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.National Library of Medicine (LM05205-13

Computational approaches to modeling the conserved structural core among distantly homologous proteins

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 95-103).Modem techniques in biology have produced sequence data for huge quantities of proteins, and 3-D structural information for a much smaller number of proteins. We introduce several algorithms that make use of the limited available structural information to classify and annotate proteins with structures that are unknown, but similar to solved structures. The first algorithm is actually a tool for better understanding solved structures themselves. Namely, we introduce the multiple alignment algorithm Matt (Multiple Alignment with Translations and Twists), an aligned fragment pair chaining algorithm that, in intermediate steps, allows local flexibility between fragments. Matt temporarily allows small translations and rotations to bring sets of fragments into closer alignment than physically possible under rigid body transformation. The second algorithm, BetaWrapPro, is designed to recognize sequences of unknown structure that belong to specific all-beta fold classes. BetaWrapPro employs a "wrapping" algorithm that uses long-distance pairwise residue preferences to recognize sequences belonging to the beta-helix and the beta-trefoil classes. It uses hand-curated beta-strand templates based on solved structures. Finally, SMURF (Structural Motifs Using Random Fields) combines ideas from both these algorithms into a general method to recognize beta-structural motifs using both sequence information and long-distance pairwise correlations involved in beta-sheet formation. For any beta-structural fold, SMURF uses Matt to automatically construct a template from an alignment of solved 3-D structures.(cont.) From this template, SMURF constructs a Markov random field that combines a profile hidden Markov model together with pairwise residue preferences of the type introduced by BetaWrapPro. The efficacy of SMURF is demonstrated on three beta-propeller fold classes.by Matthew Ewald Menke.Ph.D