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) 

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 Xray Diffraction Experiment 


11  (4) 


15  (2) 


17  (3) 


20  (1) 
Chapter 2 Xray Sources and Detectors 

21  (24) 


21  (1) 


21  (9) 


30  (1) 

2.4 Introduction to Cameras and Detectors 


31  (2) 


33  (5) 

2.6 The Rotation (Oscillation) Instrument 


38  (5) 


43  (2) 
Chapter 3 Crystals 

45  (19) 


45  (4) 


49  (7) 

3.3 Possible Symmetry for Protein Crystals 


56  (1) 

3.4 Coordinate Triplets: General and Special Positions 


56  (1) 


57  (1) 


58  (1) 


58  (2) 


60  (1) 

3.9 Characterization of the Crystals 


61  (2) 


63  (1) 
Chapter 4 Theory of Xray Diffraction by a Crystal 

64  (45) 


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) 


107  (2) 
Chapter 5 Average Reflection Intensity and Distribution of Structure Factor Data 

109  (10) 


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) 


116  (2) 


118  (1) 
Chapter 6 Special Forms of the Structure Factor 

119  (4) 


119  (1) 

6.2 The Unitary Structure Factor 


119  (1) 

6.3 The Normalized Structure Factor 


120  (2) 


122  (1) 
Chapter 7 The Solution of the Phase Problem by the Isomorphous Replacement Method 

123  (49) 


123  (1) 

7.2 The Patterson Function 


124  (9) 

7.3 The Isomorphous Replacement Method 


133  (6) 

7.4 Effect of Heavy Atoms on Xray 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) 


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) 


171  (1) 
Chapter 8 Phase Improvement 

172  (22) 


172  (1) 

8.2 The OMIT Map With and Without Sim Weighting 


173  (6) 


179  (6) 

8.4 Noncrystallographic Symmetry and Molecular Averaging 


185  (2) 


187  (3) 

8.6 wARP: Weighted Averaging of MultipleRefined Dummy Atomic Models 


190  (2) 

8.7 Further Considerations Concerning Density Modification 


192  (1) 


193  (1) 
Chapter 9 Anomalous Scattering in the Determination of the Protein Phase Angles and the Absolute Configuration 

194  (16) 


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 SingleWavelength Anomalous Diffraction (MAD and SAD) 


199  (10) 


209  (1) 
Chapter 10 Molecular Replacement 

210  (21) 


210  (1) 

10.2 The Rotation Function 


211  (6) 

10.3 The Translation Function 


217  (13) 


230  (1) 
Chapter 11 Direct Methods 

231  (10) 


231  (1) 


231  (5) 


236  (2) 

11.4 The Principle of Maximum Entropy 


238  (2) 


240  (1) 
Chapter 12 Laue Diffraction 

241  (7) 


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) 


246  (2) 
Chapter 13 Refinement of the Model Structure 

248  (31) 


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) 


278  (1) 
Chapter 14 The Combination of Phase Information 

279  (6) 


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) 


284  (1) 
Chapter 15 Checking for Gross Errors and Estimating the Accuracy of the Structural Model 

285  (12) 


285  (1) 


285  (2) 

15.3 The Ramachandran Plot 


287  (1) 

15.4 Stereochemistry Check 


287  (1) 

15.5 The 3D1D Profile Method 


288  (4) 

15.6 Quantitative Estimation of the Coordinate Error in the Final Model 


292  (4) 


296  (1) 
Chapter 16 Practical Protein Crystallization 

297  (8) 


297  (1) 

16.2 Gene Cloning and Expression 


298  (1) 

16.3 Protein Purification 


299  (3) 

16.4 Protein Crystallization 


302  (1) 


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 Xray Radiation 

314  (2) 
References 

316  (10) 
Index 

326  