A study of a hierarchical structure of proteins and ligand binding sites of receptors using the triangular spatial relationship-based structure comparison method and development of a size-filtering feature designed for comparing different sizes of protein structures

The presence of receptors and the specific binding of the ligands determine nearly all cellular responses. Binding of a ligand to its receptor causes conformational changes of the receptor that triggers the subsequent signaling cascade. Therefore, systematically studying structures of receptors will provide insight into their functions. We have developed the triangular spatial relationship (TSR)-based method where all possible triangles are constructed with C-alpha atoms of a protein as vertices. Every triangle is represented by an integer denoted as a "key" computed through the TSR algorithm. A structure is thereby represented by a vector of integers. In this study, we have first defined substructures using different types of keys. Second, using different types of keys represents a new way to interpret structure hierarchical relations and differences between structures and sequences. Third, we demonstrate the effects of sequence similarity as well as sample size on the structure-based classifications. Fourth, we show identification of structure motifs, and the motifs containing multiple triangles connected by either an edge or a vertex are mapped to the ligand binding sites of the receptors. The structure motifs are valuable resources for the researchers in the field of signal transduction. Next, we propose amino-acid scoring matrices that capture "evolutionary closeness" information based on BLOSUM62 matrix, and present the development of a new visualization method where keys are organized according to evolutionary closeness and shown in a 2D image. This new visualization opens a window for developing tools with the aim of identification of specific and common substructures by scanning pixels and neighboring pixels. Finally, we report a new algorithm called as size filtering that is designed to improve structure comparison of large proteins with small proteins. Collectively, we provide an in-depth interpretation of structure relations through the detailed analyses of different types of keys and their associated key occurrence frequencies, geometries, and labels. In summary, we consider this study as a new computational platform where keys are served as a bridge to connect sequence and structure as well as structure and function for a deep understanding of sequence, structure, and function relationships of the protein family.