Three-Dimensional Electron Microscopy of Macromolecular Assemblies

Transcription

1 Three-Dimensional Electron Microscopy of Macromolecular Assemblies Joachim Frank Wadsworth Center for Laboratories and Research State of New York Department of Health The Governor Nelson A. Rockefeller Empire State Plaza Albany, New York and Department of Biomedical Sciences State University of New York at Albany Albany, New York Academic Press San Diego New York Boston London Sydney Tokyo Toronto

2 Contents Preface xv Chapter 1 Introduction I. The Electron Microscope and Biology 1 II. Single-Particle versus Crystallographic Analysis III. Crystallography without Crystals 7 IV. Toward a Unified Approach to Structure Research V. The Electron Microscope and the Computer 10 Chapter 2 Electron Microscopy of Macromolecular Assemblies 12 I. Specimen Preparation Methods 12 A. Introduction 12 B. Negative Staining: Principle 13 C. Negative Staining: Single Layer versus Carbon Sandwich Technique 14 D. Glucose Embedment Techniques 21 E. Use of Tannic Acid 22 Vll

3 viii Contents F. Cryo-electron Microscopy of Ice-Embedded Specimens 22 G. Labeling with Gold Clusters 23 II. Principle of Image Formation in the Electron Microscope 24 A. Introduction 24 B. The Weak Phase Object Approximation 25 C. Contrast Transfer Theory 28 D. Amplitude Contrast 36 E. Optical and Computational Diffraction Analysis 38 F. Determination of the Contrast Transfer Function 41 G. Instrumental Correction of the Contrast Transfer Function 44 H. Computational Correction of the Contrast Transfer Function 45 III. Special Imaging Techniques 49 A. Low-Dose Electron Microscopy 49 B. Spot Scanning 51 C. Energy Filtering 52 Chapter 3 Two-Dimensional Averaging Techniques 54 I. Introduction 54 A. The Sources of Noise 54 B. Principle of Averaging: Historical Notes 56 C. The Role of Two-Dimensional Averaging in the Three-Dimensional Analysis of Single Molecules 59 D. A Discourse on Terminology: Views versus Projections 61 E. Origins of Orientational Preference 62 II. Digitization and Selection of Particles 67 A. The Sampling Theorem 67 B. Interactive Particle Selection 69 C. Automated Particle Selection 69 III. Alignment Methods 73 A. The Aims of Alignment 73 B. Homogeneous versus Heterogeneous Image Sets 74

4 Contents ix C. Translational and Rotational Cross-Correlation 76 D. Reference-Based Alignment Techniques 83 E. Reference-Free Techniques 93 IV. Averaging and Global Variance Analysis 101 A. The Statistics of Averaging 101 B. The Variance Map and Analysis of Significance 102 C. Signal-to-Noise Ratio 107 V. Resolution 110 A. The Concept of Resolution 110 B. Resolution Criteria 112 C. Resolution-Limiting Factors 122 VI. Validation of the Average Image: Rank Sum Analysis 123 VII. Outlier Rejection: "Odd Men Out" Strategy 124 Chapter 4 Multivariate Statistical Analysis and Classification of Images 126 I. Introduction 126 A. Heterogeneity of Image Sets 126 B. Direct Application of Multivariate Statistical Analysis to an Image Set 127 C. The Principle of Making Patterns Emerge from Data 129 D. Eigenvector Methods of Ordination: Principal Component Analysis versus Correspondence Analysis 129 II. Theory of Correspondence Analysis 135 A. Analysis of Image Vectors in R B. Analysis of Pixel Vectors in 7? N 136 C. Factorial Coordinates and Factor Maps 137 D. Reconstitution 139 E. Computational Methods 143 F. Significance Test 144 III. Correspondence Analysis in Practice 145 A. Image Sets Used for Demonstration 145 B. Eigenvalue Histogram and Factor Map 145

