (5922.95) because of the large amount of protein interactions in PPI network have these terms (Table 1).

Relationships of GO terms can be visualized in two ways, in a network or in a bubble chart, which provides intuitive understanding of similarity and relationship of GO terms. Fig. 3 shows a GO term association graph of IAS for the 48 GO terms. In this graph, GO terms are connected if they have an IAS above the threshold value (900 in this example) that can be controlled by the scale bar on the right upper corner of the panel (Fig. 3). GO terms in different categories are shown in different colors (BP: red; MF: blue; CC: yellow). The edges in bold and dashed lines are those pairs that are discussed in Table 1.

The bubble chart maps GO terms in terms of two scores users’ choice on the X- and Y-axis (Fig. 4) by a statistical dimension-reduction method named multidimensional scaling (MDS) [20, 21] implemented in R [22]. In case GO terms have the identical score, the centers of the circles/dots of the terms are shifted by a small amount to a random direction to avoid complete overlap. The bubble chart is interactive and the coordinate data is exportable. In Fig. 4, interestingly, along the Resnik score (X-axis), the GO terms are clearly separated by their GO category visualized in each different color, because the Resnik score for GO terms of different categories is 0, i.e. not defined, thus very far between them. In contrast, IAS is defined even for terms across GO categories. Thus, some GO pairs across different categories, for example, GO pairs of (GO: 0000279 from BP, GO: 007165 from CC) and (GO: 0033149 from MF, GO: 0001400 from CC) shown in the bottom half of Table 1, are close when mapped on the IAS (Y-axis) but far in Resnik (X-axis).

GO Enrichment analysis

The NaviGO server supports the analysis of GO term enrichment. For an input list of annotated genes, enriched GO terms in the genes relative to the fraction in the entire genome will be identified. This is useful for finding dominant common functions for a set of genes, which are identified, for example, by gene expression data or protein-protein interaction network. Thus, the analysis can aid to identify the associated proteins involved in certain function within an organism. The server will automatically identify the organism based on the UniProt ID [23] of the first input protein; however, users can specify the organism in the Organism window manually. NaviGO will connect to the UniProt database by using their RESTful service and automatically retrieve the organism information and the background GO annotation information of the organism.

The result page lists GO terms sorted by calculated p-value. The p-value tells how rare (significant) it is to have enrichment of the GO term in the protein set considering the number of proteins in the set, the number of proteins with that GO term in the organism, and the number of proteins in the organism. GO terms of significant p-value (0.00005) (or top 30 GO terms, whichever smaller) will be visualized in the GO hierarchy (Fig. 6). The number of GO terms to visualize can be controlled manually by users. The enriched GO terms are color-mapped according to the p-value of enrichment on the GO DAG visualizer. In the example in Fig. 6, a GO enrichment analysis is shown for 20 annotated proteins that are involved in the MAPK signalling pathway, which were found in a SNP-targeted GWAS studies as set of proteins involved in the Rheumatoid Arthritis disease [24]. Enrichment analysis helps to identify the GO terms that are prominent among these disease associated proteins. GO terms, such as GO:0051403 stress-activated MAPK cascade with p-value of 4.04E-11 and GO:0000186 activation of MAPKK activity with p-value of 3.13E-9, are in the top enriched results. Due to the fact that the activation of the TLRs signalling pathway can trigger the activation of the MAPK pathways [24], GO terms like GO:0034166 toll-like receptor 10 signaling pathway also has a low p-value (5.06E-13) and ranked the top in the list (indicated with red circle). In Fig. 6, GO terms which has e-value of less than 1.0E-10 are circled in orange and their function descriptions are shown.

