Efficient high-resolution refinement in cryo-EM with stochastic gradient descent.

IF 2.6 4区 生物学 Q2 BIOCHEMICAL RESEARCH METHODS
Bogdan Toader, Marcus A Brubaker, Roy R Lederman
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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.

低温电镜随机梯度下降的高效高分辨率细化。
电子冷冻显微镜(cryo-EM)是一种广泛应用于结构生物学的成像技术,用于从具有未知方向的嘈杂二维投影中确定生物分子的三维结构。由于典型的管道涉及处理大量数据,因此高效的算法对于快速可靠的结果至关重要。随机梯度下降(SGD)算法已被用于提高从头算重建的速度,这导致对代表感兴趣分子的体积的初始、低分辨率估计,但尚未成功应用于高分辨率领域,其中期望最大化算法以高计算成本实现了最先进的结果。在本文中,我们研究了优化问题的条件,并表明大的条件数阻碍了基于梯度下降的方法在高分辨率下的成功应用。我们的结果包括在已知单个投影方向的简化设置下对优化问题条件数的理论分析,基于使用Hutchinson对角估计器计算对角预条件的算法和数值实验,表明使用SGD估计预条件时收敛速度的提高。预条件SGD方法可以实现一种简单统一的从头开始重建和高分辨率细化方法,具有更快的收敛速度和更高的灵活性,我们的研究结果是朝着这个方向迈出的有希望的一步。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Acta Crystallographica. Section D, Structural Biology
Acta Crystallographica. Section D, Structural Biology BIOCHEMICAL RESEARCH METHODSBIOCHEMISTRY &-BIOCHEMISTRY & MOLECULAR BIOLOGY
CiteScore
4.50
自引率
13.60%
发文量
216
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.
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