Fundamentals of protein NMR spectroscopy

NMR spectroscopy has proven to be a powerful technique to study the structure and dynamics of biological macromolecules. Fundamentals of Protein NMR Spectroscopy is a comprehensive textbook that guides the reader from a basic understanding of the phenomenological properties of magnetic resonance to the application and interpretation of modern multi-dimensional NMR experiments on 15N/13C-labeled proteins. Beginning with elementary quantum mechanics, a set of practical rules is presented and used to describe many commonly employed multi-dimensional, multi-nuclear NMR pulse sequences. A modular analysis of NMR pulse sequence building blocks also provides a basis for understanding and developing novel pulse programs. This text not only covers topics from chemical shift assignment to protein structure refinement, as well as the analysis of protein dynamics and chemical kinetics, but also provides a practical guide to many aspects of modern spectrometer hardware, sample preparation, experimental set-up, and data processing. End of chapter exercises are included to emphasize important concepts. Fundamentals of Protein NMR Spectroscopy not only offer students a systematic, in-depth, understanding of modern NMR spectroscopy and its application to biomolecular systems, but will also be a useful reference for the experienced investigator.

Author Notes

Professor of Biological Sciences at Carnegie Mellon University.

Professor Rule's research is directed at understanding inter-molecular interactions in biological systems. An understanding of these interactions is required if biological systems are to be comprehended at the molecular level. The combined tools of molecular biology, NMR spectroscopy and x-ray crystallography are used to provide important information to aid in our understanding of these interactions. Our research efforts have been directed at enzyme-substrate interactions, protein-lipid interactions, antibody-antigen interactions, and protein-nucleic acid interactions

List of Figures	p. xvii
List of Tables	p. xxvi
1 NMR Spectroscopy	p. 1
1.1 Introduction to NMR Spectroscopy	p. 2
1.2 One Dimensional NMR Spectroscopy	p. 3
1.2.1 Classical Description of NMR Spectroscopy	p. 3
1.2.2 Nuclear Spin Transitions	p. 3
1.3 Detection of Nuclear Spin Transitions	p. 7
1.3.1 Continuous Wave NMR	p. 7
1.3.2 Pulsed NMR	p. 8
1.3.3 Summary of the Process of Acquiring a One Dimensional Spectrum	p. 15
1.4 Phenomenological Description of Relaxation	p. 16
1.4.1 Relaxation and the Evolution of Magnetization	p. 18
1.5 Chemical Shielding	p. 19
1.6 Characteristic [superscript 1]H, [superscript 13]C and [superscript 15]N Chemical Shifts	p. 21
1.6.1 Effect of Electronic Structure on Chemical Shifts	p. 21
1.6.2 Ring Current Effects	p. 23
1.6.3 Effects of Local Environment on Chemical Shifts	p. 25
1.6.4 Use of Chemical Shifts in Resonance Assignments	p. 25
1.6.5 Chemical Shift Dispersion & Multi-dimensional NMR	p. 26
1.7 Exercises	p. 26
1.8 Solutions	p. 26
2 Practical Aspects of Acquiring NMR Spectra	p. 29
2.1 Components of an NMR Spectrometer	p. 29
2.1.1 Magnet	p. 29
2.1.2 Computer	p. 31
2.1.3 Probe	p. 31
2.1.4 Pre-amplifier Module	p. 32
2.1.5 The Field-frequency Lock	p. 33
2.1.6 Shim System	p. 34
2.1.7 Transmitter & Pulse Generation	p. 34
2.1.8 Receiver	p. 36
2.2 Acquiring a Spectrum	p. 38
