Viral capsids are composed of multiple copies of one or a few chemically distinct capsid proteins and are mostly stabilized by inter subunit protein-protein interactions. There have been efforts to identify and analyze these protein-protein interactions, in terms of their extent and similarity, between the subunit interfaces related by quasi- and icosahedral symmetry. Here, we describe a new method to map quaternary interactions in spherical virus capsids onto polar angle space with respect to the icosahedral symmetry axes using azimuthal orthographic diagrams. This approach enables one to map the nonredundant interactions in a spherical virus capsid, irrespective of its size or triangulation number (T), onto the reference icosahedral asymmetric unit space. The resultant diagrams represent characteristic fingerprints of quaternary interactions of the respective capsids. Hence, they can be used as road maps of the protein-protein interactions to visualize the distribution and the density of the interactions. In addition, unlike the previous studies, the fingerprints of different capsids, when represented in a matrix form, can be compared with one another to quantitatively evaluate the similarity (S-score) in the subunit environments and the associated protein-protein interactions. The S-score selectively distinguishes the similarity, or lack of it, in the locations of the quaternary interactions as opposed to other well-known structural similarity metrics (e.g., RMSD, TM-score). Application of this method on a subset of T = 1 and T = 3 capsids suggests that S-score values range between 1 and 0.6 for capsids that belong to the same virus family/genus; 0.6-0.3 for capsids from different families with the same T-number and similar subunit fold; and <0.3 for comparisons of the dissimilar capsids that display different quaternary architectures (T-numbers). Finally, the sequence conserved interface residues within a virus family, whose spatial locations were also conserved have been hypothesized as the essential residues for self-assembly of the member virus capsids.
