Generating Vectors for the Lattice Structures of Tubular and Conical Viral Capsids

Retrovirus capsid is a fullerene-like lattice consisting of capsid protein hexamers and pentamers. Mathematical models for the lattice structure help understand the underlying biological mechanisms in the formation of viral capsids. It is known that viral capsids could be categorized into three major types: icosahedron, tube, and cone. While the model for icosahedral capsids is established and well-received, models for tubular and conical capsids need further investigation. This paper proposes new models for the tubular and conical capsids based on an extension of the Capser-Klug quasi-equivalence theory. In particular, two and three generating vectors are used to characterize respectively the lattice structures of tubular and conical capsids. Comparison with published HIV-1 data demonstrates a good agreement of our modeling results with experimental data.