Fast and robust single particle reconstruction in 3D fluorescence microscopy

Single particle reconstruction has recently emerged in 3D fluorescence microscopy as a powerful technique to improve the axial resolution and the degree of fluorescent labeling. It is based on the reconstruction of an average volume of a biological particle from the acquisition multiple views with unknown poses. Current methods are limited either by template bias, restriction to 2D data, high computational cost or a lack of robustness to low fluorescent labeling. In this work, we propose a single particle reconstruction method dedicated to convolutional models in 3D fluorescence microscopy that overcome these issues. We address the joint reconstruction and estimation of the poses of the particles, which translates into a challenging non-convex optimization problem. Our approach is based on a multilevel reformulation of this problem, and the development of efficient optimization techniques at each level. We demonstrate on synthetic data that our method outperforms the standard approaches in terms of resolution and reconstruction error, while achieving a low computational cost. We also perform successful reconstruction on real datasets of centrioles to show the potential of our method in concrete applications

액상에 존재하는 개별 나노입자에 대한 3차원 원자구조 분석 방법론

학위논문(박사) -- 서울대학교대학원 : 공과대학 화학생물공학부, 2023. 2. 박정원.Precise three-dimensional (3D) atomic structure determination of individual nanocrystals is a prerequisite for understanding and predicting their physical properties, because the 3D atomic arrangements of materials determine the free energy landscape. We developed a Brownian one-particle reconstruction based on imaging of ensembles of colloidal nanocrystals using graphene liquid cell electron microscopy. Nanocrystals from the same synthesis batch display what are often presumed to be small but possibly important differences in size, lattice distortions, and defects, which can only be understood by structural characterization with high spatial 3D resolution. The structures of individual colloidal platinum nanocrystals are solved by developing atomic-resolution 3D liquid-cell electron microscopy to reveal critical intrinsic heterogeneity of ligand-protected platinum nanocrystals in solution, including structural degeneracies, lattice parameter deviations, internal defects, and strain. These differences in structure lead to substantial contributions to free energies, consequential enough that they must be considered in any discussion of fundamental nanocrystal properties or applications. We introduce computational methods required for successful atomic-resolution 3D reconstruction: (i) tracking of the individual particles throughout the time series, (ii) subtraction of the interfering background of the graphene liquid cell, (iii) identification and rejection of low-quality images, and (iv) tailored strategies for 2D/3D alignment and averaging that differ from those used in biological cryo–electron microscopy. Characterization of lattice symmetry is important because the symmetry is strongly correlated with physical properties of nanomaterials. We introduce direct and quantitative analysis of lattice symmetry by using 3D atomic coordinates obtained by liquid-phase TEM. We investigate symmetry of entire unit-cells composing individual platinum nanoparticles, revealing unique structural characteristics of sub-3 nm Pt nanoparticles. We here introduce a 3D atomic structure determination method for multi-element nanoparticle systems. The method, which is based on low-pass filtration and initial 3D model generation customized for different types of multi-element systems, enables reconstruction of high-resolution 3D Coulomb density maps for ordered and disordered multi-element systems and classification of the heteroatom type. Using high-resolution image datasets obtained from TEM simulations of PbSe, CdSe, and FePt nanoparticles that are structurally relaxed with first-principles calculations in the graphene liquid cell, we show that the types and positions of the constituent atoms are precisely determined with root mean square displacement (RMSD) values less than 24 pm. Our study suggests that it is possible to investigate the 3D atomic structures of synthesized multi-element nanoparticles in liquid phase.