2.2.1 Sample Preparation	p. 38
2.2.2 Beginning the Experiment	p. 39
2.2.3 Temperature Measurement	p. 39
2.2.4 Shimming	p. 40
2.2.5 Tuning and Matching the Probe	p. 41
2.2.6 Adjusting the Transmitter	p. 42
2.2.7 Calibration of the 90[degree] Pulse Length	p. 46
2.2.8 Setting the Sweepwidth: Dwell Times and Filters	p. 48
2.2.9 Setting the Receiver Gain	p. 53
2.2.10 Spectral Resolution and Acquisition Time of the FID	p. 54
2.3 Experimental 1D-pulse Sequence: Pulse and Receiver Phase	p. 57
2.3.1 Phase Cycle	p. 58
2.3.2 Phase Cycle and Artifact Suppression	p. 61
2.4 Exercises	p. 63
2.5 Solutions	p. 64
3 Introduction to Signal Processing	p. 65
3.1 Removal of DC Offset	p. 66
3.2 Increasing Resolution by Extending the FID	p. 66
3.2.1 Increasing Resolution by Zero-filling	p. 67
3.2.2 Increasing Resolution by Linear Prediction (LP)	p. 69
3.3 Removal of Truncation Artifacts: Apodization	p. 74
3.3.1 Effect of Apodization on Resolution and Noise	p. 74
3.3.2 Using LP & Apodization to Increase Resolution	p. 77
3.4 Solvent Suppression	p. 78
3.5 Spectral Artifacts Due to Intensity Errors	p. 79
3.5.1 Errors from the Digital Fourier Transform	p. 79
3.5.2 Effect of Distorted and Missing Points	p. 80
3.5.3 Delayed Acquisition	p. 82
3.6 Phasing of the Spectrum	p. 82
3.6.1 Origin of Phase Shifts	p. 83
3.6.2 Applying Phase Corrections	p. 85
3.7 Chemical Shift Referencing	p. 86
3.8 Exercises	p. 87
3.9 Solutions	p. 87
4 Quantum Mechanical Description of NMR	p. 89
4.1 Schrodinger Equation	p. 89
4.1.1 Vector Spaces and Properties of Wavefunctions	p. 90
4.1.2 Particle in a Box	p. 92
4.2 Expectation Values	p. 93
4.3 Dirac Notation	p. 94
4.3.1 Wavefunctions in Dirac Notation	p. 94
4.3.2 Scalar Product in Dirac Notation	p. 96
4.3.3 Operators in Dirac Notation	p. 96
4.3.4 Expectation Values in Dirac Notation	p. 96
4.4 Hermitian Operators	p. 97
4.4.1 Determining Eigenvalues	p. 97
4.5 Additional Properties of Operators	p. 100
4.5.1 Commuting Observables	p. 100
4.5.2 Time Evolution of Observables	p. 100
4.5.3 Trace of an Operator	p. 100
4.5.4 Exponential Operator	p. 101
4.5.5 Unitary Operators	p. 101
4.5.6 Exponential Hermitian Operators	p. 101
4.6 Hamiltonian and Angular Momentum Operators for a Spin-1/2 Particle	p. 102
4.7 Rotations	p. 105
4.7.1 Rotation Groups	p. 105
4.7.2 Rotation Operators	p. 106
4.7.3 Rotations of Wave Functions and Operators	p. 109
4.8 Exercises	p. 112
4.9 Solutions	p. 112
5 Quantum Mechanical Description of a One Pulse Experiment	p. 113
5.1 Preparation: Evolution of the System Under B[subscript o]	p. 114
5.2 Excitation: Effect of Application of B[subscript 1]	p. 116
5.2.1 The Resonance Condition	p. 118
5.3 Detection: Evolution of the System Under B[subscript o]	p. 120
6 The Density Matrix & Product Operators	p. 121
6.1 Introduction to the Density Matrix	p. 122
6.1.1 Calculation of Expectation Values From [rho]	p. 123
6.1.2 Density Matrix for a Statistical Mixture	p. 123
6.2 One-pulse Experiment: Density Matrix Description	p. 126
6.2.1 Effect of Pulses on the Density matrix	p. 127
6.3 Product Operators	p. 129
6.3.1 Transformation Properties of Product Operators	p. 130
6.3.2 Description of the One-pulse Experiment	p. 131
6.3.3 Evaluation of Composite Pulses	p. 132
6.4 Exercises	p. 133
6.5 Solutions	p. 133
7 Scalar Coupling	p. 135
7.1 Introduction to Scalar Coupling	p. 135
7.2 Basis of Scalar Coupling	p. 136
