Crystallography made crystal clear : a guide for users of macromolecular models / Gale Rhodes.

Format:

Book

Author/Creator:

Rhodes, Gale.

Contributor:

GIC Course Text Collection (University of Pennsylvania)

Language:

English

Edition:

Third edition.

Summary:

This much admired book has been carefully revised to make crystallography even more accessible to readers who have no prior experience with crystallography and macromolecular models, or their mathematical foundations. It continues to provide clear, understandable descriptions of the principles of protein crystallography with abundant illustrations and stereo images (in full color). Coverage extends to X-ray, neutron, electron, and Laue diffraction methods, as well as NMR spectroscopy and homology modeling.

Contents:

1 Model and Molecule 1

2 An Overview of Protein Crystallography 7

2.1.1 Obtaining an image of a microscopic object 8

2.1.2 Obtaining images of molecules 9

2.1.3 A thumbnail sketch of protein crystallography 9

2.2 Crystals 10

2.2.1 The nature of crystals 10

2.2.2 Growing crystals 11

2.3 Collecting X-ray data 13

2.4 Diffraction 15

2.4.1 Simple objects 15

2.4.2 Arrays of simple objects: Real and reciprocal lattices 16

2.4.3 Intensities of reflections 16

2.4.4 Arrays of complex objects 17

2.4.5 Three-dimensional arrays 18

2.5 Coordinate systems in crystallography 19

2.6 The mathematics of crystallography: A brief description 20

2.6.1 Wave equations: Periodic functions 21

2.6.2 Complicated periodic functions: Fourier series and sums 23

2.6.3 Structure factors: Wave descriptions of X-ray reflections 24

2.6.4 Electron-density maps 26

2.6.5 Electron density from structure factors 27

2.6.6 Electron density from measured reflections 28

2.6.7 Obtaining a model 30

3 Protein Crystals 31

3.1 Properties of protein crystals 31

3.1.2 Size, structural integrity, and mosaicity 31

3.1.3 Multiple crystalline forms 33

3.1.4 Water content 34

3.2 Evidence that solution and crystal structures are similar 35

3.2.1 Proteins retain their function in the crystal 35

3.2.2 X-ray structures are compatible with other structural evidence 36

3.2.3 Other evidence 37

3.3 Growing protein crystals 37

3.3.2 Growing crystals: Basic procedure 38

3.3.3 Growing derivative crystals 40

3.3.4 Finding optimal conditions for crystal growth 41

3.4 Judging crystal quality 46

3.5 Mounting crystals for data collection 46

4 Collecting Diffraction Data 49

4.2 Geometric principles of diffraction 49

4.2.1 The generalized unit cell 49

4.2.2 Indices of the atomic planes in a crystal 50

4.2.3 Conditions that produce diffraction: Bragg's law 55

4.2.4 The reciprocal lattice 57

4.2.5 Bragg's law in reciprocal space 60

4.2.6 Number of measurable reflections 64

4.2.7 Unit-cell dimensions 65

4.2.8 Unit-cell symmetry 65

4.3 Collecting X-ray diffraction data 73

4.3.2 X-ray sources 73

4.3.3 Detectors 77

4.3.4 Cameras 80

4.3.5 Scaling and postrefinement of intensity data 85

4.3.6 Determining unit-cell dimensions 86

4.3.7 Symmetry and the strategy of collecting data 88

5 From Diffraction Data to Electron Density 91

5.2 Fourier sums and the Fourier transform 92

5.2.1 One-dimensional waves 92

5.2.2 Three-dimensional waves 94

5.2.3 The Fourier transform: General features 96

5.2.4 Fourier this and Fourier that: Review 97

5.3 Fourier mathematics and diffraction 98

5.3.1 Structure factor as a Fourier sum 98

5.3.2 Electron density as a Fourier sum 99

5.3.3 Computing electron density from data 100

5.3.4 The phase problem 101

5.4 Meaning of the Fourier equations 101

5.4.1 Reflections as terms in a Fourier sum: Eq. (5.18) 101

5.4.2 Computing structure factors from a model: Eq. (5.15) and Eq. (5.16) 104

5.4.3 Systematic absences in the diffraction pattern: Eq. (5.15) 105

5.5 Summary: From data to density 107

6 Obtaining Phases 109

6.2 Two-dimensional representation of structure factors 112

6.2.1 Complex numbers in two dimensions 112

6.2.2 Structure factors as complex vectors 112

