Automated and accurate protein structure description: Distribution of Ideal Secondary Structural Units in Natural Proteins

A new method for the Automated Protein Structure Analysis (APSA) is derived, which simplifies the protein backbone to a smooth curve in 3-dimensional space. For the purpose of obtaining this smooth line each amino acid is represented by its C$_{\alpha}$ atom, which serves as suitable anchor point for a cubic spline fit. The backbone line is characterized by arc length $s$, curvature $\kappa(s)$, and torsion $\tau(s)$. The $\kappa(s)$ and $\tau(s)$ diagrams of the protein backbone suppress, because of the level of coarse graining applied, details of the bond framework of the backbone, however reveal accurately all secondary structure features of a protein. Advantages of APSA are its quantitative representation and analysis of 3-dimensional structure in form of 2-dimensional curvature and torsion patterns, its easy visualization of complicated conformational features, and its general applicability. Typical differences between 3$_{10}$-,$\alpha$-, $\pi$-helices, and $\beta$-strands are quantified with the help of the $\kappa(s)$ and $\tau(s)$ diagrams. For a test set of 20 proteins, 63 % of all helical residues and 48.5 % of all extended residues are identified to be in ideal conformational environments with the help of APSA. APSA is compared with other methods for protein structure analysis and its applicability to higher levels of protein structure is discussed.