Statistical analysis of the internal distances of helical pairs in protein molecules

The statistical analysis of interhelical distances in pairs of connected $\alpha$-helices found in known proteins has been performed. In accordance with the certain rules, a database of the pairs found in the Protein Data Bank has been compiled. This set was subdivided into three subsets according to criterion of crossing helix projections on the parallel plane passing through the axis of the helix. It was shown that the distribution of distances between the pairs of helices whose projections are not crossed has a more long-range nature than those whose projections are overlapped. Using the regression analysis the nature of distributions is investigated. In particular, it is shown that the distributions of interhelical distances in the subset of pairs of helices without intersections belong to the gamma distributions. It is also shown that the subset of the pairs with crossing projections have a smaller ratio of the minimal distance between the helical axes to the interplanar distance that is contrast to the set without crossing projections. It was concluded that the helical pairs with crossing projections are additionally stabilized by internal interactions.