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Cryogenic electron microscopy (cryo-EM) provides a unique opportunity to study the structural heterogeneity of biomolecules. Being able to explain this heterogeneity with atomic models would help our understanding of their functional…

Cryo-electron microscopy (cryo-EM) is an experimental technique for protein structure determination that images an ensemble of macromolecules in near-physiological contexts. While recent advances enable the reconstruction of dynamic…

The computational pipelines of single-particle cryo-electron microscopy (cryo-EM) and cryo-electron tomography (cryo-ET) include an early particle-picking stage, in which a micrograph or tomogram is scanned to extract candidate particles,…

Signal Processing · Electrical Eng. & Systems 2026-04-14 Amnon Balanov , Alon Zabatani , Tamir Bendory

We revisit the topic of common lines between projection images in single particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain $2n \times n$ matrix storing properly-scaled basis vectors for the…

Optimization and Control · Mathematics 2024-06-10 Tommi Muller , Adriana L. Duncan , Eric J. Verbeke , Joe Kileel

Electron cryomicroscopy (cryo-EM) is a technique in structural biology used to reconstruct accurate volumetric maps of molecules. One step of the cryo-EM pipeline involves solving an inverse-problem. This inverse-problem, referred to as…

Quantitative Methods · Quantitative Biology 2024-11-26 Aaditya V. Rangan , Wai-Shing Tang , Pilar Cossio , Kexin Zhang , Nikolaus Grigorieff

Over the past decade, cryogenic electron microscopy (cryo-EM) has emerged as a primary method for determining near-native, near-atomic resolution 3D structures of biological macromolecules. In order to meet increasing demand for cryo-EM,…

Image and Video Processing · Electrical Eng. & Systems 2022-01-19 Paul T. Kim , Alex J. Noble , Anchi Cheng , Tristan Bepler

Cryo-EM is a transformational paradigm in molecular biology where computational methods are used to infer 3D molecular structure at atomic resolution from extremely noisy 2D electron microscope images. At the forefront of research is how to…

Quantitative Methods · Quantitative Biology 2025-06-12 Shayan Shekarforoush , David B. Lindell , Marcus A. Brubaker , David J. Fleet

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. Cryo-EM was selected by Nature Methods as Method of the…

Computational Physics · Physics 2018-03-20 Amit Singer

A main task in cryo-electron microscopy single particle reconstruction is to find a three-dimensional model of a molecule given a set of its randomly oriented and positioned noisy projection-images. In this work, we propose an algorithm for…

Computational Physics · Physics 2022-11-11 Adi Shasha Geva , Yoel Shkolnisky

In the past decade, deep conditional generative models have revolutionized the generation of realistic images, extending their application from entertainment to scientific domains. Single-particle cryo-electron microscopy (cryo-EM) is…

Computer Vision and Pattern Recognition · Computer Science 2024-10-01 Jiakai Zhang , Qihe Chen , Yan Zeng , Wenyuan Gao , Xuming He , Zhijie Liu , Jingyi Yu

Cryo-electron microscopy (cryo-EM) has become a central tool for high-resolution structural biology, yet the massive scale of datasets (often exceeding 100k particle images) renders 3D reconstruction both computationally expensive and…

Computer Vision and Pattern Recognition · Computer Science 2025-10-03 Huaizhi Qu , Xiao Wang , Gengwei Zhang , Jie Peng , Tianlong Chen

We introduce the EMC algorithm for reconstructing a particle's 3D diffraction intensity from very many photon shot-noise limited 2D measurements, when the particle orientation in each measurement is unknown. The algorithm combines a…

Data Analysis, Statistics and Probability · Physics 2010-03-04 Duane Ne-Te Loh , Veit Elser

As a critical modality for structural biology, cryogenic electron microscopy (cryo-EM) facilitates the determination of macromolecular structures at near-atomic resolution. The core computational task in single-particle cryo-EM is to…

Image and Video Processing · Electrical Eng. & Systems 2026-05-04 Suyi Chen , Haibin Ling

Cryo-EM is an increasingly popular method for determining the atomic resolution 3D structure of macromolecular complexes (eg, proteins) from noisy 2D images captured by an electron microscope. The computational task is to reconstruct the 3D…

Computer Vision and Pattern Recognition · Computer Science 2024-10-04 Shayan Shekarforoush , David B. Lindell , Marcus A. Brubaker , David J. Fleet

Cryo-electron tomography (Cryo-ET) is a 3D imaging technique that enables the systemic study of shape, abundance, and distribution of macromolecular structures in single cells in near-atomic resolution. However, the systematic and efficient…

Biomolecules · Quantitative Biology 2021-06-29 Kai Yi , Jianye Pang , Yungeng Zhang , Xiangrui Zeng , Min Xu

Cryogenic electron microscopy (cryo-EM) has become an enabling technology in drug discovery and in understanding molecular bases of disease by producing near-atomic resolution (less than 0.4 nm) 3D reconstructions of biological…

Computer Vision and Pattern Recognition · Computer Science 2020-07-23 Hong Xu , David E. Timm , Shireen Y. Elhabian

Electron cryo-tomography (cryo-ET) enables 3D imaging of complex, radiation-sensitive structures with molecular detail. However, image contrast from the interference of scattered electrons is nonlinear with atomic density and multiple…

Cryo-EM reconstruction algorithms seek to determine a molecule's 3D density map from a series of noisy, unlabeled 2D projection images captured with an electron microscope. Although reconstruction algorithms typically model the 3D volume as…

Biomolecules · Quantitative Biology 2021-07-06 Ellen D. Zhong , Adam Lerer , Joseph H. Davis , Bonnie Berger

The advent of advanced crystallographic techniques has shifted structural biology from static, single-conformer models toward probing protein dynamics. Extracting cooperative motions from temporally and spatially averaged electron density…

Quantitative Methods · Quantitative Biology 2025-09-08 Avinash Mandaiya , Veit Elser

A major challenge in single particle reconstruction methods using cryo-electron microscopy is to attain a resolution sufficient to interpret fine details in three-dimensional (3D) macromolecular structures. Obtaining high resolution 3D…

Numerical Analysis · Mathematics 2013-07-23 Lanhui Wang , Yoel Shkolnisky , Amit Singer