Structural Biology Using Electrons and X-rays (eBook)

Front Cover 1
Structural Biology Using Electrons and X-Rays 4
Copyright Page 5
Contents 6
Preface 16
Chapter 1: Overview 18
1.1 Role of Structural (Molecular) Biology 18
1.2 A Short History of Structural (Molecular) Biology 19
PART I: FOURIER TRANSFORMS 26
Chapter 2: Correlations and Convolutions 28
2.1 Introducing Correlations 28
2.2 Function Parity 35
2.3 Auto-Correlation Function 38
Chapter 3: Fourier Fundamentals 42
3.1 Component Functions 43
3.2 Fourier Analysis of Periodic Even Functions 45
3.3 Sines and Phasors 47
3.4 Fourier Transforms 56
3.5 Summary of Rules 69
Chapter 4: Digital Fourier Transforms 72
4.1 Data Preparation 73
4.2 Digital Fourier Transform Features 80
4.3 Digital Fourier Transform Calculations 84
4.4 Appendix 89
Chapter 5: Filters 92
5.1 Introduction 92
5.2 Blurring Filters 94
5.3 Digital-to-Analog Conversion 99
5.4 Correcting Blurring Filters 103
5.5 Gradients and Derivatives 106
Chapter 6: Two-Dimensional FTs 112
6.1 Two-Dimensional Fourier Transforms Rules 112
6.2 Points and Lines 118
6.3 Polygons 125
6.4 Polar Coordinates 132
PART II: OPTICS 140
Chapter 7: Microscopy with Rays 142
7.1 Light Microscopy 142
7.2 Electron Microscopy 153
7.3 Electron Lens Aberrations 158
7.4 Contrast Mechanisms 160
Chapter 8: Waves 168
8.1 Wave Properties 168
8.2 The Quantum Electron 172
8.3 Fresnel Diffraction 174
8.4 Fraunhofer Diffraction 177
8.5 Appendix 181
Chapter 9: Wave Imaging 186
9.1 Overview of Wave Imaging 186
9.2 Defocus 189
9.3 Other Aberrations 202
9.4 Appendix: Aberration Phase-Shift Geometry 205
PART III: GENERAL STRUCTURAL METHODS 206
Chapter 10: Symmetry 208
10.1 Principles 208
10.2 One-Translation Groups 215
10.3 Two-Translation Groups 220
10.4 Three-Translation Groups 228
10.5 Fourier Transforms of Crystallographic Symmetry Operations 235
Chapter 11: Statistics and Matrices 240
11.1 Statistics 240
11.2 Matrices 251
11.3 Structure Optimization and Simulation 257
11.4 Appendix 263
Chapter 12: The Third Dimension 264
12.1 Depth Through Tilting 264
12.2 Aligning Particle Images 272
12.3 Information Content of Particle Images 277
12.4 Three-Dimensional Reconstruction: Principles 284
PART IV: SYMMETRY-BASED METHODS 292
Chapter 13: X-Ray Crystallography 294
13.1 Introduction 294
13.2 Specimen and Data Collection 296
13.3 Ab Initio Phasing 302
13.4 Other Phasing Methods 311
Chapter 14: Crystalline Sheets 316
14.1 Electrons Versus X-Rays 316
14.2 Electron Diffraction 318
14.3 Two-Dimensional Imaging 323
14.4 Three-Dimensional Imaging 324
Chapter 15: Helices 328
15.1 Helical Symmetry and Structure 329
15.2 Helical Fourier Transforms 334
15.3 Getting a Structure from Helical Diffraction Data 347
Chapter 16: Icosahedral Particles 354
16.1 Deltahedra 355
16.2 Projections 361
16.3 Three-Dimensional Reconstruction 363
16.4 Appendix: Calculation of T-numbers 373
Chapter 17: Unsymmetrical ('Single') Particles 376
17.1 Introduction 376
17.2 Alignment 378
17.3 Multivariate Statistical Analysis 381
17.4 Reconstruction 386
Chapter 18: Distortion Correction 392
18.1 Introduction 392
18.2 Crystalline Sheets 394
18.3 Helices 396
PART V: MATHEMATICAL BASIS 402
Chapter 19: FT Mathematics 404
19.1 Introduction 404
19.2 Algebra 405
19.3 Geometry 407
19.4 Infinitesimals 409
19.5 Calculus 411
Chapter 20: Elementary Matrices 418
20.1 Introducing Matrices 418
20.2 Matrix Inversion 421
20.3 Eigenvectors 426
20.4 Least-Squares Fits 428
References 434
Index 444
A 444
B 444
C 444
D 445
E 445
F 446
G 446
H 446
I 447
J 447
L 447
M 447
N 448
O 448
P 448
Q 448
R 448
S 449
T 450
U 450
V 450
W 450
X 451
Z 451