During FY08, we focussed primarily on two subprojects.[unreadable] [unreadable] (1) Capsid assembly and polymorphism of retroviruses and their implications for infectivity. Retroviruses capsids are unusual in that they are assembled inside the maturing virion, not in the cytoplasm or the nucleus of the infected cell. The capsid protein is incorporated into the provirion as part of the Gag polyprotein which forms a spherical shell lining the membrane of the provirion. After the provirion has budded off, the maturational protease is activated and dissects Gag into its matrix (MA), capsid (CA) and nucleocapsid (NC) moieties. Protease inhibitors were the first antiviral drugs to be used successfully against HIV. Of the Gag fragments, CA reassembles to form the shell of the virus core, housing the viral RNA and replication enzymes. Evidence suggests that a correctly formed core is essential for infectivity; however cores are highly polymorphic. In this context, we have been using cryo-electron tomography to visualize mature virions of Rous Sarcoma Virus, the prototypic alpha-retrovirus.The virions in our[unreadable] data set range from 105 to 175 nm in diameter. Their cores are highly polymorphic. We observed angular cores, including some that are distinctively coffin-shaped and for which we propose a novel fullerene geometry; cores with continuous curvature including, rarely, fullerene cones; and tubular cores. Angular cores are the most voluminous and densely packed; tubes and some curved cores contain less material, suggesting incomplete packaging. From the tomograms, we measured the surface areas of cores and hence their contents of CA subunits. From the virion diameters, we estimated their original complements of Gag. We find that RSV virions, like HIV, contain unassembled CA subunits and the fraction of CA that is assembled correlates with core type; angular cores incorporate 80% of the available subunits and open-ended tubes, 30%. The number of glycoprotein spikes is variable ( 0 to 118) and also correlates with core type; virions with angular cores average 82 spikes, whereas those with tubular cores, 14 spikes. These observations imply that initiation of capsid assembly, in which interactions of spike endodomains with the Gag layer play a role, is a critical determinant of core morphology..[unreadable] [unreadable] (2) Retrovirus capsid geometry. Most capsid-containing viruses have capsids of uniquely defined sizes and shapes; of these, [unreadable] the most common structures observe icosahedral symmetry. In contrast, 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. For example, In the case of HIV, the appropriate structures have been proposed to be fullerene cones. On the other hand, we have found that cones are rare for Rous sarcoma virus capsids. To investigate further their polymorphism (see (1) above). we developed computational and graphical methods to construct polyhedral models that match in size and shape, RSV capsids observed within intact virions. They 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 distinct polyhedra grows rapidly with increasing quotas of hexamers, and ranks in the millions for RSV capsids, which have 150 to 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.