Self-Assembly of Icosahedral Viral Capsids: the Combinatorial Analysis Approach

An analysis of all possible icosahedral viral capsids is proposed. It takes into account the diversity of coat proteins and their positioning in elementary pentagonal and hexagonal configurations, leading to definite capsid size. We show that the self-organization of observed capsids during their production implies a definite composition and configuration of elementary building blocks. The exact number of different protein dimers is related to the size of a given capsid, labeled by its T-number. Simple rules determining these numbers for each value of T are deduced and certain consequences concerning the probabilities of mutations and evolution of capsid viruses are discussed.