{"title":"Efficient high-resolution refinement in cryo-EM with stochastic gradient descent.","authors":"Bogdan Toader, Marcus A Brubaker, Roy R Lederman","doi":"10.1107/S205979832500511X","DOIUrl":null,"url":null,"abstract":"<p><p>Electron cryo-microscopy (cryo-EM) is an imaging technique that is widely used in structural biology to determine the three-dimensional structure of biological molecules from noisy two-dimensional projections with unknown orientations. As the typical pipeline involves processing large amounts of data, efficient algorithms are crucial for fast and reliable results. The stochastic gradient descent (SGD) algorithm has been used to improve the speed of ab initio reconstruction, which results in an initial, low-resolution estimation of the volume representing the molecule of interest, but has yet to be applied successfully in the high-resolution regime, where expectation-maximization algorithms achieve state-of-the-art results, at a high computational cost. In this article, we investigate the conditioning of the optimization problem and show that the large condition number prevents the successful application of gradient descent-based methods at high resolution. Our results include a theoretical analysis of the condition number of the optimization problem in a simplified setting where the individual projection directions are known, an algorithm based on computing a diagonal preconditioner using Hutchinson's diagonal estimator and numerical experiments showing the improvement in the convergence speed when using the estimated preconditioner with SGD. The preconditioned SGD approach can potentially enable a simple and unified approach to ab initio reconstruction and high-resolution refinement with faster convergence speed and higher flexibility, and our results are a promising step in this direction.</p>","PeriodicalId":7116,"journal":{"name":"Acta Crystallographica. Section D, Structural Biology","volume":" ","pages":"327-343"},"PeriodicalIF":2.6000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Crystallographica. Section D, Structural Biology","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.1107/S205979832500511X","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/6/23 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"BIOCHEMICAL RESEARCH METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Electron cryo-microscopy (cryo-EM) is an imaging technique that is widely used in structural biology to determine the three-dimensional structure of biological molecules from noisy two-dimensional projections with unknown orientations. As the typical pipeline involves processing large amounts of data, efficient algorithms are crucial for fast and reliable results. The stochastic gradient descent (SGD) algorithm has been used to improve the speed of ab initio reconstruction, which results in an initial, low-resolution estimation of the volume representing the molecule of interest, but has yet to be applied successfully in the high-resolution regime, where expectation-maximization algorithms achieve state-of-the-art results, at a high computational cost. In this article, we investigate the conditioning of the optimization problem and show that the large condition number prevents the successful application of gradient descent-based methods at high resolution. Our results include a theoretical analysis of the condition number of the optimization problem in a simplified setting where the individual projection directions are known, an algorithm based on computing a diagonal preconditioner using Hutchinson's diagonal estimator and numerical experiments showing the improvement in the convergence speed when using the estimated preconditioner with SGD. The preconditioned SGD approach can potentially enable a simple and unified approach to ab initio reconstruction and high-resolution refinement with faster convergence speed and higher flexibility, and our results are a promising step in this direction.
期刊介绍:
Acta Crystallographica Section D welcomes the submission of articles covering any aspect of structural biology, with a particular emphasis on the structures of biological macromolecules or the methods used to determine them.
Reports on new structures of biological importance may address the smallest macromolecules to the largest complex molecular machines. These structures may have been determined using any structural biology technique including crystallography, NMR, cryoEM and/or other techniques. The key criterion is that such articles must present significant new insights into biological, chemical or medical sciences. The inclusion of complementary data that support the conclusions drawn from the structural studies (such as binding studies, mass spectrometry, enzyme assays, or analysis of mutants or other modified forms of biological macromolecule) is encouraged.
Methods articles may include new approaches to any aspect of biological structure determination or structure analysis but will only be accepted where they focus on new methods that are demonstrated to be of general applicability and importance to structural biology. Articles describing particularly difficult problems in structural biology are also welcomed, if the analysis would provide useful insights to others facing similar problems.