Principles of Protein X-Ray Crystallography

by Drenth, Jan; Mesters, Jeroen (CON)

• ISBN13: 9780387333342
• ISBN10: 0387333347
• Edition: 3rd
• Format: Hardcover
• Copyright: 2006-11-10
• Publisher: Springer Nature

Summary

X-ray crystallography has long been a vital method for studying the structure of proteins and other macromolecules. As the importance of proteins continues to grow, in fields from biochemistry and biophysics to pharmaceutical development and biotechnology, many researchers have found that a knowledge of X-ray diffraction is an indispensable tool. In this new edition of his essential work, Dr. Jan Drenth, recognized internationally for his numerous contributions to crystallographic research, has provided an up-to-date and technically rigorous introduction to the subject. Principles of Protein X-ray Crystallography provides the theoretical background necessary to understand how the structure of proteins is determined at atomic resolution. It is intended to serve as an introduction for graduate students, postdoctoral researchers, and established scientists who want to use protein crystallography in their own endeavors, or need to understand the subject in order to critically evaluate the literature. New additions to the book include a section on twinning, an additional chapter on crystal growth and a discussion of single-wavelength anomalous dispersion (SAD). About the Authors: Dr. Jan Drenth is a professor emeritus at the Laboratory of Biophysical Chemistry at the University of Groningen, The Netherlands. Contributing author Dr. Jeroen R. Mesters Ph.D. is a Senior Research Assistant at the Institute of Biochemistry, University of Luebeck, Germany.

Author Biography

Dr. Jan Drenth is a professor emeritus at the Laboratory of Biophysical Chemistry at the University of Groningen, The Netherlands.Contributing author Dr. Jeroen R. Mesters Ph.D. is a Senior Research Assistant at the Institute of Biochemistry, University of Luebeck, Germany.