7.2.1 Coupling to Multiple Spins	p. 138
7.3 Quantum Mechanical Description	p. 140
7.3.1 Analysis of an AX System	p. 140
7.3.2 Analysis of an AB System	p. 142
7.4 Decoupling	p. 145
7.4.1 Experimental Implementation of Decoupling	p. 145
7.4.2 Decoupling Methods	p. 146
7.4.3 Performance of Decoupling Schemes	p. 148
7.5 Exercises	p. 150
7.6 Solutions	p. 150
8 Coupled Spins: Density Matrix and Product Operator Formalism	p. 153
8.1 Density Matrix for Two Coupled Spins	p. 153
8.2 Product Operator Representation of the Density Matrix	p. 155
8.2.1 Detectable Elements of [rho]	p. 156
8.3 Density Matrix Treatment of a One-pulse Experiment	p. 159
8.4 Manipulation of Two-spin Product Operators	p. 162
8.5 Transformations of Two-spin Product Operators	p. 164
8.6 Product Operator Treatment of a One-pulse Experiment	p. 165
9 Two Dimensional Homonuclear J-Correlated Spectroscopy	p. 169
9.1 Multi-dimensional Experiments	p. 170
9.1.1 Elements of Multi-dimensional NMR Experiments	p. 171
9.1.2 Generation of Multi-dimensional NMR Spectra	p. 172
9.2 Homonuclear J-correlated Spectra	p. 173
9.2.1 COSY Experiment	p. 173
9.3 Double Quantum Filtered COSY (DQF-COSY)	p. 182
9.3.1 Product Operator Treatment of the DQF-COSY Experiment	p. 182
9.4 Effect of Passive Coupling on COSY Crosspeaks	p. 185
9.5 Scalar Correlation by Isotropic Mixing: TOCSY	p. 187
9.5.1 Analysis of TOCSY Pulse Sequence	p. 188
9.5.2 Isotropic Mixing Schemes	p. 191
9.5.3 Time Dependence of Magnetization Transfer by Isotropic Mixing	p. 192
9.6 Exercises	p. 194
9.7 Solutions	p. 195
10 Two Dimensional Heteronuclear J-Correlated Spectroscopy	p. 197
10.1 Introduction	p. 197
10.2 Two Dimensional Heteronuclear NMR Experiments	p. 198
10.2.1 HMQC Experiment	p. 199
10.2.2 HSQC Experiment	p. 204
10.2.3 Refocused-HSQC Experiment	p. 207
10.2.4 Comparison of HMQC, HSQC, and Refocused-HSQC Experiments	p. 209
10.2.5 Sensitivity in 2D-Heteronuclear Experiments	p. 209
10.2.6 Behavior of XH[subscript 2] Systems in HSQC-type Experiments	p. 210
11 Coherence Editing: Pulsed-Field Gradients and Phase Cycling	p. 213
11.1 Principals of Coherence Selection	p. 214
11.1.1 Spherical Basis Set	p. 214
11.1.2 Coherence Changes in NMR Experiments	p. 216
11.1.3 Coherence Pathways	p. 218
11.2 Phase Encoding With Pulsed-Field Gradients	p. 218
11.2.1 Gradient Coils	p. 218
11.2.2 Effect of Coherence Levels on Gradient Induced Phase Changes	p. 220
11.2.3 Coherence Selection by Gradients in Heteronuclear NMR Experiments	p. 222
11.3 Coherence Selection Using Phase Cycling	p. 225
11.3.1 Coherence Changes Induced by RF-Pulses	p. 226
11.3.2 Selection of Coherence Pathways	p. 229
11.3.3 Phase Cycling in the HMQC Pulse Sequence	p. 233
11.4 Exercises	p. 235
11.5 Solutions	p. 235
12 Quadrature Detection in Multi-Dimensional NMR Spectroscopy	p. 239
12.1 Quadrature Detection Using TPPI	p. 240
12.2 Hypercomplex Method of Quadrature Detection	p. 242
12.2.1 States-TPPI - Removal of Axial Peaks	p. 243
12.3 Sensitivity Enhancement	p. 245
12.4 Echo-AntiEcho Quadrature Detection: N-P Selection	p. 247
12.4.1 Absorption Mode Lineshapes with N-P Selection	p. 247
13 Resonance Assignments: Homonuclear Methods	p. 251
13.1 Overview of the Assignment Process	p. 251
13.2 Homonuclear Methods of Assignment	p. 254
13.3 [superscript 15]N Separated Homonuclear Techniques	p. 256
13.3.1 2D [superscript 15]N HSQC Experiment	p. 259
