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X-Ray Crystallography of Biomacromolecules: A Practical Guide

ISBN: 978-3-527-31396-9
318 pages
January 2007, Wiley-Blackwell
X-Ray Crystallography of Biomacromolecules: A Practical Guide (3527313966) cover image
Written by one of the most significant contributors to the progress of protein crystallography, this practical guide contains case studies, a troubleshooting section and pointers on data interpretation. It covers the theory, practice and latest achievements in x-ray crystallography, such that any researcher in structural biology will benefit from this extremely clearly written book.
Part A covers the theoretical basis and such experimental techniques as principles of x-ray diffraction, solutions for the phase problem and time-resolved x-ray crystallography. Part B includes case studies for different kinds of x-ray crystal structure determination, such as the MIRAS and MAD techniques, molecular replacement, and the difference Fourier technique.
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Preface XIII

Part I

Principles and Methods

1 Introduction 3

1.1 Crystals and Symmetry 3

1.2 Protein Solubility 13

1.2.1 Ionic Strength 13

1.2.1.1 “Salting-in” 14

1.2.1.2 “Salting-out” 15

1.2.2 pH and Counterions 15

1.2.3 Temperature 15

1.2.4 Organic Solvents 15

1.3 Experimental Techniques 16

1.3.1 Batch Crystallization 17

1.3.2 Vapor Diffusion 17

1.3.3 Crystallization by Dialysis 19

1.4 Crystallization Screenings 19

1.5 High-Throughput Crystallization, Imaging, and Analysis 20

References 22

2 Experimental Techniques 23

2.1 X-Ray Sources 23

2.1.1 Conventional X-Ray Generators 23

2.1.2 Synchrotron Radiation 24

2.1.3 Monochromators 28

2.2 Detectors 31

2.2.1 General Components of an X-Ray Diffraction Experiment 31

2.2.2 Image Plates 32

2.2.3 Gas Proportional Detectors 33

2.2.4 Charge-Coupled Device-Based Detectors 35

2.3 Crystal Mounting and Cooling 36

2.3.1 Conventional Crystal Mounting 36

2.3.2 Cryocrystallography 37

2.3.3 Crystal Quality Improvement by Humidity Control 40

2.4 Data Collection Techniques 40

2.4.1 Rotation Method 40

2.4.2 Precession Method 43

References 44

3 Principles of X-Ray Diffraction by a Crystal 45

3.1 Rational Mathematical Representation of Waves 45

3.1.1 Simple Harmonic Oscillations 45

3.1.2 Wavelike Propagation of Periodic States 49

3.2 Principles of X-Ray Diffraction by a Crystal 51

3.2.1 Scattering of X-Rays by an Electron 51

3.2.2 Scattering of X-Rays by an Atom 55

3.2.3 The Atomic Scattering Factor 58

3.2.4 Scattering of X-Rays by a Unit Cell 60

3.2.5 Scattering of X-Rays by a Crystal 61

3.2.5.1 One-Dimensional Crystal 61

3.2.5.2 Three-Dimensional Crystal 61

3.2.6 The Reciprocal Lattice and Ewald Construction 64

3.2.7 The Temperature Factor 66

3.2.8 Symmetry in Diffraction Patterns 68

3.2.9 Electron Density Equation and Phase Problem 68

3.2.10 The Patterson Function 71

3.2.11 Lorentz Factor and Integrated Intensity Diffracted by a Crystal 74

3.2.12 Intensities on an Absolute Scale 78

3.2.13 Resolution of the Structure Determination 78

References 79

4 Diffraction Data Evaluation 81

4.1 Introductory Remarks 81

4.2 Geometric Principles in the Rotation Technique with Normal Flat Detector 82

4.3 Autoindexing of Oscillation Images 84

4.4 Beam Divergence, Mosaicity, and Partiality 87

4.5 Integration of Diffraction Spots 90

4.6 Post-Refinement, Scaling, and Averaging of Diffraction Data 93

References 96

5 Methods for Solving the Phase Problem 99

5.1 Isomorphous Replacement 99

5.1.1 Preparation of Heavy-Metal Derivatives 99

5.1.2 Single Isomorphous Replacement 100

5.1.3 Multiple Isomorphous Replacement 104

5.2 Anomalous Scattering 105

5.2.1 Theoretical Background 105

5.2.2 Experimental Determination 108

5.2.3 Breakdown of Friedel’s Law 109

5.2.4 Anomalous Difference Patterson Map 110

5.2.5 Phasing Including Anomalous Scattering Information 111

5.2.6 The Multiwavelength Anomalous Diffraction (MAD) Technique 112

5.2.7 Determination of the Absolute Configuration 114

5.3 Determination of Heavy-Atom Positions 115

5.3.1 Vector Verification Procedures 115

5.3.2 Direct Methods 117

5.4 Phase Calculation 121

5.4.1 Refinement of Heavy-Atom Parameters 121

5.4.2 Protein Phases 123

5.4.3 Maximum-Likelihood Parameter Refinement and Phase Calculation 126

5.4.4 Cross-Phasing of Heavy-Atom Derivatives or Anomalous Dispersion Data 128

5.5 Patterson Search Methods (Molecular Replacement) 129

5.5.1 Rotation Function 130

5.5.2 Locked Rotation Function 133

5.5.3 Translation Function 134

5.5.3.1 R-Factor and Correlation-Coefficient Translation Functions 134

