Li Hui, He Meng, Zhang Ze
Beijing University of Technology, Beijing, 100124, People's Republic of China.
CAS Key Laboratory of Nanosystem and Hierarchical Fabrication, National Center for Nanoscience and Technology, Beijing, 100190, People's Republic of China.
Acta Crystallogr A Found Adv. 2015 Sep;71(Pt 5):526-33. doi: 10.1107/S2053273315012103. Epub 2015 Jul 22.
The core theme of X-ray crystallography is reconstructing the electron-density distribution of crystals under the constraints of observed diffraction data. Nevertheless, reconstruction of the electron-density distribution by straightforward Fourier synthesis is usually hindered due to the well known phase problem and the finite resolution of diffraction data. In analogy with optical imaging systems, the reconstructed electron-density map may be regarded as the image of the real electron-density distribution in crystals. Inspired by image definition evaluation functions applied in the auto-focusing process, two evaluation functions are proposed for the reconstructed electron-density images. One of them is based on the atomicity of the electron-density distribution and properties of Fourier synthesis. Tests were performed on synthetic data of known structures, and it was found that this evaluation function can distinguish the correctly reconstructed electron-density image from wrong ones when diffraction data of atomic resolution are available. An algorithm was established based on this evaluation function and applied in reconstructing the electron-density image from the synthetic data of known structures. The other evaluation function, which is based on the positivity of electron density and constrained power spectrum entropy maximization, was designed for cases where only diffraction data of rather limited resolution are available. Tests on the synthetic data indicate that this evaluation function may identify the correct phase set even for a data set with resolution as low as 3.5 Å. Though no algorithm for structure solution has been figured out based on the latter function, the results presented here provide a new perspective on the phase problem.
X射线晶体学的核心主题是在观测到的衍射数据的约束下重建晶体的电子密度分布。然而，由于众所周知的相位问题和衍射数据的有限分辨率，通过直接傅里叶合成重建电子密度分布通常会受到阻碍。类似于光学成像系统，重建的电子密度图可以被视为晶体中真实电子密度分布的图像。受自动聚焦过程中应用的图像清晰度评估函数的启发，为重建的电子密度图像提出了两个评估函数。其中一个基于电子密度分布的原子性和傅里叶合成的性质。对已知结构的合成数据进行了测试，发现当有原子分辨率的衍射数据时，该评估函数可以区分正确重建的电子密度图像和错误的图像。基于该评估函数建立了一种算法，并将其应用于从已知结构的合成数据中重建电子密度图像。另一个评估函数基于电子密度的正性和约束功率谱熵最大化，是为只有相当有限分辨率的衍射数据的情况设计的。对合成数据的测试表明，即使对于分辨率低至3.5 Å的数据集，该评估函数也可以识别正确的相位集。尽管尚未基于后一个函数想出结构解析算法，但此处给出的结果为相位问题提供了新的视角。
