Eppley Institute for Research in Cancer and Allied Diseases, University of Nebraska Medical Center, 986805 Nebraska Medical Center, Omaha, NE 68198-6805, USA.
Acta Crystallogr D Struct Biol. 2021 Jun 1;77(Pt 6):790-798. doi: 10.1107/S2059798321003740. Epub 2021 May 14.
Two commensurately modulated structures (PDB entries 4n3e and 6sjj) were solved using translational noncrystallographic symmetry (tNCS). The data required the use of large supercells, sevenfold and ninefold, respectively, to properly index the reflections. Commensurately modulated structures can be challenging to solve. Molecular-replacement software such as Phaser can detect tNCS and either handle it automatically or, for more challenging situations, allow the user to enter a tNCS vector, which the software then uses to place the components. Although this approach has been successful in solving these types of challenging structures, it does not make it easy to understand the underlying modulation in the structure or how these two structures are related. An alternate view of this problem is that the atoms and associated parameters are following periodic atomic modulation functions (AMFs) in higher dimensional space, and what is being observed in these supercells are the points where these higher dimensional AMFs intersect physical 3D space. In this case, the two 3D structures, with a sevenfold and a ninefold superstructure, seem to be quite different. However, describing those structures within the higher dimensional superspace approach makes a strong case that they are closely related, as they show very similar AMFs and can be described with one unique (3+1)D structure, i.e. they are two different 3D intersections of the same (3+1)D structure.
使用平移非晶学对称（tNCS）解决了两个共调制结构（PDB 条目 4n3e 和 6sjj）。数据要求分别使用七倍和九倍的大超胞来正确索引反射。共调制结构可能难以解决。分子置换软件（如 Phaser）可以检测 tNCS，自动处理或在更具挑战性的情况下允许用户输入 tNCS 向量，软件随后使用该向量来放置组件。尽管这种方法在解决这些具有挑战性的结构方面取得了成功，但它并不能轻易理解结构中的基本调制或这两种结构之间的关系。这个问题的另一种观点是，原子及其相关参数遵循更高维空间中的周期性原子调制函数（AMF），而在这些超胞中观察到的是这些更高维 AMF 与物理 3D 空间相交的点。在这种情况下，具有七倍和九倍超结构的两个 3D 结构似乎非常不同。然而，在更高维超空间方法中描述这些结构，有力地表明它们是密切相关的，因为它们显示出非常相似的 AMF，可以用一个独特的（3+1）D 结构来描述，即它们是相同的（3+1）D 结构的两个不同的 3D 交点。
