The (Fo-Fc) Fourier synthesis:: a probabilistic study
The (Fo-Fc) Fourier synthesis:: a probabilistic study
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DOI：
10.1107/s0108767308018503
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发表时间：
2008-09-01
影响因子：
1.8
通讯作者：
Siliqi, Dritan
中科院分区：
文献类型：
--
作者：
Caliandro, Rocco;Carrozzini, Benedetta;Siliqi, Dritan
（F-o - F-c）和（2F(o) - F-c）傅立叶合成被认为是恢复结构剩余部分和校正晶体结构模型的最强大的工具。采用概率方法推导了系数（F-o - F-c）期望值的方差公式。这使我们能够更好地理解差分傅立叶合成的特征；特别是，通过标准傅立叶合成将相位良好的反射子集与最佳相位的反射子集分离开来。设计了一种基于差分傅里叶映射的电子密度修正的迭代方法，以方差较小的反射集作为杠杆臂，提高方差较大反射的相位和模量估计。新程序（DEDM）已经在一系列广泛的测试结构上实现和验证，这些测试结构的部分模型是通过分子替换或应用于实验电子密度图的自动模型构建程序获得的。在所有测试用例中，差分傅立叶合成的相位和模量估计都得到了改善；因此，在目标结构偏离局部模型的区域，差分傅里叶映射的质量也得到了改善。提出了一种将DEDM与标准电子密度修饰技术相结合的新方法，可以显著降低相位误差。该程序可被视为进一步发展的起点。
(F-o - F-c) and (2F(o) - F-c) Fourier syntheses are considered the most powerful tools for recovering the remainder of a structure and for correcting crystal structure models. A probabilistic approach has been applied to derive the formula for the variance for the expected value of the coefficient (F-o - F-c). This has allowed a better understanding of the features of the difference Fourier synthesis; in particular, a subset of well phased reflections has been separated from the subset of reflections best phased by the standard Fo Fourier synthesis. An iterative procedure, based on the electron-density modification of the difference Fourier map, has been devised which aims to improve phase and modulus estimates of the reflections with higher variance value, by using as lever arm the set of reflections with lower variance value. The new procedure (DEDM) has been implemented and verified on a wide set of test structures, the partial models of which were obtained by molecular replacement or by automatic model-building routines applied to experimental electron-density maps. Phase and modulus estimates of the difference Fourier syntheses improve in all the test cases; as a consequence, the quality of the difference Fourier maps also improves in the region where the target structure deviates from the partial model. A new procedure is suggested, combining DEDM with standard electron-density modification techniques, which leads to significant reduction of the phase errors. The procedure may be considered a starting point for further developments.