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Summary
Summary
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
Table of Contents
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 |