Crystallography Made Crystal Clear

by Rhodes

• ISBN13: 9780125870733
• ISBN10: 0125870736
• Edition: 3rd
• Format: Paperback
• Copyright: 2006-02-16
• Publisher: Elsevier Science

Summary

This much admired book has been carefully revised to make crystallography even more accessible to readers who have no prior experience with crystallography and macromolecular models, or their mathematical foundations. It continues to provide clear, understandable descriptions of the principles of protein crystallography with abundant illustrations and stereo images (in full color). Coverage extends to X-ray, neutron, electron, and Laue diffraction methods, as well as NMR spectroscopy and homology modeling. Book jacket.

Table of Contents

Preface to the Third Edition	xv
Preface to the Second Edition	xix
Preface to the First Edition	xxiii
Model and Molecule	1	(6)
An Overview of Protein Crystallography	7	(24)
Introduction	7	(3)
Obtaining an image of a microscopic object	8	(1)
Obtaining images of molecules	9	(1)
A thumbnail sketch of protein crystallography	9	(1)
Crystals	10	(3)
The nature of crystals	10	(1)
Growing crystals	11	(2)
Collecting X-ray data	13	(2)
Diffraction	15	(4)
Simple objects	15	(1)
Arrays of simple objects: Real and reciprocal lattices	16	(1)
Intensities of reflections	16	(1)
Arrays of complex objects	17	(1)
Three-dimensional arrays	18	(1)
Coordinate systems in crystallography	19	(1)
The mathematics of crystallography: A brief description	20	(11)
Wave equations: Periodic functions	21	(2)
Complicated periodic functions: Fourier series and sums	23	(1)
Structure factors: Wave descriptions of X-ray reflections	24	(2)
Electron-density maps	26	(1)
Electron density from structure factors	27	(1)
Electron density from measured reflections	28	(2)
Obtaining a model	30	(1)
Protein Crystals	31	(18)
Properties of protein crystals	31	(4)
Introduction	31	(1)
Size, structural integrity, and mosaicity	31	(2)
Multiple crystalline forms	33	(1)
Water content	34	(1)
Evidence that solution and crystal structures are similar	35	(2)
Proteins retain their function in the crystal	35	(1)
X-ray structures are compatible with other structural evidence	36	(1)
Other evidence	37	(1)
Growing protein crystals	37	(9)
Introduction	37	(1)
Growing crystals: Basic procedure	38	(2)
Growing derivative crystals	40	(1)
Finding optimal conditions for crystal growth	41	(5)
Judging crystal quality	46	(1)
Mounting crystals for data collection	46	(3)
Collecting Diffraction Data	49	(42)
Introduction	49	(1)
Geometric principles of diffraction	49	(24)
The generalized unit cell	49	(1)
Indices of the atomic planes in a crystal	50	(5)
Conditions that produce diffraction: Bragg's law	55	(2)
The reciprocal lattice	57	(3)
Bragg's law in reciprocal space	60	(4)
Number of measurable reflections	64	(1)
Unit-cell dimensions	65	(1)
Unit-cell symmetry	65	(8)
Collecting X-ray diffraction data	73	(16)
Introduction	73	(1)
X-ray sources	73	(4)
Detectors	77	(3)
Cameras	80	(5)
Scaling and postrefinement of intensity data	85	(1)
Determining unit-cell dimensions	86	(2)
Symmetry and the strategy of collecting data	88	(1)
Summary	89	(2)
From Diffraction Data to Electron Density	91	(18)
Introduction	91	(1)
Fourier sums and the Fourier transform	92	(6)
One-dimensional waves	92	(2)
Three-dimensional waves	94	(2)
The Fourier transform: General features	96	(1)
Fourier this and Fourier that: Review	97	(1)
Fourier mathematics and diffraction	98	(3)
Structure factor as a Fourier sum	98	(1)
Electron density as a Fourier sum	99	(1)
Computing electron density from data	100	(1)
The phase problem	101	(1)
Meaning of the Fourier equations	101	(6)
Reflections as terms in a Fourier sum: Eq. (5.18)	101	(3)
Computing structure factors from a model: Eq. (5.15) and Eq. (5.16)	104	(1)
Systematic absences in the diffraction pattern: Eq. (5.15)	105	(2)
Summary: From data to density	107	(2)
Obtaining Phases	109	(36)
Introduction	109	(3)
Two-dimensional representation of structure factors	112	(5)
Complex numbers in two dimensions	112	(1)
Structure factors as complex vectors	112	(3)
