CRYO-EM, PART B: 3-D RECONSTRUCTION

Front Matter
......Page 0
Copyright
......Page 2
Contributors
......Page 3
Preface
......Page 7
Methods in Enzymology
......Page 9
Fundamentals of Three-Dimensional Reconstruction from Projections......Page 38
Introduction......Page 39
The Object and its Projection......Page 42
Taxonomy of Reconstruction Methods......Page 45
Discretization and Interpolation......Page 47
The Algebraic and Iterative Methods......Page 50
Filtered Backprojection......Page 55
Direct Fourier Inversion......Page 59
Implementations of Reconstruction Algorithms in EM Software Packages......Page 61
Conclusions......Page 64
References......Page 66
Image Restoration in Cryo-Electron Microscopy......Page 71
Introduction......Page 72
Image Formation Model in Electron Microscopy......Page 74
Estimation of Image Formation Model Characteristics......Page 80
Analytical model of 1D rotationally averaged PW of macromolecular complexes in solution......Page 82
Closed form solutions......Page 83
Constrained closed form restoration......Page 89
Iterative solution......Page 90
Constrained solutions-incorporation of a priori information......Page 92
Wiener filter in restoration of an image using EM data with varied defocus settings......Page 94
Wiener filter in image filtration and amplitude correction (``sharpening´´)......Page 98
Image Restoration for Sets of Heterogeneous Images......Page 100
Phase flipping......Page 101
The reciprocal space adaptive Wiener filter......Page 102
Discussion......Page 103
Acknowledgments......Page 105
References......Page 106
Resolution Measures in Molecular Electron Microscopy......Page 109
Introduction......Page 110
Optical Resolution Versus Resolution in Electron Microscopy......Page 111
Principles of Resolution Assessment in EM......Page 114
Fourier Shell Correlation and its Relation to Spectral Signal-to-Noise Ratio......Page 120
Relation Between Optical Resolution, Self-Consistency Measures, and Optimum Filtration of the Map......Page 124
Resolution Assessment in Electron Tomography......Page 128
Resolution Assessment in Practice......Page 130
References......Page 135
3D Reconstruction from 2D Crystal Image and Diffraction Data......Page 137
Introduction to Electron Crystallography Data Processing......Page 138
Algorithms for Electron Crystallography......Page 140
Initialization of a project......Page 143
Processing of crystal images......Page 145
Processing of electron diffraction patterns......Page 148
Scaling......Page 149
Lattice line fitting by matrix transformation and SVD......Page 150
Molecular replacement and model building......Page 152
Project initialization in 2dx......Page 153
Processing of an individual image in 2dx......Page 154
Project initialization in XDP......Page 156
Processing of an individual electron diffraction pattern in XDP......Page 157
Merging in XDP......Page 158
Processing of an individual electron diffraction pattern in IPLT......Page 159
Merging in IPLT......Page 160
Conclusions......Page 161
References......Page 163
Fourier-Bessel Reconstruction of Helical Assemblies......Page 166
Introduction......Page 167
Mathematical description of a helix......Page 168
Fourier transform of a helix......Page 170
Advantages of helical symmetry for 3D reconstruction......Page 172
Scanning the film image......Page 173
Orient, mask, and center the helix......Page 175
Determine repeat distance and interpolate the image......Page 177
Indexing of layer lines......Page 178
Extract layer line data and calculate phase statistics......Page 180
Determine defocus and apply the contrast transfer function......Page 181
Averaging data from multiple images......Page 182
Correcting distortions in the helical assembly (unbending)......Page 183
Create final averaged data set and correct CTF......Page 184
Map calculation and display......Page 185
Case Study of Helical Reconstruction of Ca-ATPase......Page 186
Real-space averaging of different helical symmetries......Page 187
Alternative real-space averaging of gn,(r) of different helical symmetries......Page 188
Comparison with the iterative helical real-space reconstruction method......Page 189
Conclusions......Page 191
Definition of a Fourier transform......Page 192
Fourier transform in cylindrical coordinates......Page 193
Helical symmetry......Page 195
Example: tobacco mosaic virus......Page 196
References......Page 197
Reconstruction of Helical Filaments and Tubes......Page 201
The Iterative Helical Real Space Reconstruction Approach......Page 203
Using IHRSR......Page 205
Intrinsic Ambiguities in Helical Symmetry......Page 208
Acknowledgments......Page 215
References......Page 216
Three-Dimensional Asymmetric Reconstruction of Tailed Bacteriophage......Page 218
Introduction: 3D Asymmetric Reconstruction of Tailed Bacteriophage......Page 219
Symmetry mismatch in phage structure......Page 220
