Optimal architectures of elongated viruses

Many viruses protect their genetic material by a closed elongated protein shell. Unlike spherical viruses, the structure of these prolates is not yet well understood, and only a few of them have been fully characterized. We present the results of a simple phenomenological model, which describes the remarkable structures of prolate or bacilliform viral shells. Surprisingly, we find that the special well-defined geometry of these elongated viruses arises just as a consequence of free-energy minimization of a generic interaction between the structural units of the capsid. Hemispherical T-number caps centered along the 5-, 3-, and 2-fold axes with hexagonally ordered cylindrical bodies are found to be local energy minima, thus justifying their occurrence as optimal viral structures. Moreover, closed elongated viruses show a sequence of magic numbers for the end-caps, leading to strict selection rules for the length and structure of the body as well as for the number of capsomers and proteins of the capsid. The model reproduces the architecture of spherical and bacilliform viruses, both in vivo and in vitro, and constitutes an important step towards understanding viral assembly and its potential control for biological and nanotechnological applications.