Unveiling the Hidden Rules of Spherical Viruses Using Point Arrays

Abstract

Since its introduction, the Triangulation number has been the most successful and ubiquitous scheme for classifying spherical viruses. However, despite its many successes, it fails to describe the relative angular orientations of proteins, as well as their radial mass distribution within the capsid. It also fails to provide any critical insight into sites of stability, modifications or possible mutations. We show how classifying spherical viruses using icosahedral point arrays, introduced by Keef and Twarock, unveils new geometric rules and constraints for understanding virus stability and key locations for exterior and interior modifications. We present a modified fitness measure which classifies viruses in an unambiguous and rigorous manner, irrespective of local surface chemistry, steric hinderance, solvent accessibility or Triangulation number. We then use these point arrays to explain the immutable surface loops of bacteriophage MS2, the relative reactivity of surface lysine residues in CPMV and the non-quasi-equivalent flexibility of the HBV dimers. We then explain how point arrays can be used as a predictive tool for site-directed modifications of capsids. This success builds on our previous work showing that viruses place their protruding features along the great circles of the asymmetric unit, demonstrating that viruses indeed adhere to these geometric constraints.

Viral Phrenology

“…These constraints are radially-distributed representations of icosahedral rotation symmetry which set limits on the angular orientation and distribution of virus capsid proteins, see Figure 1. While in principle, viruses could conform to multiple point arrays, in practice we find most viruses conform to only one or two arrays [2]. This classification is powerful, as it indicates geometric locations where viruses need to be modified with care, as well as other potential geometric locations where modifications should be relatively easy to accomplish.…”

“…Gauge point 19 imposes inflexible restrictions on the choice of point arrays, either ICO 2 or IDD 5 , are the only two point arrays available to this gauge point [2,14]. These are known as sister arrays, and are identical except for a single radial level and without more coordinate information on the genome, are indistinguishable at this level [2]. Each of these point arrays specify restrictions on three of the four protein chains A, C & D. ( b ) The capsid proteins pair up to form two dimers (AB & CD) which molecular dynamics simulations have shown to have different vibrational frequencies [22].…”

“…Icosahedral point arrays offer a novel tool for analyzing viruses [3,4,14]. We have shown previously that amino acids near these geometric locations are likely critical to capsid stability and that many modifications, from amino acid substitution to ligand attachment are either prohibited or requires more care than expected by standard analysis such as steric hindrance and solvent accessibility [2]. Point arrays are constructed by applying an affine extension to a base icosahedron (ICO), dodecahedron (DOD) or icosadodecahedron (IDD) along the 2-, 3- or 5-fold symmetry axes direction then re-applying icosahedral symmetry.…”

“…There are two potential structural protrusions within the AU, located along the 5-2 arc (purple) and the 3-5 arc (orange). We find that only the point arrays corresponding to purple protrusion GP 19 have corresponding arrays which meet the criteria for a proper fit [2], so there is only one structural protrusion in HBV.…”

“…We have previously shown that all protruding features of spherical viruses are located on the gauge points of these arrays, though it was not yet known that these locations also indicated the genomic composition. The gauge points determine the overall radial scaling of a point array and are all located on the 15 icosahedral great circles which subtend neighboring symmetry axes in the asymmetric unit [2,14]. We also show that not all gauge points are used for both DNA and RNA viruses.…”