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E-grāmata: Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

5.00/5 (1 ratings by Goodreads)

Dennis Sherwood (Managing Director, The Silver Bullet Machine Manufacturing Company), Jon Cooper (Professor of Structural Biology, Division of Medicine, University College London)

Formāts: PDF+DRM
Izdošanas datums: 05-Nov-2010
Izdevniecība: Oxford University Press
Valoda: eng
ISBN-13: 9780191035524

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Formāts: PDF+DRM
Izdošanas datums: 05-Nov-2010
Izdevniecība: Oxford University Press
Valoda: eng
ISBN-13: 9780191035524

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A complete account of the theory of the diffraction of X-rays by crystals, with particular reference to the processes of determining the structures of protein molecules. This book is aimed primarily at structural biologists and biochemists but will also be valuable to those entering the field with a background in physical sciences or chemistry. It may be used at any post-school level, and develops from first principles all relevant mathematics, diffraction and wave theory, assuming no mathematical knowledge beyond integral calculus.

`Crystals, X-rays and Proteins was my favourite book for learning the theory of macromolecular crystallography as a starting PhD student, since no assumptions were made to prior knowledge of necessary physics and maths. The book was very self contained. All derivations were given in a very clear mathematical nomenclature. I am very excited that Dennis Sherwood and Jon Cooper have updated the whole volume.' Mark Sanderson, King's College London

A complete account of the theory of the diffraction of x-rays by crystals with particular reference to the processes of determining the structures of protein molecules, this book is aimed primarily at structural biologists and biochemists but will also be valuable to those entering the field with a background in physical sciences or chemistry. It may be used at any post-school level, and develops from first principles all relevant mathematics, diffraction and wave theory, assuming no mathematical knowledge beyond integral calculus.

The book covers a host of important topics in the area, including:
- The practical aspects of sample preparation and x-ray data collection, using both laboratory and synchrotron sources
- Data analysis at both theoretical and practical levels
- The important role played by the Patterson function in structure analysis by both molecular replacement and experimental phasing approaches
- Methods for improving the resulting electron density map
- The theoretical basis of methods used in refinement of protein crystal structures
- In-depth explanation of the crucial task of defining the binding sites of ligands and drug molecules
- The complementary roles of other diffraction methods which reveal further detail of great functional importance in a crystal structure.

Recenzijas

The first two-thirds of this book was like a thriller to me. Even though I knew the answer, I wanted to see how the author would address the next topic and I could not put it down. * Joseph D. Ferrara, Ph.D, Crystallography Times * This is one of the best crystallography books ever written, and it is with pleasure that I wholeheartedly recommend it. * Nicholas M. Glykos, Democritus University of Thrace, Greece * The authors have nicely brought the bibliography up to date and mention recent method developments, giving a good first grasp of what is involved in solving a structure. The text also makes good use of accompanying, illustrative figures, which is most essential when developing the complex concepts of diffraction, Fourier transformation and convolution. * E. von Castelmur and A. Perrakis, Crystallography Reviews * In my opinion, this book would be the perfect textbook for a theoretical course on macromolecular crystallography * Manfred S. Weiss, Acta Crystallographica Section D * A welcome addition to any structural biology laboratory, [ and] an invaluable reference, answering questions in an accurate and transparent manner * Karen McLuskey, Chemistry World *

List of symbols

xiv

PART I FUNDAMENTALS

1 The crystalline state and its study

(20)

1.1 States of matter

(1)

1.2 Anisotropy

(2)

1.3 The significance of order

(3)

1.4 Crystals

(2)

1.5 Solids which are not crystals

(2)

1.6 Crystal defects

(1)

1.7 Analysing the structure of crystals and molecules

(4)

1.8 Why do we use X-rays?

(3)

1.9 Why do we use diffraction?

(1)

1.10 Protein crystals

(1)

Summary

(1)

Bibliography

(2)

2 Vector analysis and complex algebra

(35)

Vectors

(1)

2.1 What is a vector?

(2)

2.2 Vector addition

(2)

2.3 Multiplication by a scalar

(1)

2.4 Unit vectors

(3)

2.5 Components

(2)

2.6 Vector subtraction

(1)

