A New Type of φ, ψ Representation of the Protein Tertiary Structure and the Analysis of the Amino Acid Preferences for Specific Locations at Type-II β-Turn by Using 8000 Possible Kinds of Amino Acid Residues

φ, ψ Representations of three-dimensional structures of 125 globular proteins were depicted for analyzing conformational details in their secondary and tertiary structures. They can be drawn in the form of a two-dimensional diagram. The new type of representation of the protein tertiary structure can be used as a stereotyped finger printing for 125 protein molecules. It is powerful for a precise comparison of the relationship of the primary, secondary, and tertiary structures of homologous proteins. The precise or broad similarity between the patterns of proteins classified into the same family is obvious. This representation is also useful in readily recognizing all of the secondary structures as one progresses along the chain. Complicated three-dimensional structures of 125 globular proteins are easily recognized to be built up from only four secondary structures: helix, β-strand, β-turn, and unordered structure. A combination of intersegments hydrogen bonds among β-strands was also shown in the diagram. In order to demonstrate the usefulness of the diagram, 195 type-II β-turns were extracted from 125 proteins using the new type of two-dimensional φ, ψ diagrams. Their amino acid sequences were surveyed so as better to understand amino acid preferences previously observed. For their analysis, a normalized preference (NP) value of an amino acid residue at a particular position of the secondary structure is defined as the ratio of the average percentage composition at the position based on average percentage composition at large. The statistical significance of the NP-value used in this study is more simple and clearer than that of the d-test based on a normal distribution, which was used in the previous study. It is clearly shown that a high NP-value (5.0) of a single P residue for the position i + 1 of the type-II β-turn is an average preference of a variety of P residues in the middle of triplets consisting of consecutive amino acid residues. The NP-values of P residues, in the middle of 25 particular triplets are outstandingly high. Out of 400 possible P residues 322 kinds of P residues were found in 125 proteins. A remarkable high NP-value (8.8) of a single G residue for the position i + 2 is also an average preference of G residues in the middle of various triplets.