Geometry of phage head construction

Abstract

The process of phage capsid assembly is reviewed, with particular attention to the probable role of curvature in helping to determine head size and shape. Both measures of curvature (mean curvature and Gaussian curvature, explained in Appendix I), should act best when the assembling shell is spherical, which could account for procapsids having this shape. Procapsids are also relatively thick, which should help head size determination by the mean curvature. The accessory role of inner and outer scaffolds in size determination and head nucleation is also reviewed. Nucleation failure generates various malformations, including non-closure, but the most common is the tube or polyhead, where the subunits’ inherent curvature is expressed as a constant mean curvature. This induces lattice distortions that only partly understood. An extra tubular section in normal heads leads to the prolate shape, with a more complex and variable geometry. Newly assembled procapsids are both enlarged and toughened by the head transformation. In the procapsid the Gaussian curvature is uniformly distributed. But toughening tends to equalize bond lengths, so all the Gaussian curvature gets concentrated in the vertices, being zero elsewhere. This explains head angularization. Because of this change in Gaussian curvature, the regular subunit packing in the polyhedral head cannot be mapped onto the procapsid. This explains part of the hexon distortions found in this region. The implications of translocase-induced DNA twist, end rotation and the coiling of packaged DNA, are discussed. The symmetry mismatches between the head, connector and tail are discussed in relation to the possible α-helical structures of their DNA channels.