The protein stoichiometry of viral capsids via tiling theory

A vital part of an infectious virus particles is the viral capsid, that is a protein shell that protects the viral genome. It is formed from so-called morphological units, which are entities composed of usually five or six proteins. The derivation of mathematical models for the location and the types of these morphological units in the viral capsids is important as this information is key for an understanding of the viral assembly process and hence for the design of anti-viral therapeutics. For a large class of viruses this problem is solved by Caspar-Klug theory [1], and the corresponding results are presently used in the classification and evaluation of experimental data. However, for a significant number of viruses, including for example important cases such as polyoma virus – the causative agent for cervical cancer in women – this theory does not apply. In [2, 3] a new theory has been introduced that uses a combination of group theory and tiling theory – a theory investigating tessellations of surfaces in terms of a finite set of building blocks called tiles – to generalise Caspar-Klug theory. This new theory not only accommodates all open cases that have been discovered experimentally until present, but also makes predictions about novel viral structures. Furthermore, it predicts the bonding structure between protein subunits in the capsid, which is a result that could not be obtained within the framework of Caspar-Klug theory. In this contribution, we demonstrate the new theory for the example of polyoma virus based on [2].