Projecting Three-dimensional Protein Structure into a One-dimensional Character Code Utilizing the Automated Protein Structure Analysis Method

The protein backbone is described as a smooth curved and twisted line in three-dimensional (3D) space and characterized by its curvature $\kappa(s)$ and torsion $\tau(s)$ both expressed as a function of arc length s. It is shown that the function $\tau(s)$ is sufficient to analyze the contributions of all amino acids to the conformation of the protein backbone. The characteristic peak and trough patterns of the $\tau(s)$ diagrams can be translated into a 16-letter code, which provides a rapid identification of helices, strands, and turns, specifies entry and exit points of secondary structural units, and determines their regularity in terms of distortions, kinks or breaks. Via computer encoding, 3D protein structure is projected into a 1D string of conformational letters. The 3D-1D-projection procedure represents an extension of the Automated Protein Structure Analysis (APSA) method. APSA has been applied to describe 155 super secondary structures from 94 proteins and to compare results with Efimov's classification system of super secondary structure. The applicability of the latter is demonstrated.