In a past journal club, I presented a paper by Xu et al on their method of quantifying semantic similarity of proteins based on the Gene Ontology. The Gene Ontology (GO) is a directed acyclic graph (DAG, c.f. Figure 1) of terms with which a protein or a gene can be annotated. These terms are designed to describe the process the protein is involved in, what role it fulfils in this process, and where in the cell it is localized. Thus, when comparing the function of two proteins in a quantifiable way, it has become standard to refer back to the GO terms these proteins are annotated with and compare these based on their relationship in the DAG.

Figure 1: Schematic Diagram of a Directed Acyclic Graph (DAG).

As opposed to many methods, which measure the importance of a node (GO-term) in the DAG as its information content given an external database, the method proposed by Xu et al measures semantic similarity independently of external resources, which gives it the appearance of an independent measure. Furthermore, it claims to be good at dealing with badly annotated proteins, which is often a big problem in functional similarity calculations.

The similarity measure is a hybrid between node-based and edge-based methods, and is seemingly inspired by Wang et al’s 2007 paper and Shen et al’s 2010 paper. It is based on what they call “Shortest Semantic Differentiation Distance” or (SSDD), which is calculated over the shortest distance between two GO-terms on the DAG. When comparing the GO-terms A and B, the shortest path is measured by traversing the DAG upwards from node A to the lowest common ancestor of both nodes and down to node B.

The SSDD calculation over the shortest path is based on their so-called semantic Totipotency values assigned to the terms in the DAG that are part of the shortest path. The semantic Totipotency, T, of a term is calculated by:

Semantic Totipotency Measure

where the weight, ω, is given by:

Weight, ω

Here, Dst(t) denotest the number of descendents of the term t, and t_p denotes the parent term of term t. Thus, the T-value of every node is both an expression of the depth of the DAG in this area and the coverage.

Finally, the SSDD is calculated by:

Shortest Semantic Differentiation Distance

And subsequently the similarity of two GO terms is measured by:

Results

In their paper Xu et al showed the method to be competitive compared to other methods which compute protein functional similarity by pairwise GO-term comparisons, while also outperforming a common graph-based method in simUI. While these results look promising, the biological interpretability of such a semantic similarity measure remains difficult.

The strongest advantage of the SSDD method proposed was however its alleged invariance to annotation richness of proteins, which was presented as shown in Figure 2 below (Figure 5 in the paper).

Figure 2: The performance of difference methods dealing with sets of proteins with difference annotation richness.

The results in this figure show that SSDD exhibits only a slight decrease in Pearson Correlation Coefficient to a set of reference similarity values for proteins which are less well annotated. This ability to deal with badly annotated proteins is the true value of the SSDD method proposed by Xu et al. However, this investigation was performed by sets of proteins selected by the authors, and should thus be validated independently to confirm these surprising results.