Wilson statistics: derivation, generalization and applications to electron cryomicroscopy
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 20, 2021
- Source ID
- 10.1107/s205327332100752x
Entities
People
- Amit Singer
Organizations
- Air Force Office of Scientific Research
- Gordon and Betty Moore Foundation
- National Institute of General Medical Sciences
- National Science Foundation Directorate for Mathematical & Physical Sciences
- National Science Foundation Directorate of Computer and Information Science and Engineering
- Simons Foundation