Orientational distributions of contact clusters in proteins closely resemble those of an icosahedron.

The orientational geometry of residue packing in proteins was studied in the past by superimposing clusters of neighboring residues with several simple lattices (Bagci et al., Proteins 2003;53:56-67; Raghunathan et al., Protein Sci 1997;6:2072-2083). In this work, instead of a lattice we use the regular polyhedron, the icosahedron, as the model to describe the orientational distribution of contacts in clusters derived from a high-resolution protein dataset (522 protein structures with high resolution < 1.5 A). We find that the order parameter (orientation function) measuring the angular overlap of directions in coordination clusters with directions of the icosahedron is 0.91, which is a significant improvement in comparison with the value 0.82 for the order parameter with the face-centered cubic (fcc) lattice. Close packing tendencies and patterns of residue packing in proteins are considered in detail and a theoretical description of these packing regularities is proposed.