2.7 Multiplication by a vector to give a scalar

(3)

2.8 Multiplication by a vector to give a vector

(3)

2.9 The scalar triple product and the vector triple product

(3)

Complex Algebra

(1)

2.10 What is a complex number?

(1)

2.11 The Argand diagram

(2)

2.12 The addition of complex numbers

(1)

2.13 Multiplication of complex numbers

(1)

2.14 The complex conjugate

(1)

2.15 The complex exponential representation

(2)

2.16 Complex exponentials and trigonometric functions

(1)

Summary

(3)

Appendix: Determinants

(2)

Bibliography

(1)

3 Crystal systematics

(35)

3.1 What is a crystal?

(3)

3.2 Symmetry

(1)

3.3 The description of the lattice

(10)

3.4 Crystal directions

(1)

3.5 Lattice planes

(4)

3.6 Symmetry operations and symmetry elements

(8)

3.7 Point groups and Laue groups

(3)

3.8 Space groups

(4)

Summary

(1)

Bibliography

(1)

4 Waves and electromagnetic radiation

(40)

4.1 Mathematical functions

(1)

4.2 What is a wave?

(3)

4.3 The mathematical description of a wave

(7)

4.4 The wave equation

104

(2)

4.5 The solution of the wave equation

106

(5)

4.6 The principle of superposition

111

(3)

4.7 Phase

114

(4)

4.8 Waves and complex exponentials

118

(2)

4.9 Intensity

120

(1)

4.10 Waves which are not plane

121

(1)

4.11 Electromagnetic waves

122

(2)

4.12 The form of electromagnetic waves

124

(2)

4.13 The interaction of electromagnetic radiation with matter

126

(5)

Summary

131

(1)

Bibliography

132

(1)

5 Fourier transforms and convolutions

133

(51)

5.1 Integrals

133

(2)

5.2 Curve sketching

135

(6)

5.3 Fourier transforms

141

(5)

5.4 Mathematical conventions and physical reality

146

(2)

5.5 The inverse transform

148

(3)

5.6 Real space and Fourier space

151

(1)

5.7 Delta functions

152

(2)

5.8 Fourier transforms and delta functions

154

(10)

5.9 Symmetrical and antisymmetrical functions

164

(2)

5.10 Convolutions

166

(6)

5.11 The Fourier transform of a convolution

172

(1)

5.12 The Patterson function

173

(3)

Summary

176

(3)

Appendix I Proof of Fourier's theorem

179

(1)

Appendix II Proof of convolution theorem

180

(3)

Bibliography

183

(1)

6 Diffraction

184

(32)

6.1 The interaction of waves with obstacles

184

(1)

6.2 The diffraction of water waves

185

(4)

6.3 Diffraction and information

189

(1)

6.4 The diffraction of light

190

(2)

6.5 X-ray diffraction

192

(1)

6.6 The mathematics of diffraction

192

(6)

6.7 Diffraction and Fourier transforms

198

(2)

6.8 The significance of the Fourier transform

200

(3)

6.9 Fourier transforms and phase

203

(2)

6.10 Fourier transforms and the wave equation

205

(1)

6.11 Fourier transforms and information

206

(2)

6.12 The inverse transform

208

(2)

6.13 The significance of the inverse transform

210

(3)

6.14 Experimental limitations

213

(1)

Summary

214

(1)

Bibliography

215

(1)

REVIEW I

216

(5)

PART II DIFFRACTION THEORY

7 Diffraction by one-dimensional obstacles

221

(33)

7.1 The geometrical arrangement

221

(3)

7.2 One narrow slit

224

(2)

7.3 One wide slit

226

(1)

7.4 Two narrow slits

227

(1)

7.5 Young's experiment

228

(4)

7.6 Two wide slits

232

(3)

7.7 Three narrow slits

235

(1)

7.8 Three wide slits

236

(1)

7.9 N narrow slits

237

(1)

7.10 N wide slits

238

(1)

7.11 An infinite number of narrow slits

239

(1)

7.12 An infinite number of wide slits

240

(1)

7.13 The significance of the diffraction pattern

241

(5)

7.14 Another way of looking at N wide slits

246

(4)

Summary

250

(3)

Bibliography

253

(1)

8 Diffraction by a three-dimensional lattice

254

(43)

8.1 The diffraction pattern of a crystal

254

(1)

8.2 Non-normally incident waves

255

(3)

8.3 The diffraction pattern of a finite three-dimensional lattice

258

(2)

8.4 The diffraction pattern of an infinite lattice

260

(5)

8.5 The Laue equations

265

(1)

8.6 The solution of the Laue equations

266

(3)

8.7 The reciprocal lattice

269

(5)

8.8 Reciprocal-lattice vectors and real-lattice planes

274

(3)

8.9 Bragg's law

277

(1)

8.10 The Ewald circle

278

(3)

8.11 The reciprocal lattice and diffraction

281

(4)

8.12 Why X-ray diffraction works

285

(1)

8.13 The Ewald sphere

286

(2)

8.14 The Ewald sphere and diffraction

288

(3)

8.15 Bragg's law and crystal planes

291

(2)

8.16 The effect of finite crystal size

293

(1)

Summary

294

(3)

9 The contents of the unit cell

297

(42)

9.1 The scattering of X-rays by a single electron

297

(3)

9.2 The scattering of X-rays by a distribution of electrons

300

(4)

9.3 The diffraction pattern of the motif

304

(3)

9.4 The calculation of the electron density function

307

(1)

9.5 Fourier synthesis

308

(3)

9.6 The calculation of structure factors

311

(6)

9.7 Atomic scattering factors

317

(5)

9.8 Anomalous scattering

322

(1)

9.9 Crystal symmetry and X-ray diffraction

323

(1)

9.10 Diffraction pattern symmetry

324

(2)

9.11 Friedel's law

326

(2)

9.12 The breakdown of Friedel's law

328

(3)

9.13 Friedel's law and electron density calculations

331

(1)

9.14 Systematic absences

332

(3)

9.15 The determination of crystal symmetry

335

(1)

Summary

336

(3)

REVIEW II

339

(4)

PART III STRUCTURE SOLUTION

10 Experimental techniques: sample preparation

343

(19)

10.1 Protein expression

343

(4)

10.2 Protein purification

347

(5)

10.3 Crystallisation

352

(4)

10.4 Crystal mounting

356

(4)

Summary

360

(1)

References

360

(2)

11 Experimental techniques: data collection and analysis

362

(69)

11.1 The origin of X-rays

362

(1)

11.2 Laboratory X-ray sources

363

(5)

11.3 Synchrotron sources

368

(2)

11.4 Optimising the X-ray beam

370

(5)

11.5 The rotation method

375

(3)

11.6 Electronic detectors

378

(3)

11.7 Other aspects of data collection

381

(2)

11.8 Data processing

383

(9)

11.9 The basis of intensity data corrections

392

(5)

11.10 The polarisation factor

397

(1)

11.11 The Lorentz factor

398

(3)

11.12 Absorption

401

(4)

11.13 The temperature factor

405

(8)

11.14 Scaling and merging intensity measurements

413

(3)

11.15 Conversion of intensities to structure factor amplitudes

416

(2)

11.16 Normalised structure factors

418

(1)

11.17 Completeness of the data

419

(1)

11.18 Estimating the solvent content

420

(2)

11.19 Misindexing and twinning

422

(4)

Summary

426

(2)

References

428

(3)

12 The phase problem and the Patterson function

431

(18)

12.1 The nature of the problem

431

(1)

12.2 Why is phase not detectable?

432

(1)

12.3 The Fourier transform of the intensities

433

(1)

12.4 The Patterson function and the crystal structure

434

(3)

12.5 The form of the Patterson function

437

(1)

12.6 The meaning of the Patterson function

438

(1)

12.7 Patterson maps

439

(4)

12.8 Patterson map symmetry

443

(2)

12.9 The use of Patterson maps

445

(2)

Summary

447

(1)

Bibliography

448

(1)

13 Molecular replacement

449

(26)

13.1 Solving the phase problem when the structure of a related protein is known

449

(2)

13.2 The rotation function

451

(4)

13.3 Choice of variables in the rotation function

455

(5)

13.4 Testing the rotation function

460

(1)

13.5 Refining the rotation function solution

460

(1)

13.6 Symmetry of the rotation function

461

(1)

13.7 The translation function

461

(1)

13.8 Patterson-based translation methods

462

(2)

13.9 Reciprocal-space translation searches

464

(3)

13.10 Asymmetric unit of the translation function

467

(1)

13.11 Non-crystallographic symmetry

468

(2)

13.12 The packing function

470

(1)

13.13 Verifying the results

471

(1)

13.14 Wider applications of molecular replacement

472

(1)

Summary

473

(1)

References

473

(2)

14 Solving the phase problem experimentally

475

(70)

14.1 The techniques of solution

475

(1)

14.2 Isomorphism and the preparation of heavy-atom derivatives

476

(3)

14.3 Scaling and analysing derivative data

479

(4)

14.4 The difference Patterson function

483

(10)

14.5 The methods of Patterson solution

493

(3)

14.6 Direct methods for locating sites

496

(9)

14.7 Refinement of heavy-atom sites

505

(2)

14.8 Cross-phasing

507

(2)

14.9 The isomorphous replacement method

509

(10)

14.10 Exploiting anomalous scattering effects in phasing

519

(11)

14.11 Density modification

530

(8)

Summary

538

(3)

References

541

(4)

15 Refinement

545

(50)

15.1 The necessity for refinement

545

(3)

15.2 Obtaining the trial structure

548

(3)

15.3 Assessing the trial structure

551

(3)

15.4 Least-squares refinement

554

(1)

15.5 Theory of the least-squares method

555

(10)

15.6 The use of stereochemical restraints

565

(6)

15.7 The benefits of non-crystallographic symmetry

571

(1)

15.8 Modelling rigid-group displacement

572

(1)

15.9 Simulated annealing

572

(2)

15.10 Cross-validation

574

(2)

15.11 Use of Fourier maps in refinement

576

(2)

15.12 The difference Fourier synthesis

578

(8)

15.13 The maximum-likelihood method in refinement

586

(1)

15.14 Validation and deposition

587

(2)

Summary

589

(2)

References

591

(4)

16 Complementary diffraction methods

595

(19)

16.1 Finding hydrogen atoms in X-ray structures

595

(2)

16.2 Neutron protein crystallography

597

(4)

16.3 Neutron data collection

601

(3)

16.4 Neutron applications

604

(2)

16.5 Advantages of perdeuteration

606

(1)

16.6 X-ray Laue diffraction

607

(1)

16.7 Laue data processing

608

(1)

Summary

609

(1)

References

610

(4)

REVIEW III

614

(2)

General bibliography

616

(1)

Index

617

Dennis Sherwood read Natural Sciences as a scholar at Clare College, Cambridge, and subsequently won a Mellon Fellowship to the Department of Molecular Biophysics and Biochemistry at Yale University (MPhil), and a Calbiochem Scholarship to the University of California at San Diego (PhD). After a brief period as an ICI Post-doctoral Fellow at the University of Sussex, Dennis changed career, and joined Deloitte Haskins & Sells as a trainee consultant, and where, for 12 years, he was a consulting partner. Dennis was subsequently an Executive Director with Goldman Sachs, a partner in Bossard Consultants, and Managing Director in the UK of SRI Consulting. Dennis now runs his own business, The Silver Bullet Machine Manufacturing Company Limited , which specialises in organizational creativity and innovation. Dennis participates in a number of academic programmes at institutions such as London Business School, the London School of Economics, the University of St Gallen, and London South Bank University.

Jon Cooper is a Professor of Structural Biology at UCL Department of Medicine who specialises in expression and X-ray structure analysis of proteins. Previously he was based in the School of Biological Sciences at the University of Southampton where he taught biochemistry and structural biology on undergraduate programmes and at the post-graduate level. He has been working in the protein crystallography field since the mid-1980s when he started a PhD at Birkbeck College London where he later became a post-doctoral fellow and subsequently a lecturer. He is a member of Biological Structures Group of the British Crystallographic Association (BCA) and has been a tutor at the BCA Protein Crystallography Summer School.

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E-grāmata: Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

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