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.
Highlights
We present a modified fitting method for classifying spherical viruses using the icosahedral point arrays introduced by Keef and Twarock [1,2]
We showed that viruses place their protruding features at discrete gauge points along the 15 icosahedral great circles which are used to create the asymmetric unit (Figure 1), a direct consequence of viruses conforming to the geometric constraints of point arrays [4]
We begin by reviewing icosahedral symmetry and the construction of the 55 icosahedral point arrays generated by affine extensions of the base icosahedral polyhedra developed in the seminal papers by Keef and Twarock [1,2]
Summary
We present a modified fitting method for classifying spherical viruses using the icosahedral point arrays introduced by Keef and Twarock [1,2]. These point arrays reveal an interdependence between the location of viral protrusions, capsid proteins and the geometric packaging of the viral genome. For example L-A virus, is a 120 protein capsid ( T = 2) with the same architecture as a T = 1 capsid, though it has 10 proteins making up its pentameric unit and no hexamers. SV40 is composed entirely of pentameric subunits, with 60 pentamers residing where the 60 hexamers would
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