Rhodes Crystallography Made Crystal Clear

A Guide for Users of Macromolecular Models
3. Auflage 2010
ISBN: 978-0-08-045554-9
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 352 Seiten

Crystallography Made Crystal Clear makes crystallography accessible to readers who have no prior knowledge of the field or its mathematical basis. This is the most comprehensive and concise reference for beginning Macromolecular crystallographers, written by a leading expert in the field. Rhodes' uses visual and geometric models to help readers understand the mathematics that form the basis of x-ray crystallography. He has invested a great deal of time and effort on World Wide Web tools for users of models, including beginning-level tutorials in molecular modeling on personal computers. Rhodes' personal CMCC Home Page also provides access to tools and links to resources discussed in the text. Most significantly, the final chapter introduces the reader to macromolecular modeling on personal computers-featuring SwissPdbViewer, a free, powerful modeling program now available for PC, Power Macintosh, and Unix computers. This updated and expanded new edition uses attractive four-color art, web tool access for further study, and concise language to explain the basis of X-ray crystallography, increasingly vital in today's research labs.
* Helps readers to understand where models come from, so they don't use them blindly and
inappropriately
* Provides many visual and geometric models for understanding a largely mathematical method
* Allows readers to judge whether recently published models are of sufficiently high quality and detail to be useful in their own work
* Allows readers to study macromolecular structure independently and in an open-ended fashion on their own computers, without being limited to textbook or journals illustrations
* Provides access to web tools in a format that will not go out of date. Links will be updated and added as existing resources change location or are added

Gale Rhodes earned a B.S. in applied mathematics at North Carolina State University, and then a Ph.D. in Chemistry at the University of North Carolina. He is currently a professor of chemistry at the University of Southern Maine, Portland. His main duty, and first love, is teaching undergraduate biochemistry. He has received awards for outstanding teaching at three different colleges. His best known publication is the first edition of Crystallography Made Crystal Clear, which received very complimentary reviews in several journals. He has also published three book chapters, three book reviews, and about 30 articles on diverse subjects, including research articles in biochemistry, and articles on chemistry, science, and interdisciplinary education.

Autoren/Hrsg.

