The study of interhelical distances of helical pairs in protein molecules

In this paper the study of interhelical distances in pairs of connected $\alpha$-helices found in known proteins has been performed. A number of rules for selection of the helical pairs from a set of protein structures obtained from the Protein Data Bank (PDB) have been developed. The set of helical pairs has been analyzed for the purpose of classification and finding out the features of protein structural organization. A point model of a double-helix motif has been proposed. All pairs of connected helices were 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. In this work histograms of the distribution of all types of helical pairs are obtained depending on the interhelical distances. The statistical estimates of the interplanar and minimal distance distributions for helical pairs of various types belonging to different sets are presented.