Ang Kai-Siang, Schaposnik Laura P
The Harker School, San Jose, CA 95128, USA.
University of Illinois, Chicago, IL 60607, USA.
J Struct Biol. 2017 Mar;197(3):340-349. doi: 10.1016/j.jsb.2017.01.001. Epub 2017 Jan 19.
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.
大型二十面体病毒衣壳由对称子组成，对称子是衣壳粒的有序排列。有三种类型的对称子：双对称子、三对称子和五对称子，它们具有不同的形状，分别以二十面体的二次、三次和五次对称轴为中心。辛科维茨和贝克（2010年）给出了仅由三对称子和五对称子构建二十面体结构的所有可能方式的分类，这要求三角剖分数T为奇数。在本文中，我们纳入双对称子，以获得由规则的五对称子、三对称子和双对称子形成的大型二十面体病毒的几何分类，给出所有数学上一致且理论上可能的解决方案。对于每一类解决方案，我们还提供了对称子大小的公式以及对h、k和T数的奇偶性限制。我们还介绍了几种可以使用不变量对给定构型进行分类的方法。
