THREE-DIMENSIONA L ELECTRON MICROSCOP Y OF MACROMOLECULAR ASSEMBLIE S Visualization of Biological Molecules in Their Native Stat e Joachim Frank
CHAPTER 1 Introduction 1 1 The Electron Microscope and Biology 1 1.1 General Remarks 1 1.2 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 1 0 6 The Electron Microscope and the Computer 1 2 CHAPTER 2 Electron Microscopy of Macromolecular Assemblies 1 5 1 Principle of the Transmission Electron Microscope 1 5 2 Specimen Preparation Methods 1 9 2.1 Introduction 1 9 2.2 Negative Staining 2 0 2.3 Glucose Embedment 2 7 2.4 Use of Tannic Acid 28 2.5 Ice-Embedded Specimens 2 8 2.6 Hybrid Techniques : Cryo-Negative Staining 31
2.7 Labeling with Gold Clusters 3 3 2.8 Support Grids 3 3 3 Principle of Image Formation in the Transmissio n Electron Microscope 3 4 3.1 Introduction 3 4 3.2 The Weak-Phase Object Approximation 3 5 3.3 The Contrast Transfer Theory 3 9 3.4 Amplitude Contrast 4 7 3.5 Formulation of Bright-Field Image Formation Usin g Complex Atomic Scattering Amplitudes 4 9 3.6 Optical and Computational Diffraction Analysi s The Power Spectrum 50 3.7 Determination of the Contrast Transfer Function 5 3 3.8 Instrumental Correction of the Contrast Transfer Function 5 7 3.9 Computational Correction of the Contrast Transfer Function 5 8 3.10 Locally Varying CTF and Image Quality 62 4 Special Imaging Techniques and Devices 6 4 4.1 Low-Dose Electron Microscopy 64 4.2 Spot Scanning 66 4.3 Energy Filtration 6 7 4.4 Direct Image Readout and Automated Data Collection 6 8 CHAPTER 3 Two-Dimensional Averaging Techniques 7 1 1 Introduction 7 2 1.1 The Different Sources and Types of Noise 7 2 1.2 Principle of Averaging: Historical Notes 7 4 1.3 Equivalence between Averaging an d Quasi-Optical Fourier Filtration 7 5 1.4 A Discourse on Terminology : Views Versus Projections 78 1.5 The Role of Two-Dimensional Averaging in th e Three-Dimensional Analysis of Single Molecules 7 8 1.6 Origins of Orientational Preferences 79 2 Digitization and Selection of Particles 8 3 2.1 Hardware for Digitization 8 3 2.2 The Sampling Theorem 8 4 2.3 Interactive Particle Selection 8 6 2.4 Automated Particle Selection 8 7 3 Alignment Methods 9 1 3.1 Quantitative Definitions of Alignment 9 1 3.2 Homogeneous Versus Heterogeneous Image Sets 9 2 3.3 Translational and Rotational Cross-Correlation 9 4 3.4 Reference-Based Alignment Techniques 100 3.5 Reference-Free Alignment Techniques 10 9 3.6 Alignment Using the Radon Transform 115
4 Averaging and Global Variance Analysis 11 5 4.1 The Statistics of Averaging 11 5 4.2 The Variance Map and the Analysis of Statistical Significance 11 7 4.3 Signal-to-Noise Ratio 12 1 5 Resolution 12 4 5.1 The Concept of Resolution 12 4 5.2 Resolution Criteria 12 6 5.3 Resolution and Cross-Resolution 13 7 5.4 Resolution-Limiting Factors 13 8 5.5 Statistical Requirements following the Physic s of Scattering 13 9 5.6 Noise Filtering 140 6 Validation of the Average Image 142 CHAPTER 4 Multivariate Data Analysis and Classification of Images 14 5 1 Introduction 14 5 1.1 Heterogeneity of Image Sets 146 1.2 Images as a Set of Multivariate Data 14 7 1.3 The Principle of Making Patterns Emerge from Data 14 8 1.4 Multivariate Data Analysis : Principal Componen t Analysis Versus Correspondence Analysis 14 9 2 Theory of Correspondence Analysis 15 3 2.1 Analysis of Image Vectors in R' 15 4 2.2 Analysis of Pixel Vectors in R N 155 2.3 Factorial Coordinates and Factor Maps 15 6 2.4 Reconstitution 15 7 2.5 Computational Methods 16 1 2.6 Significance Test 16 1 3 Correspondence Analysis in Practice 16 2 3.1 A Model Image Set Used for Demonstration 16 2 3.2 Definition of the Image Region to Be Analyzed 16 2 3.3 Eigenvalue Histogram and Factor Map 16 6 3.4 Case Study: Ribosome Images 169 3.5 Use of Explanatory Tools 17 2 4 Classification 17 6 4.1 Background 17 6 4.2 Overview over Different Approaches and Goals of Classification 177 4.3 K-Means Clustering 17 8 4.4 Hierarchical Ascendant Classification 18 0 4.5 Hybrid Clustering Techniques 182 4.6 Inventories 184 4.7 Analysis of Trends 185
