Contents -- CHAPTER 1 Introduction -- 1 The Electron Microscope and Biology -- 1.1 General Remarks -- 1.2 Three-Dimensional Electron Microscopy -- 2 Single-Particle Versus Crystallographic Analysis -- 3 Crystallography without Crystals -- 4 Toward a Unified Approach to Structural Analysis of Macromolecules -- 5 Single-Particle Reconstruction, Macromolecular Machines, and Structural Proteomics -- 6 The Electron Microscope and the Computer -- CHAPTER 2 Electron Microscopy of Macromolecular Assemblies -- 1 Principle of the Transmission Electron Microscope -- 2 Specimen Preparation Methods -- 2.1 Introduction -- 2.2 Negative Staining -- 2.3 Glucose Embedment -- 2.4 Use of Tannic Acid -- 2.5 Ice-Embedded Specimens -- 2.6 Hybrid Techniques: Cryo-Negative Staining -- 2.7 Labeling with Gold Clusters -- 2.8 Support Grids -- 3 Principle of Image Formation in the Transmission Electron Microscope -- 3.1 Introduction -- 3.2 The Weak-Phase Object Approximation -- 3.3 The Contrast Transfer Theory -- 3.4 Amplitude Contrast -- 3.5 Formulation of Bright-Field Image Formation Using Complex Atomic Scattering Amplitudes -- 3.6 Optical and Computational Diffraction Analysis-The Power Spectrum -- 3.7 Determination of the Contrast Transfer Function -- 3.8 Instrumental Correction of the Contrast Transfer Function -- 3.9 Computational Correction of the Contrast Transfer Function -- 3.10 Locally Varying CTF and Image Quality -- 4 Special Imaging Techniques and Devices -- 4.1 Low-Dose Electron Microscopy -- 4.2 Spot Scanning -- 4.3 Energy Filtration -- 4.4 Direct Image Readout and Automated Data Collection -- CHAPTER 3 Two-Dimensional Averaging Techniques -- 1 Introduction -- 1.1 The Different Sources and Types of Noise -- 1.2 Principle of Averaging: Historical Notes -- 1.3 Equivalence between Averaging and Quasi-Optical Fourier Filtration.

1.4 A Discourse on Terminology: Views Versus Projections -- 1.5 The Role of Two-Dimensional Averaging in the Three-Dimensional Analysis of Single Molecules -- 1.6 Origins of Orientational Preferences -- 2 Digitization and Selection of Particles -- 2.1 Hardware for Digitization -- 2.2 The Sampling Theorem -- 2.3 Interactive Particle Selection -- 2.4 Automated Particle Selection -- 3 Alignment Methods -- 3.1 Quantitative Definitions of Alignment -- 3.2 Homogeneous Versus Heterogeneous Image Sets -- 3.3 Translational and Rotational Cross-Correlation -- 3.4 Reference-Based Alignment Techniques -- 3.5 Reference-Free Alignment Techniques -- 3.6 Alignment Using the Radon Transform -- 4 Averaging and Global Variance Analysis -- 4.1 The Statistics of Averaging -- 4.2 The Variance Map and the Analysis of Statistical Significance -- 4.3 Signal-to-Noise Ratio -- 5 Resolution -- 5.1 The Concept of Resolution -- 5.2 Resolution Criteria -- 5.3 Resolution and Cross-Resolution -- 5.4 Resolution-Limiting Factors -- 5.5 Statistical Requirements following the Physics of Scattering -- 5.6 Noise Filtering -- 6 Validation of the Average Image -- CHAPTER 4 Multivariate Data Analysis and Classification of Images -- 1 Introduction -- 1.1 Heterogeneity of Image Sets -- 1.2 Images as a Set of Multivariate Data -- 1.3 The Principle of Making Patterns Emerge from Data -- 1.4 Multivariate Data Analysis: Principal Component Analysis Versus Correspondence Analysis -- 2 Theory of Correspondence Analysis -- 2.1 Analysis of Image Vectors in R[sup(J)] -- 2.2 Analysis of Pixel Vectors in R[sup(N)] -- 2.3 Factorial Coordinates and Factor Maps -- 2.4 Reconstitution -- 2.5 Computational Methods -- 2.6 Significance Test -- 3 Correspondence Analysis in Practice -- 3.1 A Model Image Set Used for Demonstration -- 3.2 Definition of the Image Region to Be Analyzed.