Alternative strategies to determine the structures of asymmetric viruses......Page 221
Cryo-TEM of phi29......Page 222
Image reconstruction software......Page 223
Particle Boxing......Page 225
Expanding the box to include the tail......Page 226
Generating a Starting Model of the Complete phi29 Phage......Page 227
Hybrid head-tail model of phi29......Page 228
Origin and orientation determination and refinement with FREALIGN......Page 230
Origin and orientation refinement in AUTO3DEM......Page 231
Model docking......Page 233
Map segmentation......Page 235
Streamlined processing......Page 237
Future prospects......Page 238
References......Page 239
Single Particle Analysis at High Resolution......Page 244
Introduction......Page 245
Orientation......Page 246
High-resolution image acquisition......Page 247
Introduction to EMAN......Page 250
Particle Selection/Boxing......Page 251
CTF and Envelope Correction......Page 252
Initial Model Building......Page 257
Refinement......Page 259
3D reconstruction......Page 260
Eliminating particles......Page 262
Resolution and Assessing Results......Page 263
Required Computational Capacity and Emerging Methods......Page 265
References......Page 266
The Orthogonal Tilt Reconstruction Method......Page 269
Introduction......Page 270
Random Conical Tilt and the "missing cone" problem......Page 272
The test sample: The yeast exosome......Page 277
Sample preparation......Page 278
Data collection......Page 280
Selection of particles......Page 281
Does the sample adopt enough orientations to satisfy OTR requirements?......Page 283
CTF correction......Page 284
Alignment and classification......Page 285
Reconstruction......Page 287
Comparison between OTR and RCT reconstructions......Page 289
References......Page 292
An Introduction to Maximum-Likelihood Methods in Cryo-EM......Page 295
Maximum-likelihood estimates......Page 296
Introduction to the EM-ML algorithm......Page 297
Relevance to SPR problems......Page 301
The maximum-likelihood estimator......Page 302
An example of direct MLE calculation in cryo-EM......Page 303
An example of an incomplete data problem in cryo-EM......Page 305
The EM-ML algorithm......Page 307
An example of EM-ML in cryo-EM......Page 308
Comparison with conventional methods......Page 309
EM-ML Approaches in Cryo-EM......Page 310
Single-particle analysis......Page 311
Icosahedral viruses......Page 313
2D crystallography......Page 315
Tomography......Page 316
The Statistical Data Model......Page 318
Reducing Computational Requirements......Page 321
Outlook......Page 322
Acknowledgments......Page 323
References......Page 324
Classification of Structural Heterogeneity by Maximum-Likelihood Methods......Page 327
Introduction......Page 328
Data Preprocessing......Page 330
Micrograph preprocessing......Page 331
Particle extraction......Page 332
Normalization......Page 333
Data cleaning......Page 335
2D Classification......Page 336
ML2D......Page 337
kerdenSOM......Page 338
3D Classification......Page 339
Preparing the starting model......Page 340
Multi-reference refinement......Page 342
Interpretation of the classification results......Page 344
High-Performance Computing......Page 347
Outlook......Page 349
References......Page 350
Methods for Three-Dimensional Reconstruction of Heterogeneous Assemblies......Page 353
Introduction......Page 354
Theoretical Background......Page 356
Model data......Page 358
Small heat shock proteins......Page 361
Statistical Analysis of Particles with Variable Ligand Occupancy......Page 362
Model data......Page 363
Chaperonin-substrate complexes......Page 365
70S ribosome with elongation factor G......Page 367
Conclusions......Page 369
References......Page 372
Alignment of Cryo-Electron Tomography Datasets......Page 374
Introduction......Page 375
Notation......Page 376
Marker detection......Page 377
IMOD: Iterate projection model and marker detection......Page 379
RAPTOR: Corresponding groups of markers......Page 380
Number of markers to track......Page 382
Projection model estimation......Page 383
Marker-Free Alignment......Page 387
Allignator......Page 388
Alignment from extended-features in TxBR......Page 390
3D model-based approach......Page 391
Reconstruction Using the Projection Model......Page 393
Summary......Page 395
References......Page 396
Correcting for the Ewald Sphere in High-Resolution Single-Particle Reconstructions......Page 399
Introduction......Page 400
The Ewald Curvature Problem and Symbols Used......Page 401
The Paraboloid Method in the Context of 3D Reconstruction......Page 403
The Prec Algorithm......Page 404
Implementation of the Prec Algorithm......Page 405
Application to Experimental Reconstructions......Page 407
References......Page 409
Software Tools for Molecular Microscopy: An Open-Text Wikibook......Page 411
References......Page 419
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