Statistical characters of mean backbone torsion angles of proteins

Based on the high resolution protein structures taken from the Protein Data Bank, the mean backbone torsion angle of each protein is calculated. Then the statistical characters of the mean backbone torsion angles of proteins are investigated. On φ-ψ plane, the representing points of the proteins, i.e., the mean backbone torsion angles (φ¯,ψ¯), separate into four clusters according to four main structural classes. Each cluster has a determinate centroid, which associates to the relative content of two types of popular secondary structural elements, α-helices and β-strands. It is also found that α/β structural class exhibits greater concentricity of the partial mean backbone torsion angle relative to other classes. An intuitive explanation is that the α/β structural class has high level of average lengths of both α-helices and β-strands. These results provide a further understanding of protein structures.