title: On the geometry of regular icosahedral capsids containing disymmetrons.
abstract: Large icosahedral virus capsids are composed of symmetrons, organized arrangements of capsomers. There are three types of symmetrons: disymmetrons, trisymmetrons, and pentasymmetrons, which have different shapes and are centered on the icosahedral 2-fold, 3-fold and 5-fold axes of symmetry, respectively. Sinkovits and Baker (2010) gave a classification of all possible ways of building an icosahedral structure solely from trisymmetrons and pentasymmetrons, which requires the triangulation number T to be odd. In the present paper we incorporate disymmetrons to obtain a geometric classification of large icosahedral viruses formed by regular penta-,tri-, and disymmetrons, giving all mathematically consistent and theoretically possible solutions. For every class of solutions, we further provide formulas for symmetron sizes and parity restrictions on h, k, and T numbers. We also present several methods in which invariants may be used to classify a given configuration.
authors.affiliation: The Harker School, San Jose, CA 95128, USA.
authors.forename: Kai-Siang
authors.initials: KS
authors.lastname: Ang
authors.affiliation: University of Illinois, Chicago, IL 60607, USA. Electronic address: schapos@uic.edu.
authors.forename: Laura P
authors.initials: LP
authors.lastname: Schaposnik
mesh_terms: D002213:Capsid / Q000737:chemistry*; D036022:Capsid Proteins / Q000737:chemistry*; D008958:Models, Molecular; D008962:Models, Theoretical; D014771:Virion / Q000737:chemistry
chemical_list: D036022:Capsid Proteins
keywords: Capsomer; Disymmetron; Icosahedral symmetry; Icosahedral viruses; Pentasymmetron; Triangulation number; Trisymmetron; Virus capsid structure