재료의 3D 원자 배열이 자유 에너지 환경을 결정한다는 점을 고려했을 때, 개별 나노결정의 정확한 3차원(3D) 원자 구조 분석은 물리적 특성을 이해하고 예측하기 위해 필수 불가결하다. 본 연구자는 그래핀 액체 세포 투과 전자 현미경을 사용하여 콜로이드 나노입자의 앙상블 이미징을 기반으로 하는 "브라운 단일 입자 재구성"을 개발했다. 동일한 합성 배치의 나노입자는 크기, 격자 왜곡 및 결함 등에서 종종 작지만 중요한 것으로 추정되는 것으로 간주되는 구조적 차이점이 있으며, 이는 3D 고해상도 구조 분석에 의해서만 이해할 수 있다. 구조적 퇴화, 격자 매개변수 편차, 내부 결함 및 변형을 포함한 개별 콜로이드 백금 나노입자의 구조적 특성은 원자 분해능 3D 액체 세포 전자 현미경을 개발하여 풀어낼 수 있다. 이러한 구조의 차이는 자유 에너지에 상당한 기여를 하므로 결과적으로 기본적인 나노입자 특성 또는 응용에 대한 논의에서 고려되어야 한다. 본 논문에서는 성공적인 원자 해상도 3D 재구성에 필요한 계산 방법론을 소개한다. 그 방법론에는 다음과 같은 알고리즘이 포함된다. (1) 시계열 이미지에서 개별 나노입 자를 추적하는 알고리즘, (2) 그래핀 액체 셀의 배경 노이즈를 제거하는 알고리즘, (3) 저해상도 이미지를 검출 및 제거하는 알고리즘, (4) 극저온 전자현미경을 이용한 바이오 입자의 재구성에 쓰이는 알고리즘과는 다른 나노입자만을 위해서 고안된 2차원/3차원 정렬 알고리즘. 격자 대칭성은 나노 물질의 물리적 특성과 강한 상관관계가 있기 때문에, 격자 대칭성 분석은 중요하다. 본 논문에서는 액상 투과 전자 현미경을 통해서 얻은 3차원 원자 좌표를 이용하여 격자 대칭을 직접적, 정량적으로 분석할 수 있는 방법론을 소개하고자 한다. 개별 백금 나노입자를 구성하는 전체 unit cell의 대칭성을 조사함으로써, 3 나노미터 이하의 백금 나노입자가 갖는 독특한 구조적 특징을 밝혀내였다. 본 논문에서는 다원소 나노입자 시스템을 위한 3차원 원자 구조 분석법을 소개하고자 한다. 제시된 low-pass filtering과 initial 3D modeling 방법은 다양한 유형의 다원소 시스템에 맞춰져 있으며, 이를 통해 ordered multi-element system과 disordered multi-element system에서 원자의 위치를 파악하고 원소의 종류를 구분할 수 있다. First-principles calculation을 통해 얻은 PbSe, CdSe, FePt 나노입자 구조로부터 그래핀 액체 셀 안에서의 TEM 시뮬레이션 이미지를 얻고, 이를 활용하여 구성 원자의 유형과 위치를 24 피코미터 미만의 오차로 정확도 높게 판별할 수 있음을 확인하였다. 우리의 연구는 액상에서 합성된 다원소 나노입자의 3차원 원자 구조를 조사하는 것이 가능함을 시사한다.Chapter 1. Introdution 1 1.1. Atomic structure property relationships in nanoparticles 1 1.2. Toward atomic structure characterization 2 1.3. Direct observation of 3D atomic structures of individual nanoparticles: Electron tomography and Brownian one-particle reconstruction 3 1.4. Purpose of Research 4 Chapter 2. 3D atomic structures of individual ligand-protected Pt nanoparticles in solution 7 2.1. Introduction 7 2.2. 3D reconstruction from electron microscopy images of Pt nanoparticles in liquid 8 2.2.1. Synthesis of Pt nanoparticles 8 2.2.2. Preparation of graphene liquid cells 9 2.2.3. Acquisition of TEM images 9 2.2.4. 3D reconstruction 10 2.2.5. Atomic position assignment 11 2.2.6. Validation 11 2.2.7. Atomic structure analysis 13 2.3. Atomic structural characteristics of Pt nanoparticles in liquid 16 2.2.1. Effect of surface ligands on the 3D atomic structures of Pt nanoparticles 16 2.3.2. Structural heterogeneity of Pt nanoparticles 18 2.3.3. Strain analysis of individual Pt nanoparticles from the 3D atomic maps 19 2.4. Conclusion 21 Chapter 3. SINGLE: Computational methods for atomic-resolution 3D reconstruction 57 3.1. Introduction 57 3.2. Results 58 3.2.1. Overview of 3D SINGLE 58 3.2.2. The SINGLE workflow 58 3.3. Conclusion 66 Chapter 4. 3-Dimensional scanning of unit cell symmetries in individual nanoparticles by using Brownian one-particle reconstruction 75 4.1. Introduction 75 4.2. Results 77 4.2.1. Quantitative symmetry analysis from 3D atomic coordinates 77 4.2.2. Direction of symmetry breakage 79 4.2.3. Structural heterogeneity 80 4.2.4. Relationship between symmetry and surface interactions 80 4.3. Conclusion 84 Chapter 5. Method for 3D atomic structure determination of multi-element nanoparticles with graphene liquid-cell TEM 102 5.1. Introduction 102 5.2. Results 104 5.2.1. Overview of multi-element nanoparticle 3D reconstruction 104 5.2.2. Principles for multi-element nanoparticle reconstruction 105 5.2.3. Demonstration using simulated TEM images 106 5.3. Conclusion 111 Bibliography 136 국 문 초 록 144박