5 x Contents C. Explanatory Tools I: Local Averages 149 D. Explanatory Tools II: Eigenimages and Reconstitution 150 E. Preparation of Masks 156 F. Demonstration of Reconstitution for a Molecule Set 159 IV. Classification 160 A. Background 160 B. Classification of the Different Approaches to Classification 163 C. Partitional Methods: K-Means Technique 164 D. Hard versus Fuzzy Classification 165 E. Hierarchical Ascendant Classification 165 F. Hybrid Techniques 171 G. Intrinsically Parallel Methods 173 H. Inventories and Analysis of Trends 175 I. Nonlinear Mapping 176 J. Supervised Classification: Use of Templates 179 K. Inference, through Classification, from Two to Three Dimensions 180 Chapter 5 Three-Dimensional Reconstruction 182 I. Introduction 182 II. General Mathematical Principles 183 A. The Projection Theorem, Radon's Theorem, and Resolution 183 B. Projection Geometries 186 III. Rationales of Data Collection: Reconstruction Schemes 188 A. Introduction 188 B. Cylindrically Averaged Reconstruction 190 C. Compatibility of Projections 192 D. Relating Projections to One Another Using Common Lines 193 E. The Random-Conical Data Collection Method 199 F. Reconstruction Schemes Based on Uniform Angular Coverage 202

6 Contents xi IV. Overview of Existing Reconstruction Techniques 202 A. Preliminaries 202 B. Weighted Back-Projection 203 C. Fourier Methods 208 D. Iterative Algebraic Reconstruction Methods 209 V. The Random-Conical Reconstruction Scheme in Practice 211 A. Overview 211 B. Optical Diffraction Screening 211 C. Interactive Tilted/Untilted Particle Selection 213 D. Density Scaling 214 E. Processing of Untilted-Particle Images 217 F. Processing of Tilted-Particle Images 219 G. Reconstruction 222 H. Resolution Assessment 222 VI. Merging of Reconstructions 225 A. The Rationale of Merging 225 B. Preparation-Induced Deformations 226 C. Three-Dimensional Orientation Search 227 D. Reconstruction from the Full Projection Set 230 VII. Three-Dimensional Restoration 231 A. Introduction 231 B. Theory of Projection onto Convex Sets 231 C. Projection onto Convex Sets in Practice 233 VIII. Angular Refinement Techniques 235 A. Introduction 235 B. Three-Dimensional Projection Matching Method 237 C. Three-Dimensional Radon Transform Method 241 D. The Size of Angular Deviations 243 IX. Transfer Function Correction 245 Chapter 6 Interpretation of Three-Dimensional Images of Macromolecules 247 I. Preliminaries: Significance, Experimental Validity, and Meaning 247

7 xii Contents II. Assessment of Statistical Significance 248 A. Introduction 248 B. Three-Dimensional Variance Estimation from Projections 250 C. Significance of Features in a Three-Dimensional Map 252 D. Significance of Features in a Difference Map 253 III. Validation and Consistency 254 A. A Structure and Its Component Reconstructed Separately: 80S Mammalian Ribosome and the 40S Ribosomal Subunit 254 B. Three-Dimensional Structural Features Inferred from Variational Pattern: Half-Molecules of Limulus polyphemus Hemocyanin 257 C. Concluding Remarks 260 IV. Visualization and Segmentation 260 A. Segmentation 260 B. Visualization and Rendering Tools 263 C. Definition of Boundaries 266 V. Juxtaposition with Existing Knowledge 268 A. The Organization of Knowledge 268 B. Fitting of Electron Microscopy with X-Ray Results 269 C. Use of Envelopes of Three-Dimensional Electron Microscopy Data 271 D. Public Sharing of Low-Resolution Volume Data: The Three-Dimensional Density Database 272 Chapter 7 Example for an Application: Calcium Release Channel 273 I. Introduction 273 II. Image Processing and Three-Dimensional Reconstruction of the Calcium Release Channel 275

8 Contents xiii Appendix 1 Software Implementations 282 I. Introduction 282 II. Basic Design Features 282 A. Modular Design 283 B. Hierarchical Calling Structure 283 C. Bookkeeping Capabilities and Data Storage Organization 284 D. User Interfaces 285 III. Existing Packages 285 IV. Interfacing to Other Software 287 V. Documentation 288 Appendix 2 Macromolecular Assemblies Reconstructed from Images of Single Macromolecules 289 Bibliography 293 Index 333