The structure of elongated viral capsids

There are many viruses whose genetic material is protected by a closed elongated protein shell. Unlike spherical viruses, the structure and construction principles of these elongated capsids are not fully known. In this article, we have developed a general geometrical model to describe the structure of prolate or bacilliform capsids. We show that only a limited set of tubular architectures can be built closed by hemispherical icosahedral caps. In particular, the length and number of proteins adopt a very special set of discrete values dictated by the axial symmetry (fivefold, threefold, or twofold) and the triangulation number of the caps. The results are supported by experimental observations and simulations of simplified physical models. This work brings about a general classification of elongated viruses that will help to predict their structure, and to design viral cages with tailored geometrical properties for biomedical and nanotechnological applications.