Electron density as a function of intensities and phases	115	(2)
Isomorphous replacement	117	(11)
Preparing heavy-atom derivatives	117	(2)
Obtaining phases from heavy-atom data	119	(5)
Locating heavy atoms in the unit cell	124	(4)
Anomalous scattering	128	(8)
Introduction	128	(1)
Measurable effects of anomalous scattering	128	(2)
Extracting phases from anomalous scattering data	130	(2)
Summary	132	(1)
Multiwavelength anomalous diffraction phasing	133	(2)
Anomalous scattering and the hand problem	135	(1)
Direct phasing: Application of methods from small-molecule crystallography	135	(1)
Molecular replacement: Related proteins as phasing models	136	(7)
Introduction	136	(1)
Isomorphous phasing models	137	(2)
Nonisomorphous phasing models	139	(1)
Separate searches for orientation and location	139	(2)
Monitoring the search	141	(2)
Summary of molecular replacement	143	(1)
Iterative improvement of phases (preview of Chapter 7)	143	(2)
Obtaining and Judging the Molecular Model	145	(34)
Introduction	145	(1)
Iterative improvement of maps and models---overview	146	(3)
First maps	149	(4)
Resources for the first map	149	(1)
Displaying and examining the map	150	(1)
Improving the map	151	(2)
The Model becomes molecular	153	(6)
New phases from the molecular model	153	(1)
Minimizing bias from the model	154	(2)
Map fitting	156	(3)
Structure refinement	159	(9)
Least-squares methods	159	(1)
Crystallographic refinement by least squares	160	(1)
Additional refinement parameters	161	(1)
Local minima and radius of convergence	162	(1)
Molecular energy and motion in refinement	163	(1)
Bayesian methods: Ensembles of models	164	(4)
Convergence to a final model	168	(5)
Producing the final map and model	168	(3)
Guides to convergence	171	(2)
Sharing the model	173	(6)
A User's Guide to Crystallographic Models	179	(32)
Introduction	179	(2)
Judging the quality and usefulness of the refined model	181	(11)
Structural parameters	181	(2)
Resolution and precision of atomic positions	183	(2)
Vibration and disorder	185	(2)
Other limitations of crystallographic models	187	(2)
Online validation tools: Do it yourself!	189	(3)
Summary	192	(1)
Reading a crystallography paper	192	(17)
Introduction	192	(1)
Annotated excerpts of the preliminary (8/91) paper	193	(5)
Annotated excerpts from the full structure-determination (4/92) paper	198	(11)
Summary	209	(2)
Other Diffraction Methods	211	(26)
Introduction	211	(1)
Fiber diffraction	211	(8)
Diffraction by amorphous materials (scattering)	219	(3)
Neutron diffraction	222	(5)
Electron diffraction and cryo-electron microscopy	227	(4)
Laue diffraction and time-resolved crystallography	231	(4)
Summary	235	(2)
Other Kinds of Macromolecular Models	237	(32)
Introduction	237	(1)
NMR models	238	(21)
Introduction	238	(1)
Principles	239	(12)
Assigning resonances	251	(1)
Determining conformation	252	(5)
PDB files for NMR models	257	(1)
Judging model quality	257	(2)
Homology models	259	(8)
Introduction	259	(1)
Principles	260	(3)
Databases of homology models	263	(2)
Judging model quality	265	(2)
Other theoretical models	267	(2)
Tools for Studying Macromolecules	269	(24)
Introduction	269	(1)
Computer models of molecules	269	(6)
Two-dimensional images from coordinates	269	(1)
Into three dimensions: Basic modeling operations	270	(2)
Three-dimensional display and perception	272	(1)
Types of graphical models	273	(2)
Touring a molecular modeling program	275	(13)
Importing and exporting coordinate files	276	(2)
Loading and saving models	278	(1)
Viewing models	278	(2)
Editing and labeling the display	280	(1)
Coloring	281	(1)
Measuring	281	(1)
Exploring structural change	282	(1)
Exploring the molecular surface	282	(4)
Exploring intermolecular interactions: Multiple models	286	(1)
Displaying crystal packing	287	(1)
Building models from scratch	287	(1)
Scripts and macros: Automating routine structure analysis	287	(1)
Other tools for studying structure	288	(3)
Tools for structure analysis and validation	288	(2)
Tools for modeling protein action	290	(1)
Final note	291	(2)
Appendix Viewing Stereo Images	293	(2)
Index	295