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# Structural Biology Using Electrons and X-rays

## An Introduction for Biologists

- 1st Edition - January 19, 2011
- Editor: Michael F Moody
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 3 7 0 5 8 1 - 5
- 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 o… Read more

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Request a sales quote*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

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
- Edition: 1
- Published: January 19, 2011
- Imprint: Academic Press
- Paperback ISBN: 9780123705815
- eBook ISBN: 9780080919454

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