Graphlet Kernels for Prediction of Functional Residues in Protein Structures

Abstract

We introduce a novel graph-based kernel method for annotating functional residues in protein structures. A structure is first modeled as a protein contact graph, where nodes correspond to residues and edges connect spatially neighboring residues. Each vertex in the graph is then represented as a vector of counts of labeled non-isomorphic subgraphs (graphlets), centered on the vertex of interest. A similarity measure between two vertices is expressed as the inner product of their respective count vectors and is used in a supervised learning framework to classify protein residues. We evaluated our method on two function prediction problems: identification of catalytic residues in proteins, which is a well-studied problem suitable for benchmarking, and a much less explored problem of predicting phosphorylation sites in protein structures. The performance of the graphlet kernel approach was then compared against two alternative methods, a sequence-based predictor and our implementation of the FEATURE framework. On both tasks the graphlet kernel performed favorably; however, the margin of difference was considerably higher on the problem of phosphorylation site prediction. While there is data that phosphorylation sites are preferentially positioned in intrinsically disordered regions, we provide evidence that for the sites that are located in structured regions, neither the surface accessibility alone nor the averaged measures calculated from the residue microenvironments utilized by FEATURE were sufficient to achieve high accuracy. The key benefit of the graphlet representation is its ability to capture neighborhood similarities in protein structures via enumerating the patterns of local connectivity in the corresponding labeled graphs.

Recurrent Subgraph Prediction

“…Graph embedding has been used in [17], but the scope of the embedding has been limited to the subgraph itself; whereas, our method embeds the entire network state. Structure prediction in temporal networks has been studied in [18], but it considers interactions which occur across time-steps; our approach aims to predict any arbitrarily defined subgraph for a future instance.…”

Fingerprint Kernels for Protein Structure Comparison

“…As an alternative, graph kernels have gained attention in bioinformatics, since they can offer an error‐tolerant measure of similarity along with a the possibility of being more runtime efficient. Different works in this field are available such as random walk,27 shortest path,28 graphlet29,30 or diffusion kernels 31. Other kernels are based e.g.…”

GUISE: Uniform Sampling of Graphlets for Large Graph Analysis

“…Since then, graphlet frequencies have been used for comparing structures of different biological networks [3], characterizing biological networks using graphlet degree distribution [3], obtaining a structural to functional mapping for biological networks [11], and for relating various kinds of graphlets with different information cascades [14]. Frequencies of various graphlets have also been used for designing effective graph kernels [15], [16].…”

“…In the few exceptions that we have, such as [14], [15] and [16], the high computation cost is dealt with a compromise that considers graphlets that have up to four vertices. N. Przulj's team built a software called GraphCrunch2 [17], which is the only existing tool that counts the frequencies of all graphlets with three, four, and five vertices.…”