Crystallography Made Crystal Clear : A Guide for Users of Macromolecular Models

by Rhodes, Gale

• ISBN13: 9780125870757
• ISBN10: 0125870752
• Format: Paperback
• Copyright: 1993-03-01
• Publisher: Academic Pr

Summary

Crystallography Made Crystal Clear is designed to meet the need for an X-ray analysis that is between brief textbook sections and complete treatments. The book provides non-crystallographers with an intellectually satisfying explanation of the principles of how protein models are gleaned from X-ray analysis. The understanding of these concepts will foster wise use of the models, including the recognition of the strengths and weaknesses of pictures or computer graphics. Since proteins comprise the majority of the mass of macromolecules in cells and carry out biologically important tasks, the book will be of interest to biologists. Provides accessible descriptions of principles of x-ray crystallography, built on simple foundations for anyone with a basic science background Leads the reader through clear, thorough, unintimidating explanations of the mathematics behind crystallography Explains how to read crystallography papers in research journals If you use computer-generated models of proteins or nucleic acids for: Studying molecular interactions Designing ligands, inhibitors, or drugs Engineering new protein functions Interpreting chemical, kinetic, thermodynamic, or spectroscopic data Studying protein folding Teaching macromolecule structure,and if you want to read new structure papers intelligently; become a wiser user of macromolecular models; and want to introduce undergraduates to the important subject of x-ray crystallography, then this book is for you.