5.5.3.2 Patterson-Correlation Translation Function 135

5.5.3.3 Phased Translation Function 136

5.5.4 Computer Programs for Molecular Replacement 137

References 137

6 Phase Improvement by Density Modification and Phase Combination 141

6.1 Introduction 141

6.2 Solvent Flattening 142

6.3 Histogram Matching 145

6.4 Molecular Averaging 148

6.5 Sayre’s Equation 151

6.6 Atomization 152

6.7 Phase Combination 152

6.8 Difference Fourier Technique 153

References 156

7 Model Building and Refinement 157

7.1 Model Building 157

7.2 Crystallographic Refinement 160

7.2.1 Introduction 160

7.2.2 Principles of Least Squares 161

7.2.3 Constraints and Restraints in Refinement 163

7.2.4 Refinement by Simulated Annealing 167

7.2.5 The Maximum Likelihood Method 169

7.2.6 Refinement at Atomic Resolution 171

7.3 Verification and Accuracy of Structure Determination 174

7.3.1 Free R-Factor as a Tool for Cross-Validation in Structure Determination 174

7.3.2 Determination of Coordinate Uncertainty 175

7.3.2.1 Unrestrained Least-Squares Refinement 175

7.3.2.2 Restrained Least-Squares Refinement 177

7.3.2.3 Rough Estimation of Coordinate Uncertainties 177

7.3.3 Validation of the Geometric and Stereochemical Parameters of the Structural Model 179

7.3.4 Validation of the Structural Model against the Experimental Data 182

7.3.5 Deposition of Structural Data with the Protein Data Bank 183

References 183

8 Crystal Structure Determination of the Time-Course of Reactions and of Unstable Species 187

8.1 Introduction 187

8.2 Triggering Methods 188

8.2.1 Photolysis 189

8.2.2 Diffusion 189

8.2.3 Radiolysis 190

8.3 Trapping Methods 190

8.3.1 Physical Trapping 190

8.3.2 Chemical Trapping 191

8.4 Laue Diffraction 191

8.4.1 Principles of the Laue Technique 191

8.4.2 Advantages and Disadvantages 197

8.4.3 Practical Aspects 197

References 201

9 Structural Genomics 203

9.1 Introduction 203

9.2 Target Selection 204

9.3 Production of Recombinant Proteins 205

9.3.1 Introduction 205

9.3.2 Engineering an Appropriate Expression Construct 206

9.3.3 Expression Systems 210

9.3.3.1 E. coli 210

9.3.3.2 Eukaryotic Expression Systems 212

9.3.4 Protein Purification 214

9.3.4.1 Precipitation 215

9.3.4.2 Chromatography 216

9.3.5 Quality Control of the Purified Protein 217

9.4 Aspects of Automation 218

References 219

Part II Practical Examples Introductory Remarks 221

10 Data Evaluation 223

10.1 Autoindexing, Refinement of Cell Parameters, and Reflection Integration 223

10.2 Scaling of Intensity Diffraction Data 231

10.3 A Complex Example of Space Group Determination 235

References 238

11 Determination of Anomalous Scatterer or Heavy Atom Positions 239

11.1 Application of Direct Methods 239

11.2 Vector Verification Methods 244

11.3 Comparison of the Results from SnB and RSPS 250

References 251

12 MIRAS and MAD Phasing with the Program SHARP 253

12.1 MAD Phasing with the Program SHARP for 4-BUDH 253

References 259

13 Molecular Replacement 261

13.1 Phase Determination of PKC-iota with Program Molrep 261

References 266

14 Averaging about Non-Crystallographic Symmetry (NCS) for 4-BUDH 267

14.1 Determination of NCS Operators for 4-BUDH 268

14.2 Electron Density Map Averaging for 4-BUDH 274

References 275

15 Model Building and More 277

15.1 A Very Personal Short Introduction to the Computer Graphics Modeling Program “O” 277

15.2 Introduction of the Four Fe-Sites per Fe–S-Cluster and New SHARP-Phasing for 4-BUDH 285

15.3 Crystallographic Refinement and Final Steps 286

References 290

Subject Index 293

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Professor Dr. Albrecht Messerschmidt is group leader at the Max Planck Institute for Biochemistry, Marinsried, Germany.

His main reserach interest is in the determination of X-ray structures of metalloproteins and -enzymes, PLP-dependent enzymes, CoA-transferases and other proteins. His group is part of the department of X-ray structure determination of proteins headed by nobel laureate Robert Huber.
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"This is clearly going to be a very useful book for students and researchers coming from across all the relevant disciplines." (Crystallography Reviews, July 2008)

"…this book is reasonably well organized and covers all the relevant theory and much of the practical applications of the field." (Journal of the American Chemical Association, August 6, 2008)

I would highly recommend this book to someone who is thinking about or already using X-ray crystallography. (The Yale Journal of Biology and Medicine, March 2008)

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