Numerical Geometry of Map and Model Assessment

We are describing best practices and assessment strategies for the atomic interpretation of cryo-electron microscopy (cryo-EM) maps. Multiscale numerical geometry strategies in the Situs package and in secondary structure detection software are currently evolving due to the recent increases in cryo-EM resolution. Criteria that aim to predict the accuracy of fitted atomic models at low (worse than 8 angstrom) and medium (4-8 angstrom) resolutions remain challenging. However, a high level of confidence in atomic models can be achieved by combining such criteria. The observed errors are due to map-model discrepancies and due to the effect of imperfect global docking strategies. Extending the earlier motion capture approach developed for flexible fitting, we use simulated fiducials (pseudoatoms) at varying levels of coarse-graining to track the local drift of structural features. We compare three tracking approaches: naive vector quantization, a smoothly deformable model, and a tessellation of the structure into rigid Voronoi cells, which are fitted using a multi-fragment refinement approach. The lowest error is an upper bound for the (small) discrepancy between the crystal structure and the EM map due to different conditions in their structure determination. When internal features such as secondary structures are visible in medium-resolution EM maps, it is possible to extend the idea of point-based fiducials to more complex geometric representations such as helical axes, strands, and skeletons. We propose quantitative strategies to assess map-model pairs when such secondary structure patterns are prominent

Cryo-EM structures of herpes simplex virus type 1 portal vertex and packaged genome.

Herpesviruses are enveloped viruses that are prevalent in the human population and are responsible for diverse pathologies, including cold sores, birth defects and cancers. They are characterized by a highly pressurized pseudo-icosahedral capsid-with triangulation number (T) equal to 16-encapsidating a tightly packed double-stranded DNA (dsDNA) genome1-3. A key process in the herpesvirus life cycle involves the recruitment of an ATP-driven terminase to a unique portal vertex to recognize, package and cleave concatemeric dsDNA, ultimately giving rise to a pressurized, genome-containing virion4,5. Although this process has been studied in dsDNA phages6-9-with which herpesviruses bear some similarities-a lack of high-resolution in situ structures of genome-packaging machinery has prevented the elucidation of how these multi-step reactions, which require close coordination among multiple actors, occur in an integrated environment. To better define the structural basis of genome packaging and organization in herpes simplex virus type 1 (HSV-1), we developed sequential localized classification and symmetry relaxation methods to process cryo-electron microscopy (cryo-EM) images of HSV-1 virions, which enabled us to decouple and reconstruct hetero-symmetric and asymmetric elements within the pseudo-icosahedral capsid. Here we present in situ structures of the unique portal vertex, genomic termini and ordered dsDNA coils in the capsid spooled around a disordered dsDNA core. We identify tentacle-like helices and a globular complex capping the portal vertex that is not observed in phages, indicative of herpesvirus-specific adaptations in the DNA-packaging process. Finally, our atomic models of portal vertex elements reveal how the fivefold-related capsid accommodates symmetry mismatch imparted by the dodecameric portal-a longstanding mystery in icosahedral viruses-and inform possible DNA-sequence recognition and headful-sensing pathways involved in genome packaging. This work showcases how to resolve symmetry-mismatched elements in a large eukaryotic virus and provides insights into the mechanisms of herpesvirus genome packaging

Conformational states of macromolecular assemblies explored by integrative structure calculation

A detailed description of macromolecular assemblies in multiple conformational states can be very valuable for understanding cellular processes. At present, structural determination of most assemblies in different biologically relevant conformations cannot be achieved by a single technique and thus requires an integrative approach that combines information from multiple sources. Different techniques require different computational methods to allow efficient and accurate data processing and analysis. Here, we summarize the latest advances and future challenges in computational methods that help the interpretation of data from two techniques—mass spectrometry and three-dimensional cryo-electron microscopy (with focus on alignment and classification of heterogeneous subtomograms from cryo-electron tomography). We evaluate how new developments in these two broad fields will lead to further integration with atomic structures to broaden our picture of the dynamic behavior of assemblies in their native environment

Expansion-enhanced super-resolution radial fluctuations enable nanoscale molecular profiling of pathology specimens

