Discrete Groups and Internal Symmetries of Icosahedral Viral Capsids

Abstract

A classification of all possible icosahedral viral capsids is proposed. It takes into account the diversity of hexamers’ compositions, leading to definite capsid size.We showhowthe self-organization of observed capsids during their production results from definite symmetries of constituting hexamers. The division of all icosahedral capsids into four symmetry classes is given. New subclasses implementing the action of symmetry groups Z2, Z3 and S3 are found and described. They concern special cases of highly symmetric capsids whose T = p2 + pq + q2-number is of particular type corresponding to the cases (p, 0) or (p, p).

Keywords

• viral capsid growth
• self-organized agglomeration
• symmetry