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Wilson statistics: derivation, generalization and applications to electron cryomicroscopy

Wilson statistics: derivation, generalization and applications to electron cryomicroscopy 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Crystallographica Section A Foundations of Crystallography Wiley

Wilson statistics: derivation, generalization and applications to electron cryomicroscopy

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Publisher
Wiley
Copyright
Copyright © 2021 Wiley Subscription Services, Inc., A Wiley Company
ISSN
0108-7673
eISSN
1600-5724
DOI
10.1107/s205327332100752x
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Crystallographica Section A Foundations of CrystallographyWiley

Published: Sep 1, 2021

Keywords: power spectrum

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