Janner A
Institute for Theoretical Physics, Radboud University, Toernooiveld, 6525 ED Nijmegen, The Netherlands.
Acta Crystallogr D Biol Crystallogr. 2005 Mar;61(Pt 3):256-68. doi: 10.1107/S0907444904032706. Epub 2005 Feb 24.
The investigation of the geometry of the molecular envelope and channel in the proteins discussed in part I [Janner (2005a), Acta Cryst. D61, 247-255] is extended to axial-symmetric proteins with orders of rotation N = 5, 7, 8, 9 and 11, non-crystallographic in dimension 3. In these cases also, the vertices of the molecular form which encapsulate the C(alpha) backbone have integral coordinates (indices) in a symmetry-adapted basis which generates a polygonal lattice. As in the crystallographic case of part I, a characteristic rational axial ratio squared is observed that reduces to one the number of free lattice parameters and enhances the symmetry. Furthermore, there is a crystallographic scaling relation between the envelope and the channel which depends on the order of the axial symmetry and is expressible in terms of star polygons. Possible biological implications are suggested within a more general context.
在第一部分[詹纳（2005a），《晶体学报》D61卷，247 - 255页]中所讨论的蛋白质分子包膜和通道几何结构的研究，扩展到了三维非晶体学的、具有5、7、8、9和11次旋转对称性的轴对称蛋白质。在这些情况下，封装α - 碳骨架的分子形状的顶点，在一个生成多边形晶格的对称适配基中具有整数坐标（指标）。与第一部分的晶体学情况一样，观察到一个特征性的有理轴向比平方，它减少了自由晶格参数的数量并增强了对称性。此外，包膜和通道之间存在一种晶体学缩放关系，该关系取决于轴对称的次数，并且可以用星形多边形来表示。在更广泛的背景下提出了可能的生物学意义。
