×

Cryo-EM reconstruction of continuous heterogeneity by Laplacian spectral volumes. (English) Zbl 07161831


MSC:

94Axx Communication, information
92Cxx Physiological, cellular and medical topics
65Kxx Numerical methods for mathematical programming, optimization and variational techniques
PDF BibTeX XML Cite
Full Text: DOI arXiv Link

References:

[1] Frank J 2006 Three-Dimensional Electron Microscopy of Macromolecular Assemblies (Oxford: Oxford University Press)
[2] Vulović M, Ravelli R B, van Vliet L J, Koster A J, Lazić I, Lücken U, Rullgård H, Öktem O and Rieger B 2013 Image formation modeling in cryo-electron microscopy J. Struct. Biol.183 19-32
[3] Kühlbrandt W 2014 The resolution revolution Science343 1443-4
[4] Amunts A, Brown A, Bai X-C, Llácer J L, Hussain T, Emsley P, Long F, Murshudov G, Scheres S H W and Ramakrishnan V 2014 Structure of the yeast mitochondrial large ribosomal subunit Science343 1485-9
[5] Liao M, Cao E, Julius D and Cheng Y 2013 Structure of the TRPV1 ion channel determined by electron cryo-microscopy Nature504 107-12
[6] Bartesaghi A et al 2018 Atomic resolution cryo-EM structure of β-galactosidase Structure26 848-56.e3
[7] Barnett A, Greengard L, Pataki A and Spivak M 2017 Rapid solution of the cryo-EM reconstruction problem by frequency marching SIAM J. Imaging Sci.10 1170-95 · Zbl 1380.92036
[8] Cheng Y, Grigorieff N, Penczek P A and Walz T 2015 A primer to single-particle cryo-electron microscopy Cell161 438-49
[9] Milne J L, Borgnia M J, Bartesaghi A, Tran E E H, Earl L A, Schauder D M, Lengyel J, Pierson J, Patwardhan A and Subramaniam S 2012 Cryo-electron microscopy—a primer for the non-microscopist FEBS J.280 28-45
[10] Vinothkumar K R and Henderson R 2016 Single particle electron cryomicroscopy: trends, issues and future perspective Q. Rev. Biophys.49 1-25
[11] Scheres S H 2012 A Bayesian view on cryo-EM structure determination J. Mol. Biol.415 406-18
[12] Yasuda R, Noji H, Kinosita K and Yoshida M 1998 F1-ATPase is a highly efficient molecular motor that rotates with discrete 120° Steps Cell93 1117-24
[13] Scheres S H 2012 RELION: implementation of a Bayesian approach to cryo-EM structure determination J. Struct. Biol.180 519-30
[14] Punjani A, Rubinstein J L, Fleet D J and Brubaker M A 2017 cryoSPARC: algorithms for rapid unsupervised cryo-EM structure determination Nat. Methods14 290-6
[15] Lyumkis D, Brilot A F, Theobald D L and Grigorieff N 2013 Likelihood-based classification of cryo-EM images using FREALIGN J. Struct. Biol.183 377-88
[16] Grant T, Rohou A and Grigorieff N 2018 cisTEM, user-friendly software for single-particle image processing Elife7 377-88
[17] Tang G, Peng L, Baldwin P R, Mann D S, Jiang W, Rees I and Ludtke S J 2007 EMAN2: an extensible image processing suite for electron microscopy J. Struct. Biol.157 38-46
[18] Liu W and Frank J 1995 Estimation of variance distribution in three-dimensional reconstruction I Theory J. Opt. Soc. Am. A 12 2615
[19] Penczek P A 2002 Variance in three-dimensional reconstructions from projections Proc. IEEE Int. Symp. on Biomedical Imaging pp 749-52
[20] Penczek P A, Yang C, Frank J and Spahn C M 2006 Estimation of variance in single-particle reconstruction using the bootstrap technique J. Struct. Biol.154 168-83
[21] Penczek P A, Frank J and Spahn C M 2006 A method of focused classification, based on the bootstrap 3D variance analysis, and its application to EF-G-dependent translocation J. Struct. Biol.154 184-94
[22] Penczek P A, Kimmel M and Spahn C M 2011 Identifying conformational states of macromolecules by eigen-analysis of resampled cryo-EM images Structure19 1582-90
[23] Liao H Y and Frank J 2010 Classification by bootstrapping in single particle methods IEEE Int. Symp. on Biomedical Imaging From Nano to Macrovol 29169 pp 169-72
[24] Katsevich E, Katsevich A and Singer A 2015 Covariance matrix estimation for the cryo-EM heterogeneity problem SIAM J. Imaging Sci.8 126-85 · Zbl 1362.92036
