A novel measure to analyze protein structures: Aspect ratio in protein alpha shapes

Proteins' three-dimensional (3D) structures are analyzed traditionally using geometric descriptors such as torsional angles and inter-atomic distances. In this study a measure that is borrowed from computational geometry, aspect ratio of each tetrahedron in alpha shapes of proteins, is utilized. This geometric descriptor differentiates alpha and beta structural classes of proteins when combined with principal components analysis. The method converts the structures of individual proteins, 3D coordinates of the atoms, to points on a plane. It has a high degree of accuracy in differentiating R and T structures of hemoglobin. Therefore, it is anticipated that the geometric measure can be used successfully in a method that is extended to solve classification problems in machine learning.