Quantifying functional association of proteins

This functionality available from the “Protein Set” tab in the NaviGO website, takes a list of annotated proteins as input and computes functional relevance between each protein pair. This function help identifying functional groups in a set of proteins. The server can take a function annotation file in the CAFA format. The result will be provided in a table as well as an interactive clustering view. An example result shown in Fig. 7 are for the 33 protein pairs that have high IAS mong all the protein pairs from the human genome. Since IAS are defined for GO term pairs taken from physically interacting proteins, protein pairs with a high IAS are highly likely to be interacting with each other. In the result table (Fig. 7a), significance of similarity predictions is classified into five levels shown in a color-scale (red to pink for high to low). The scale indicates that the score is within top 1, 5, 10 and 20%, which are computed relative to the score distribution of all the protein pairs of the organism chosen by the user at the pull-down menu. The median option in the pull-down menu shows significance based on the average values of 5^th and 6^th genomes (i.e. median) when the 10 genomes in the list are sorted in the descending order of their corresponding cut-off values. The full result table is available to download in the CSV format.

In Fig. 7a, pairs are sorted by IAS. Notice that pairs with high IAS do not always have significant scores in terms of the other scores, e.g. ALL (functional similarity of proteins using Relevance Similarity scores (Eq. 6), indicating that IAS captures a unique feature of GO annotations of proteins, which are different from functional similarity. Figure 7b shows the fraction of physically interacting protein pairs among pairs with IAS above cutoffs. The graph shows that IAS has a substantial correlation to the fraction of interacting proteins, indicating IAS indeed detects physically interacting protein pairs. For example, all three protein pairs with a score above 850 actually interact with each other, and 68.4% (13 pairs) among 19 pairs that have an IAS over 650 have physical interactions between each other. Figure 7c provides the network view of the 33 protein pairs, where nodes are proteins and edges indicate pairs with IAS above a custom similarity cut-off value (200 is used). Pairs with significant scores, 850, 650, and 450, are highlighted in, red, green, and blue, respectively.

Analysing function prediction results with NaviGO

NaviGO is linked from two function prediction servers, PFP [12, 13] and ESG [14], so that predicted GO terms for a gene by the servers can be easily further analysed. These two servers were ranked among top in gene function prediction contests held in recent years, the function prediction category in the Critical Assessment of techniques in protein Structure Prediction (CASP7) [26] and in the two rounds of the Critical Assessment of Function Annotation (CAFA) [27, 28]. PFP and ESG are available at http://kiharalab.org/pfp.php and http://kiharalab.org/esg.php [8]. Function prediction have become increasingly important because a substantial fraction of genes in a genome are unannotated [13].

In the output page of PFP and ESG, where predicted GO terms are listed with confidence scores, the GO terms will be sent to NaviGO by clicking a link “Analyze with NaviGO” (Fig. 8a). Here we show a case that the analysis of predicted function by NaviGO revealed that a query protein has two distinct functions. The function prediction was performed by the ESG server for human aconitase (UniProt ID: Q99798). This protein is known as a moonlighting protein, which has two distinct independent functions [29, 30]. The primary function of this protein is an enzyme as aconitase while it is also known to be involved in iron homeostasis [29, 30]. Visualization of the predicted GO terms by NaviGO shows that the predicted GO terms in the MF category (Fig. 8b) are indeed separated in two branches, one on the left with the enzymatic activity (including lyase activity, aconitase hydrolase) and another branch on the right, iron-sulfer clustering binding, which is related to iron homeostasis (Fig. 8c), showing that the prediction correctly captured two distinct functions of this protein. The network view of the predicted GO terms also clarified that the protein has two distinct MF functions (shown in blue nodes), indicated by the two clusters.

GO similarity/association scores

In NaviGO, six scores can be used to quantify similarity or association relationship of GO terms. Three scores are for quantifying semantic similarity of GO terms: Resnik’s, Lin’s, and the relevant semantic similarity score. The other three scores, CAS, PAS, and IAS are for quantifying GO associations. Detailed explanation of the scores is provided in separate sections below.

To quantify the functional similarity of two genes, the funsim score [4, 5] is used. Funsim of two sets of terms, i.e. GO annotations of two genes, is calculated from an all-by-all similarity matrix, where each entry of the matrix is a similarity score of users’ choice between a GO pair.