4.8 Nonlinear Mapping 18 5 4.9 Self-Organized Maps 18 6 4.10 Supervised Classification : Use of Templates 18 8 4.11 Inference from Two to Three Dimensions 18 9 CHAPTER 5 Three-Dimensional Reconstruction 19 3 1 Introduction 19 3 2 General Mathematical Principles 19 4 2.1 The Projection Theorem and Radon's Theorem 19 4 2.2 Object Boundedness, Shape Transform, and Resolution 196 2.3 Definition of Eulerian Angles, and Specia l Projection Geometries : Single-Axis and Conical Tilting 19 8 3 The Rationales of Data Collection: Reconstruction Schemes 20 1 3.1 Introduction 20 1 3.2 Cylindrically Averaged Reconstruction 20 2 3.3 Compatibility of Projections 20 5 3.4 Relating Projections to One Another Using Common Lines 20 6 3.5 The Random-Conical Data Collection Method 21 0 3.6 Comparison of Common Lines Versu s Random-Conical Methods 21 2 3.7 Reconstruction Schemes Based on Uniform Angular Coverage 21 3 4 Overview of Existing Reconstruction Techniques 21 3 4.1 Preliminaries 21 3 4.2 Weighted Back-Projection 21 4 4.3 Fourier Reconstruction Methods 21 9 4.4 Iterative Algebraic Reconstruction Methods 22 1 5 The Random-Conical Reconstruction in Practice 22 2 5.1 Overview 222 5.2 Optical Diffraction Screening 22 2 5.3 Interactive Tilted/Untilted Particle Selection 22 5 5.4 Optical Density Scaling 22 6 5.5 Processing of Untitled-Particle Images 22 7 5.6 Processing of Tilted-Particle Images 22 8 5.7 Carrying Out the Reconstruction 23 1 6 Common-Lines Methods (or "Angular Reconstitution") in Practice 23 2 7 Reference-Based Methods and Refinement 23 2 7.1 Introduction 23 2 7.2 Three-Dimensional Projection Matching 23 6 7.3 Numerical Aspects 24 0 7.4 Three-Dimensional Radon Transform Method 24 2 7.5 The Size of Angular Deviations 243 7.6 Model Dependence of the Reconstruction 24 6 7.7 Consistency Check by Reprojection 247
8 Resolution Assessment 247 8.1 Theoretical Resolution of the 3D Reconstruction 24 7 8.2 Practically Achieved Resolution 24 8 8.3 Cross-Validation Using Excision of Fourier Data from th e 3D Reference 25 3 9 Contrast Transfer Function and Fourier Amplitude Correction 25 5 9.1 Introduction 25 5 9.2 Contrast Transfer Function Correction 25 5 9.3 Fourier Amplitude Correction 25 9 10 Three-Dimensional Restoration 26 1 10.1 Introduction 26 1 10.2 Theory of Projection onto Convex Sets 26 2 10.3 Projection onto Convex Sets in Practice 264 11 Reconstructions from Heterogeneous Data Sets 26 6 11.1 Introduction 266 11.2 Separating Ligand-Bound from Ligand-Free Complexes 26 6 11.3 Separating Populations with Different Conformations 26 7 12 Merging and Averaging of Reconstructions 27 0 12.1 The Rationale for Merging 27 0 12.2 Negatively Stained Specimens : Complications due to Preparation-Induced Deformations 27 1 12.3 Alignment of Volumes 27 2 12.4 Merging of Reconstructions through Merging of Projection Sets into a Common Coordinate Frame 27 5 12.5 Classification of 3D Volumes 27 6 CHAPTER 6 Interpretation of Three-Dimensional Images o f Macromolecules 27 7 1 Introduction 27 7 2 Assessment of Statistical Significance 27 9 2.1 Introduction 27 9 2.2 Three-Dimensional Variance Estimation from Projections 28 0 2.3 Use of the 3D Variance Estimate to Ascertain th e Statistical Significance 28 4 3 Validation and Consistency 28 6 3.1 Internal Consistency 28 6 3.2 Reconstructions from the Same Data Set wit h Different Algorithms 28 6 3.3 Consistency with X=Ray Structures 28 7 3.4 Concluding Remarks 29 1 4 Visualization and Rendering 29 3 4.1 Surface Rendering 294 4.2 Definition of Boundaries 296
4.3 Volume Rendering 29 7 5 Segmentation of Volumes 29 8 5.1 Manual (Interactive) Segmentation 299 5.2 Segmentation Based on Density Alone 29 9 5.3 Knowledge-Based Segmentation, and Identification of Regions 30 3 6 Methods for Docking and Fitting 30 8 6.1 Manual Fitting 309 6.2 Quantitative Fitting 31 1 7 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