Rhodes, Gale

Inhaltsverzeichnis

1;Front cover;1
2;Title page;6
3;Copyright page;7
4;Table of contents;10
5;Preface to the Third Edition;16
6;Preface to the Second Edition;20
7;Preface to the First Edition;24
8;1 Model and Molecule;28
9;2 An Overview of Protein Crystallography;34
9.1;Introduction;34
9.1.1;Obtaining an image of a microscopic object;35
9.1.2;Obtaining images of molecules;36
9.1.3;A thumbnail sketch of protein crystallography;36
9.2;Crystals;37
9.2.1;The nature of crystals;37
9.2.2;Growing crystals;38
9.3;Collecting X-ray data;40
9.4;Diffraction;42
9.4.1;Simple objects;42
9.4.2;Arrays of simple objects: Real and reciprocal lattices;43
9.4.3;Intensities of reflections;43
9.4.4;Arrays of complex objects;44
9.4.5;Three-dimensional arrays;45
9.5;Coordinate systems in crystallography;46
9.6;The mathematics of crystallography: A brief description;47
9.6.1;Wave equations: Periodic functions;48
9.6.2;Complicated periodic functions: Fourier series and sums;50
9.6.3;Structure factors: Wave descriptions of X-ray reflections;51
9.6.4;Electron-density maps;53
9.6.5;Electron density from structure factors;54
9.6.6;Electron density from measured reflections;55
9.6.7;Obtaining a model;57
10;3 Protein Crystals;58
10.1;Properties of protein crystals;58
10.1.1;Introduction;58
10.1.2;Size, structural integrity, and mosaicity;58
10.1.3;Multiple crystalline forms;60
10.1.4;Water content;61
10.2;Evidence that solution and crystal structures are similar;62
10.2.1;Proteins retain their function in the crystal;62
10.2.2;X-ray structures are compatible with other structural evidence;63
10.2.3;Other evidence;64
10.3;Growing protein crystals;64
10.3.1;Introduction;64
10.3.2;Growing crystals: Basic procedure;65
10.3.3;Growing derivative crystals;67
10.3.4;Finding optimal conditions for crystal growth;68
10.4;Judging crystal quality;73
10.5;Mounting crystals for data collection;73
11;4 Collecting Diffraction Data;76
11.1;Introduction;76
11.2;Geometric principles of diffraction;76
11.2.1;The generalized unit cell;76
11.2.2;Indices of the atomic planes in a crystal;77
11.2.3;Conditions that produce diffraction: Bragg's law;82
11.2.4;The reciprocal lattice;84
11.2.5;Bragg's law in reciprocal space;87
11.2.6;Number of measurable reflections;91
11.2.7;Unit-cell dimensions;92
11.2.8;Unit-cell symmetry;92
11.3;Collecting X-ray diffraction data;100
11.3.1;Introduction;100
11.3.2;X-ray sources;100
11.3.3;Detectors;104
11.3.4;Cameras;107
11.3.5;Scaling and postrefinement of intensity data;112
11.3.6;Determining unit-cell dimensions;113
11.3.7;Symmetry and the strategy of collecting data;115
11.4;Summary;116
12;5 From Diffraction Data to Electron Density;118
12.1;Introduction;118
12.2;Fourier sums and the Fourier transform;119
12.2.1;One-dimensional waves;119
12.2.2;Three-dimensional waves;121
12.2.3;The Fourier transform: General features;123
12.2.4;Fourier this and Fourier that: Review;124
12.3;Fourier mathematics and diffraction;125
12.3.1;Structure factor as a Fourier sum;125
12.3.2;Electron density as a Fourier sum;126
12.3.3;Computing electron density from data;127
12.3.4;The phase problem;128
12.4;Meaning of the Fourier equations;128
12.4.1;Reflections as terms in a Fourier sum: Eq. (5.18);128
12.4.2;Computing structure factors from a model: Eq. (5.15) and Eq. (5.16);131
12.4.3;Systematic absences in the diffraction pattern: Eq. (5.15);132
12.5;Summary: From data to density;134
13;6 Obtaining Phases;136
13.1;Introduction;136
13.2;Two-dimensional representation of structure factors;139
13.2.1;Complex numbers in two dimensions;139
13.2.2;Structure factors as complex vectors;139
13.2.3;Electron density as a function of intensities and phases;142
13.3;Isomorphous replacement;144
13.3.1;Preparing heavy-atom derivatives;144
13.3.2;Obtaining phases from heavy-atom data;146
13.3.3;Locating heavy atoms in the unit cell;151
13.4;Anomalous scattering;155
13.4.1;Introduction;155
13.4.2;Measurable effects of anomalous scattering;155
