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

by Rhodes

• ISBN13: 9780125870726
• ISBN10: 0125870728
• Edition: 2nd
• Format: Paperback
• Copyright: 1999-11-29
• Publisher: Elsevier Science & Technology

Summary

Macromolecules are the proteins and nucleic acids upon which life depends. Understanding the action of biological macromolecules (giant molecules) requires detailed knowledge of their structures. Most of the more than ten thousand known structures of protein and nucleic acids were obtained by x-ray crystallography, the standard mechanism for determining protein structure. Essentially, proteins are frozen into rigid crystals, which can be stacked up in a repeating pattern--like supermarket displays. The structure of each individual crystal can be determined by the way x-rays are bent when they pass through the composite crystal. Protein structure is essential when investigating protein interactions and planning drug development. Crystallography Made Crystal Clear, Second Edition explains how scientists discover the structures of the macromolecules. Scientists do not see these molecules directly. Instead, they build models as a means of interpreting data from x-ray diffraction by crystals, or by irradiation by other forms of energy. Users of these models need to know how they are obtained in order to know what they are seeing when they study a model of a macromolecule. They also need to know how to judge whether conclusions they draw from the molecular models are really supported by the models. This book uses visual and geometric models to help readers understand the mathematics that forms the basis of x-ray crystallography. The field of protein crystallography is growing every day and has been instrumental in discovering the molecular principles of biology and in discovering new drugs, such as the recent protease inhibitors for AIDS. The field includes the largest percentage of Nobel prizes than any other scientific discipline. Every major university and drug company has a protein crystallography laboratory and this book is an invaluable aid to those wishing to practice protein crystallography or just learn more about how it is actually done.