Improved methods for single-particle cryogenic electron microscopy

Biological macromolecules such as enzymes are nanoscale machines. This is true in a concrete sense: if the atomic structure of a biological macromolecule can be obtained, the theories of mechanics and intermolecular forces can be applied to explain how the machine works in terms that engineers would understand, including motors, ratchets, gates and transducers. Nevertheless, biological macromolecules are complex, fragile and extremely small, so obtaining their structures is a challenging experimental endeavor. Single-particle cryogenic electron microscopy (cryo-EM) is a technique for determining the 3D structure of a biological macromolecule from a large set of 2D electron micrographs of individual structurally-identical particles. To obtain such images, a solution of the macromolecules must be prepared in the frozen-hydrated state, embedded in a thin electron-transparent glassy film of water. This specimen must then be imaged with a very short exposure to avoid radiation damage. A powerful computer must then be used to sort, align, and average the 2D particle images to back-calculate the 3D structure. At its best, cryo-EM can determine the structures of biological macromolecules to atomic resolution. In practice, this goal is usually not achieved. Cryo-EM has gotten significantly more powerful in the past few years due to improvements in equipment and methodology. Several of the most significant advances originated in the labs of David Agard and Yifan Cheng at UCSF. When I began my PhD with Yifan, the spirit in the lab was that cryo-EM could keep getting better and better: with enough engineering, determining the 3D structure of an arbitrary biological macromolecule would be as routine an experiment as gel electrophoresis or DNA sequencing. Inspired, I took on projects in the lab that I thought would move the field closer to that goal. In the first chapter of this thesis, I describe work I did supporting a project initiated by David Agard and his long-time scientific programmer Shawn Zheng. They developed and implemented an algorithm, MotionCor2, for correcting the complex, anisotropic movements that occur when a frozen-hydrated specimen interacts with the high-energy electron beam. My role was to benchmark MotionCor2 on a panel of real-world 3D reconstruction tasks. I was able to show that MotionCor2 restored the highest resolution details in the images, ultimately yielding significantly better structures than simpler algorithms. For me, this projected highlighted the importance of benchmarking an algorithm for use in routine real-world conditions with the right metrics. In chapter 1, I include the manuscript for the MotionCor2 study, formatted to highlight my contributions that were moved to the supplement in the original publication by Nature Methods. One of the major remaining issues with cryo-EM is sample preparation: preparing the thin freestanding films of frozen-hydrated particles necessarily exposes those particles to air-water interfaces. Many fragile macromolecular complexes denature when exposed to such interfaces, preventing structure determination with cryo-EM. In chapters 2 and 3, I describe my efforts to develop a simple, robust approach to stabilizing fragile macromolecular complexes during the vitrification process. In chapter 2, I develop a method for coating EM grids with an electron-transparent and functionalizable graphene-oxide support film. I demonstrate that such GO grids are compatible with high-resolution structure determination. This work was published in the Journal of Structural Biology in 2018. In chapter 3, I extend this work by functionalizing GO grids with nucleic acids, enabling routine structure determination of uncrosslinked chromatin specimens. In on-going work, I used nucleic acid grids to solve high-resolution structures of a highly fragile specimen, the snf2h-nucleosome complex, and analyzed the conformational heterogeneity of the nucleosome substrate. These results were made possible by the nucleic acid grid, as the other major approach for stabilizing chromatin specimens, chemical crosslinking, not work for this specimen.Perhaps the most fundamental problem with single-particle cryo-EM is the radiation sensitivity of frozen-hydrated macromolecules. To image biological matter with electrons is to destroy it, so obtaining images of undamaged specimens requires very short, highly under sampled exposures. The resultant images are extremely noisy and low contrast, with most particles barely visible from the background. In chapter 4, I describe a novel computational approach to generating contrast in cryo-EM. Using a recently described machine learning strategy for training a parameterized denoising algorithm, I developed a computer program, restore, that denoises cryo-EM images, greatly enhancing their contrast and interpretability. This program leverages recent advances in computer vision and deep learning which have not yet been widely used in cryo-EM image processing algorithms. To characterize the performance of the algorithm on real-world data, I extended conventional metrics for image resolution to measure how an arbitrary transformation affects images at different spatial frequencies. These novel metrics are general and may be useful for characterizing other nonlinear reconstruction algorithms in cryo-EM and medical imaging. Finally, I showed that denoised cryo-EM images maintain the high-resolution information required for accurate 3D reconstruction. Denoising can be applied to conventional cryo-EM images and can be reversed whenever necessary. I have made the software for restore program publicly available and have submitted a manuscript for peer-reviewed publication

