Keef T, Twarock R
Department of Mathematics, University of York, York, YO10 5DD, UK.
J Math Biol. 2009 Sep;59(3):287-313. doi: 10.1007/s00285-008-0228-5. Epub 2008 Nov 1.
Since the seminal work of Caspar and Klug on the structure of the protein containers that encapsulate and hence protect the viral genome, it has been recognised that icosahedral symmetry is crucial for the structural organisation of viruses. In particular, icosahedral symmetry has been invoked in order to predict the surface structures of viral capsids in terms of tessellations or tilings that schematically encode the locations of the protein subunits in the capsids. Whilst this approach is capable of predicting the relative locations of the proteins in the capsids, information on their tertiary structures and the organisation of the viral genome within the capsid are inaccessible. We develop here a mathematical framework based on affine extensions of the icosahedral group that allows us to describe those aspects of the three-dimensional structure of simple viruses. This approach complements Caspar-Klug theory and provides details on virus structure that have not been accessible with previous methods, implying that icosahedral symmetry is more important for virus architecture than previously appreciated.
自卡斯帕（Caspar）和克鲁格（Klug）关于封装并因此保护病毒基因组的蛋白质容器结构的开创性工作以来，人们已经认识到二十面体对称性对于病毒的结构组织至关重要。特别是，二十面体对称性已被用于根据镶嵌或平铺来预测病毒衣壳的表面结构，这些镶嵌或平铺示意性地编码了衣壳中蛋白质亚基的位置。虽然这种方法能够预测衣壳中蛋白质的相对位置，但关于它们的三级结构以及衣壳内病毒基因组的组织信息却无法获得。我们在此开发了一个基于二十面体群仿射扩展的数学框架，该框架使我们能够描述简单病毒三维结构的那些方面。这种方法补充了卡斯帕 - 克鲁格理论，并提供了以前方法无法获得的病毒结构细节，这意味着二十面体对称性对病毒结构的重要性比以前所认识到的更高。