Table of Contents

Preface to the Second Edition	xiii
Preface to the First Edition	xvii
Model and Molecule	1	(4)
An Overview of Protein Crystallography	5	(24)
Introduction	5	(3)
Obtaining an image of a microscopic object	6	(1)
Obtaining images of molecules	7	(1)
A thumbnail sketch of protein crystallography	7	(1)
Crystals	8	(2)
The nature of crystals	8	(1)
Growing crystals	9	(1)
Collecting X-ray data	10	(2)
Diffraction	12	(5)
Simple objects	12	(1)
Arrays of simple objects: Real and reciprocal lattices	13	(1)
Intensities of reflections	14	(1)
Arrays of complex objects	15	(1)
Three-dimensional arrays	16	(1)
Coordinate systems in crystallography	17	(2)
The mathematics of crystallography: A brief description	19	(10)
Wave equations: Periodic functions	19	(1)
Complicated periodic functions: Fourier series	20	(4)
Structure factors: Wave descriptions of X-ray reflections	24	(1)
Electron-density maps	24	(1)
Electron density from structure factors	25	(2)
Electron density from measured reflections	27	(1)
Obtaining a model	28	(1)
Protein Crystals	29	(16)
Properties of protein crystals	29	(4)
Introduction	29	(1)
Size, structural integrity, and mosaicity	29	(2)
Multiple crystalline forms	31	(1)
Water content	32	(1)
Evidence that solution and crystal structures are similar	33	(2)
Proteins retain their function in the crystal	33	(1)
X-ray structures are compatible with other structural evidence	34	(1)
Other evidence	34	(1)
Growing protein crystals	35	(6)
Introduction	35	(1)
Growing crystals: Basic procedure	35	(1)
Introduction	35	(1)
Growing crystals: Basic procedure	35	(2)
Growing derivative crystals	37	(1)
Finding optimal conditions for crystal growth	37	(4)
Judging crystal quality	41	(2)
Mounting crystals for data collection	43	(2)
Collecting Diffraction Data	45	(40)
Introduction	45	(1)
Geometric principles of diffraction	45	(19)
The generalized unit cell	46	(1)
Indices of the atomic planes in a crystal	47	(3)
Conditions that produce diffraction: Bragg's law	50	(2)
The reciprocal lattice	52	(3)
Bragg's law in reciprocal space	55	(3)
The number of measurable reflections	58	(2)
Unit-cell dimensions	60	(1)
Unit-cell symmetry	60	(4)
Collecting X-ray diffraction data	64	(19)
Introduction	64	(1)
X-ray sources	65	(4)
Detectors	69	(3)
Diffractometers and cameras	72	(7)
Scaling and postrefinement of intensity data	79	(1)
Determining unit-cell dimensions	80	(2)
Symmetry and the strategy of collecting data	82	(1)
Summary	83	(2)
From Diffraction Data to Electron Density	85	(16)
Introduction	85	(1)
Fourier series and the Fourier transform	86	(6)
One-dimensional waves	86	(2)
Three-dimensional waves	88	(2)
The Fourier transform: General features	90	(2)
Fourier this and Fourier that: Review	92	(1)
Fourier mathematics and diffraction	92	(3)
Stucture factor as a Fourier series	92	(2)
Electron density as a Fourier series	94	(1)
Computing electron density from data	95	(1)
The phase problem	95	(1)
The meaning of the Fourier equations	95	(5)
Reflections as Fourier terms: Equation (5.18)	95	(1)
Computing structure factors from a model: Equations (5.15) and (5.16)	96	(2)
Systematic absences in the diffraction pattern: Equation (5.15)	98	(2)
Summary: From data to density	100	(1)
Obtaining Phases	101	(32)
Introduction	101	(1)
Two-dimensional representation of structure factors	102	(5)
Complex numbers in two dimensions	102	(1)
Structure factors as complex vectors	103	(3)
Electron density as a function of intensities and phases	106	(1)
The heavy-atom method (isomorphous replacement)	107	(11)
A. Preparing heavy-atom derivatives	108	(1)
Obtaining phases from heavy-atom data	109	(5)
Locating heavy atoms in the unit cell	114	(4)
Anomalous scattering	118	(9)
Introduction	118	(1)
The measurable effects of anomalous scattering	119	(1)
Extracting phases from anomalous scattering data	120	(3)
Summary	123	(1)
Multiwavelength anomalous diffraction phasing	124	(1)
Anomalous scattering and the hand problem	125	(1)
Direct phasing: Application of methods from small-molecule crystallography	126	(1)
Molecular replacement: Related proteins as phasing models	127	(5)
Introduction	127	(1)
Isomorphous phasing models	128	(1)
Nonisomorphous phasing models	129	(1)
Separate searches for orientation and location	129	(1)
Monitoring the search	130	(1)
Summary	131	(1)
Iterative improvement of phases (preview of Chapter 7)	132	(1)
Obtaining and Judging the Molecular Model	133	(26)
Introduction	133	(1)
Iterative improvement of maps and models: Overview	133	(4)
First maps	137	(4)
Resources for the first map	137	(1)
Displaying and examining the map	138	(1)
Improving the map	139	(2)
The model becomes molecular	141	(5)
New phases from the molecular model	141	(1)
Minimizing bias from the model	142	(2)
Map fitting	144	(2)
Structure refinement	146	(5)
Least-squares methods	146	(1)
Crystallographic refinement	147	(1)
Additional refinement parameters	147	(2)
Local minima and radius of convergence	149	(1)
Molecular energy and motion in refinement	150	(1)
Convergence to a final structure	151	(3)
Producing the final map and model	151	(2)
Guides to convergence	153	(1)
Sharing the model	154	(5)
A User's Guide to Crystallographic Models	159	(28)
Introduction	159	(1)
Judging the quality and usefulness of the refined model	160	(10)
Structural parameters	160	(2)
Resolution and precision of atomic positions	162	(2)
Vibration and disorder	164	(2)
Other limitations of crystallographic models	166	(3)
Summary	169	(1)
Reading a crystallography paper	170	(16)
Introduction	170	(1)
Annotated excerpts of the preliminary (8/91) paper	170	(5)
Annotated excerpts from the full structure determination (4/92) paper	175	(11)
Summary	186	(1)
Other Diffraction Methods	187	(28)
Introduction	187	(1)
Fiber diffraction	188	(8)
Diffraction by amorphous materials (scattering)	196	(4)
Neutron diffraction	200	(5)
Electron diffraction	205	(4)
Lane diffraction and time-resolved crystallography	209	(4)
Conclusion	213	(2)
Other Kinds of Macromolecular Models	215	(32)
Introduction	215	(1)
NMR models	216	(21)
Introduction	216	(1)
Principles	217	(13)
Assigning resonances	230	(2)
Determining conformation	232	(3)
PDB files for NMR models	235	(1)
Judging model quality	235	(2)
Homology models	237	(9)
Introduction	237	(1)
Principles	238	(4)
Databases of homology models	242	(1)
Judging model quality	243	(3)
Other theoretical models	246	(1)
Tools for Studying Macromolecules	247	(18)
Introduction	247	(1)
Computer models of molecules	248	(4)
Two-dimensional images from coordinates	248	(1)
Into three dimensions: Basic modeling operations	249	(1)
Three-dimensional display and perception	250	(1)
Types of graphical models	251	(1)
Touring a typical molecular modeling program	252	(9)
Importing and exporting coordinates files	253	(1)
Loading and saving models	253	(1)
Viewing models	254	(1)
Editing and labeling the display	255	(1)
Coloring	256	(1)
Measuring	257	(1)
Exploring structural change	257	(1)
Exploring the molecular surface	258	(1)
Exploring intermolecular interactions: Multiple models	259	(1)
Displaying crystal packing	260	(1)
Building models from scratch	260	(1)
Other tools for studying structure	261	(2)
Tools for structure analysis	261	(2)
Tools for modeling protein action	263	(1)
A final note	263	(2)
Index	265