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Computational and Mathematical Methods in Medicine
Volume 9, Issue 3-4, Pages 197-210
Original Article

Irregular and Semi-Regular Polyhedral Models for Rous Sarcoma Virus Cores

1Laboratory of Structural Biology Research, National Institute for Arthritis, Musculoskeletal and Skin Diseases, National Institutes of Health, Bethesda, MD, USA
2Department of Microbiology and Immunology, The Pennsylvania State University College of Medicine, Hershey, PA, USA

Received 18 March 2008; Accepted 2 April 2008

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 3D structures of individual retrovirus capsids may be determined by cryo-electron tomography, albeit at lower resolution. Here, we describe computational and graphical methods used to construct polyhedral models that match in size and shape, capsids of Rous sarcoma virus (RSV) observed within intact virions. 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 particles in the size range of RSV capsids, which typically have 150–300 hexamers. Unlike the CAs 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.