3.3 Eigenvalue Histogram and Factor Map -- 3.4 Case Study: Ribosome Images -- 3.5 Use of Explanatory Tools -- 4 Classification -- 4.1 Background -- 4.2 Overview over Different Approaches and Goals of Classification -- 4.3 K-Means Clustering -- 4.4 Hierarchical Ascendant Classification -- 4.5 Hybrid Clustering Techniques -- 4.6 Inventories -- 4.7 Analysis of Trends -- 4.8 Nonlinear Mapping -- 4.9 Self-Organized Maps -- 4.10 Supervised Classification: Use of Templates -- 4.11 Inference from Two to Three Dimensions -- CHAPTER 5 Three-Dimensional Reconstruction -- 1 Introduction -- 2 General Mathematical Principles -- 2.1 The Projection Theorem and Radon's Theorem -- 2.2 Object Boundedness, Shape Transform, and Resolution -- 2.3 Definition of Eulerian Angles, and Special Projection Geometries: Single-Axis and Conical Tilting -- 3 The Rationales of Data Collection: Reconstruction Schemes -- 3.1 Introduction -- 3.2 Cylindrically Averaged Reconstruction -- 3.3 Compatibility of Projections -- 3.4 Relating Projections to One Another Using Common Lines -- 3.5 The Random-Conical Data Collection Method -- 3.6 Comparison of Common Lines Versus Random-Conical Methods -- 3.7 Reconstruction Schemes Based on Uniform Angular Coverage -- 4 Overview of Existing Reconstruction Techniques -- 4.1 Preliminaries -- 4.2 Weighted Back-Projection -- 4.3 Fourier Reconstruction Methods -- 4.4 Iterative Algebraic Reconstruction Methods -- 5 The Random-Conical Reconstruction in Practice -- 5.1 Overview -- 5.2 Optical Diffraction Screening -- 5.3 Interactive Tilted/Untilted Particle Selection -- 5.4 Optical Density Scaling -- 5.5 Processing of Untitled-Particle Images -- 5.6 Processing of Tilted-Particle Images -- 5.7 Carrying Out the Reconstruction -- 6 Common-Lines Methods (or ''Angular Reconstitution'') in Practice -- 7 Reference-Based Methods and Refinement -- 7.1 Introduction.

7.2 Three-Dimensional Projection Matching -- 7.3 Numerical Aspects -- 7.4 Three-Dimensional Radon Transform Method -- 7.5 The Size of Angular Deviations -- 7.6 Model Dependence of the Reconstruction -- 7.7 Consistency Check by Reprojection -- 8 Resolution Assessment -- 8.1 Theoretical Resolution of the 3D Reconstruction -- 8.2 Practically Achieved Resolution -- 8.3 Cross-Validation Using Excision of Fourier Data from the 3D Reference -- 9 Contrast Transfer Function and Fourier Amplitude Correction -- 9.1 Introduction -- 9.2 Contrast Transfer Function Correction -- 9.3 Fourier Amplitude Correction -- 10 Three-Dimensional Restoration -- 10.1 Introduction -- 10.2 Theory of Projection onto Convex Sets -- 10.3 Projection onto Convex Sets in Practice -- 11 Reconstructions from Heterogeneous Data Sets -- 11.1 Introduction -- 11.2 Separating Ligand-Bound from Ligand-Free Complexes -- 11.3 Separating Populations with Different Conformations -- 12 Merging and Averaging of Reconstructions -- 12.1 The Rationale for Merging -- 12.2 Negatively Stained Specimens: Complications due to Preparation-Induced Deformations -- 12.3 Alignment of Volumes -- 12.4 Merging of Reconstructions through Merging of Projection Sets into a Common Coordinate Frame -- 12.5 Classification of 3D Volumes -- CHAPTER 6 Interpretation of Three-Dimensional Images of Macromolecules -- 1 Introduction -- 2 Assessment of Statistical Significance -- 2.1 Introduction -- 2.2 Three-Dimensional Variance Estimation from Projections -- 2.3 Use of the 3D Variance Estimate to Ascertain the Statistical Significance -- 3 Validation and Consistency -- 3.1 Internal Consistency -- 3.2 Reconstructions from the Same Data Set with Different Algorithms -- 3.3 Consistency with X-Ray Structures -- 3.4 Concluding Remarks -- 4 Visualization and Rendering -- 4.1 Surface Rendering -- 4.2 Definition of Boundaries.

4.3 Volume Rendering -- 5 Segmentation of Volumes -- 5.1 Manual (Interactive) Segmentation -- 5.2 Segmentation Based on Density Alone -- 5.3 Knowledge-Based Segmentation, and Identification of Regions -- 6 Methods for Docking and Fitting -- 6.1 Manual Fitting -- 6.2 Quantitative Fitting -- 7 Classification of Volumes -- Appendix 1 Some Important Definitions and Theorems -- Appendix 2 Profiles, Point-Spread Functions, and Effects of Commonly Used Low-Pass Filters -- Appendix 3 Bibliography of Methods -- Appendix 4 Bibliography of Structures -- Appendix 5 Special Journal Issues on Image Processing Techniques -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z.