13.3.2 3D [superscript 15]N Separated TOCSY Experiment	p. 259
13.3.3 The HNHA Experiment - Identifying H[subscript alpha] Protons	p. 262
13.3.4 The HNHB Experiment- Identifying H[subscript beta] Protons	p. 265
13.3.5 Establishing Spin-system Connectivities with Dipolar Coupling	p. 267
13.4 Exercises	p. 272
13.5 Solutions	p. 273
14 Resonance Assignments: Heteronuclear Methods	p. 277
14.1 Mainchain Assignments	p. 278
14.1.1 Strategy	p. 278
14.1.2 Methods for Mainchain Assignments	p. 279
14.2 Description of Triple-resonance Experiments	p. 282
14.2.1 HNCO Experiment	p. 282
14.2.2 HNCA Experiment	p. 290
14.3 Selective Excitation and Decoupling of [superscript 13]C	p. 294
14.3.1 Selective 90[degree] Pulses	p. 294
14.3.2 Selective 180[degree] Pulses	p. 297
14.3.3 Selective Decoupling: SEDUCE	p. 298
14.3.4 Frequency Shifted Pulses	p. 299
14.4 Sidechain Assignments	p. 300
14.4.1 Triple-resonance Methods for Sidechain Assignments	p. 301
14.4.2 The HCCH Experiment	p. 302
14.5 Exercises	p. 308
14.6 Solutions	p. 310
15 Practical Aspects of N-Dimensional Data Acquisition and Processing	p. 313
15.1 Sample Preparation	p. 313
15.1.1 NMR Sample Tubes	p. 313
15.1.2 Sample Requirements	p. 313
15.2 Solvent Considerations - Water Suppression	p. 315
15.2.1 Amide Exchange Rates	p. 315
15.2.2 Solvent Suppression	p. 316
15.3 Instrument Configuration	p. 324
15.3.1 Probe Tuning	p. 324
15.4 Calibration of Pulses	p. 326
15.4.1 Proton Pulses	p. 326
15.4.2 Heteronuclear Pulses	p. 326
15.5 T[subscript 1], T[subscript 2] and Experimental Parameters	p. 328
15.5.1 Fundamentals of Nuclear Spin Relaxation	p. 328
15.5.2 Effect of Molecular Weight and Magnetic Field Strength on T[subscript 1] and T[subscript 2]	p. 330
15.5.3 Effect of Temperature on T[subscript 2]	p. 332
15.5.4 Relaxation Interference: TROSY	p. 332
15.5.5 Determination of T[subscript 1] and T[subscript 2]	p. 337
15.6 Acquisition of Multi-Dimensional Spectra	p. 338
15.6.1 Setting Polarization Transfer Delays	p. 338
15.6.2 Defining the Directly Detected Dimension: t[subscript 3]	p. 339
15.6.3 Defining Indirectly Detected Dimensions	p. 340
15.7 Processing 3-Dimensional Data	p. 346
15.7.1 Data Structure	p. 346
15.7.2 Defining the Spectral Matrix	p. 346
15.7.3 Data Processing	p. 348
15.7.4 Processing the Directly Detected Domain	p. 348
15.7.5 Variation in Processing	p. 349
15.7.6 Useful Manipulations of the Free Induction Decay	p. 351
16 Dipolar Coupling	p. 353
16.1 Introduction	p. 353
16.1.1 Energy of Interaction	p. 353
16.1.2 Effect of Isotropic Tumbling on Dipolar Coupling	p. 356
16.1.3 Effect of Anisotropic Tumbling	p. 357
16.2 Measurement of Inter-proton Distances	p. 358
16.2.1 NOESY Experiment	p. 360
16.2.2 Crosspeak Intensity in the NOESY Experiment	p. 363
16.2.3 Effect of Molecular Weight on the Intensity of NOESY Crosspeaks	p. 364
16.2.4 Experimental Determination of Inter-proton Distances	p. 366
16.3 Residual Dipolar Coupling (RDC)	p. 368
16.3.1 Generating Partial Alignment of Macromolecules	p. 369
16.3.2 Theory of Dipolar Coupling	p. 371
16.3.3 Measurement of Residual Dipolar Couplings	p. 375
16.3.4 Estimation of the Alignment Tensor	p. 380
17 Protein Structure Determination	p. 383
17.1 Energy Functions	p. 385
17.1.1 Experimental Data	p. 385
17.1.2 Covalent and Non-covalent Interactions	p. 391
17.2 Energy Minimization and Simulated Annealing	p. 392