Correlated Multimodal Imaging in Life Sciences:Expanding the Biomedical Horizon

International audienceThe frontiers of bioimaging are currently being pushed toward the integration and correlation of several modalities to tackle biomedical research questions holistically and across multiple scales. Correlated Multimodal Imaging (CMI) gathers information about exactly the same specimen with two or more complementary modalities that-in combination-create a composite and complementary view of the sample (including insights into structure, function, dynamics and molecular composition). CMI allows to describe biomedical processes within their overall spatio-temporal context and gain a mechanistic understanding of cells, tissues, diseases or organisms by untangling their molecular mechanisms within their native environment. The two best-established CMI implementations for small animals and model organisms are hardware-fused platforms in preclinical imaging (Hybrid Imaging) and Correlated Light and Electron Microscopy (CLEM) in biological imaging. Although the merits of Preclinical Hybrid Imaging (PHI) and CLEM are well-established, both approaches would benefit from standardization of protocols, ontologies and data handling, and the development of optimized and advanced implementations. Specifically, CMI pipelines that aim at bridging preclinical and biological imaging beyond CLEM and PHI are rare but bear great potential to substantially advance both bioimaging and biomedical research. CMI faces three mai

Multireference Alignment is Easier with an Aperiodic Translation Distribution

In the multireference alignment model, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. The goal is to recover the signal's orbit by accessing multiple independent observations. Of particular interest is the sample complexity, i.e., the number of observations/samples needed in terms of the signal-to-noise ratio (the signal energy divided by the noise variance) in order to drive the mean-square error (MSE) to zero. Previous work showed that if the translations are drawn from the uniform distribution, then, in the low SNR regime, the sample complexity of the problem scales as $\omega(1/\text{SNR}^3)$. In this work, using a generalization of the Chapman--Robbins bound for orbits and expansions of the $\chi^2$ divergence at low SNR, we show that in the same regime the sample complexity for any aperiodic translation distribution scales as $\omega(1/\text{SNR}^2)$. This rate is achieved by a simple spectral algorithm. We propose two additional algorithms based on non-convex optimization and expectation-maximization. We also draw a connection between the multireference alignment problem and the spiked covariance model