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Structural Biology Using Electrons and X-rays
An Introduction for Biologists
1st Edition - January 19, 2011
Editor: Michael F Moody
eBook ISBN:
9 7 8 - 0 - 0 8 - 0 9 1 9 4 5 - 4
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… Read more
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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
Graduate and advanced undergraduate students in biochemistry, molecular biology, and biological and medical physics; research biologists using electron microscopy
Preface
Chapter 1: Overview
1.1 Role of Structural (Molecular) Biology
1.2 A Short History of Structural (Molecular) Biology
1.2.1 The Nature of the Problem
1.2.2 ‘Imaging’ Techniques
1.2.3 Nuclear Magnetic Resonance
1.2.4 Fundamental Limitations to Finding Macromolecule Structures
Part I: Fourier Transforms
Chapter 2: Correlations and Convolutions
2.1 Introducing Correlations
2.2 Function Parity
2.3 Auto-Correlation Function
Chapter 3: Fourier Fundamentals
3.1 Component Functions
3.2 Fourier Analysis of Periodic Even Functions
3.3 Sines and Phasors
3.4 Fourier Transforms
3.5 Summary of Rules
Chapter 4: Digital Fourier Transforms
4.1 Data Preparation
4.2 Digital Fourier Transform Features
4.3 Digital Fourier Transform Calculations
4.4 Appendix
Chapter 5: Filters
5.1 Introduction
5.2 Blurring Filters
5.3 Digital-to-Analog Conversion
5.4 Correcting Blurring Filters
5.5 Gradients and Derivatives
Chapter 6: Two-Dimensional FTs
6.1 Two-Dimensional Fourier Transforms Rules
6.2 Points and Lines
6.3 Polygons
6.4 Polar Coordinates
Part II: Optics
Chapter 7: Microscopy with Rays
7.1 Light Microscopy
7.2 Electron Microscopy
7.3 Electron Lens Aberrations
7.4 Contrast Mechanisms
Chapter 8: Waves
8.1 Wave Properties
8.2 The Quantum Electron
8.3 Fresnel Diffraction
8.4 Fraunhofer Diffraction
8.5 Appendix
Chapter 9: Wave Imaging
9.1 Overview of Wave Imaging
9.2 Defocus
9.3 Other Aberrations
9.4 Appendix: Aberration Phase-Shift Geometry
Part III: General Structural Methods
Chapter 10: Symmetry
10.1 Principles
10.2 One-Translation Groups
10.3 Two-Translation Groups
10.4 Three-Translation Groups
10.5 Fourier Transforms of Crystallographic Symmetry Operations
Chapter 11: Statistics and Matrices
11.1 Statistics
11.2 Matrices
11.3 Structure Optimization and Simulation
11.4 Appendix
Chapter 12: The Third Dimension
12.1 Depth Through Tilting
12.2 Aligning Particle Images
12.3 Information Content of Particle Images
12.4 Three-Dimensional Reconstruction: Principles
Part IV: Symmetry-Based Methods
Chapter 13: X-Ray Crystallography
13.1 Introduction
13.2 Specimen and Data Collection
13.3 Ab Initio Phasing
13.4 Other Phasing Methods
Chapter 14: Crystalline Sheets
14.1 Electrons Versus X-Rays
14.2 Electron Diffraction
14.3 Two-Dimensional Imaging
14.4 Three-Dimensional Imaging
Chapter 15: Helices
15.1 Helical Symmetry and Structure
15.2 Helical Fourier Transforms
15.3 Getting a Structure from Helical Diffraction Data
Chapter 16: Icosahedral Particles
16.1 Deltahedra
16.2 Projections
16.3 Three-Dimensional Reconstruction
16.4 Appendix: Calculation of T-numbers
Chapter 17: Unsymmetrical (‘Single’) Particles
17.1 Introduction
17.2 Alignment
17.3 Multivariate Statistical Analysis
17.4 Reconstruction
Chapter 18: Distortion Correction
18.1 Introduction
18.2 Crystalline Sheets
18.3 Helices
Part V: Mathematical Basis
Chapter 19: FT Mathematics
19.1 Introduction
19.2 Algebra
19.3 Geometry
19.4 Infinitesimals
19.5 Calculus
Chapter 20: Elementary Matrices
20.1 Introducing Matrices
20.2 Matrix Inversion
20.3 Eigenvectors
20.4 Least-Squares Fits
References
Index
- No. of pages: 450
- Language: English
- Published: January 19, 2011
- Imprint: Academic Press
- eBook ISBN: 9780080919454