Analysis of torsion angles between helical axes in pairs of helices in protein molecules

In this study, an analysis of distribution of the torsion angles $\Omega$ between helical axes 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. The database was analyzed in order to elaborate its classification and find out novel structural features in helix packing. The database was subdivided into three subsets according to criterion of crossing helix projections on the parallel planes passing through the axes of the helices. It was shown that helical pairs not having crossing projections are distributed along whole range of angles $\Omega$, although there are two maxima at $\Omega=0^\circ$ and $\Omega=180^\circ$. Most of helical pairs of this subset are pairs formed by $\alpha$-helices and $3_{10}$- helices. It is shown that the distribution of all the helical pairs having the crossing helix projections has a maximum at $20^\circ < \Omega < 25^\circ$. In this subset, most helical pairs are formed by $\alpha$-helices. The distribution of only $\alpha$-helical pairs having crossing axes projections has three maxima, at $-50^\circ < \Omega < -25^\circ$, $20^\circ < \Omega < 25^\circ$, and $70^\circ < \Omega < 110^\circ$.