Statistical analysis of internal distances of helical pairs in protein molecules

In this paper, a statistical analysis of a distribution of interhelical distances in the helical pairs of known proteins is carried out. A set of helical pairs of the protein molecules which was selected from the Protein Data Bank according to certain rules was subdivided into three subsets according to the criterion of crossing helix projections onto parallel planes passing through the helical axes. It is shown that the distributions of the distances for the helical pairs not having crossing projections have more long-range character than those whose projections cross. Using regression analysis we analyze the character of distributions, in particular, we show that in the subsets which do not have crossing projections, distributions of different distances between helical axes are gamma distributions. It is demonstrated that in the subsets having crossing projections, the ratio between the minimum distance and the interplane one is likely to be small as distinct from the subset not having crossing projections where the opposite is the case. The conclusion is proved that helical pairs having crossing axes projections are additionally stabilized due to internal interactions.