GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging

Tomography has made a radical impact on diverse fields ranging from the study of 3D atomic arrangements in matter to the study of human health in medicine. Despite its very diverse applications, the core of tomography remains the same, that is, a mathematical method must be implemented to reconstruct the 3D structure of an object from a number of 2D projections. In many scientific applications, however, the number of projections that can be measured is limited due to geometric constraints, tolerable radiation dose and/or acquisition speed. Thus it becomes an important problem to obtain the best-possible reconstruction from a limited number of projections. Here, we present the mathematical implementation of a tomographic algorithm, termed GENeralized Fourier Iterative REconstruction (GENFIRE). By iterating between real and reciprocal space, GENFIRE searches for a global solution that is concurrently consistent with the measured data and general physical constraints. The algorithm requires minimal human intervention and also incorporates angular refinement to reduce the tilt angle error. We demonstrate that GENFIRE can produce superior results relative to several other popular tomographic reconstruction techniques by numerical simulations, and by experimentally by reconstructing the 3D structure of a porous material and a frozen-hydrated marine cyanobacterium. Equipped with a graphical user interface, GENFIRE is freely available from our website and is expected to find broad applications across different disciplines.Comment: 18 pages, 6 figure

Biological application of Compressed Sensing Tomography in the Scanning Electron Microscope

The three-dimensional tomographic reconstruction of a biological sample, namely collagen fibrils in human dermal tissue, was obtained from a set of projection-images acquired in the Scanning Electron Microscope. A tailored strategy for the transmission imaging mode was implemented in the microscope and proved effective in acquiring the projections needed for the tomographic reconstruction. Suitable projection alignment and Compressed Sensing formulation were used to overcome the limitations arising from the experimental acquisition strategy and to improve the reconstruction of the sample. The undetermined problem of structure reconstruction from a set of projections, limited in number and angular range, was indeed supported by exploiting the sparsity of the object projected in the electron microscopy images. In particular, the proposed system was able to preserve the reconstruction accuracy even in presence of a significant reduction of experimental projections

Zernike Phase Contrast Cryo-Electron Microscopy and Tomography for Structure Determination at Nanometer and Subnanometer Resolutions

Zernike phase contrast cryo-electron microscopy (ZPC-cryoEM) is an emerging technique that is capable of producing higher image contrast than conventional cryoEM. By combining this technique with advanced image processing methods, we achieved subnanometer resolution for two biological specimens: 2D bacteriorhodopsin crystal and epsilon15 bacteriophage. For an asymmetric reconstruction of epsilon15 bacteriophage, ZPC-cryoEM can reduce the required amount of data by a factor of ~3, compared with conventional cryoEM. The reconstruction was carried out to 13 Å resolution without the need to correct the contrast transfer function. New structural features at the portal vertex of the epsilon15 bacteriophage are revealed in this reconstruction. Using ZPC cryo-electron tomography (ZPC-cryoET), a similar level of data reduction and higher resolution structures of epsilon15 bacteriophage can be obtained relative to conventional cryoET. These results show quantitatively the benefits of ZPC-cryoEM and ZPC-cryoET for structural determinations of macromolecular machines at nanometer and subnanometer resolutions.National Institutes of Health (U.S.) (Grant P41RR002250)National Institutes of Health (U.S.) (Grant R01AI0175208)National Institutes of Health (U.S.) (Grant PN1EY016525)Robert Welch Foundation (Q1242

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

In situ structure of virus capsids within cell nuclei by correlative light and cryo-electron tomography

Cryo electron microscopy (cryo-EM), a key method for structure determination involves imaging purified material embedded in vitreous ice. Images are then computationally processed to obtain three-dimensional structures approaching atomic resolution. There is increasing interest in extending structural studies by cryo-EM into the cell, where biological structures and processes may be imaged in context. The limited penetrating power of electrons prevents imaging of thick specimens (> 500 nm) however. Cryo-sectioning methods employed to overcome this are technically challenging, subject to artefacts or involve specialised and costly equipment. Here we describe the first structure of herpesvirus capsids determined by sub-tomogram averaging from nuclei of eukaryotic cells, achieved by cryo-electron tomography (cryo-ET) of re-vitrified cell sections prepared using the Tokuyasu method. Our reconstructions confirm that the capsid associated tegument complex is present on capsids prior to nuclear egress. We demonstrate that this method is suited to both 3D structure determination and correlative light/electron microscopy, thus expanding the scope of cryogenic cellular imaging

Automatic Differentiation for Inverse Problems in X-ray Imaging and Microscopy

Computational techniques allow breaking the limits of traditional imaging methods, such as time restrictions, resolution, and optics flaws. While simple computational methods can be enough for highly controlled microscope setups or just for previews, an increased level of complexity is instead required for advanced setups, acquisition modalities or where uncertainty is high; the need for complex computational methods clashes with rapid design and execution. In all these cases, Automatic Differentiation, one of the subtopics of Artificial Intelligence, may offer a functional solution, but only if a GPU implementation is available. In this paper, we show how a framework built to solve just one optimisation problem can be employed for many different X-ray imaging inverse problems