Structural Biology Using Electrons and X-rays (eBook)

An Introduction for Biologists

Michael F Moody (Herausgeber)

eBook Download: PDF | EPUB

2011 | 1. Auflage
450 Seiten
Elsevier Science (Verlag)
978-0-08-091945-4 (ISBN)

Infos

Structural Biology Using Electrons and X-Rays discusses the diffraction and image-based methods used for the determination of complex biological macromolecules. The book focuses on the Fourier transform theory, which is a mathematical function that is computed to transform signals between time and frequency domain. Composed of five parts, the book examines the development of nuclear magnetic resonance (NMR), which allows the calculation of the images of a certain protein. Parts 1 to 4 provide the basic information and the applications of Fourier transforms, as well as the different methods used for image processing using X-ray crystallography and the analysis of electron micrographs. Part 5 focuses entirely on the mathematical aspect of Fourier transforms. In addition, the book examines detailed structural analyses of a specimen's symmetry (i.e., crystals, helices, polyhedral viruses and asymmetrical particles). This book is intended for the biologist or biochemist who is interested in different methods and techniques for calculating the images of proteins using nuclear magnetic resonance (NMR). It is also suitable for readers without a background in physical chemistry or mathematics. - Emphasis on common principles underlying all diffraction-based methods - Thorough grounding in theory requires understanding of only simple algebra - Visual representations and explanations of challenging content - Mathematical detail offered in short-course form to parallel the text

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 3.3.2011
• Sprache: englisch
• Themenwelt: Informatik ► Weitere Themen ► Bioinformatik
• Themenwelt: Naturwissenschaften ► Biologie ► Biochemie
• Themenwelt: Naturwissenschaften ► Biologie ► Genetik / Molekularbiologie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik
• Themenwelt: Technik
• ISBN-10: 0-08-091945-6 / 0080919456
• ISBN-13: 978-0-08-091945-4 / 9780080919454