[25] Andén J, Katsevich E and Singer A 2015 Covariance estimation using conjugate gradient for 3D classification in cryo-EM IEEE 12th Int. Symp. on Biomedical Imaging pp 200-4
[26] Andén J and Singer A 2018 Structural variability from noisy tomographic projections SIAM J. Imaging Sci.11 1441-92 · Zbl 1401.92117
[27] Tagare H D, Kucukelbir A, Sigworth F J, Wang H and Rao M 2015 Directly reconstructing principal components of heterogeneous particles from cryo-EM images J. Struct. Biol.191 245-62
[28] Dashti A et al 2014 Trajectories of the ribosome as a Brownian nanomachine Proc. Natl. Acad. Sci.111 17492-7
[29] Schwander P, Fung R and Ourmazd A 2014 Conformations of macromolecules and their complexes from heterogeneous datasets Phil. Trans. R. Soc. B 369 1-8
[30] Frank J and Ourmazd A 2016 Continuous changes in structure mapped by manifold embedding of single-particle data in cryo-EM Methods100 61-7
[31] Dashti A, Ben Hail D, Mashayekhi G, Schwander P, des Georges A, Frank J and Ourmazd A 2018 Functional pathways of biomolecules retrieved from single-particle snapshots Technical Report (https://doi.org/10.1101/291922)
[32] Coifman R R, Lafon S, Lee A B, Maggioni M, Nadler B, Warner F and Zucker S W 2005 Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps Proc. Natl. Acad. Sci.102 7426-31 · Zbl 1405.42043
[33] Coifman R R and Lafon S 2006 Diffusion maps Appl. Comput. Harmon. Anal.21 5-30 · Zbl 1095.68094
[34] Wang C and Mahadevan S 2009 Manifold alignment without correspondence Int. Jt. Conf. Artif. Intell.1 1273-8
[35] Cui Z, Chang H, Shan S and Chen X 2014 Generalized unsupervised manifold alignment Neural Information Processing Systems pp 2429-37
[36] Nakane T, Kimanius D, Lindahl E and Scheres S H 2018 Characterisation of molecular motions in cryo-EM single-particle data by multi-body refinement in RELION eLife7 1-18
[37] Jin Q, Sorzano C O S, de la Rosa J M, Bilbao-Castro J R, Núñez-Ramírez R, Llorca O, Tama F and Jonić S 2014 Iterative elastic 3D-to-2D alignment method using normal modes for studying structural dynamics of large macromolecular complexes Structure22 496-506
[38] Schilbach S, Hantsche M, Tegunov D, Dienemann C, Wigge C, Urlaub H and Cramer P 2017 Structures of transcription pre-initiation complex with TFIIH and mediator Nature551 204-9
[39] Sorzano C O S et al 2019 Survey of the analysis of continuous conformational variability of biological macromolecules by electron microscopy Acta Crystallogr. F 75 19-32
[40] Wang L, Shkolnisky Y and Singer A 2013 A Fourier-based approach for iterative 3D reconstruction from cryo-EM images (arXiv:1307.5824)
[41] Dutt A and Rokhlin V 1993 Fast Fourier transforms for nonequispaced data SIAM J. Sci. Comput.14 1368-93 · Zbl 0791.65108
[42] Greengard L and Lee J-Y 2004 Accelerating the nonuniform fast Fourier transform SIAM Rev.46 443-54 · Zbl 1064.65156
[43] Belkin M and Niyogi P 2003 Laplacian eigenmaps for dimensionality reduction and data representation Neural Comput.15 1373-96 · Zbl 1085.68119
[44] Natterer F 2001 The Mathematics of Computerized Tomography (https://doi.org/10.1137/1.9780898719284) · Zbl 0973.92020
[45] Grebenkov D S and Nguyen B T 2013 Geometrical structure of Laplacian eigenfunctions SIAM Rev.55 601-67 · Zbl 1290.35157
[46] Aflalo Y, Brezis H and Kimmel R 2015 On the optimality of shape and data representation in the spectral domain SIAM J. Imaging Sci.8 1141-60 · Zbl 1360.94038
[47] Greblicki W and Pawlak M 1985 Fourier and Hermite series estimates of regression functions Ann. Inst. Stat. Math.37 443 · Zbl 0623.62029
[48] Liao H Y, Hashem Y and Frank J 2015 Efficient estimation of three-dimensional covariance and its application in the analysis of heterogeneous samples in cryo-electron microscopy Structure23 1129-37
