Abstract
Whereas many viruses have capsids of uniquely defined sizes that observe icosahedral symmetry, retrovirus capsids are highly polymorphic. Nevertheless, they may also be described as polyhedral foldings of a fullerene lattice on which the capsid protein (CA) is arrayed. Lacking the high order of symmetry that facilitates the reconstruction of icosahedral capsids from cryo-electron micrographs, the three-dimensional structures of individual retrovirus capsids may be determined by cryo-electron tomography, albeit at lower resolution. Here we describe computational and graphical methods to construct polyhedral models that match in size and shape, capsids of Rous sarcoma virus (RSV) observed within intact virions [8]. The capsids fall into several shape classes, including tubes, "lozenges", and "coffins". The extent to which a capsid departs from icosahedral symmetry reflects the irregularity of the distribution of pentamers, which are always 12 in number for a closed polyhedral capsid. The number of geometrically distinct polyhedra grows rapidly with increasing quotas of hexamers, and ranks in the millions for RSV capsids, which typically have 150 - 300 hexamers. Unlike the capsid proteins of icosahedral viruses that assume a minimal number of quasi-equivalent conformations equal to the triangulation number (T), retroviral CAs exhibit a near-continuum of quasi-equivalent conformations - a property that may be attributed to the flexible hinge linking the N- and C-terminal domains.
Highlights
The ability of capsid proteins (CAs) to assemble into closed hollow shells is a remarkable and still incompletely understood phenomenon
We describe our approach to modelling and apply it to our data set of Rous sarcoma virus (RSV) virions to further explore their capsid geometry
We wrote a small tool in Chimera [36], called the ‘Triangle Net’ tool, which allows the user to go through these steps
Summary
The ability of capsid proteins (CAs) to assemble into closed hollow shells is a remarkable and still incompletely understood phenomenon. Continuous closure requires that T should comply with the selection rule T 1⁄4 (h 2 þ h · k þ k 2) where h and k are non-negative integers These structures may alternatively be considered as foldings of a planar hexagonal lattice of equilateral triangles or as honeycomb lattices of hexagons and pentagons (the latter is called a fullerene lattice). These are dual representations [11]. The same geometrical rules apply in the case of retroviral cores as for carbon fullerenes and other naturally occurring polyhedra. We describe our approach to modelling and apply it to our data set of Rous sarcoma virus (RSV) virions to further explore their capsid geometry
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