THE NUCLEAR OVERHAUSER EFFECT IN STRUCTURAL AND CONFORMATIONAL ANALYSIS

David Neuhaus and Michael P. Williamson

VCH

CONTENTS

Preface v

Acknowledgments vii

Symbols, Abbreviations, and Units xvii

Introduction xxi

P A R T

THEORY

C H A P T E R 1

Background 3

1.1 Energy Levels, Populations, and Intensities 3 1.2 Relaxation, T, and T2 8 1.3 The Nature of Relaxation 12 1.4 The Local Field and Dipole-Dipole Relaxation 13 1.5 Pulses and Saturation 14 1.6 References 22

C H A P T E R 2

The Steady-State NOE for Two Spins 23 2.1 The Origin and Form of the NOE 23

2.1.1 Qualitative Considerations 23 2.1.2 The Solomon Equations 27

2.2 Dependence of the NOE on Molecular Motion 30 2.2.1 Correlation Times, Spectral Density Functions,

and Transition Probabilities 31 2.2.2 Anisotropie Tumbling 38

2.3 What the Symbols Mean for Two Spins and for Many Spins 39 2.3.1 Relaxation Rates 39 2.3.2 7", Measurements and Cross-Relaxation 43

ix

X CONTENTS

2.4 Effects of Other Relaxation Sources 46 2.4.1 The External Relaxation Rate p* 47 2.4.2 Intermolecular Dipole-Dipole Relaxation 51 2.4.3 Quadrupolar Relaxation 53 2.4.4 Chemical Shift Anisotropy (CSA) Relaxation 54 2.4.5 Scalar Relaxation 55 2.4.6 Spin-Rotation Relaxation 55

2.5 The Heteronuclear NOE 56 2.6 References 60

C H A P T E R 3

The Steady-State NOE in Rigid Multispin Systems 63 3.1 The Equations 64

3.1.1 The Solomon Equations for More Than Two Spins 64

3.1.2 Cross-Correlation 67 3.1.3 Two General Solutions to the Multispin Solomon

Equations 69 3.1.3.1 Saturation of One Spin 69 3.1.3.2 Saturation of All Spins Except One 70

3.1.4 Internuclear Distances and Steady-State NOE Enhancements 72

3.2 What the Equations Mean 74 3.2.1 General; Direct Enhancements and Spin Diffusion 74 3.2.2 Interpretation at the Extreme Narrowing Limit

(anc < 1) 77 3.2.2.1 Direct Effects 77 3.2.2.2 Indirect Effects 81 3.2.2.3 When Do Indirect Effects Matter? 82 3.2.2.4 Magnetic Equivalence 85 3.2.2.5 T, and the 3/2 Effect 87 3.2.2.6 Chemical Equivalence 87

3.2.3 Away from the Extreme Narrowing Limit 89 3.3 In Practice 95

3.3.1 Incomplete Saturation 95 3.3.2 Failure to Reach Steady State 97 3.3.3 Competition from Other Relaxation Sources 97

3.4 References WO

C H A P T E R 4

The Kinetics of the NOE 103 4.1 The Initial Rate Approximation 104 4.2 The Truncated Driven NOE (TOE) 105

4.2.1 The Reference Distance 109

CONTENTS xi

4.2.2 Noninstantaneous Saturation 109 4.2.3 Correlation Times 109 4.2.4 Internal Motion 110 4.2.5 Noninitial Conditions 110 4.2.6 Practical Implications 117

4.3 Further Implications for Interpretation 119 4.3.1 What Is the Steady State? 119 4.3.2 r , Values as an Aid to Interpretation 122

4.4 Transient and NOESY Experiments 123 4.5 Calculated Examples of Multispin Systems 135 4.6 References 139

C H A P T E R 5

The Effects of Exchange and Internal Motion 141 5.1 Transfer of Saturation 143 5.2 General Equations for the NOE in Systems of Two-Site

Exchange 148 5.2.1 Exchange in a Two-Spin System 148 5.2.2 Exchange in Dimethylformamide 157

5.3 Applications to More Complicated Cases of Exchange 160 5.3.1 Averaging of Rates Rather Than Enhancements 161 5.3.2 Two-Site Exchange in a Multispin System 163

5.3.2.1 Olefinic Methoxy Conformations 163 5.3.2.2 Nucleotide Conformations: A Simple

Model 164 5.3.2.3 Nucleotide Conformations: The "Best Fit"

Approach 757 5.3.3 Allowing for Averaging 170

5.4 Exchange Rates Faster Than Molecular Tumbling 173 5.5 The Transferred NOE 175 5.6 References 181

C H A P T E R 6

Complications from Spin-Spin Coupling 183 6.1 Decoupling 183 6.2 Selective Population Transfer 184

6.2.1 Theory 185 6.2.2 Consequences 193

6.3 Strong Coupling 194 6.3.1 A{B} Enhancements 195 6.3.2 AB{X} Enhancements 196 6.3.3 Scalar Relaxation 203

6.3.3.1 Scalar Relaxation of the First Kind 205 6.3.3.2 Scalar Relaxation of the Second Kind 207

6.4 References 208

xii CONTENTS

EXPERIMENTAL 209

C H A P T E R 7

One-Dimensional Experiments 211 7.1 Sample Preparation 211

7.1.1 Solvent 211 7.1.2 Solute Concentration 214 7.1.3 Sample Purification 215

7.2 Setting Up the Steady-State Difference Experiment 217 7.2.1 Introduction to the Difference Experiment 218 7.2.2 Minimizing Subtraction Artifacts 220 7.2.3 Automatic Multiple Experiments 224 7.2.4 Irradiation Power and Selectivity 227 7.2.5 Multiplet Irradiation and SPT Suppression 231 7.2.6 Timing 236

