Structural Biology Using Electrons and X-rays book cover

Structural Biology Using Electrons and X-rays

An Introduction for Biologists

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.

Audience
Graduate and advanced undergraduate students in biochemistry, molecular biology, and biological and medical physics; research biologists using electron microscopy

Paperback, 450 Pages

Published: January 2011

Imprint: Academic Press

ISBN: 978-0-12-370581-5

Contents


  • 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








Advertisement

advert image