ArticleActa crystallographica. Section A, Foundations and advances2021
Wilson statistics: derivation, generalization and applications to electron cryomicroscopy.
Article in Acta crystallographica. Section A, Foundations and advances, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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11 citing papers in PubMed.
- Confidence-guided cryo-EM map optimisation with LocScale-2.0.Nature communications · 2026Article
- Subspace Method of Moments forSIAM journal on imaging sciences · 2026Article
- Sensitive detection of structural dynamics using a statistical framework for comparative crystallography.Science advances · 2025Article
- Robust and automatic beamstop shadow outlier rejection: combining crystallographic statistics with modern clustering under a semi-supervised learning strategy.Acta crystallographica. Section D, Structural biology · 2024Article
- Cryo-EM Heterogeneity Analysis using Regularized Covariance Estimation and Kernel Regression.bioRxiv : the preprint server for biology · 2024Article
- Moment-based metrics for molecules computable from cryogenic electron microscopy images.Biological imaging · 2024Article
- Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Transformations between rotational and translational invariants formulated in reciprocal spaces.Journal of structural biology: X · 2023Article
- Toward Single Particle Reconstruction without Particle Picking: Breaking the Detection Limit.SIAM journal on imaging sciences · 2023Article
- Electron scattering properties of biological macromolecules and their use for cryo-EM map sharpening.Faraday discussions · 2022Review
- A molecular prior distribution for Bayesian inference based on Wilson statistics.Computer methods and programs in biomedicine · 2022Article
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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.
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