ArticleSIAM journal on imaging sciences2015
Covariance Matrix Estimation for the Cryo-EM Heterogeneity Problem.
Article in SIAM journal on imaging sciences, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 33 papers.
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Who cites it
33 citing papers in PubMed, 69 citations in OpenAlex.
- How many (distinguishable) classes can we identify in single-particle analysis?Acta crystallographica. Section D, Structural biology · 2025Article
- Cryo-EM heterogeneity analysis using regularized covariance estimation and kernel regression.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Cryo-EM Heterogeneity Analysis using Regularized Covariance Estimation and Kernel Regression.bioRxiv : the preprint server for biology · 2024Article
- Algebraic constraints and algorithms for common lines in cryo-EM.Biological imaging · 2024Article
- MDSPACE and MDTOMO Software for Extracting Continuous Conformational Landscapes from Datasets of Single Particle Images and Subtomograms Based on Molecular Dynamics Simulations: Latest Developments in ContinuousFlex Software Package.International journal of molecular sciences · 2023Article
- Methods for Cryo-EM Single Particle Reconstruction of Macromolecules Having Continuous Heterogeneity.Journal of molecular biology · 2023Review
- Deep generative modeling for volume reconstruction in cryo-electron microscopy.Journal of structural biology · 2022Review
- Emerging Themes in CryoEM─Single Particle Analysis Image Processing.Chemical reviews · 2022Review
- Visualizing Conformational Space of Functional Biomolecular Complexes by Deep Manifold Learning.International journal of molecular sciences · 2022Article
- Data-driven determination of number of discrete conformations in single-particle cryo-EM.Computer methods and programs in biomedicine · 2022Article
- Probing Structural Perturbation of Biomolecules by Extracting Cryo-EM Data Heterogeneity.Biomolecules · 2022Review
- Refinement of AlphaFold2 models against experimental and hybrid cryo-EM density maps.QRB discovery · 2022Article
- A Bayesian approach to extracting free-energy profiles from cryo-electron microscopy experiments.Scientific reports · 2021Article
- Principal component analysis is limited to low-resolution analysis in cryoEM.Acta crystallographica. Section D, Structural biology · 2021Article
- HEMNMA-3D: Cryo Electron Tomography Method Based on Normal Mode Analysis to Study Continuous Conformational Variability of Macromolecular Complexes.Frontiers in molecular biosciences · 2021Article
- A Representation Theory Perspective on Simultaneous Alignment and Classification.Applied and computational harmonic analysis · 2020Article
- Computational Methods for Single-Particle Electron Cryomicroscopy.Annual review of biomedical data science · 2020Review
- Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes.Inverse problems · 2020Article
- Hybrid Electron Microscopy Normal Mode Analysis with Scipion.Protein science : a publication of the Protein Society · 2020Article
- Separating distinct structures of multiple macromolecular assemblies from cryo-EM projections.Journal of structural biology · 2020Article
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Authors and funding
3 authors at 2 institutions in 1 country.
Funding
Abstract
In cryo-electron microscopy (cryo-EM), a microscope generates a top view of a sample of randomly oriented copies of a molecule. The problem of single particle reconstruction (SPR) from cryo-EM is to use the resulting set of noisy two-dimensional projection images taken at unknown directions to reconstruct the three-dimensional (3D) structure of the molecule. In some situations, the molecule under examination exhibits structural variability, which poses a fundamental challenge in SPR. The heterogeneity problem is the task of mapping the space of conformational states of a molecule. It has been previously suggested that the leading eigenvectors of the covariance matrix of the 3D molecules can be used to solve the heterogeneity problem. Estimating the covariance matrix is challenging, since only projections of the molecules are observed, but not the molecules themselves. In this paper, we formulate a general problem of covariance estimation from noisy projections of samples. This problem has intimate connections with matrix completion problems and high-dimensional principal component analysis. We propose an estimator and prove its consistency. When there are finitely many heterogeneity classes, the spectrum of the estimated covariance matrix reveals the number of classes. The estimator can be found as the solution to a certain linear system. In the cryo-EM case, the linear operator to be inverted, which we term the projection covariance transform, is an important object in covariance estimation for tomographic problems involving structural variation. Inverting it involves applying a filter akin to the ramp filter in tomography. We design a basis in which this linear operator is sparse and thus can be tractably inverted despite its large size. We demonstrate via numerical experiments on synthetic datasets the robustness of our algorithm to high levels of noise.
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