Analysis of the areas and perimeters of polygons of the helices projections intersection in helical pairs of protein molecules

In this study, an analysis of distribution of the areas and perimeters of polygons of the helices projections intersection in pairs of connected helices found in known proteins has been performed. The database for helical pairs was compiled using the Protein Data Bank taking into account the definite rules suggested earlier. It was shown that helical pairs of all types that belong to a subset of pairs that have helices projections intersection and not having their axes intersection have polygons intersection areas and perimeters whose values are small or close to zero. Among all types of helical pairs belonging to a subset of pairs with helices projections intersections and axes intersections, there were no pairs that have small or close to zero values of areas and perimeters of helices projections intersection polygons. The maximum of the distribution of pairs formed by two $\alpha$-helices and belonging to a given subset was found at the values of polygons of the helices projections intersection areas and perimeters in the region (70–150) Å and (30–45) Å, respectively.