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Maximum likelihood for high-noise group orbit estimation and single-particle cryo-EM [article]

Zhou Fan and Roy R. Lederman and Yi Sun and Tianhao Wang and Sheng Xu
2021 arXiv   pre-print
Motivated by applications to single-particle cryo-electron microscopy (cryo-EM), we study several problems of function estimation in a low SNR regime, where samples are observed under random rotations  ...  of cryo-EM as introduced by Bandeira, Blum-Smith, Kileel, Perry, Weed, and Wein.  ...  We would like to thank Fred Sigworth for helpful discussions about cryo-EM, and for suggesting to us the hemoglobin example. ZF was supported in part by NSF DMS-1916198.  ... 
arXiv:2107.01305v1 fatcat:mxfmbmytirhcpj4zg5t2yavse4

Estimation of Orientation and Camera Parameters from Cryo-Electron Microscopy Images with Variational Autoencoders and Generative Adversarial Networks [article]

Nina Miolane, Frédéric Poitevin, Yee-Ting Li, Susan Holmes
2021 arXiv   pre-print
This analysis leads us to design an estimation method for orientation and camera parameters of single-particle cryo-EM images, together with an outliers detection procedure.  ...  As such, it opens the door to geometric approaches for unsupervised estimations of orientations and camera parameters, making possible fast cryo-EM biomolecule reconstruction.  ...  Acknowledgments We thank Khanh Dao Duc and TJ Lane for very helpful comments on an earlier draft of the manuscript, and Daniel Ratner and Cornelius Gati for stimulating discussions and support throughout  ... 
arXiv:1911.08121v2 fatcat:l2snznfj6bgoznvkbotzyx4c6y

Single-particle cryo-electron microscopy: Mathematical theory, computational challenges, and opportunities [article]

Tamir Bendory, Alberto Bartesaghi, Amit Singer
2019 arXiv   pre-print
Based on these abstractions, we discuss some recent intriguing results in the mathematical theory of cryo-EM, and delineate relations with group theory, invariant theory, and information theory.  ...  Determining molecular structures requires a wide range of computational tools in a variety of fields, including signal processing, estimation and detection theory, high-dimensional statistics, convex and  ...  ACKNOWLEDGMENT We thank the anonymous reviewers and the editor for their valuable comments and suggestions.  ... 
arXiv:1908.00574v2 fatcat:lwbbis37e5ctjngflw3opjl4sy

Mathematics for cryo-electron microscopy [article]

Amit Singer
2018 arXiv   pre-print
Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules.  ...  This paper focuses on the mathematical principles underlying existing algorithms for structure determination using single particle cryo-EM.  ...  There are two aspects that make single particle reconstruction (SPR) from cryo-EM more challenging compared to classical CT.  ... 
arXiv:1803.06714v1 fatcat:cg5a2zhwkjfmzeqj44lunrhspa

The generalized method of moments for multi-reference alignment [article]

Asaf Abas, Tamir Bendory, Nir Sharon
2021 arXiv   pre-print
We begin by proving that the GMM estimator maintains its asymptotic optimality for statistical models with group symmetry, including MRA.  ...  We also formulate the GMM to estimate a three-dimensional molecular structure using cryo-electron microscopy and present numerical results on simulated data.  ...  GMM FOR CRYO-EM: A PROOF OF CONCEPT As aforementioned, the main motivation of this work stems from the task of reconstructing the 3-D structure of molecular structures using single-particle cryo-EM.  ... 
arXiv:2103.02215v2 fatcat:gwntrj32tfdopkkxzz3yok2d34

Dihedral multi-reference alignment [article]

Tamir Bendory, Dan Edidin, William Leeb, Nir Sharon
2022 arXiv   pre-print
This implies that the optimal estimation rate in the high noise regime is proportional to the square of the variance of the noise.  ...  Based on tools from invariant theory and algebraic geometry, we also delineate conditions for unique orbit recovery for multi-reference alignment models over finite groups (namely, when the dihedral group  ...  To estimate the signal in high noise levels, we also suggest maximizing the marginalized maximum likelihood using expectation-maximization (EM).  ... 
arXiv:2107.05262v2 fatcat:bmugkzqtr5ew5ppmu3l5eeseeq

Structural Analysis of Macromolecular Assemblies by Electron Microscopy

E. V. Orlova, H. R. Saibil
2011 Chemical Reviews  
Gohlke, and Stephen Fuller for providing figures, and Andrew Service and Anne-Cecile Maffat for help with manuscript preparation.  ...  ACKNOWLEDGMENT We thank Joachim Frank, Richard Henderson, Ronald Milligan, and Peter Rosenthal for helpful comments on the manuscript, Dan Clare, Maud Dumoux, Richard Hayward, Maya Topf, Neil Ranson, Uli  ...  Single-particle cryo-EM becomes very difficult when the particle is less than a few hundred kDa in mass.  ... 
doi:10.1021/cr100353t pmid:21919528 pmcid:PMC3239172 fatcat:bx7j3f6dajalzitk63mgx3nxhq

Deep manifold learning reveals hidden dynamics of proteasome autoregulation [article]

Zhaolong Wu, Shuwen Zhang, Wei Li Wang, Yinping Ma, Yuanchen Dong, Youdong Mao
2021 arXiv   pre-print
By using AlphaCryo4D to analyze a single experimental cryo-EM dataset, we identified 64 conformers of the substrate-bound human 26S proteasome, revealing conformational entanglement of two regulatory particles  ...  Here we introduce a deep manifold learning framework, named AlphaCryo4D, which enables atomic-level cryogenic electron microscopy (cryo-EM) reconstructions of nonequilibrium conformational continuum and  ...  Figure 1 . 1 Conceptual framework of AlphaCryo4D for 4D cryo-EM reconstruction. a, Schematic showing the major conceptual steps of single-particle cryo-EM data processing in AlphaCryo4D. b, Illustration  ... 
arXiv:2012.12854v2 fatcat:g3xx3xzfinbutgmkwcrjkyikga

