In this paper a statistical analysis of distributions of inter-helical angles in pairs of consequtive and connected α-helices in spatial structures of proteins are presented. A number of rules for selection of the helical pairs from a set of protein structures obtained from Protein Data Bank (PDB) are developed. The set of helical pairs has been analyzed for the purpose of classification and finding out the features of protein structural organization. All the pairs of connected helices are divided into three subsets according to the criterion of crossing of projections of the helices on parallel planes, which pass through the axes of the helices. It is shown that the distribution of all the types of helical pairs, whose projections do not cross each other, covers almost the entire range of inter-helical angles. The distribution has a single minimum which is close to right angle. Most pairs in this set constitute helical pairs consisting of α- and 3₁₀-helices, and most pairs with the crossing projections of helices are helical pairs formed by two α-helices. It is also shown that a great amount of the pairs of connected α-helices has accute angle between the axes of the helices. The distribution of all the types of helical pairs depending on the length of the inter-helical connections is also analyzed. It is shown that the structures with short connections occur most often in all the subsets.

structural motifs of proteins, point model, helical pairs, angle between the axes of the helices

Mathematical modelling in actual problems of science and technics

Tikhonov Dmitry Anatol’evich,  ,  orcid.org/0000-0002-1779-464X,  KIAM RAS

Kulikova Liudmila Ivanovna,  ,  orcid.org/0000-0002-7293-1504,  KIAM RAS

Efimov Alexander Vasil’evich,  ,  orcid.org/0000-0002-9539-270X,  Институт белка РАН