Simplified representation of proteins

The conventional methods for characterizing the secondary structures of proteins based on hydrogen bonding patterns and phi,phi torsions are not fully specific in determining the spatial arrangements of various secondary structural elements. This fact motivates a search for an efficient description of the various secondary structures and their interactions. The successive identical repeating units of a polypeptide chain, namely the atoms of the peptide plane may be superposed using a method based on the mathematical quaternion. The superposition angle then characterizes different secondary structures. The distortions in protein alpha-helices such as kinks and bends are also precisely determined. The twist in beta-sheets is quantified and reverse turns are found to have characteristic variations. This new representation might pave the way for a better understanding of the final folding conformation of the polypeptide chain.