Deep manifold learning reveals hidden dynamics of proteasome autoregulation [article]

Zhaolong Wu, Shuwen Zhang, Wei Li Wang, Yinping Ma, Yuanchen Dong, Youdong Mao
2020 bioRxiv   pre-print
By using AlphaCryo4D to analyze a single experimental cryo-EM dataset, we identified 64 conformers of the substrate-bound human 26S proteasome, revealing conformational entanglement of two regulatory particles  ...  Here we introduce a deep manifold learning framework, named AlphaCryo4D, which enables atomic-level cryogenic electron microscopy (cryo-EM) reconstructions of nonequilibrium conformational continuum and  ...  Figure 1 . 1 Conceptual framework of AlphaCryo4D for 4D cryo-EM reconstruction. a,539 Schematic showing the major conceptual steps of single-particle cryo-EM data processing in540 AlphaCryo4D. b, Illustration  ... 
doi:10.1101/2020.12.22.423932 fatcat:txhdd7nborh35orefd4ovpoyrq

Multi-reference alignment in high dimensions: sample complexity and phase transition [article]

Elad Romanov, Tamir Bendory, Or Ordentlich
2020 arXiv   pre-print
Motivated by single-particle cryo-electron microscopy, we analyze the sample complexity of the problem in the high-dimensional regime L→∞.  ...  Namely, the number of measurements required to achieve a desired accuracy ε approaches σ^2/ε for small ε; this is the sample complexity of estimating a signal in additive white Gaussian noise, which does  ...  Therefore, we can only estimate the orbit of X under the group of circular shifts Z L .  ... 
arXiv:2007.11482v1 fatcat:ifqn22nwtbb5jd7ctp2t26mzge

Multireference Alignment is Easier with an Aperiodic Translation Distribution [article]

Emmanuel Abbe, Tamir Bendory, William Leeb, João Pereira, Nir Sharon, Amit Singer
2018 arXiv   pre-print
In this work, using a generalization of the Chapman--Robbins bound for orbits and expansions of the χ^2 divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation  ...  In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise.  ...  ACKNOWLEDGMENTS We would like to thank Afonso Bandeira, Nicolas Boumal, Joseph Kileel, Roy Lederman and Zhizhen Zhao for many insightful discussions.  ... 
arXiv:1710.02793v3 fatcat:pv6wbujrpzfz7eahzadubjr2ee

Method of moments for 3-D single particle ab initio modeling with non-uniform distribution of viewing angles [article]

Nir Sharon, Joe Kileel, Yuehaw Khoo, Boris Landa, Amit Singer
2019 arXiv   pre-print
Single-particle reconstruction in cryo-electron microscopy (cryo-EM) is an increasingly popular technique for determining the 3-D structure of a molecule from several noisy 2-D projections images taken  ...  For unknown, non-uniform distributions, we use non-convex optimization methods to solve for both the molecule and distribution.  ...  The authors thank Nicolas Boumal, Peter Bürgisser, Eitan Levin, Dilano Saldin and Yoel Shkolnisky for stimulating conversations, and the anonymous referees for their valuable comments.  ... 
arXiv:1907.05377v2 fatcat:5hovat6mpbhadnevzdik6cl3fq

Likelihood landscape and maximum likelihood estimation for the discrete orbit recovery model [article]

Zhou Fan, Yi Sun, Tianhao Wang, Yihong Wu
2021 arXiv   pre-print
We study the non-convex optimization landscape for maximum likelihood estimation in the discrete orbit recovery model with Gaussian noise.  ...  We show that fundamental properties of the likelihood landscape depend on the signal-to-noise ratio and the group structure.  ...  We would like to thank Roy Lederman for helpful conversations at the onset of this work. Z. F. was supported in part by NSF Grant DMS-1916198. Y.  ... 
arXiv:2004.00041v4 fatcat:jjoklj6rknfihhuzaot524hhje

Measuring image resolution in optical nanoscopy

Robert P J Nieuwenhuizen, Keith A Lidke, Mark Bates, Daniela Leyton Puig, David Grünwald, Sjoerd Stallinga, Bernd Rieger
2013 Nature Methods  
for assistance with experiments; and V. van Ravesteijn and P. Kruit for providing scanning electron microscope data.  ...  We appreciate the thoughtful comments of T. reprints and permissions information is available online at http://www.nature. com/reprints/index.html.  ...  It is centered on the FRC (or, equivalently, the spectral signal-to-noise ratio), which is commonly used in the field of cryo-electron microscopy (cryo-EM) to assess single-particle reconstructions of  ... 
doi:10.1038/nmeth.2448 pmid:23624665 pmcid:PMC4149789 fatcat:v3vyc77xk5bzfbfbf5ebi2ho2a

On random tomography with unobservable projection angles

Victor M. Panaretos
2009 Annals of Statistics  
The problem arises in single particle electron microscopy, a powerful method that biophysicists employ to learn the structure of biological macromolecules.  ...  projections in random and unobservable directions.  ...  Finally, my thanks go to an Associate Editor and the referees for their thorough and constructive comments.  ... 
doi:10.1214/08-aos673 fatcat:ng3dsio4kncdjj7jcy7ybghhwq
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