13.4.3;Extracting phases from anomalous scattering data;157
13.4.4;Summary;159
13.4.5;Multiwavelength anomalous diffraction phasing;160
13.4.6;Anomalous scattering and the hand problem;162
13.4.7;Direct phasing: Application of methods from small-molecule crystallography;162
13.5;Molecular replacement: Related proteins as phasing models;163
13.5.1;Introduction;163
13.5.2;Isomorphous phasing models;164
13.5.3;Nonisomorphous phasing models;166
13.5.4;Separate searches for orientation and location;166
13.5.5;Monitoring the search;168
13.5.6;Summary of molecular replacement;170
13.6;Iterative improvement of phases (preview of Chapter 7);170
14;7 Obtaining and Judging the Molecular Model;172
14.1;Introduction;172
14.2;Iterative improvement of maps and models - overview;173
14.3;First maps;176
14.3.1;Resources for the first map;176
14.3.2;Displaying and examining the map;177
14.3.3;Improving the map;178
14.4;The Model becomes molecular;180
14.4.1;New phases from the molecular model;180
14.4.2;Minimizing bias from the model;181
14.4.3;Map fitting;183
14.5;Structure refinement;186
14.5.1;Least-squares methods;186
14.5.2;Crystallographic refinement by least squares;187
14.5.3;Additional refinement parameters;188
14.5.4;Local minima and radius of convergence;189
14.5.5;Molecular energy and motion in refinement;190
14.5.6;Bayesian methods: Ensembles of models;191
14.6;Convergence to a final model;195
14.6.1;Producing the final map and model;195
14.6.2;Guides to convergence;198
14.7;Sharing the model;200
15;8 A User’s Guide to Crystallographic Models;206
15.1;Introduction;206
15.2;Judging the quality and usefulness of the refined model;208
15.2.1;Structural parameters;208
15.2.2;Resolution and precision of atomic positions;210
15.2.3;Vibration and disorder;212
15.2.4;Other limitations of crystallographic models;214
15.2.5;Online validation tools: Do it yourself!;216
15.2.6;Summary;219
15.3;Reading a crystallography paper;219
15.3.1;Introduction;219
15.3.2;Annotated excerpts of the preliminary (8/91) paper;220
15.3.3;Annotated excerpts from the full structure-determination (4/92) paper;225
15.4;Summary;236
16;9 Other Diffraction Methods;238
16.1;Introduction;238
16.2;Fiber diffraction;238
16.3;Diffraction by amorphous materials (scattering);246
16.4;Neutron diffraction;249
16.5;Electron diffraction and cryo-electron microscopy;254
16.6;Laue diffraction and time-resolved crystallography;258
16.7;Summary;262
17;10 Other Kinds of Macromolecular Models;264
17.1;Introduction;264
17.2;NMR models;265
17.2.1;Introduction;265
17.2.2;Principles;266
17.2.3;Assigning resonances;278
17.2.4;Determining conformation;279
17.2.5;PDB files for NMR models;284
17.2.6;Judging model quality;284
17.3;Homology models;286
17.3.1;Introduction;286
17.3.2;Principles;287
17.3.3;Databases of homology models;290
17.3.4;Judging model quality;292
17.4;Other theoretical models;294
18;11 Tools for Studying Macromolecules;296
18.1;Introduction;296
18.2;Computer models of molecules;296
18.2.1;Two-dimensional images from coordinates;296
18.2.2;Into three dimensions: Basic modeling operations;297
18.2.3;Three-dimensional display and perception;299
18.2.4;Types of graphical models;300
18.3;Touring a molecular modeling program;302
18.3.1;Importing and exporting coordinate files;303
18.3.2;Loading and saving models;305
18.3.3;Viewing models;305
18.3.4;Editing and labeling the display;307
18.3.5;Coloring;308
18.3.6;Measuring;308
18.3.7;Exploring structural change;309
18.3.8;Exploring the molecular surface;309
18.3.9;Exploring intermolecular interactions: Multiple models;313
18.3.10;Displaying crystal packing;314
18.3.11;Building models from scratch;314
18.3.12;Scripts and macros: Automating routine structure analysis;314
18.4;Other tools for studying structure;315
18.4.1;Tools for structure analysis and validation;315
18.4.2;Tools for modeling protein action;317
18.5;Final note;318
19;Appendix: Viewing Stereo Images;320
20;Index;322
21;Complementary Science Series;335