17.2.1 Energy Minimization	p. 393
17.2.2 Simulated Annealing	p. 393
17.3 Generation of Starting Structures	p. 395
17.3.1 Random Coordinates	p. 395
17.3.2 Distance Geometry	p. 395
17.3.3 Refinement	p. 397
17.4 Illustrative Example of Protein Structure Determination	p. 399
18 Exchange Processes	p. 403
18.1 Introduction	p. 403
18.2 Chemical Exchange	p. 404
18.3 General Theory of Chemical Exchange	p. 407
18.3.1 Fast Exchange Limit	p. 409
18.3.2 Slow Exchange Limit	p. 410
18.3.3 Intermediate Time Scales	p. 410
18.4 Measurement of Chemical Exchange	p. 411
18.4.1 Very Slow Exchange: k[subscript ex]	p. 411
18.4.2 Slow Exchange: k[subscript ex]	p. 413
18.4.3 Slow to Intermediate Exchange: k[subscript ex approximate Delta nu]	p. 414
18.4.4 Fast Exchange: k[subscript ex] > [Delta nu]	p. 414
18.4.5 Measurement of Exchange Using CPMG Methods	p. 419
18.5 Distinguishing Fast from Slow Exchange	p. 425
18.5.1 Effect of Temperature	p. 425
18.5.2 Magnetic Field Dependence	p. 426
18.6 Ligand Binding Kinetics	p. 427
18.6.1 Slow Exchange	p. 428
18.6.2 Intermediate Exchange	p. 429
18.6.3 Fast Exchange	p. 429
18.7 Exercises	p. 430
18.8 Solutions	p. 430
19 Nuclear Spin Relaxation and Molecular Dynamics	p. 431
19.1 Introduction	p. 431
19.1.1 Relaxation of Excited States	p. 432
19.2 Time Dependent Field Fluctuations	p. 434
19.2.1 Chemical Shift Anisotropy	p. 434
19.2.2 Dipolar Coupling	p. 437
19.2.3 Frequency Components from Molecular Rotation	p. 438
19.3 Spin-lattice (T[subscript 1]) and Spin-spin (T[subscript 2]) Relaxation	p. 442
19.3.1 Spin-lattice Relaxation	p. 442
19.3.2 Spin-lattice Relaxation of Like Spins	p. 445
19.3.3 Spin-lattice Relaxation of Unlike Spins	p. 445
19.3.4 Spin-spin Relaxation	p. 446
19.3.5 Heteronuclear NOE	p. 447
19.4 Motion and the Spectral Density Function	p. 448
19.4.1 Random Isotropic Motion	p. 448
19.4.2 Anisotropic Motion - Non-spherical Protein	p. 448
19.4.3 Constrained Internal Motion	p. 449
19.4.4 Combining Internal and External Motion	p. 451
19.5 Effect of Internal Motion on Relaxation	p. 451
19.5.1 Anisotropic Rotational Diffusion	p. 454
19.6 Measurement and Analysis of Relaxation Data	p. 455
19.6.1 Pulse Sequences	p. 455
19.6.2 Measuring Heteronuclear T[subscript 1]	p. 457
19.6.3 Measuring Heteronuclear T[subscript 2]	p. 459
19.7 Data Analysis and Model Fitting	p. 463
19.7.1 Defining Rotational Diffusion	p. 463
19.7.2 Determining Internal Rotation	p. 466
19.7.3 Systematic Errors in Model Fitting	p. 467
19.8 Statistical Tests	p. 468
19.8.1 X[superscript 2] Test for Goodness-of-fit	p. 468
19.8.2 Test for Inclusion of Additional Parameters	p. 470
19.8.3 Alternative Methods of Model Selection	p. 472
19.8.4 Error Propagation	p. 472
19.9 Exercises	p. 473
19.10 Solutions	p. 474
Appendices	p. 475
A Fourier Transforms	p. 475
A.1 Fourier Series	p. 475
A.2 Non-periodic Functions - The Fourier Transform	p. 476
B Complex Variables, Scalars, Vectors, and Tensors	p. 485
B.1 Complex Numbers	p. 485
B.2 Representation of Signals with Complex Numbers	p. 486
B.3 Scalars, Vectors, and Tensors	p. 487
C Solving Simultaneous Differential Equations: Laplace Transforms	p. 491
C.1 Laplace Transforms	p. 491
D Building Blocks of Pulse Sequences	p. 497
D.1 Product operators	p. 497
D.2 Common Elements of Pulse Sequences	p. 498
References	p. 505
Index	p. 519

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents