Visible Volume: a Robust Measure for Protein Structure Characterization

We propose a new characterization of protein structure based on the natural tetrahedral geometry of the β carbon and a new geometric measure of structural similarity, called visible volume. In our model, the side-chains are replaced by an ideal tetrahedron, the orientation of which is fixed with respect to the backbone and corresponds to the preferred rotamer directions. Visible volume is a measure of the non-occluded empty space surrounding each residue position after the side-chains have been removed. It is a robust, parameter-free, locally-computed quantity that accounts for many of the spatial constraints that are of relevance to the corresponding position in the native structure. When computing visible volume, we ignore the nature of both the residue observed at each site and the ones surrounding it. We focus instead on the space that, together, these residues could occupy. By doing so, we are able to quantify a new kind of invariance beyond the apparent variations in protein families, namely, the conservation of the physical space available at structurally equivalent positions for side-chain packing. Corresponding positions in native structures are likely to be of interest in protein structure prediction, protein design, and homology modeling. Visible volume is related to the degree of exposure of a residue position and to the actual rotamers in native proteins. In this article, we discuss the properties of this new measure, namely, its robustness with respect to both crystallographic uncertainties and naturally occurring variations in atomic coordinates, and the remarkable fact that it is essentially independent of the choice of the parameters used in calculating it. We also show how visible volume can be used to align protein structures, to identify structurally equivalent positions that are conserved in a family of proteins, and to single out positions in a protein that are likely to be of biological interest. These properties qualify visible volume as a powerful tool in a variety of applications, from the detailed analysis of protein structure to homology modeling, protein structural alignment, and the definition of better scoring functions for threading purposes.

Integration of relational and hierarchical network information for protein function prediction

BACKGROUND:In the current climate of high-throughput computational biology, the inference of a protein's function from related measurements, such as protein-protein interaction relations, has become a canonical task. Most existing technologies pursue this task as a classification problem, on a term-by-term basis, for each term in a database, such as the Gene Ontology (GO) database, a popular rigorous vocabulary for biological functions. However, ontology structures are essentially hierarchies, with certain top to bottom annotation rules which protein function predictions should in principle follow. Currently, the most common approach to imposing these hierarchical constraints on network-based classifiers is through the use of transitive closure to predictions.RESULTS:We propose a probabilistic framework to integrate information in relational data, in the form of a protein-protein interaction network, and a hierarchically structured database of terms, in the form of the GO database, for the purpose of protein function prediction. At the heart of our framework is a factorization of local neighborhood information in the protein-protein interaction network across successive ancestral terms in the GO hierarchy. We introduce a classifier within this framework, with computationally efficient implementation, that produces GO-term predictions that naturally obey a hierarchical 'true-path' consistency from root to leaves, without the need for further post-processing.CONCLUSION:A cross-validation study, using data from the yeast Saccharomyces cerevisiae, shows our method offers substantial improvements over both standard 'guilt-by-association' (i.e., Nearest-Neighbor) and more refined Markov random field methods, whether in their original form or when post-processed to artificially impose 'true-path' consistency. Further analysis of the results indicates that these improvements are associated with increased predictive capabilities (i.e., increased positive predictive value), and that this increase is consistent uniformly with GO-term depth. Additional in silico validation on a collection of new annotations recently added to GO confirms the advantages suggested by the cross-validation study. Taken as a whole, our results show that a hierarchical approach to network-based protein function prediction, that exploits the ontological structure of protein annotation databases in a principled manner, can offer substantial advantages over the successive application of 'flat' network-based methods.