Principles of Protein X-Ray Crystallography

by Drenth, Jan

• ISBN13: 9780387985879
• ISBN10: 0387985875
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-02-01
• Publisher: Springer Verlag

Summary

X-ray crystallography has been a vital method for studying the structure of proteins and other macromolecules for many years. As the importance of proteins continues to grow in a wide range of research fields from basic biochemistry and biophysics to pharmaceutical development and biotechnology, more and more researchers have found a knowledge of X-ray diffraction to be an indispensable tool. Professor Drenth, recognized internationally for his numerous contributions to crystallographic research, has provided a technically rigorous introduction to the subject. This book provides the theoretical background necessary to understand how the structure of proteins is determined at atomic resolution. It is intended to be an introduction for graduate students, postdoctoral researchers, and established scientists who want to apply protein crystallography in their own endeavors, or need to understand the subject in order to critically evaluate the literature. Principles of Protein X-ray Crystallography is appropriate as a textbook for courses in biochemistry and biophysics, including protein structure and function, structural biology, and macromolecular structure.

Table of Contents

Series Preface	v	(2)
Preface to the Second Edition	vii	(2)
Preface to the First Edition	ix
Chapter 1 Crystallizing a Protein	1	(21)
1.1 Introduction	1	(1)
1.2 Principles of Protein Crystallization	1	(3)
1.3 Crystallization Techniques	4	(4)
1.4 Crystallization of Lysozyme	8	(3)
1.5 A Preliminary Note on Crystals	11	(1)
1.6 Preparation for an X-ray Diffraction Experiment	12	(4)
1.7 Cryocooling	16	(2)
1.8 Notes	18	(3)
Summary	21	(1)
Chapter 2 X-ray Sources and Detectors	22	(28)
2.1 Introduction	22	(1)
2.2 X-ray Sources	22	(10)
2.3 Monochromators	32	(2)
2.4 Introduction to Cameras and Detectors	34	(1)
2.5 Detectors	35	(6)
2.6 The Rotation (Oscillation) Instrument	41	(6)
2.7 Electronic Area Detectors	47	(2)
Summary	49	(1)
Chapter 3 Crystals	50	(20)
3.1 Introduction	50	(5)
3.2 Symmetry	55	(3)
3.3 Possible Symmetry for Protein Crystals	58	(4)
3.4 Coordinate Triplets: General and Special Positions	62	(1)
3.5 Asymmetric Unit	63	(1)
3.6 Point Groups	64	(1)
3.7 Crystal Systems	64	(2)
3.8 Radiation Damage	66	(1)
3.9 Characterization of the Crystals	67	(2)
Summary	69	(1)
Chapter 4 The Theory of X-ray Diffraction by a Crystal	70	(47)
4.1 Introduction	70	(1)
4.2 Waves and Their Addition	71	(3)
4.3 A System of Two Electrons	74	(4)
4.4 Scattering by an Atom	78	(2)
4.5 Scattering by a Unit Cell	80	(1)
4.6 Scattering by a Crystal	81	(1)
4.7 Diffraction Conditions	82	(2)
4.8 Reciprocal Lattice and Ewald Construction	84	(5)
4.9 The Temperature Factor	89	(3)
4.10 Calculation of the Electron Density p (x y z)	92	(6)
4.11 Comparison of F(h k l) and F(h k l)	98	(1)
4.12 Symmetry in the Diffraction Pattern	99	(4)
4.13 Integral Reflection Conditions for Centered Lattices	103	(1)
4.14 The Intensity Diffracted by a Crystal	103	(8)
4.15 Scattering by a Plane of Atoms	111	(2)
4.16 Choice of Wavelength, Size of Unit Cell, and Correction of the Diffracted Intensity	113	(2)
Summary	115	(2)
Chapter 5 Average Reflection Intensity and Distribution of Structure Factor Data	117	(8)
5.1 Introduction	117	(3)
5.2 Average Intensity; Wilson Plots	120	(2)
5.3 The Distribution of Structure Factors F and Structure Factor Amplitudes F	122	(2)
Summary	124	(1)
Chapter 6 Special Forms of the Structure Factor	125	(4)