7.3 Display and Calculation of Results 240 7.4 Other 1D Experiments 241

7.4.1 CW Steady-State Integration 241 7.4.2 The Truncated Driven NOE (TOE) Experiment 243 7.4.3 Transient Experiments 247

7.4.3.1 Selective Pulses 247 7.4.3.2 Other Considerations 250

7.5 References 251

C H A P T E R 8

The Two-Dimensional NOESY Experiment 253 8.1 One Dimension or Two? 253

8.1.1 The Negative NOE Regime (anc > 1.12) 253 8.1.2 The Positive NOE Regime (COTC < 1.12) 254

8.2 Basic Principles 256 8.3 Acquiring a NOESY Spectrum 264

8.3.1 Fixed Delays and Pulse Widths 264 8.3.2 Acquisition Times ?, and t2 and Spectral Widths SW\

and SW2 266 8.3.3 Quadrature Detection in F, and F2 269 8.3.4 Phase-Sensitive NOESY 277

8.4 Phase Cycling, Signal Selection, and Artifact Suppression 283 8.4.1 Rejection of Nonlongitudinal Contributions during tm;

/-Peak Suppression 284 8.4.2 Other Forms of 7-Peaks; Zero Quantum Coherences

and Pulse Angle Effects 285 8.4.3 Axial Peaks 288

CONTENTS xiii

8.4.4 Quadrature Images 288 8.4.5 ?, Noise 290

8.5 Data Processing 293 8.5.1 Zero Filling 293 8.5.2 Window Functions 294 8.5.3 Symmetrization and f, Noise Removal 296 8.5.4 Integration 298

8.6 Variations 2P£ 8.6.1 Combination with Other 2D Experiments 298 8.6.2 Semiselective Experiments 301 8.6.3 Heteronuclear Experiments 302 8.6.4 Other Variants 303

8.7 References 304

C H A P T E R 9

Other Developments 307 9.1 Heteronuclear Experiments 307 9.2 Rotating Frame NOE Experiments 312

9.2.1 Theory 313 9.2.1.1 Spin Locking and Transverse

Cross-Relaxation 313 9.2.1.2 Other Effects during Spin Locking 318

9.2.2 Practice 324 9.2.3 Summary 326

9.3 Variation of u>xc 327 9.4 Editing and Spectral Simplification 330 9.5 Coping with Large Solvent Signals 337

9.5.1 Methods That Suppress the Solvent Signal 339 9.5.2 Methods That Do Not Excite the Solvent Signal 342 9.5.3 Data Processing 345 9.5.4 Special Problems of 2D Experiments 346

9.6 References 347

P A R T I I I

APPLICATIONS 351

C H A P T E R 10

Applications of the NOE to Structure Elucidation 353 10.1 General Considerations 353

10.1.1 Why Structural and Conformational Problems Are the Same 354

10.1.2 Spectra and Assignments 355

xiv CONTENTS

10.1.3 Reporting Results and Interpretation 357 10.1.4 Miscellaneous 359

10.2 Aromatic Substitution and Ring Fusion Patterns: Simple Cases 359

10.3 Aromatic Substitution and Ring Fusion Patterns: More Complex Cases 370 10.3.1 Petroporphyrins 370 10.3.2 Isoquinoline and Related Alkaloids 374

10.4 Double Bond Isomers 380 10.5 Saturated Ring Systems: Simple Cases 386

10.5.1 Substituent Stereochemistry 387 10.5.2 Ring Fusion Stereochemistry 396

10.6 Saturated Ring Systems: More Complex Cases 408 10.6.1 Pulvomycin 410 10.6.2 Penitrem A 413 10.6.3 Other Examples 416

10.7 References 419

C H A P T E R 11

Applications of the NOE to Conformational Analysis 421 11.1 General Considerations 421

11.1.1 Why Structural and Conformational Problems Are Different 421

11.1.2 Multiple Conformations 423 11.2 Local Conformational Detail in Small Molecules 424

11.2.1 Slowly Exchanging Equilibria 424 11.2.2 Rapidly Exchanging Equilibria: A Hypothetical

Example, X—CH2OH 426 11.2.3 Rapidly Exchanging Equilibria: Real Examples 428

11.3 Conformational Analysis of Medium-Sized Molecules 437 11.4 References 448

C H A P T E R 12

Biopolymers 4SI 12.1 Peptides and Proteins 451

12.1.1 Assignment: General 453 12.1.2 Sequential Assignment Method 457 12.1.3 Crystal/Sequence Method 458

12.1.3.1 Techniques Requiring No Structural Assumptions 459

12.1.3.2 Techniques Requiring Structural Assumptions 459

CONTENTS

12.1.4 Structure Determination 460 12.1.4.1 Small Cyclic Peptides 462 12.1.4.2 Acyclic Peptides 463 12.1.4.3 Small Proteins: General 463 12.1.4.4 BUSI IIA: Distance Geometry 464 12.1.4.5 Metallothionein-2 467 12.1.4.6 Lac Repressor Headpiece: Molecular

Dynamics 469 12.1.4.7 Large Proteins 473

12.2 Polynucleotides 474 12.2.1 Structures and Conformations 477 12.2.2 A, B, or Z? 482 12.2.3 Sequential Assignment 484 12.2.4 Sequence-Dependent Conformation 488 12.2.5 Interactions with Other Molecules 493

12.3 Oligosaccharides 494 12.3.1 Sequence and Linkage Determination 495 12.3.2 Conformation 496

12.4 References 498

A P P E N D I X I

Equations for Enhancements Involving Groups of Equivalent Spins 503

A P P E N D I X I I

Quantum Mechanics and Transition Probabilities 505

Index 515