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| List of Figures | |
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| List of Tables | |
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| NMR Spectroscopy | |
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| Introduction to NMR Spectroscopy | |
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| One Dimensional NMR Spectroscopy | |
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| Classical Description of NMR Spectroscopy | |
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| Nuclear Spin Transitions | |
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| Detection of Nuclear Spin Transitions | |
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| Continuous Wave NMR | |
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| Pulsed NMR | |
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| Summary of the Process of Acquiring a One Dimensional Spectrum | |
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| Phenomenological Description of Relaxation | |
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| Relaxation and the Evolution of Magnetization | |
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| Chemical Shielding | |
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| Characteristic [superscript 1]H, [superscript 13]C and [superscript 15]N Chemical Shifts | |
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| Effect of Electronic Structure on Chemical Shifts | |
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| Ring Current Effects | |
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| Effects of Local Environment on Chemical Shifts | |
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| Use of Chemical Shifts in Resonance Assignments | |
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| Chemical Shift Dispersion & Multi-dimensional NMR | |
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| Exercises | |
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| Solutions | |
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| Practical Aspects of Acquiring NMR Spectra | |
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| Components of an NMR Spectrometer | |
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| Magnet | |
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| Computer | |
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| Probe | |
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| Pre-amplifier Module | |
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| The Field-frequency Lock | |
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| Shim System | |
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| Transmitter & Pulse Generation | |
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| Receiver | |
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| Acquiring a Spectrum | |
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| Sample Preparation | |
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| Beginning the Experiment | |
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| Temperature Measurement | |
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| Shimming | |
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| Tuning and Matching the Probe | |
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| Adjusting the Transmitter | |
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| Calibration of the 90[degree] Pulse Length | |
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| Setting the Sweepwidth: Dwell Times and Filters | |
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| Setting the Receiver Gain | |
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| Spectral Resolution and Acquisition Time of the FID | |
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| Experimental 1D-pulse Sequence: Pulse and Receiver Phase | |
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| Phase Cycle | |
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| Phase Cycle and Artifact Suppression | |
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| Exercises | |
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| Solutions | |
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| Introduction to Signal Processing | |
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| Removal of DC Offset | |
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| Increasing Resolution by Extending the FID | |
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| Increasing Resolution by Zero-filling | |
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| Increasing Resolution by Linear Prediction (LP) | |
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| Removal of Truncation Artifacts: Apodization | |
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| Effect of Apodization on Resolution and Noise | |
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| Using LP & Apodization to Increase Resolution | |
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| Solvent Suppression | |
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| Spectral Artifacts Due to Intensity Errors | |
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| Errors from the Digital Fourier Transform | |
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| Effect of Distorted and Missing Points | |
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| Delayed Acquisition | |
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| Phasing of the Spectrum | |
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| Origin of Phase Shifts | |
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| Applying Phase Corrections | |
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| Chemical Shift Referencing | |
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| Exercises | |
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| Solutions | |
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| Quantum Mechanical Description of NMR | |
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| Schrodinger Equation | |
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| Vector Spaces and Properties of Wavefunctions | |
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| Particle in a Box | |
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| Expectation Values | |
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| Dirac Notation | |
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| Wavefunctions in Dirac Notation | |
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| Scalar Product in Dirac Notation | |
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| Operators in Dirac Notation | |
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| Expectation Values in Dirac Notation | |
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| Hermitian Operators | |
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| Determining Eigenvalues | |
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| Additional Properties of Operators | |
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| Commuting Observables | |
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| Time Evolution of Observables | |
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| Trace of an Operator | |
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| Exponential Operator | |
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| Unitary Operators | |
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| Exponential Hermitian Operators | |
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| Hamiltonian and Angular Momentum Operators for a Spin-1/2 Particle | |
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| Rotations | |
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| Rotation Groups | |
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| Rotation Operators | |
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| Rotations of Wave Functions and Operators | |
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| Exercises | |
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| Solutions | |
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| Quantum Mechanical Description of a One Pulse Experiment | |
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| Preparation: Evolution of the System Under B[subscript o] | |
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| Excitation: Effect of Application of B[subscript 1] | |
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| The Resonance Condition | |
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| Detection: Evolution of the System Under B[subscript o] | |
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| The Density Matrix & Product Operators | |
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| Introduction to the Density Matrix | |
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| Calculation of Expectation Values From [rho] | |
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| Density Matrix for a Statistical Mixture | |
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| One-pulse Experiment: Density Matrix Description | |
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| Effect of Pulses on the Density matrix | |
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| Product Operators | |
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| Transformation Properties of Product Operators | |
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| Description of the One-pulse Experiment | |
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| Evaluation of Composite Pulses | |
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| Exercises | |
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| Solutions | |
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| Scalar Coupling | |
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| Introduction to Scalar Coupling | |
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| Basis of Scalar Coupling | |
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| Coupling to Multiple Spins | |
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| Quantum Mechanical Description | |
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| Analysis of an AX System | |
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| Analysis of an AB System | |
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| Decoupling | |
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| Experimental Implementation of Decoupling | |
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| Decoupling Methods | |
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| Performance of Decoupling Schemes | |
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| Exercises | |
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| Solutions | |
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| Coupled Spins: Density Matrix and Product Operator Formalism | |
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| Density Matrix for Two Coupled Spins | |
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| Product Operator Representation of the Density Matrix | |
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| Detectable Elements of [rho] | |
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| Density Matrix Treatment of a One-pulse Experiment | |
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| Manipulation of Two-spin Product Operators | |
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| Transformations of Two-spin Product Operators | |
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| Product Operator Treatment of a One-pulse Experiment | |
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| Two Dimensional Homonuclear J-Correlated Spectroscopy | |
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| Multi-dimensional Experiments | |
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| Elements of Multi-dimensional NMR Experiments | |
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| Generation of Multi-dimensional NMR Spectra | |
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| Homonuclear J-correlated Spectra | |
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| COSY Experiment | |
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| Double Quantum Filtered COSY (DQF-COSY) | |
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| Product Operator Treatment of the DQF-COSY Experiment | |
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| Effect of Passive Coupling on COSY Crosspeaks | |
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| Scalar Correlation by Isotropic Mixing: TOCSY | |
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| Analysis of TOCSY Pulse Sequence | |
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| Isotropic Mixing Schemes | |
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| Time Dependence of Magnetization Transfer by Isotropic Mixing | |
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| Exercises | |
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| Solutions | |
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| Two Dimensional Heteronuclear J-Correlated Spectroscopy | |
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| Introduction | |
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| Two Dimensional Heteronuclear NMR Experiments | |
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| HMQC Experiment | |
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| HSQC Experiment | |
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| Refocused-HSQC Experiment | |
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| Comparison of HMQC, HSQC, and Refocused-HSQC Experiments | |
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| Sensitivity in 2D-Heteronuclear Experiments | |
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| Behavior of XH[subscript 2] Systems in HSQC-type Experiments | |
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| Coherence Editing: Pulsed-Field Gradients and Phase Cycling | |
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| Principals of Coherence Selection | |
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| Spherical Basis Set | |
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| Coherence Changes in NMR Experiments | |
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| Coherence Pathways | |
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| Phase Encoding With Pulsed-Field Gradients | |
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| Gradient Coils | |
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| Effect of Coherence Levels on Gradient Induced Phase Changes | |
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| Coherence Selection by Gradients in Heteronuclear NMR Experiments | |
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| Coherence Selection Using Phase Cycling | |
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| Coherence Changes Induced by RF-Pulses | |
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| Selection of Coherence Pathways | |
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| Phase Cycling in the HMQC Pulse Sequence | |
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| Exercises | |
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| Solutions | |
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| Quadrature Detection in Multi-Dimensional NMR Spectroscopy | |
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| Quadrature Detection Using TPPI | |
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| Hypercomplex Method of Quadrature Detection | |
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| States-TPPI - Removal of Axial Peaks | |
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| Sensitivity Enhancement | |
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| Echo-AntiEcho Quadrature Detection: N-P Selection | |
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| Absorption Mode Lineshapes with N-P Selection | |
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| Resonance Assignments: Homonuclear Methods | |
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| Overview of the Assignment Process | |
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| Homonuclear Methods of Assignment | |
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| [superscript 15]N Separated Homonuclear Techniques | |
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| 2D [superscript 15]N HSQC Experiment | |
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| 3D [superscript 15]N Separated TOCSY Experiment | |
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| The HNHA Experiment - Identifying H[subscript alpha] Protons | |
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| The HNHB Experiment- Identifying H[subscript beta] Protons | |
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| Establishing Spin-system Connectivities with Dipolar Coupling | |
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| Exercises | |
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| Solutions | |
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| Resonance Assignments: Heteronuclear Methods | |
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| Mainchain Assignments | |
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| Strategy | |
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| Methods for Mainchain Assignments | |
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| Description of Triple-resonance Experiments | |
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| HNCO Experiment | |
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| HNCA Experiment | |
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| Selective Excitation and Decoupling of [superscript 13]C | |
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| Selective 90[degree] Pulses | |
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| Selective 180[degree] Pulses | |
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| Selective Decoupling: SEDUCE | |
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| Frequency Shifted Pulses | |
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| Sidechain Assignments | |
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| Triple-resonance Methods for Sidechain Assignments | |
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| The HCCH Experiment | |
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| Exercises | |
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| Solutions | |
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| Practical Aspects of N-Dimensional Data Acquisition and Processing | |
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| Sample Preparation | |
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| NMR Sample Tubes | |
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| Sample Requirements | |
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| Solvent Considerations - Water Suppression | |
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| Amide Exchange Rates | |
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| Solvent Suppression | |
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| Instrument Configuration | |
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| Probe Tuning | |
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| Calibration of Pulses | |
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| Proton Pulses | |
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| Heteronuclear Pulses | |
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| T[subscript 1], T[subscript 2] and Experimental Parameters | |
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| Fundamentals of Nuclear Spin Relaxation | |
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| Effect of Molecular Weight and Magnetic Field Strength on T[subscript 1] and T[subscript 2] | |
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| Effect of Temperature on T[subscript 2] | |
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| Relaxation Interference: TROSY | |
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| Determination of T[subscript 1] and T[subscript 2] | |
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| Acquisition of Multi-Dimensional Spectra | |
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| Setting Polarization Transfer Delays | |
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| Defining the Directly Detected Dimension: t[subscript 3] | |
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| Defining Indirectly Detected Dimensions | |
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| Processing 3-Dimensional Data | |
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| Data Structure | |
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| Defining the Spectral Matrix | |
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| Data Processing | |
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| Processing the Directly Detected Domain | |
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| Variation in Processing | |
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| Useful Manipulations of the Free Induction Decay | |
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| Dipolar Coupling | |
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| Introduction | |
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| Energy of Interaction | |
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| Effect of Isotropic Tumbling on Dipolar Coupling | |
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| Effect of Anisotropic Tumbling | |
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| Measurement of Inter-proton Distances | |
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| NOESY Experiment | |
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| Crosspeak Intensity in the NOESY Experiment | |
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| Effect of Molecular Weight on the Intensity of NOESY Crosspeaks | |
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| Experimental Determination of Inter-proton Distances | |
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| Residual Dipolar Coupling (RDC) | |
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| Generating Partial Alignment of Macromolecules | |
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| Theory of Dipolar Coupling | |
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| Measurement of Residual Dipolar Couplings | |
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| Estimation of the Alignment Tensor | |
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| Protein Structure Determination | |
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| Energy Functions | |
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| Experimental Data | |
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| Covalent and Non-covalent Interactions | |
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| Energy Minimization and Simulated Annealing | |
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| Energy Minimization | |
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| Simulated Annealing | |
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| Generation of Starting Structures | |
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| Random Coordinates | |
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| Distance Geometry | |
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| Refinement | |
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| Illustrative Example of Protein Structure Determination | |
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| Exchange Processes | |
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| Introduction | |
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| Chemical Exchange | |
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| General Theory of Chemical Exchange | |
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| Fast Exchange Limit | |
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| Slow Exchange Limit | |
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| Intermediate Time Scales | |
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| Measurement of Chemical Exchange | |
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| Very Slow Exchange: k[subscript ex] << [Delta nu] | |
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| Slow Exchange: k[subscript ex] < [Delta nu] | |
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| Slow to Intermediate Exchange: k[subscript ex approximate Delta nu] | |
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| Fast Exchange: k[subscript ex] > [Delta nu] | |
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| Measurement of Exchange Using CPMG Methods | |
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| Distinguishing Fast from Slow Exchange | |
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| Effect of Temperature | |
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| Magnetic Field Dependence | |
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| Ligand Binding Kinetics | |
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| Slow Exchange | |
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| Intermediate Exchange | |
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| Fast Exchange | |
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| Exercises | |
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| Solutions | |
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| Nuclear Spin Relaxation and Molecular Dynamics | |
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| Introduction | |
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| Relaxation of Excited States | |
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| Time Dependent Field Fluctuations | |
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| Chemical Shift Anisotropy | |
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| Dipolar Coupling | |
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| Frequency Components from Molecular Rotation | |
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| Spin-lattice (T[subscript 1]) and Spin-spin (T[subscript 2]) Relaxation | |
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| Spin-lattice Relaxation | |
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| Spin-lattice Relaxation of Like Spins | |
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| Spin-lattice Relaxation of Unlike Spins | |
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| Spin-spin Relaxation | |
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| Heteronuclear NOE | |
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| Motion and the Spectral Density Function | |
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| Random Isotropic Motion | |
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| Anisotropic Motion - Non-spherical Protein | |
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| Constrained Internal Motion | |
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| Combining Internal and External Motion | |
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| Effect of Internal Motion on Relaxation | |
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| Anisotropic Rotational Diffusion | |
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| Measurement and Analysis of Relaxation Data | |
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| Pulse Sequences | |
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| Measuring Heteronuclear T[subscript 1] | |
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| Measuring Heteronuclear T[subscript 2] | |
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| Data Analysis and Model Fitting | |
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| Defining Rotational Diffusion | |
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| Determining Internal Rotation | |
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| Systematic Errors in Model Fitting | |
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| Statistical Tests | |
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| X[superscript 2] Test for Goodness-of-fit | |
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| Test for Inclusion of Additional Parameters | |
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| Alternative Methods of Model Selection | |
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| Error Propagation | |
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| Exercises | |
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| Solutions | |
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| Appendices | |
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| Fourier Transforms | |
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| Fourier Series | |
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| Non-periodic Functions - The Fourier Transform | |
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| Complex Variables, Scalars, Vectors, and Tensors | |
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| Complex Numbers | |
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| Representation of Signals with Complex Numbers | |
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| Scalars, Vectors, and Tensors | |
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| Solving Simultaneous Differential Equations: Laplace Transforms | |
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| Laplace Transforms | |
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| Building Blocks of Pulse Sequences | |
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| Product operators | |
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| Common Elements of Pulse Sequences | |
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| References | |
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| Index | |