Leseproben

  Chapter 2

 An Overview of Protein Crystallography 2.1 Introduction
The most common experimental means of obtaining a detailed model of a large molecule, allowing the resolution of individual atoms, is to interpret the diffraction of X-rays from many identical molecules in an ordered array like a crystal. This method is called single-crystal X-ray crystallography. As of January 2005, the Protein Data Bank (PDB), the world’s largest repository of macromolecular models obtained from experimental data (called experimental models), contains roughly 25,000 protein and nucleic-acid models determined by X-ray crystallography. In addition, the PDB holds roughly 4500 models, mostly proteins of fewer than 200 residues, that have been solved by nuclear magnetic resonance (NMR) spectroscopy, which provides a model of the molecule in solution, rather than in the crystalline state. (Because many proteins appear in multiple forms—for example, wild types and mutants, or solo and also as part of protein-ligand or multiprotein complexes—the number of unique proteins represented in the PDB is only a fraction of the almost 30,000 models.) Finally, there are theoretical models, either built by analogy with the structures of known proteins having similar sequence, or based on simulations of protein folding. (Theoretical models are available from databases other than the PDB.) All methods of obtaining models have their strengths and weaknesses, and they coexist happily as complementary methods. One of the goals of this book is to make users of crystallographic models aware of the strengths and weaknesses of X-ray crystallography, so that users’ expectations of the resulting models are in keeping with the limitations of crystallographic methods. Chapter 10 provides, in brief, complementary information about other types of models. In this chapter, I provide a simplified overview of how researchers use the technique of X-ray crystallography to obtain models of macromolecules. Chapters 3 through 8 are simply expansions of the material in this chapter. In order to keep the language simple, I will speak primarily of proteins, but the concepts I describe apply to all macromolecules and macromolecular assemblies that possess ordered structure, including carbohydrates, nucleic acids, and nucleoprotein complexes like ribosomes and whole viruses. 2.1.1 Obtaining an image of a microscopic object
When we see an object, light rays bounce off (are diffracted by) the object and enter the eye through the lens, which reconstructs an image of the object and focuses it on the retina. In a simple microscope, an illuminated object is placed just beyond one focal point of a lens, which is called the objective lens. The lens collects light diffracted from the object and reconstructs an image beyond the focal point on the opposite side of the lens, as shown in Fig. 2.1. Figure 2.1 Action of a simple lens. Rays parallel to the lens axis strike the lens and are refracted into paths passing through a focus (F or F’). Rays passing through a focus strike the lens and are refracted into paths parallel to the lens axis. As a result, the lens produces an image at I of an object at O such that (OF)(IF’) = (FL)(F’L). For a simple lens, the relationship of object position to image position in Fig. 2.1 is (OF)(IF’) = (FL)(F’L). Because the distances FL and F’L are constants (but not necessarily equal) for a fixed lens, the distance OF is inversely proportional to the distance IF’. Placing the object just beyond the focal point F results in a magnified image produced at a considerable distance from F’ on the other side of the the lens, which is convenient for viewing. In a compound microscope, the most common type, an additional lens, the eyepiece, is added to magnify the image produced by the objective lens. 2.1.2 Obtaining images of molecules
In order for the object to diffract light and thus be visible under magnification, the wavelength (?) of the light must be, roughly speaking, no larger than the object. Visible light, which is electromagnetic radiation with wavelengths of 400–700 nm (nm = 10–9 m), cannot produce an image of individual atoms in protein molecules, in which bonded atoms are only about 0.15 nm or 1.5 angstroms (Å = 10–10 m) apart. Electromagnetic radiation of this wavelength falls into the X-ray range, so X-rays are diffracted by even the smallest molecules. X-ray analysis of proteins seldom resolves the hydrogen atoms, so the protein models described in this book include elements on only the second and higher rows of the periodic table. The positions of all hydrogen atoms can be deduced on the assumption that bond lengths, bond angles, and conformational angles in proteins are just like those in small organic molecules. Even though individual atoms diffract X-rays, it is still not possible to produce a focused image of a single molecule, for two reasons. First, X-rays cannot be focused by lenses. Crystallographers sidestep this problem by measuring the directions and strengths (intensities) of the diffracted X-rays and then using a computer to simulate an image-reconstructing lens. In short, the computer acts as the lens, computing the image of the object and then displaying it on a screen (Fig. 2.2). Figure 2.2 Crystallographic analogy of lens action. X-rays diffracted from the object are received and measured by a detector. The measurements are fed to a computer, which simulates the action of a lens to produce a graphics image of the object. Compare Fig. 2.2 with Fig. 2.1 and you will see that to magnify molecules, you merely have to replace the light bulb with a synchrotron X-ray source (175 feet in diameter), replace the glass lens with the equivalent of a 5- to 10-megapixel camera, and connect the camera output to a computer running some of the world’s most complex and sophisticated software. Oh, yes, and you will need to spend somewhere between a few days and the rest of your life getting your favorite protein to form satisfactory crystals. No, it’s not quite as simple as microscopy. Second, a single molecule is a very weak scatterer of X-rays. Most of the X-rays will pass through a single molecule without being diffracted, so the diffracted beams are too weak to be detected. Analyzing diffraction from crystals, rather than individual molecules, solves this problem. A crystal of a protein contains many ordered molecules in identical orientations, so each molecule diffracts identically, and the diffracted beams for all molecules augment each other to produce strong, detectable X-ray beams. 2.1.3 A thumbnail sketch of protein crystallography
In brief, determining the structure of a protein by X-ray crystallography entails growing high-quality crystals of the purified protein, measuring the directions and intensities of X-ray beams diffracted from the crystals, and using a computer to simulate the effects of an objective lens and thus produce an image of the crystal’s contents, like the small section of a molecular image shown in Fig. 2.3a. Finally, the crystallographer must interpret that image, which entails displaying it by computer graphics and building a molecular model that is consistent with the image (Fig. 2.3b). Figure 2.3 (a) Small section of molecular image displayed on a computer. (b) Image (a) is interpreted by building a molecular model to fit within the image. Computer graphics programs allow the crystallographer to add parts to the model and adjust their positions and conformations to fit the image. The protein shown here is adipocyte lipid binding protein (ALBP, PDB 1alb). The resulting model is often the only product of crystallography that the user sees. It is therefore easy to think of the model as a real entity that has been directly observed. In fact, our “view” of the molecule is quite indirect. Understanding just how the crystallographer obtains models of protein molecules from diffraction measurements is essential to fully understanding how to use models properly. 2.2 Crystals
2.2.1 The nature of crystals
Under certain circumstances, many molecular substances, including proteins, solidify to form crystals. In entering the crystalline state from solution, individual molecules of the substance adopt one or a few identical orientations. The resulting crystal is an orderly three-dimensional array of molecules, held together by noncovalent interactions. Figure 2.4 depicts such a crystalline array of molecules. Figure 2.4 Six unit cells in a crystalline lattice. Each unit cell contains two molecules of alanine (hydrogen atoms not shown) in different orientations. The lines in the figure divide the crystal into identical unit cells. The array of points at the corners or vertices of unit cells is called the lattice. The unit cell is the smallest and simplest volume element that is completely representative of the whole crystal. If we know the exact contents of the unit cell, we can imagine the whole crystal as an efficiently packed array of many unit cells stacked beside and on top of each other, more or less like identical boxes in a...