Refaat L S, Tate C, Woolfson M M
Physics Department, University of York, Heslington, England.
Acta Crystallogr D Biol Crystallogr. 1996 Mar 1;52(Pt 2):252-6. doi: 10.1107/S0907444995008456.
In the conventional histogram-matching technique for phase extension and refinement for proteins a simple one-to-one transformation is made in the protein region to modify calculated density so that it will have some target histogram in addition to solvent flattening. This work describes an investigation where the density modification takes into account not only the current calculated density at a grid point but also some characteristic of the environment of the grid point within some distance R. This characteristic can be one of the local maximum density, the local minimum density or the local variance of density. The grid points are divided into ten groups, each containing the same number of grid points, for ten different ranges of value of the local characteristic. The ten groups are modified to give different histograms, each corresponding to that obtained under the same circumstances from a structure similar to the one under investigation. This process is referred to as the double-histogram matching method. Other processes which have been investigated are the weighting of structure factors when calculating maps with estimated phases and also the use of a factor to dampen the change of density and so control the refinement process. Two protein structures were used in numerical trials, RNApl [Bezborodova, Ermekbaeva, Shlyapnikov, Polyakov & Bezborodov (1988). Biokhimiya, 53, 965-973] and 2-Zn insulin [Baker, Blundell, Cutfield, Cutfield, Dodson, Dodson, Hodgkin, Hubbard, lsaacs, Reynolds, Sakabe, Sakabe & Vijayan (1988). Philos. Trans. R. Soc. London Ser. B, 319, 456--469]. Comparison of the proposed procedures with the normal histogram-matching technique without structure-factor weighting or damping gives mean phase errors reduced by up to 10 degrees with map correlation coefficients improved by as much as 0.14. Compared to the normal histogram used with weighting of structure factors and damping, the improvement due to the use of the double-histogram method is usually of order 4 degrees in mean phase error and an increase of 0.06-0.08 in the map correlation coefficient. It is concluded that the most reliable results are found with the local-maximum condition and with R in the range 0.5-0.6 A.
在用于蛋白质相位扩展和优化的传统直方图匹配技术中，在蛋白质区域进行简单的一对一变换，以修改计算得到的密度，使其除了溶剂扁平化之外还具有某种目标直方图。本文描述了一项研究，其中密度修改不仅考虑了网格点处当前计算得到的密度，还考虑了在距离R内网格点环境的某些特征。该特征可以是局部最大密度、局部最小密度或密度的局部方差之一。网格点被分为十组，每组包含相同数量的网格点，对应于局部特征值的十个不同范围。对这十组进行修改，以给出不同的直方图，每组直方图都对应于在相同情况下从与所研究结构相似的结构中获得的直方图。这个过程被称为双直方图匹配方法。研究过的其他过程包括在使用估计相位计算图谱时对结构因子进行加权，以及使用一个因子来抑制密度变化从而控制优化过程。在数值试验中使用了两种蛋白质结构，RNApl [Bezborodova, Ermekbaeva, Shlyapnikov, Polyakov & Bezborodov (1988). Biokhimiya, 53, 965 - 973] 和2 - Zn胰岛素 [Baker, Blundell, Cutfield, Cutfield, Dodson, Dodson, Hodgkin, Hubbard, lsaacs, Reynolds, Sakabe, Sakabe & Vijayan (1988). Philos. Trans. R. Soc. London Ser. B, 319, 456 - 469]。将所提出的程序与未进行结构因子加权或阻尼的正常直方图匹配技术进行比较，平均相位误差最多降低了10度，图谱相关系数提高了多达0.14。与使用结构因子加权和阻尼的正常直方图相比，使用双直方图方法带来的改进通常是平均相位误差降低约4度，图谱相关系数增加0.06 - 0.08。得出的结论是，在局部最大条件且R在0.5 - 0.6 Å范围内时能得到最可靠的结果。