6.1 Introduction	125	(1)
6.2 The Unitary Structure Factor	125	(1)
6.3 The Normalized Structure Factor	126	(2)
Summary	128	(1)
Chapter 7 The Solution of the Phase Problem by the Isomorphous Replacement Method	129	(51)
7.1 Introduction	129	(1)
7.2 The Patterson Function	130	(9)
7.3 The Isomorphous Replacement Method	139	(6)
7.4 Effect of Heavy Atoms on X-ray Intensities	145	(4)
7.5 Determination of the Heavy Atom Parameters from Centrosymmetric Projections	149	(2)
7.6 Parameters of Heavy Atoms Derived from Acentric Reflections	151	(1)
7.7 The Difference Fourier Summation	152	(3)
7.8 Anomalous Scattering	155	(4)
7.9 The Anomalous Patterson Summation	159	(2)
7.10 One Common Origin for All Derivatives	161	(4)
7.11 Refinement of the Heavy Atom Parameters Using Preliminary Protein Phase Angles	165	(3)
7.12 Protein Phase Angles	168	(6)
7.13 The Remaining Error in the Best Fourier Map	174	(4)
7.14 The Single Isomorphous Replacement (SIR) Method	178	(1)
Summary	179	(1)
Chapter 8 Phase Improvement	180	(23)
8.1 Introduction	180	(1)
8.2 The OMIT Map with and Without Sim Weighting	181	(7)
8.3 Solvent Flattening	188	(6)
8.4 Noncrystallographic Symmetry and Molecular Averaging	194	(4)
8.5 Histogram Matching	198	(1)
8.6 wARP: Weighted Averaging of Multiple-Refined Dummy Atomic Models	199	(1)
8.7 Further Considerations Concerning Density Modification	200	(2)
Summary	202	(1)
Chapter 9 Anomalous Scattering in the Determination of the Protein Phase Angles and the Absolute Configuration	203	(16)
9.1 Introduction	203	(1)
9.2 Protein Phase Angle Determination with Anomalous Scattering	203	(2)
9.3 Improvement of Protein Phase Angles with Anomalous Scattering	205	(2)
9.4 The Determination of the Absolute Configuration	207	(2)
9.5 Multiple Wavelength Anomalous Dispersion (MAD)	209	(9)
Summary	218	(1)
Chapter 10 Molecular Replacement	219	(25)
10.1 Introduction	219	(1)
10.2 The Rotation Function	220	(9)
10.3 The Translation Function	229	(14)
Summary	243	(1)
Chapter 11 Direct Methods	244	(9)
11.1 Introduction	244	(1)
11.2 Shake-and-Bake	244	(5)
11.3 The Principle of Maximum Entropy	249	(3)
Summary	252	(1)
Chapter 12 Laue Diffraction	253	(7)
12.1 Introduction	253	(1)
12.2 The Accessible Region of Reciprocal Space	254	(1)
12.3 The Multiple Problem	255	(1)
12.4 Unscrambling of Multiple Intensities	256	(1)
12.5 The Spatial Overlap Problem	257	(1)
12.6 Wavelength Normalization	257	(2)
Summary	259	(1)
Chapter 13 Refinement of the Model Structure	260	(32)
13.1 Introduction	260	(3)
13.2 The Mathematics of Refinement	263	(12)
13.3 The Principle of the Fast Fourier Transform (FFT) Method	275	(2)
13.4 Specific Refinement Methods	277	(14)
Summary	291	(1)
Chapter 14 The Combination of Phase Information	292	(6)
14.1 Introduction	292	(1)
14.2 Phase Information from Isomorphous Replacement	293	(2)
14.3 Phase Information from Anomalous Scattering	295	(1)
14.4 Phase Information from MAD	296	(1)
14.5 Phase Information from Partial Structure Data, Solvent Flattening, and Molecular Averaging	297	(1)
Summary	297	(1)
Chapter 15 Checking for Gross Errors and Estimating the Accuracy of the Structural Model	298	(13)
15.1 Introduction	298	(1)
15.2 R-Factors	298	(2)
15.3 The Ramachandran Plot	300	(2)
15.4 Stereochemistry Check	302	(1)
15.5 The 3D-1D Profile Method	303	(2)
15.6 Quantitative Estimation of the Coordinate Error in the Final Model	305	(5)
Summary	310	(1)
Appendix 1 A Compilation of Equations for Calculating Electron Density Maps	311	(4)
Appendix 2 A Compilation of Reliability Indices	315	(6)
Appendix 3 The Variation in the Intensity of X-ray Radiation	321	(2)
References	323	(8)
Index	331