[Relationship between the Interhelical Packing Angles and the Length of α-Helices in Proteins]

Mutual arrangement, or packing, of α-helices in proteins depends on several factors, but, tight packing and the chemical nature of the polypeptide chain are the most important. This study shows, for the first time, that the torsion packing angles between axes of α-helices depend on their length. A database of helical pairs formed by two connected and juxtaposed α-helices has been compiled using the Protein Data Bank. These helical pairs have been subdivided into four types: (1) 10474 pairs formed by long helices; (2) 3665 pairs in which the first α-helix is long and the second is short; (3) 3648 pairs in which the first α-helix is short and the second is long; 4) 1895 pairs in which both helices are short. Analysis of the database showed that most helical pairs in which both the helices are long form α-hairpins having interhelical packing angles of Ω. ≈ 20°. Most helical pairs in which one α-helix is long and the other is short or both helices are short form αα-corners having orthogonal (Ω ≈ -70°...-90°) or slanted (Ω ≈ -50°) packing of α-helices. The possible reasons for this relationship between interhelical angles (Ω) and the length of α-helices are discussed. These results are of great importance in protein modeling and prediction since they enable the determination of the mutual arrangement of α-helices in protein molecules.