Wilson statistics: derivation, generalization and applications to electron cryomicroscopy
Wilson statistics: derivation, generalization and applications to electron cryomicroscopy
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DOI：
10.1107/s205327332100752x
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发表时间：
2021-09-01
影响因子：
1.8
通讯作者：
Singer, Amit
中科院分区：
文献类型：
--
作者：
Singer, Amit
蛋白质在高频下的功率谱可以用平坦的威尔逊统计量很好地描述。因此，威尔逊统计在X射线晶体学和最近的电子低温显微镜（cryo-EM）中起着重要作用。具体而言，现代计算方法的三维地图锐化和原子建模的大分子单粒子cryo-EM是基于威尔逊统计。在这里，第一个严格的数学推导威尔逊统计提供。推导精确地指出了威尔逊统计的有效性在大分子的大小方面的制度。此外，分析自然会导致统计量的协方差和高阶谱的概括。这些反过来又提供了一个理论基础的假设基础广泛的贝叶斯推理框架三维细化和解释的限制，基于自相关的方法在冷冻EM。
The power spectrum of proteins at high frequencies is remarkably well described by the flat Wilson statistics. Wilson statistics therefore plays a significant role in X-ray crystallography and more recently in electron cryomicroscopy (cryo-EM). Specifically, modern computational methods for three-dimensional map sharpening and atomic modelling of macromolecules by single-particle cryo-EM are based on Wilson statistics. Here the first rigorous mathematical derivation of Wilson statistics is provided. The derivation pinpoints the regime of validity of Wilson statistics in terms of the size of the macromolecule. Moreover, the analysis naturally leads to generalizations of the statistics to covariance and higher-order spectra. These in turn provide a theoretical foundation for assumptions underlying the widespread Bayesian inference framework for three-dimensional refinement and for explaining the limitations of autocorrelation-based methods in cryo-EM.