CAS and PAS

Here, Pub(i,j) is the number of PubMed abstracts which contain both the GO terms i and j. Similarly, Pub(i) is the number of abstracts that contain GO term i and the same is applicable for Pub(j). The numerator of Eq. 2, \( \frac{Pub\left( i, j\right)}{{\displaystyle {\sum}_{ij\;} Pub\left( i, j\right)}} \), is the fraction of abstracts in PubMed that mention two particular GO terms, i and j, among all the abstracts in the PubMed database. The denominator multiplies the fraction (probability) of abstracts in PubMed that mention GO term i and the fraction of abstracts that mention GO term j. Thus, it is the expected fraction of abstracts in the database with the two GO annotations, i and j, if i and j randomly show up in abstracts. Altogether, PAS quantifies how often two GO terms i and j are co-mentioned in PubMed abstracts relative to the random chance. PAS = 1 means that GO term i and j are not related, and a larger value indicates that i and j are related and frequently co-mentioned in biological contexts. Importantly, it is possible that GO terms that do not have a high functional similar scores (Resnik, Lin’s, and Relevance Similarity scores) have a high CAS or PAS. High PAS and CAS implies that proteins with the GO term annotation are functionally related and play roles in the same biological context, e.g. pathways.

IAS

The Interaction Association Score (IAS) [7] captures the propensity of GO term pairs to occur in interacting proteins by counting the number of GO term pair that occur in interacting proteins normalized by random chance. Thus, high IAS between a protein pair indicates a high possibility that the protein pairs interact with each other. The GO_IAS for each GO term pair was computed as follows:

$$ GO\_ I A S\left( GOx, GOy\right)=\frac{\frac{N\left( GOx, GOy\right)}{\# T. Edges}}{\left(\frac{N(GOx)}{\# T. Nodes}\right)\left(\frac{N(GOy)}{\# T. Nodes}\right)} $$

(3)

where N(GOx-GOy) is the number of times GO term pair GOx and GOy interact in PPI networks, #T.Edges is the total number of interactions (edges) in PPI networks, N(GOx) and N(GOy) are the number of times GOx and GOy independently occur in proteins the networks, and #T.Nodes is the total number of proteins in the PPI networks. Figure 9 shows an example of a small PPI network. This network has 5 edges between 5 proteins; 3 proteins are annotated with GO:1, and 2 proteins with GO:2. There are 2 edges that connects between GO:1 and GO:2 (P1 to P2 and P2 to P4). From this network, GO_IAS for GO:1 and GO:2 is computed as (2/5)/((3/5)(2/5)) = 1.67. Similar to PAS and CAS, IAS quantifies how often two GO terms i and j are observed in physically interacting proteins in a protein-protein interaction network relative to the expected number of observations by the random chance. If two proteins are annotated with GO terms that have high IAS, it suggests that the proteins may physically interact with each other.

Significant difference between CAS, PAS, and IAS from conventional GO functional similarity scores described in the next section is that the former three scores quantifies functional relevance of GO term pairs in biological contexts, co-annotation to genes (CAS), co-mention in PubMed abstracts (PAS), and interacting protein pairs (IAS). Due to the design, these scores are capable of identifying proteins in the same pathways (CAS, PAS) [3] and physical interacting proteins (IAS) [7]. Correlation of CAS/PAS/IAS to regular functional similarity scores (below) is not very high [3, 7], because proteins in the same pathway and physically interacting proteins are not necessarily have similar function.

Resnik, Lin’s, and relevance similarity scores

Here p(c) is the probability of a GO term c, which is defined as the fraction of the occurrence of c in the GO Database. s(c1,c2) is the set of common ancestors of the GO terms c1 and c2. The root of the ontology has a probability of 1.0.

The first term considers the relative depth of the common ancestor c to the average depth of the two terms c1 and c2 while the second term takes into account how rare it is to identify the common ancestor c by chance.

Functional similarity score of gene pairs

Gene ontology enrichment analysis