THREE-DIMENSIONA L ELECTRON MICROSCOP Y OF MACROMOLECULAR ASSEMBLIE S. Visualization of Biological Molecules in Their Native Stat e.

Transcription

1 THREE-DIMENSIONA L ELECTRON MICROSCOP Y OF MACROMOLECULAR ASSEMBLIE S Visualization of Biological Molecules in Their Native Stat e Joachim Frank

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3 CHAPTER 1 Introduction 1 1 The Electron Microscope and Biology General Remarks Three-Dimensional Electron Microscopy 2 2 Single-Particle Versus Crystallographic Analysis 5 3 Crystallography without Crystals 7 4 Toward a Unified Approach to Structural Analysis of Macromolecules 9 5 Single-Particle Reconstruction, Macromolecular Machines, and Structural Proteomics The Electron Microscope and the Computer 1 2 CHAPTER 2 Electron Microscopy of Macromolecular Assemblies Principle of the Transmission Electron Microscope Specimen Preparation Methods Introduction Negative Staining Glucose Embedment Use of Tannic Acid Ice-Embedded Specimens Hybrid Techniques : Cryo-Negative Staining 31

4 2.7 Labeling with Gold Clusters Support Grids Principle of Image Formation in the Transmissio n Electron Microscope Introduction The Weak-Phase Object Approximation The Contrast Transfer Theory Amplitude Contrast Formulation of Bright-Field Image Formation Usin g Complex Atomic Scattering Amplitudes Optical and Computational Diffraction Analysi s The Power Spectrum Determination of the Contrast Transfer Function Instrumental Correction of the Contrast Transfer Function Computational Correction of the Contrast Transfer Function Locally Varying CTF and Image Quality 62 4 Special Imaging Techniques and Devices Low-Dose Electron Microscopy Spot Scanning Energy Filtration Direct Image Readout and Automated Data Collection 6 8 CHAPTER 3 Two-Dimensional Averaging Techniques Introduction The Different Sources and Types of Noise Principle of Averaging: Historical Notes Equivalence between Averaging an d Quasi-Optical Fourier Filtration A Discourse on Terminology : Views Versus Projections The Role of Two-Dimensional Averaging in th e Three-Dimensional Analysis of Single Molecules Origins of Orientational Preferences 79 2 Digitization and Selection of Particles Hardware for Digitization The Sampling Theorem Interactive Particle Selection Automated Particle Selection Alignment Methods Quantitative Definitions of Alignment Homogeneous Versus Heterogeneous Image Sets Translational and Rotational Cross-Correlation Reference-Based Alignment Techniques Reference-Free Alignment Techniques Alignment Using the Radon Transform 115

5 4 Averaging and Global Variance Analysis The Statistics of Averaging The Variance Map and the Analysis of Statistical Significance Signal-to-Noise Ratio Resolution The Concept of Resolution Resolution Criteria Resolution and Cross-Resolution Resolution-Limiting Factors Statistical Requirements following the Physic s of Scattering Noise Filtering Validation of the Average Image 142 CHAPTER 4 Multivariate Data Analysis and Classification of Images Introduction Heterogeneity of Image Sets Images as a Set of Multivariate Data The Principle of Making Patterns Emerge from Data Multivariate Data Analysis : Principal Componen t Analysis Versus Correspondence Analysis Theory of Correspondence Analysis Analysis of Image Vectors in R' Analysis of Pixel Vectors in R N Factorial Coordinates and Factor Maps Reconstitution Computational Methods Significance Test Correspondence Analysis in Practice A Model Image Set Used for Demonstration Definition of the Image Region to Be Analyzed Eigenvalue Histogram and Factor Map Case Study: Ribosome Images Use of Explanatory Tools Classification Background Overview over Different Approaches and Goals of Classification K-Means Clustering Hierarchical Ascendant Classification Hybrid Clustering Techniques Inventories Analysis of Trends 185

6 4.8 Nonlinear Mapping Self-Organized Maps Supervised Classification : Use of Templates Inference from Two to Three Dimensions 18 9 CHAPTER 5 Three-Dimensional Reconstruction Introduction General Mathematical Principles The Projection Theorem and Radon's Theorem Object Boundedness, Shape Transform, and Resolution Definition of Eulerian Angles, and Specia l Projection Geometries : Single-Axis and Conical Tilting The Rationales of Data Collection: Reconstruction Schemes Introduction Cylindrically Averaged Reconstruction Compatibility of Projections Relating Projections to One Another Using Common Lines The Random-Conical Data Collection Method Comparison of Common Lines Versu s Random-Conical Methods Reconstruction Schemes Based on Uniform Angular Coverage Overview of Existing Reconstruction Techniques Preliminaries Weighted Back-Projection Fourier Reconstruction Methods Iterative Algebraic Reconstruction Methods The Random-Conical Reconstruction in Practice Overview Optical Diffraction Screening Interactive Tilted/Untilted Particle Selection Optical Density Scaling Processing of Untitled-Particle Images Processing of Tilted-Particle Images Carrying Out the Reconstruction Common-Lines Methods (or "Angular Reconstitution") in Practice Reference-Based Methods and Refinement Introduction Three-Dimensional Projection Matching Numerical Aspects Three-Dimensional Radon Transform Method The Size of Angular Deviations Model Dependence of the Reconstruction Consistency Check by Reprojection 247

7 8 Resolution Assessment Theoretical Resolution of the 3D Reconstruction Practically Achieved Resolution Cross-Validation Using Excision of Fourier Data from th e 3D Reference Contrast Transfer Function and Fourier Amplitude Correction Introduction Contrast Transfer Function Correction Fourier Amplitude Correction Three-Dimensional Restoration Introduction Theory of Projection onto Convex Sets Projection onto Convex Sets in Practice Reconstructions from Heterogeneous Data Sets Introduction Separating Ligand-Bound from Ligand-Free Complexes Separating Populations with Different Conformations Merging and Averaging of Reconstructions The Rationale for Merging Negatively Stained Specimens : Complications due to Preparation-Induced Deformations Alignment of Volumes Merging of Reconstructions through Merging of Projection Sets into a Common Coordinate Frame Classification of 3D Volumes 27 6 CHAPTER 6 Interpretation of Three-Dimensional Images o f Macromolecules Introduction Assessment of Statistical Significance Introduction Three-Dimensional Variance Estimation from Projections Use of the 3D Variance Estimate to Ascertain th e Statistical Significance Validation and Consistency Internal Consistency Reconstructions from the Same Data Set wit h Different Algorithms Consistency with X=Ray Structures Concluding Remarks Visualization and Rendering Surface Rendering Definition of Boundaries 296

8 4.3 Volume Rendering Segmentation of Volumes Manual (Interactive) Segmentation Segmentation Based on Density Alone Knowledge-Based Segmentation, and Identification of Regions Methods for Docking and Fitting Manual Fitting Quantitative Fitting Classification of Volumes 31 6 Appendix 1 Some Important Definitions and Theorems 31 9 Appendix 2 Profiles, Point-Spread Functions, and Effects o f Commonly Used Low-Pass Filters 32 7 Appendix 3 Bibliography of Methods 33 1 Appendix 4 Bibliography of Structures 33 7 Appendix 5 Special Journal Issues on Image Processing Techniques 34 3 References 345 Index 399