Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces
Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces
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分子替换的数学方面。
DOI：
10.1107/s2053273317007227
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Zucker, Steven M.
中科院分区：
文献类型：
--
作者：
Chirikjian, Gregory S.;Sajjadi, Sajdeh;Shiffman, Bernard;Zucker, Steven M.
在分子置换（MR）搜索中，探索运动空间以确定晶体学不对称单元中大分子刚体模型的适当位置。MR搜索中的非冗余运动空间的属性，称为“运动空间”，是这一系列论文的主题。本文，在该系列的第四，建立在其他显示，当一个大分子晶体的空间群可以被分解成两个空间子群的产品，只有共享晶格平移组，组的分解提供了不同的分解相应的运动空间。然后，可以通过在平移子空间和旋转子空间的区域之间进行权衡来实现MR搜索。本文的结果限制了这些子空间的形状和大小。当空间群被分解为正常比伯巴赫子群和对称子群的乘积时，就会产生特殊的选择（这在蛋白质晶体学中遇到的空间群中很常见）。Sohncke空间群的例子被用来说明三维情况下的一般理论（这是MR的相关情况），但本文中的一般理论适用于任何维度。
In molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension.