admin@chemistrydocs.com

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

Free Download Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens – Volume 5

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

 

Authors:
GORDON S. RULE
Department of Biological Sciences,
Carnegie Mellon University, Pittsburgh, PA, U.S.A.
KEVIN HITCHENS
Pittsburgh NMR Center for Biomedical Research,
Carnegie Mellon University, Pittsburgh, PA, U.S.A.

 

Table of Contents

List of Figures xvii

List of Tables xxvi

  1. NMR SPECTROSCOPY 1

1.1 Introduction to NMR Spectroscopy 2

1.2 One Dimensional NMR Spectroscopy 3

1.2.1 Classical Description of NMR Spectroscopy 3

1.2.2 Nuclear Spin Transitions 3

1.3 Detection of Nuclear Spin Transitions 7

1.3.1 Continuous Wave NMR 7

1.3.2 Pulsed NMR 8

1.4 Phenomenological Description of Relaxation 16

1.4.1 Relaxation and the Evolution of Magnetization 18

1.5 Chemical Shielding 19

1.6 Characteristic 1H, 13C, and 15N Chemical Shifts 21

1.6.1 Effect of Electronic Structure on Chemical Shifts 21

1.6.2 Ring Current Effects 23

1.6.3 Effects of Local Environment on Chemical Shifts 25

1.6.4 Use of Chemical Shifts in Resonance Assignments 25

1.6.5 Chemical Shift Dispersion & Multi-dimensional NMR 26

1.7 Exercises 26

1.8 Solutions 26

  1. PRACTICAL ASPECTS OF ACQUIRING NMR SPECTRA 29

2.1 Components of an NMR Spectrometer 29

2.1.1 Magnet 29

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

Summary of the Process of Acquiring a One Dimensional Spectrum

2.1.2 Computer 31

2.1.3 Probe 31

2.1.4 Pre-amplifier Module 32

2.1.5 The Field-frequency Lock 33

2.1.6 Shim System 34

2.1.7 Transmitter & Pulse Generation 34

2.1.8 Receiver 36

2.2 Acquiring a Spectrum 38

2.2.1 Sample Preparation 38

2.2.2 Beginning the Experiment 39

2.2.3 Temperature Measurement 39

2.2.4 Shimming 40

2.2.5 Tuning and Matching the Probe 41

2.2.6 Adjusting the Transmitter 42

2.2.7 Calibration of the 90 Pulse Length 46

2.2.8 Setting the Sweepwidth: Dwell Times and Filters 48

2.2.9 Setting the Receiver Gain 53

2.2.10 Spectral Resolution and Acquisition Time of the FID 54

2.3 Experimental 1D-pulse Sequence: Pulse and Receiver Phase 57

2.3.1 Phase Cycle 58

2.3.2 Phase Cycle and Artifact Suppression 61

2.4 Exercises 63

2.5 Solutions 64

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

  1. INTRODUCTION TO SIGNAL PROCESSING 65

3.1 Removal of DC Offset 66

3.2 Increasing Resolution by Extending the FID 66

3.2.1 Increasing Resolution by Zero-filling 67

3.2.2 Increasing Resolution by Linear Prediction (LP) 69

3.3 Removal of Truncation Artifacts: Apodization 74

3.3.1 Effect of Apodization on Resolution and Noise 74

3.3.2 Using LP & Apodization to Increase Resolution 77

3.4 Solvent Suppression 78

3.5 Spectral Artifacts Due to Intensity Errors 79

3.5.1 Errors from the Digital Fourier Transform 79

3.5.2 Effect of Distorted and Missing Points 80

3.5.3 Delayed Acquisition 82

3.6 Phasing of the Spectrum 82

3.6.1 Origin of Phase Shifts 83

3.6.2 Applying Phase Corrections 85

3.7 Chemical Shift Referencing 86

3.8 Exercises 87

3.9 Solutions 87

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

  1. QUANTUM MECHANICAL DESCRIPTION OF NMR 89

4.1 Schrödinger Equation 89

4.1.1 Vector Spaces and Properties of Wavefunctions 90

4.1.2 Particle in a Box 92

4.2 Expectation Values 93

4.3 Dirac Notation 94

4.3.1 Wavefunctions in Dirac Notation 94

4.3.2 Scalar Product in Dirac Notation 96

4.3.3 Operators in Dirac Notation 96

4.3.4 Expectation Values in Dirac Notation 96

4.4 Hermitian Operators 97

4.4.1 Determining Eigenvalues 97

4.5 Additional Properties of Operators 100

4.5.1 Commuting Observables 100

4.5.2 Time Evolution of Observables 100

4.5.3 Trace of an Operator 100

4.5.4 Exponential Operator 101

4.5.5 Unitary Operators 101

4.5.6 Exponential Hermitian Operators 101

4.7 Rotations 105

4.7.1 Rotation Groups 105

4.7.2 Rotation Operators 106

4.7.3 Rotations of Wave Functions and Operators 109

4.8 Exercises 112

4.9 Solutions 112

  1. QUANTUM MECHANICAL DESCRIPTION OF A ONE PULSE

EXPERIMENT 113

5.1 Preparation: Evolution of the System Under Bo 114

5.2 Excitation: Effect of Application of B1 116

5.2.1 The Resonance Condition 118

Hamiltonian and Angular Momentum Operators for a Spin-1/2 Particle

5.3 Detection: Evolution of the System Under Bo 120

  1. THE DENSITYMATRIX&PRODUCTOPERATORS 121

6.1 Introduction to the Density Matrix 122

6.1.1 Calculation of Expectation Values From ρ 123

6.1.2 Density Matrix for a Statistical Mixture 123

6.2 One-pulse Experiment: Density Matrix Description 126

6.2.1 Effect of Pulses on the Density matrix 127

6.3 Product Operators 129

6.3.1 Transformation Properties of Product Operators 130

6.3.2 Description of the One-pulse Experiment 131

6.3.3 Evaluation of Composite Pulses 132

6.4 Exercises 133

6.5 Solutions 133

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

  1. SCALAR COUPLING 135

7.1 Introduction to Scalar Coupling 135

7.2 Basis of Scalar Coupling 136

7.2.1 Coupling to Multiple Spins 138

7.3 Quantum Mechanical Description 140

7.3.1 Analysis of an AX System 140

7.4 Decoupling 145

7.4.1 Experimental Implementation of Decoupling 145

7.4.2 Decoupling Methods 146

7.4.3 Performance of Decoupling Schemes 148

7.5 Exercises 150

7.6 Solutions 150

  1. COUPLED SPINS: DENSITY MATRIX AND

PRODUCT OPERATOR FORMALISM 153

8.1 Density Matrix for Two Coupled Spins 153

8.2 Product Operator Representation of the Density Matrix 155

8.2.1 Detectable Elements of ρ 156

8.3 Density Matrix Treatment of a One-pulse Experiment 159

8.4 Manipulation of Two-spin Product Operators 162

8.5 Transformations of Two-spin Product Operators 164

8.6 Product Operator Treatment of a One-pulse Experiment 165

Analysis of an AB System

9.1 Multi-dimensional Experiments 170

9.1.1 Elements of Multi-dimensional NMR Experiments 171

9.1.2 Generation of Multi-dimensional NMR Spectra 172

9.2 Homonuclear J-correlated Spectra 173

9.2.1 COSY Experiment 173

9.3 Double Quantum Filtered COSY (DQF-COSY) 182

9.4 Effect of Passive Coupling on COSY Crosspeaks 185

9.5 Scalar Correlation by Isotropic Mixing: TOCSY 187

9.5.1 Analysis of TOCSY Pulse Sequence 188

9.5.2 Isotropic Mixing Schemes 191

9.6 Exercises 194

9.7 Solutions 195

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens
10.1 Introduction 197

10.2 Two Dimensional Heteronuclear NMR Experiments 198

10.2.1 HMQC Experiment 199

10.2.2 HSQC Experiment 204

10.2.3 Refocused-HSQC Experiment 207

10.2.5 Sensitivity in 2D-Heteronuclear Experiments 209

10.2.6 Behavior of XH2 Systems in HSQC-type Experiments 210

  1. TWO DIMENSIONAL HETERONUCLEAR J-CORRELATED

SPECTROSCOPY

Experiments

Comparison of HMQC, HSQC, and Refocused-HSQC

  1. COHERENCE EDITING: PULSED-FIELD GRADIENTS

AND PHASE CYCLING
11.1 Principals of Coherence Selection 214

11.1.1 Spherical Basis Set 214

11.1.2 Coherence Changes in NMR Experiments 216

11.1.3 Coherence Pathways 218

11.2 Phase Encoding With Pulsed-Field Gradients 218

11.2.1 Gradient Coils 218

TWO DIMENSIONAL HOMONUCLEAR J-CORRELATED

SPECTROSCOPY

Fundamentals of Protein NMR Spectroscopy by Gordon S. Rule and T. Kevin Hitchens

Product Operator Treatment of the DQF-COSY

Experiment

Time Dependence of Magnetization Transfer by

Isotropic Mixing

11.3 Coherence Selection Using Phase Cycling 225

11.3.1 Coherence Changes Induced by RF-Pulses 226

11.3.2 Selection of Coherence Pathways 229 on Gradient Induced Phase Changes

Establishing Spin-system Connectivities with Dipolar Coupling 267

Coherence Selection by Gradients in Heteronuclear

Effect of Coherence Levels

NMR Experiments

11.3.3 Phase Cycling in the HMQC Pulse Sequence 233

11.4 Exercises 235

11.5 Solutions 235

  1. QUADRATURE DETECTION IN MULTI-DIMENSIONAL

NMR SPECTROSCOPY 239

12.1 Quadrature Detection Using TPPI 240

12.2 Hypercomplex Method of Quadrature Detection 242

12.2.1 States-TPPI – Removal of Axial Peaks 243

12.3 Sensitivity Enhancement 245

12.4 Echo-AntiEcho Quadrature Detection: N-P Selection 247

12.4.1 Absorption Mode Lineshapes with N-P Selection 247

  1. RESONANCE ASSIGNMENTS: HOMONUCLEAR METHODS 251

13.1 Overview of the Assignment Process 251

13.2 Homonuclear Methods of Assignment 254

13.3 15N Separated Homonuclear Techniques 256

13.3.1 2D 15N HSQC Experiment 259

13.3.2 3D 15N Separated TOCSY Experiment 259

13.3.3 The HNHA Experiment – Identifying Hα Protons 262

13.3.4 The HNHB Experiment- Identifying Hβ Protons 265

13.4 Exercises 272

13.5 Solutions 273

  1. RESONANCE ASSIGNMENTS:

HETERONUCLEAR METHODS 277

14.1 Mainchain Assignments 278

14.1.1 Strategy 278

14.1.2 Methods for Mainchain Assignments 279

14.2 Description of Triple-resonance Experiments 282

14.2.1 HNCO Experiment 282

14.2.2 HNCA Experiment 290

14.3 Selective Excitation and Decoupling of 13C 294
14.3.1 Selective 90 Pulses 294

14.3.2 Selective 180 Pulses 297

14.3.3 Selective Decoupling: SEDUCE 298

14.3.4 Frequency Shifted Pulses 299

14.4 Sidechain Assignments 300
14.4.1 Triple-resonance Methods for Sidechain Assignments 301

14.4.2 The HCCH Experiment 302

14.5 Exercises 308

14.6 Solutions 310

15.1 Sample Preparation 313

15.1.1 NMR Sample Tubes 313

15.1.2 Sample Requirements 313

15.2 Solvent Considerations – Water Suppression 315

15.2.1 Amide Exchange Rates 315

15.2.2 Solvent Suppression 316

15.3 Instrument Configuration 324

15.3.1 Probe Tuning 324

15.4 Calibration of Pulses 326

15.4.1 Proton Pulses 326

15.4.2 Heteronuclear Pulses 326

15.5 T1, T2 and Experimental Parameters 328

15.5.1 Fundamentals of Nuclear Spin Relaxation 328

15.5.2 Effect of MolecularWeight and Magnetic Field Strength on 330

15.5.3 Effect of Temperature on T2 332

15.5.4 Relaxation Interference: TROSY 332

15.5.5 Determination of T1 and T2 337

15.6 Acquisition of Multi-Dimensional Spectra 338

15.6.1 Setting Polarization Transfer Delays 338

15.6.2 Defining the Directly Detected Dimension: t3 339

15.6.3 Defining Indirectly Detected Dimensions 340

15.7 Processing 3-Dimensional Data 346

15.7.1 Data Structure 346

15.7.2 Defining the Spectral Matrix 346

15.7.3 Data Processing 348

15.7.4 Processing the Directly Detected Domain 348
15.7.5 Variation in Processing 349

15.7.6 Useful Manipulations of the Free Induction Decay 351

  1. PRACTICAL ASPECTS OF N-DIMENSIONAL DATA

ACQUISITION AND PROCESSING

T1 and T2

  1. DIPOLAR COUPLING 353

16.1 Introduction 353

16.1.1 Energy of Interaction 353

16.1.2 Effect of Isotropic Tumbling on Dipolar Coupling 356

16.1.3 Effect of Anisotropic Tumbling 357

16.2 Measurement of Inter-proton Distances 358

16.2.1 NOESY Experiment 360

16.2.2 Crosspeak Intensity in the NOESY Experiment 363

16.2.4 Experimental Determination of Inter-proton Distances 366

16.3 Residual Dipolar Coupling (RDC) 368

16.3.1 Generating Partial Alignment of Macromolecules 369

16.3.2 Theory of Dipolar Coupling 371

16.3.3 Measurement of Residual Dipolar Couplings 375

16.3.4 Estimation of the Alignment Tensor 380

  1. PROTEIN STRUCTURE DETERMINATION 383

17.1 Energy Functions 385

17.1.1 Experimental Data 385

17.1.2 Covalent and Non-covalent Interactions 391

17.2 Energy Minimization and Simulated Annealing 392

17.2.1 Energy Minimization 393

17.2.2 Simulated Annealing 393

17.3 Generation of Starting Structures 395

17.3.1 Random Coordinates 395

17.3.2 Distance Geometry 395

17.3.3 Refinement 397

17.4 Illustrative Example of Protein Structure Determination 399

  1. EXCHANGE PROCESSES 403

18.1 Introduction 403

18.2 Chemical Exchange 404

18.3 General Theory of Chemical Exchange 407

18.3.1 Fast Exchange Limit 409

18.3.2 Slow Exchange Limit 410

18.3.3 Intermediate Time Scales 410

18.4 Measurement of Chemical Exchange 411

18.4.1 Very Slow Exchange:kex << Δν 411

18.4.2 Slow Exchange: kex < Δν 413

Effect of Molecular Weight on the Intensity of NOESY Crosspeaks

18.4.3 Slow to Intermediate Exchange: kex Δν 414

18.4.4 Fast Exchange: kex > Δν 414

18.4.5 Measurement of Exchange Using CPMG Methods 419

18.5 Distinguishing Fast from Slow Exchange 425

18.5.1 Effect of Temperature 425

18.5.2 Magnetic Field Dependence 426

18.6 Ligand Binding Kinetics 427

18.6.1 Slow Exchange 428

Fundamentals of Protein NMR Spectroscopy

18.6.2 Intermediate Exchange 429

18.6.3 Fast Exchange 429

18.7 Exercises 430

18.8 Solutions 430

19.1 Introduction 431

19.1.1 Relaxation of Excited States 432

19.2 Time-Dependent Field Fluctuations 434

19.2.1 Chemical Shift Anisotropy 434

19.2.2 Dipolar Coupling 437

19.2.3 Frequency Components from Molecular Rotation 438

19.3 Spin-lattice (T1) and Spin-spin (T2) Relaxation 442

19.3.1 Spin-lattice Relaxation 442

19.3.2 Spin-lattice Relaxation of Like Spins 445
19.3.3 Spin-lattice Relaxation of Unlike Spins 445
19.3.4 Spin-spin Relaxation 446
19.3.5 Heteronuclear NOE 447
19.4 Motion and the Spectral Density Function 448
19.4.1 Random Isotropic Motion 448
19.4.2 Anisotropic Motion – Non-spherical Protein 448
19.4.3 Constrained Internal Motion 449
19.4.4 Combining Internal and External Motion 451
19.5 Effect of Internal Motion on Relaxation 451
19.5.1 Anisotropic Rotational Diffusion 454
19.6 Measurement and Analysis of Relaxation Data 455
19.6.1 Pulse Sequences 455
19.6.2 Measuring Heteronuclear T1 457

Fundamentals of Protein NMR Spectroscopy

  1. NUCLEAR SPIN RELAXATION AND MOLECULAR DYNAMICS
    19.7.1 Defining Rotational Diffusion 463
    19.7.2 Determining Internal Rotation 466

19.7.3 Systematic Errors in Model Fitting 467
19.8 Statistical Tests 468
19.8.1 χ2 Test for Goodness-of-fit 468
19.8.2 Test for Inclusion of Additional Parameters 470
19.8.3 Alternative Methods of Model Selection 472
19.8.4 Error Propagation 472
19.9 Exercises 473
19.10 Solutions 474
19.6.3 Measuring Heteronuclear T2 459
19.7 Data Analysis and Model Fitting 463
19.7.1 Defining Rotational Diffusion 463
19.7.2 Determining Internal Rotation 466
19.7.3 Systematic Errors in Model Fitting 467
19.8 Statistical Tests 468
19.8.1 χ2 Test for Goodness-of-fit 468
19.8.2 Test for Inclusion of Additional Parameters 470
19.8.3 Alternative Methods of Model Selection 472
19.8.4 Error Propagation 472
19.9 Exercises 473
19.10 Solutions 474
Appendices 475
A Fourier Transforms 475
A.1 Fourier Series 475
A.2 Non-periodic Functions – The Fourier Transform 476
A.2.1 Examples of Fourier Transforms 477
A.2.2 Linearity 481

Fundamentals of Protein NMR Spectroscopy

B Complex Variables, Scalars, Vectors, and Tensors 485
B.1 Complex Numbers 485
B.2 Representation of Signals with Complex Numbers 486
B.3 Scalars, Vectors, and Tensors 487
B.3.1 Scalars 487
B.3.2 Vectors 487
B.3.3 Tensors 488

Fundamentals of Protein NMR Spectroscopy

C Solving Simultaneous Differential Equations: Laplace Transforms 491
C.1 Laplace Transforms 491
C.1.1 Example Calculation 492
C.1.2 Application to Chemical Exchange 493
C.1.3 Application to Spin-lattice Relaxation 494
C.1.4 Spin-lattice Relaxation of Two Different Spins 495

Fundamentals of Protein NMR Spectroscopy

D Building Blocks of Pulse Sequences 497
D.1 Product operators 497
D.1.1 Pulses 497
D.1.2 Evolution by J-coupling 497
D.1.3 Evolution by Chemical Shift 498
D.2 Common Elements of Pulse Sequences 498
D.2.1 INEPT Polarization Transfer 498
D.2.2 HMQC Polarization Transfer 499
D.2.3 Constant Time Evolution 499
D.2.4 Constant Time Evolution with J-coupling 500
D.2.5 Sequential Chemical Shift & J-coupling Evolution 501
D.2.6 Semi-constant Time Evolution of Chemical

Shift & J-Coupling 501
References 505

Index 519

File Size: 5.44 MB. Pages: 543. Please read Disclaimer.

Download Link 1

 

 

 

You may also likeAnalytical Chemistry by Gary D. Christian 7th edition”.

 

Free download hundreds of chemistry books in pdf from HERE.

Please Subscribe to our Email list and get notified of our latest uploads (Books, documents) and new updates. Email Subscription Box is provided on the sidebar (for PC) and on the bottom of this post (for Android Devices).

Kindly Like, Follow and Share our social media pages so that maximum people can get the benefit from this public service!

Facebook   Instagram    LinkedIn    Twitter    Pinterest

P.S: If the download link(s) is/are not working, kindly drop a comment below, so we’ll update the download link for you.

Happy reading!

Leave a Reply

Your email address will not be published.