Abstract—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.

中文翻译：

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蛋白质间螺旋堆积角与α-螺旋长度的关系

摘要-蛋白质中α螺旋的相互排列或堆积取决于几个因素，但是紧密堆积和多肽链的化学性质是最重要的。这项研究首次表明，α螺旋轴之间的扭转堆积角取决于其长度。使用蛋白质数据库已编译了由两个相互连接且并置的α螺旋形成的螺旋对数据库。这些螺旋对又分为四种类型：（1）由长螺旋形成的10474对；（2）3665对，其中第一个α螺旋长而第二个短。（3）3648对，其中第一个α螺旋短而第二个长。4）1895对，两个螺旋均短。对数据库的分析表明，两个螺旋都是长螺旋的大多数螺旋对形成的α-发夹的螺旋间堆积角为Ω≈20°。大多数螺旋对，其中一个α螺旋较长，而另一个则较短，或者两个螺旋均为短螺旋形式，具有正交（Ω≈–70°…–90°）或倾斜（Ω≈–50°）堆积的αα角-螺旋。讨论了螺旋间角（Ω）与α螺旋长度之间这种关系的可能原因。这些结果在蛋白质建模和预测中非常重要，因为它们可以确定蛋白质分子中α螺旋的相互排列。讨论了螺旋间角（Ω）与α螺旋长度之间这种关系的可能原因。这些结果在蛋白质建模和预测中非常重要，因为它们可以确定蛋白质分子中α螺旋的相互排列。讨论了螺旋间角（Ω）与α螺旋长度之间这种关系的可能原因。这些结果在蛋白质建模和预测中非常重要，因为它们可以确定蛋白质分子中α螺旋的相互排列。