Table of Contents

Preface to the Third Edition	v
Preface to the Second Edition	vi
Preface to the First Edition	vii
Chapter 1 Crystallizing a Protein	1	(20)
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	(1)
1.5 A Preliminary Note on Crystals	9	(2)
1.6 Preparation for an X-ray Diffraction Experiment	11	(4)
1.7 Cryocooling	15	(2)
1.8 Notes	17	(3)
Summary	20	(1)
Chapter 2 X-ray Sources and Detectors	21	(24)
2.1 Introduction	21	(1)
2.2 X-ray Sources	21	(9)
2.3 Monochromators	30	(1)
2.4 Introduction to Cameras and Detectors	31	(2)
2.5 Detectors	33	(5)
2.6 The Rotation (Oscillation) Instrument	38	(5)
Summary	43	(2)
Chapter 3 Crystals	45	(19)
3.1 Introduction	45	(4)
3.2 Symmetry	49	(7)
3.3 Possible Symmetry for Protein Crystals	56	(1)
3.4 Coordinate Triplets: General and Special Positions	56	(1)
3.5 Asymmetric Unit	57	(1)
3.6 Point Groups	58	(1)
3.7 Crystal Systems	58	(2)
3.8 Radiation Damage	60	(1)
3.9 Characterization of the Crystals	61	(2)
Summary	63	(1)
Chapter 4 Theory of X-ray Diffraction by a Crystal	64	(45)
4.1 Introduction	64	(1)
4.2 Waves and Their Addition	65	(3)
4.3 A System of Two Electrons	68	(3)
4.4 Scattering by an Atom	71	(2)
4.5 Scattering by a Unit Cell	73	(1)
4.6 Scattering by a Crystal	74	(2)
4.7 Diffraction Conditions	76	(1)
4.8 Reciprocal Lattice and Ewald Construction	77	(4)
4.9 The Temperature Factor	81	(3)
4.10 Calculation of the Electron Density p(x y z)	84	(6)
4.11 Comparison of F(h k 1) and F(h k l)	90	(1)
4.12 Symmetry in the Diffraction Pattern	91	(4)
4.13 Integral Reflection Conditions for Centered Lattices	95	(1)
4.14 Intensity Diffracted by a Crystal	96	(7)
4.15 Scattering by a Plane of Atoms	103	(2)
4.16 Choice of Wavelength, Size of Unit Cell, and Correction of the Diffracted Intensity	105	(2)
Summary	107	(2)
Chapter 5 Average Reflection Intensity and Distribution of Structure Factor Data	109	(10)
5.1 Introduction	109	(2)
5.2 Average Intensity; Wilson Plots	111	(3)
5.3 The Distribution of Structure Factors F and Structure Factor Amplitudes |F|	114	(2)
5.4 Crystal Twinning	116	(2)
Summary	118	(1)
Chapter 6 Special Forms of the Structure Factor	119	(4)
6.1 Introduction	119	(1)
6.2 The Unitary Structure Factor	119	(1)
6.3 The Normalized Structure Factor	120	(2)
Summary	122	(1)
Chapter 7 The Solution of the Phase Problem by the Isomorphous Replacement Method	123	(49)
7.1 Introduction	123	(1)
7.2 The Patterson Function	124	(9)
7.3 The Isomorphous Replacement Method	133	(6)
7.4 Effect of Heavy Atoms on X-ray Intensities	139	(3)
7.5 Determination of the Heavy Atom Parameters from Centrosymmetric Projections	142	(2)
7.6 Parameters of Heavy Atoms Derived from Acentric Reflections	144	(2)
7.7 The Difference Fourier Summation	146	(2)
7.8 Anomalous Scattering	148	(4)
7.9 The Anomalous Patterson Summation	152	(2)
7.10 One Common Origin for All Derivatives	154	(3)
7.11 Refinement of the Heavy Atom Parameters Using Preliminary Protein Phase Angles	157	(3)
7.12 Protein Phase Angles	160	(7)
7.13 The Remaining Error in the Best Fourier Map	167	(3)
7.14 The Single Isomorphous Replacement Method	170	(1)
Summary	171	(1)
Chapter 8 Phase Improvement	172	(22)
8.1 Introduction	172	(1)
8.2 The OMIT Map With and Without Sim Weighting	173	(6)
8.3 Solvent Flattening	179	(6)
8.4 Noncrystallographic Symmetry and Molecular Averaging	185	(2)
8.5 Histogram Matching	187	(3)
8.6 wARP: Weighted Averaging of Multiple-Refined Dummy Atomic Models	190	(2)
8.7 Further Considerations Concerning Density Modification	192	(1)
Summary	193	(1)
Chapter 9 Anomalous Scattering in the Determination of the Protein Phase Angles and the Absolute Configuration	194	(16)
9.1 Introduction	194	(1)
9.2 Protein Phase Angle Determination with Anomalous Scattering	194	(2)
9.3 Improvement of Protein Phase Angles with Anomalous Scattering	196	(2)
9.4 The Determination of the Absolute Configuration	198	(1)
9.5 Multiple- and Single-Wavelength Anomalous Diffraction (MAD and SAD)	199	(10)
Summary	209	(1)
Chapter 10 Molecular Replacement	210	(21)
10.1 Introduction	210	(1)
10.2 The Rotation Function	211	(6)
10.3 The Translation Function	217	(13)
Summary	230	(1)
Chapter 11 Direct Methods	231	(10)
11.1 Introduction	231	(1)
11.2 Shake-and-Bake	231	(5)
11.3 SHELXD	236	(2)
11.4 The Principle of Maximum Entropy	238	(2)
Summary	240	(1)
Chapter 12 Laue Diffraction	241	(7)
12.1 Introduction	241	(1)
12.2 The Accessible Region of Reciprocal Space	242	(1)
12.3 The Multiple Problem	243	(1)
12.4 Unscrambling of Multiple Intensities	244	(1)
12.5 The Spatial Overlap Problem	245	(1)
12.6 Wavelength Normalization	245	(1)
Summary	246	(2)
Chapter 13 Refinement of the Model Structure	248	(31)
13.1 Introduction	248	(3)
13.2 The Mathematics of Refinement	251	(11)
13.3 The Principle of the Fast Fourier Transform Method	262	(2)
13.4 Specific Refinement Methods	264	(14)
Summary	278	(1)
Chapter 14 The Combination of Phase Information	279	(6)
14.1 Introduction	279	(1)
14.2 Phase Information from Isomorphous Replacement	280	(2)
14.3 Phase Information from Anomalous Scattering	282	(1)
14.4 Phase Information from Partial Structure Data, Solvent Flattening, and Molecular Averaging	283	(1)
14.5 Phase Information from SAD	284	(1)
Summary	284	(1)
Chapter 15 Checking for Gross Errors and Estimating the Accuracy of the Structural Model	285	(12)
15.1 Introduction	285	(1)
15.2 R-Factors	285	(2)
15.3 The Ramachandran Plot	287	(1)
15.4 Stereochemistry Check	287	(1)
15.5 The 3D-1D Profile Method	288	(4)
15.6 Quantitative Estimation of the Coordinate Error in the Final Model	292	(4)
Summary	296	(1)
Chapter 16 Practical Protein Crystallization	297	(8)
16.1 Introduction	297	(1)
16.2 Gene Cloning and Expression	298	(1)
16.3 Protein Purification	299	(3)
16.4 Protein Crystallization	302	(1)
Summary	303	(2)
Appendix 1 A Compilation of Equations for Calculating Electron Density Maps	305	(3)
Appendix 2 A Compilation of Reliability Indexes	308	(6)
Appendix 3 The Variation in the Intensity of X-ray Radiation	314	(2)
References	316	(10)
Index	326