Table of Contents

Preface to the Second Edition	p. xiii
Preface to the First Edition	p. xvii
Model and Molecule	p. 1
An Overview of Protein Crystallography	p. 5
Introduction	p. 5
Obtaining an image of a microscopic object	p. 6
Obtaining images of molecules	p. 7
A thumbnail sketch of protein crystallography	p. 7
Crystals	p. 8
The nature of crystals	p. 8
Growing crystals	p. 9
Collecting X-ray data	p. 10
Diffraction	p. 12
Simple objects	p. 12
Arrays of simple objects: Real and reciprocal lattices	p. 13
Intensities of reflections	p. 14
Arrays of complex objects	p. 15
Three-dimensional arrays	p. 16
Coordinate systems in crystallography	p. 17
The mathematics of crystallography: A brief description	p. 19
Wave equations: Periodic functions	p. 19
Complicated periodic functions: Fourier series	p. 20
Structure factors: Wave descriptions of X-ray reflections	p. 24
Electron-density maps	p. 24
Electron density from structure factors	p. 25
Electron density from measured reflections	p. 27
Obtaining a model	p. 28
Protein Crystals	p. 29
Properties of protein crystals	p. 29
Introduction	p. 29
Size, structural integrity, and mosaicity	p. 29
Multiple crystalline forms	p. 31
Water content	p. 32
Evidence that solution and crystal structures are similar	p. 33
Proteins retain their function in the crystal	p. 33
X-ray structures are compatible with other structural evidence	p. 34
Other evidence	p. 34
Growing protein crystals	p. 35
Introduction	p. 35
Growing crystals: Basic procedure	p. 35
Growing derivative crystals	p. 37
Finding optimal conditions for crystal growth	p. 37
Judging crystal quality	p. 41
Mounting crystals for data collection	p. 43
Collecting Diffraction Data	p. 45
Introduction	p. 45
Geometric principles of diffraction	p. 45
The generalized unit cell	p. 46
Indices of the atomic planes in a crystal	p. 47
Conditions that produce diffraction: Bragg's law	p. 50
The reciprocal lattice	p. 52
Bragg's law in reciprocal space	p. 55
The number of measurable reflections	p. 58
Unit-cell dimensions	p. 60
Unit-cell symmetry	p. 60
Collecting X-ray diffraction data	p. 64
Introduction	p. 64
X-ray sources	p. 65
Detectors	p. 69
Diffractometers and cameras	p. 72
Scaling and postrefinement of intensity data	p. 79
Determining unit-cell dimensions	p. 80
Symmetry and the strategy of collecting data	p. 82
Summary	p. 83
From Diffraction Data to Electron Density	p. 85
Introduction	p. 85
Fourier series and the Fourier transform	p. 86
One-dimensional waves	p. 86
Three-dimensional waves	p. 88
The Fourier transform: General features	p. 90
Fourier this and Fourier that: Review	p. 92
Fourier mathematics and diffraction	p. 92
Stucture factor as a Fourier series	p. 92
Electron density as a Fourier series	p. 94
Computing electron density from data	p. 95
The phase problem	p. 95
The meaning of the Fourier equations	p. 95
Reflections as Fourier terms: Equation (5.18)	p. 95
Computing structure factors from a model: Equations (5.15) and (5.16)	p. 96
Systematic absences in the diffraction pattern: Equation (5.15)	p. 98
Summary: From data to density	p. 100
Obtaining Phases	p. 101
Introduction	p. 101
Two-dimensional representation of structure factors	p. 102
Complex numbers in two dimensions	p. 102
Structure factors as complex vectors	p. 103
Electron density as a function of intensities and phases	p. 106
The heavy-atom method (isomorphous replacement)	p. 107
Preparing heavy-atom derivatives	p. 108
Obtaining phases from heavy-atom data	p. 109
Locating heavy atoms in the unit cell	p. 114
Anomalous scattering	p. 118
Introduction	p. 118
The measurable effects of anomalous scattering	p. 119
Extracting phases from anomalous scattering data	p. 120
Summary	p. 123
Multiwavelength anomalous diffraction phasing	p. 124
Anomalous scattering and the hand problem	p. 125
Direct phasing: Application of methods from small-molecule crystallography	p. 126
Molecular replacement: Related proteins as phasing models	p. 127
Introduction	p. 127
Isomorphous phasing models	p. 128
Nonisomorphous phasing models	p. 129
Separate searches for orientation and location	p. 129
Monitoring the search	p. 130
Summary	p. 131
Iterative improvement of phases (preview of Chapter 7)	p. 132
Obtaining and Judging the Molecular Model	p. 133
Introduction	p. 133
Iterative improvement of maps and models: Overview	p. 133
First maps	p. 137
Resources for the first map	p. 137
Displaying and examining the map	p. 138
Improving the map	p. 139
The model becomes molecular	p. 141
New phases from the molecular model	p. 141
Minimizing bias from the model	p. 142
Map fitting	p. 144
Structure refinement	p. 146
Least-squares methods	p. 146
Crystallographic refinement	p. 147
Additional refinement parameters	p. 147
Local minima and radius of convergence	p. 149
Molecular energy and motion in refinement	p. 150
Convergence to a final structure	p. 151
Producing the final map and model	p. 151
Guides to convergence	p. 153
Sharing the model	p. 154
A User's Guide to Crystallographic Models	p. 159
Introduction	p. 159
Judging the quality and usefulness of the refined model	p. 160
Structural parameters	p. 160
Resolution and precision of atomic positions	p. 162
Vibration and disorder	p. 164
Other limitations of crystallographic models	p. 166
Summary	p. 169
Reading a crystallography paper	p. 170
Introduction	p. 170
Annotated excerpts of the preliminary (8/91) paper	p. 170
Annotated excerpts from the full structure determination (4/92) paper	p. 175
Summary	p. 186
Other Diffraction Methods	p. 187
Introduction	p. 187
Fiber diffraction	p. 188
Diffraction by amorphous materials (scattering)	p. 196
Neutron diffraction	p. 200
Electron diffraction	p. 205
Lane diffraction and time-resolved crystallography	p. 209
Conclusion	p. 213
Other Kinds of Macromolecular Models	p. 215
Introduction	p. 215
NMR models	p. 216
Introduction	p. 216
Principles	p. 217
Assigning resonances	p. 230
Determining conformation	p. 232
PDB files for NMR models	p. 235
Judging model quality	p. 235
Homology models	p. 237
Introduction	p. 237
Principles	p. 238
Databases of homology models	p. 242
Judging model quality	p. 243
Other theoretical models	p. 246
Tools for Studying Macromolecules	p. 247
Introduction	p. 247
Computer models of molecules	p. 248
Two-dimensional images from coordinates	p. 248
Into three dimensions: Basic modeling operations	p. 249
Three-dimensional display and perception	p. 250
Types of graphical models	p. 251
Touring a typical molecular modeling program	p. 252
Importing and exporting coordinates files	p. 253
Loading and saving models	p. 253
Viewing models	p. 254
Editing and labeling the display	p. 255
Coloring	p. 256
Measuring	p. 257
Exploring structural change	p. 257
Exploring the molecular surface	p. 258
Exploring intermolecular interactions: Multiple models	p. 259
Displaying crystal packing	p. 260
Building models from scratch	p. 260
Other tools for studying structure	p. 261
Tools for structure analysis	p. 261
Tools for modeling protein action	p. 263
A final note	p. 263
Index	p. 265
Table of Contents provided by Syndetics. All Rights Reserved.