Expansion microscopy physically enlarges biological specimens to achieve nanoscale resolution using diffraction-limited microscopy systems1. However, optimal performance is usually reached using laser-based systems (for example, confocal microscopy), restricting its broad applicability in clinical pathology, as most centres have access only to light-emitting diode (LED)-based widefield systems. As a possible alternative, a computational method for image resolution enhancement, namely, super-resolution radial fluctuations (SRRF)2,3, has recently been developed. However, this method has not been explored in pathology specimens to date, because on its own, it does not achieve sufficient resolution for routine clinical use. Here, we report expansion-enhanced super-resolution radial fluctuations (ExSRRF), a simple, robust, scalable and accessible workflow that provides a resolution of up to 25 nm using LED-based widefield microscopy. ExSRRF enables molecular profiling of subcellular structures from archival formalin-fixed paraffin-embedded tissues in complex clinical and experimental specimens, including ischaemic, degenerative, neoplastic, genetic and immune-mediated disorders. Furthermore, as examples of its potential application to experimental and clinical pathology, we show that ExSRRF can be used to identify and quantify classical features of endoplasmic reticulum stress in the murine ischaemic kidney and diagnostic ultrastructural features in human kidney biopsies.</p

Normal Mode Flexible Fitting of High-Resolution Structures of Biological Molecules Toward SAXS Data

We present a method to reconstruct a three-dimensional protein structure from an atomic pair distribution function derived from the scattering intensity profile from SAXS data by flexibly fitting known x-ray structures. This method uses a linear combination of low-frequency normal modes from an elastic network description of the molecule in an iterative manner to deform the structure to conform optimally to the target pair distribution function derived from SAXS data. For computational efficiency, the protein and water molecules included in the protein first hydration shell are coarse-grained. In this paper, we demonstrate the validity of our coarse-graining approach to study SAXS data. Illustrative results of our flexible fitting studies on simulated SAXS data from five different proteins are presented

Improved biological annotation of EMDB data

Curs 2015-2016In this Final degree Project are explained all processes required to create the segmentation and biological annotation parts of Segmentation File Format (SFF) project. The segmentation file format is an Electron Microscope Data Base (EMDB) project, which is a combination of two projects, the “OMERO volume slicer” and the “Segmentation annotation tool”. This project was developed in order to build the segmentation and annotation sets for the “Segmentation annotation tool” step. The project was divided into two steps, Segmentation using Chimera, that permitted the downloading of the EMDB and PDB structure and proceed to do the segmentation, then this segmentation was saved as an Segger or HDF5 file. The segmentation of a structure is the decomposition by the different components that forms it. The second part consisted to create a biological annotation of the components previously segmented and building a link with other databases in order to identify them. The objective of this project was to create a SFF, this application would permit to the user to visualize segmentations on a EM tomogram, in order to identify and distinguish all the components that composed it. The annotation and segmentation that is explained in this project was made as a data set to build this new EMDB application. On the end of the project a collection of 100 segmentation and annotation sets were obtained, three types of structures can be distinguished; Helicases, Chaperones and Ribosomes

Ball-and-chain inactivation in a calcium-gated potassium channel

Inactivation is the process by which ion channels terminate ion flux through their pores while the opening stimulus is still present1. In neurons, inactivation of both sodium and potassium channels is crucial for the generation of action potentials and regulation of firing frequency1,2. A cytoplasmic domain of either the channel or an accessory subunit is thought to plug the open pore to inactivate the channel via a ‘ball-and-chain’ mechanism3–7. Here we use cryo-electron microscopy to identify the molecular gating mechanism in calcium-activated potassium channels by obtaining structures of the MthK channel from Methanobacterium thermoautotrophicum—a purely calcium-gated and inactivating channel—in a lipid environment. In the absence of Ca2+, we obtained a single structure in a closed state, which was shown by atomistic simulations to be highly flexible in lipid bilayers at ambient temperature, with large rocking motions of the gating ring and bending of pore-lining helices. In Ca2+-bound conditions, we obtained several structures, including multiple open-inactivated conformations, further indication of a highly dynamic protein. These different channel conformations are distinguished by rocking of the gating rings with respect to the transmembrane region, indicating symmetry breakage across the channel. Furthermore, in all conformations displaying open channel pores, the N terminus of one subunit of the channel tetramer sticks into the pore and plugs it, with free energy simulations showing that this is a strong interaction. Deletion of this N terminus leads to functionally non-inactivating channels and structures of open states without a pore plug, indicating that this previously unresolved N-terminal peptide is responsible for a ball-and-chain inactivation mechanism

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

Geometric analysis of macromolecule organization within cryo-electron tomograms

Cryo-electron tomography (CET) provides unprecedented views into the native cellular environment at molecular resolution. While subtomogram analysis yields high-resolution native structures of molecular complexes, it also determines the precise positions and orientations of these macromolecules within the cell. Analyzing the geometric relationships between adjacent macromolecules can offer structural insights into molecular interactions and identify supramolecular ensembles. However, computation..