Global secondary structure packing angle bias in proteins

While studies of secondary structure interactions have focused on local interacting features, there is a need for a more global characterization of packing-induced aligned packing of secondary structures. This study presents an analysis of the distribution of globally sampled secondary structures within selected subunits of a selected set of multimeric proteins. Comparisons are made between the distribution of the cosines of angles between triplets of linear segments associated to secondary structures and a theoretically obtained distribution for triplets of random uniformly distributed unit vectors. We show that, among all pairs of helix or strand segments, planar configurations appear more frequently than expected for uniformly distributed vectors, and alignment is strongly preferred compared to that expected for uniformly distributed vector triplets. Among all secondary structure triplets, pairs of angle cosines between helix strand segments deviate from uniformity corresponding to alignment and anti-alignment. Furthermore, among all helix or strand segments, including non-interacting secondary structures, the distribution of a single angle cosine indicates a strong preference for alignment and anti-alignment. Selection for interactive triplets shows results consistent with prior studies. Lastly, angle pairs are not statistically independent, indicating that alignment between two helix or strand segments is more likely if another helix or strand is aligned with either of the first two helices or strands. Selection for interactive segment triplets shows results consistent with prior studies.