[49] Herman G T and Kalinowski M 2008 Classification of heterogeneous electron microscopic projections into homogeneous subsets Ultramicroscopy108 327-38
[50] Shatsky M, Hall R J, Nogales E, Malik J and Brenner S E 2010 Automated multi-model reconstruction from single-particle electron microscopy data J. Struct. Biol.170 98-108
[51] Mallat S 2009 A Wavelet Tour of Signal Processing (Amsterdam: Elsevier) (https://doi.org/10.1016/B978-0-12-374370-1.X0001-8) · Zbl 1170.94003
[52] Kay S M 1993 Fundamentals of Statistical Signal Processing: Estimation Theory (Upper Saddle River, NJ: Prentice-Hall) · Zbl 0803.62002
[53] von Luxburg U 2007 A tutorial on spectral clustering Stat. Comput.17 395-416
[54] Friedman J H, Bentley J L and Finkel R A 1977 An algorithm for finding best matches in logarithmic expected time ACM Trans. Math. Softw.3 209-26 · Zbl 0364.68037
[55] Stewart G W 2002 A Krylov-Schur algorithm for large eigenproblems SIAM J. Matrix Anal. Appl.23 601-14 · Zbl 1003.65045
[56] McQueen J, Meilă M, VanderPlas J and Zhang Z 2016 Megaman: scalable manifold learning in python J. Mach. Learn. Res.17 5176-80
[57] Olson L N and Schroder J B 2018 PyAMG: algebraic multigrid solvers in python v4.0
[58] Barnett A H, Magland J F and af Klinteberg L 2019 A parallel non-uniform fast Fourier transform library based on an ‘exponential of semicircle’ kernel SIAM J. Sci. Comput. Press. 1-25 · Zbl 07123199
[59] Golub G H and Van Loan C F 2013 Matrix Computations 4th edn (Baltimore, MD: Johns Hopkins University Press) · Zbl 1268.65037
[60] Trefethen L N and Bau D 1997 Numerical Linear Algebra (Philadelphia, PA: SIAM)
[61] von Luxburg U, Belkin M and Bousquet O 2008 Consistency of spectral clustering Ann. Stat.36 555-86 · Zbl 1133.62045
[62] Rosasco L, Belkin M and De Vito E 2010 On learning with integral operators J. Mach. Learn. Res.11 905-34 · Zbl 1242.62059
[63] Lee A B and Izbicki R 2016 A spectral series approach to high-dimensional nonparametric regression Electron. J. Stat.10 423-63 · Zbl 1332.62133
[64] Nadler B, Lafon S, Coifman R R and Kevrekidis I G 2005 Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators Neural Information Processing Systems pp 955-62
[65] Ting D, Huang L and Jordan M 2010 An analysis of the convergence of graph laplacians Int. Conf. on Machine Learning
[66] Henderson R et al 2012 Outcome of the first electron microscopy validation task force meeting Structure20 205-14
[67] Belkin M and Niyogi P 2004 Semi-supervised learning on Riemannian manifolds Mach. Learn.56 209-39 · Zbl 1089.68086
[68] Zhou X and Srebro N 2011 Error analysis of Laplacian eigenmaps for semi-supervised learning Int. Conf. on Artificial Intelligence and Statisticsvol 15 pp 901-8
[69] Moscovich A, Jaffe A and Nadler B 2017 Minimax-optimal semi-supervised regression on unknown manifolds Int. Conf. on Artificial Intelligence and Statisticsvol 54 pp 933-42
[70] Villoutreix P, Andén J, Lim B, Lu H, Kevrekidis I G, Singer A and Shvartsman S Y 2017 Synthesizing developmental trajectories PLOS Comput. Biol.13 1-15
[71] Singer A and Wu H-T 2013 Two-dimensional tomography from noisy projections taken at unknown random directions SIAM J. Imaging Sci.6 136-75 · Zbl 1279.68339
[72] Singer A 2006 Spectral independent component analysis Appl. Comput. Harmon. Anal.21 135-44 · Zbl 1095.94010
[73] Lederman R R and Singer A 2017 Continuously heterogeneous hyper-objects in cryo-EM and 3-D movies of many temporal dimensions (arXiv:1704.02899)
[74] Lederman R R, Andén J and Singer A 2019 Hyper-molecules: on the representation and recovery of dynamical structures, with application to flexible macro-molecular structures in cryo-EM Inverse Problems accepted
[75] Pettersen E F, Goddard T D, Huang C C, Couch G S, Greenblatt D M, Meng E C and Ferrin T E 2004 UCSF Chimera—a visualization system for exploratory research and analysis J. Comput. Chem.25 1605-12
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.