"Observed protein structures usually represent energetically favorable conformations. While not all observed structures are necessarily functional, it is generally agreed that protein structure is closely related to protein function. Given a collection of proteins sharing a common global structure, variations in their local structures at specific, critical locations may result in different biological functions. Structural relationships among proteins are important in the study of the evolution of proteins as well as in drug design and development. Analysis of geometrical 3D protein structure has been shown to be effective with respect to classifying proteins. Prior work has shown that the Double Centroid Reduced Representation (DCRR) model is a useful geometric representation for protein structure with respect to visual models, reducing the quantity of modeled information for each amino acid, yet retaining the most important geometrical and chemical features of each: the centroids of the backbone and of the side-chain. DCRR has not yet been applied in the calculation of geometric structural similarity. Meanwhile, multi-dimensional indexing (MDI) of protein structure combines protein structural analysis with distance metrics to facilitate structural similarity queries and is also used for clustering protein structures into related groups. In this respect, the combination of geometric models with MDI has been shown to be effective. Prior work, notably Distance and Density-based Protein Indexing (DDPIn), applies MDI to protein models based on the geometry of the C-alpha backbone. DDPIn's distance metrics are based on radial and density functions that incorporate spherical-based metrics, and the indices are built from metric-tree (M-tree) structures. This work combines DCRR with DDPIn for the development of new DCRR centroid-based metrics: spherical binning distance and inter-centroid spherical distance. The use of DCRR models will provide additional significant structural information via the inclusion of side-chain centroids. Additionally, the newly developed distance metric functions combined with DCRR and M-tree indexing attempt to improve upon the performance of prior work (DDPIn), given the same data set, with respect to both individual k-nearest neighbor (kNN) search queries as well as clustering all proteins in the index."--Abstract.