6.2.3 Electron density as a function of intensities and phases 115

6.3 Isomorphous replacement 117

6.3.1 Preparing heavy-atom derivatives 117

6.3.2 Obtaining phases from heavy-atom data 119

6.3.3 Locating heavy atoms in the unit cell 124

6.4 Anomalous scattering 128

6.4.2 Measurable effects of anomalous scattering 128

6.4.3 Extracting phases from anomalous scattering data 130

6.4.5 Multiwavelength anomalous diffraction phasing 133

6.4.6 Anomalous scattering and the hand problem 135

6.4.7 Direct phasing: Application of methods from small-molecule crystallography 135

6.5 Molecular replacement: Related proteins as phasing models 136

6.5.2 Isomorphous phasing models 137

6.5.3 Nonisomorphous phasing models 139

6.5.4 Separate searches for orientation and location 139

6.5.5 Monitoring the search 141

6.5.6 Summary of molecular replacement 143

6.6 Iterative improvement of phases (preview of Chapter 7) 143

7 Obtaining and Judging the Molecular Model 145

7.2 Iterative improvement of maps and models-overview 146

7.3 First maps 149

7.3.1 Resources for the first map 149

7.3.2 Displaying and examining the map 150

7.3.3 Improving the map 151

7.4 The Model becomes molecular 153

7.4.1 New phases from the molecular model 153

7.4.2 Minimizing bias from the model 154

7.4.3 Map fitting 156

7.5 Structure refinement 159

7.5.1 Least-squares methods 159

7.5.2 Crystallographic refinement by least squares 160

7.5.3 Additional refinement parameters 161

7.5.4 Local minima and radius of convergence 162

7.5.5 Molecular energy and motion in refinement 163

7.5.6 Bayesian methods: Ensembles of models 164

7.6 Convergence to a final model 168

7.6.1 Producing the final map and model 168

7.6.2 Guides to convergence 171

7.7 Sharing the model 173

8 A User's Guide to Crystallographic Models 179

8.2 Judging the quality and usefulness of the refined model 181

8.2.1 Structural parameters 181

8.2.2 Resolution and precision of atomic positions 183

8.2.3 Vibration and disorder 185

8.2.4 Other limitations of crystallographic models 187

8.2.5 Online validation tools: Do it yourself! 189

8.3 Reading a crystallography paper 192

8.3.2 Annotated excerpts of the preliminary (8/91) paper 193

8.3.3 Annotated excerpts from the full structure-determination (4/92) paper 198

9 Other Diffraction Methods 211

9.2 Fiber diffraction 211

9.3 Diffraction by amorphous materials (scattering) 219

9.4 Neutron diffraction 222

9.5 Electron diffraction and cryo-electron microscopy 227

9.6 Laue diffraction and time-resolved crystallography 231

10 Other Kinds of Macromolecular Models 237

10.2 NMR models 238

10.2.3 Assigning resonances 251

10.2.4 Determining conformation 252

10.2.5 PDB files for NMR models 257

10.2.6 Judging model quality 257

10.3 Homology models 259

10.3.3 Databases of homology models 263

10.3.4 Judging model quality 265

10.4 Other theoretical models 267

11 Tools for Studying Macromolecules 269

11.2 Computer models of molecules 269

11.2.1 Two-dimensional images from coordinates 269

11.2.2 Into three dimensions: Basic modeling operations 270

11.2.3 Three-dimensional display and perception 272

11.2.4 Types of graphical models 273

11.3 Touring a molecular modeling program 275

11.3.1 Importing and exporting coordinate files 276

11.3.2 Loading and saving models 278

11.3.3 Viewing models 278

11.3.4 Editing and labeling the display 280

11.3.5 Coloring 281

11.3.6 Measuring 281

11.3.7 Exploring structural change 282

11.3.8 Exploring the molecular surface 282

11.3.9 Exploring intermolecular interactions: Multiple models 286

11.3.10 Displaying crystal packing 287

11.3.11 Building models from scratch 287

11.3.12 Scripts and macros: Automating routine structure analysis 287

11.4 Other tools for studying structure 288

11.4.1 Tools for structure analysis and validation 288

11.4.2 Tools for modeling protein action 290

11.5 Final note 291

Appendix Viewing Stereo Images 293.

ISBN:

9780125870733