Structures of Spherical Viral Capsids as Quasicrystalline Tilings

TL;DR

This paper introduces a novel geometrical approach to modeling spherical viral capsids as quasicrystalline tilings, unifying existing models and explaining structures that deviate from traditional theories.

Contribution

It presents a new geometrical framework for viral capsid structures that minimizes conformations and applies to both Caspar-Klug compliant and non-compliant structures.

Findings

Derived idealized coordinates for six capsid types.

Unified description of Caspar-Klug and non-Caspar-Klug structures.

Demonstrated the minimal tile type approach for protein bonding.

Abstract

Spherical viral shells with icosahedral symmetry have been considered as quasicrystalline tilings. Similarly to known Caspar-Klug quasi-equivalence theory, the presented approach also minimizes the number of conformations necessary for the protein molecule bonding with its neighbors in the shell, but is based on different geometrical principles. It is assumed that protein molecule centers are located at vertices of tiles with identical edges, and the number of different tile types is minimal. Idealized coordinates of nonequivalent by symmetry protein positions in six various capsid types are obtained. The approach describes in a uniform way both the structures satisfying the well-known Caspar-Klug geometrical model and the structures contradicting this model.