Two-Dimensional (2D) NMR Methods

Two-Dimensional (2D) NMR Methods
Dedication
Contents
List of Contributors
Preface
1 Basics of Two-dimensional NMR
1.1 Introduction
1.1.1 Time-domain NMR
1.1.2 Hans Primas and the “Correlation Function of the Spectrum”
1.2 Spin Dynamics
1.2.1 Density Operator
1.2.2 Spin Hamiltonian
1.2.3 Liouville Space
1.2.4 Liouvillian
1.2.5 Propagation Superoperator
1.3 One-dimensional Fourier NMR
1.3.1 The One-dimensional NMR Experiment
1.3.2 One-dimensional NMR Spectrum
1.4 Two-dimensional NMR
1.4.1 The Two-dimensional NMR Experiment
1.4.2 Two-dimensional NMR Signal
1.4.3 Two-dimensional NMR Spectrum
1.4.4 Two-dimensional Experiments
1.5 Summary
Acknowledgments
References
2 Data Processing Methods: Fourier and Beyond
2.1 Introduction
2.2 Time-domain NMR Signal
2.3 NMR Spectrum
2.4 The Most Important Features of FT
2.5 Distortion: Phase
2.6 Kramers-Kronig Relations and Hilbert Transform
2.7 Distortion: Truncation
2.8 Distortion: Noise and Multiple Scans
2.9 Distortion: Sampling and DFT
2.10 Quadrature Detection
2.11 Processing: Weighting
2.12 Processing: Zero Filling
2.13 Fourier Transform in Multiple Dimensions
2.14 Quadrature Detection in Multiple Dimensions
2.15 Projection Theorem
2.16 ND Sampling Aspects and Sparse Sampling
2.17 Reconstructing Sparsely Sampled Data Sets
2.18 Deconvolution
References
3 Product Operator Formalism
3.1 Introduction
3.2 Product Operators and Time Evolution
3.2.1 Advantages of Product Operators
3.3 Time Evolution of the Product Operators
3.3.1 Effect of Pulses
3.3.2 Effect of Evolution Under the Hamiltonian
3.4 Applications
3.4.1 Spin-echo Experiments
3.4.2 Multiple-quantum Coherence
3.4.3 Composite Pulses
3.5 Two-dimensional Experiments
3.5.1 Two-dimensional J-Resolved
3.5.2 COSY
3.5.3 Two-dimensional NOE
3.5.4 Double-quantum Filtered COSY
3.5.5 Two-dimensional Double-quantum Spectroscopy
3.5.6 Relayed-COSY
3.5.7 TOCSY or Homonuclear Hartmann-Hahn Transfer
3.5.8 INEPT and HSQC
3.5.9 HMQC and HMBC
References
4 Relaxation in NMR Spectroscopy
4.1 Introduction
4.2 Theory
4.2.1 Bloch Equations
4.2.2 Transition-rate Theory
4.2.3 Semi-classical Relaxation Theory
4.2.4 Quantum-mechanical Relaxation Theory – Lindblad Formulation
4.3 Relaxation in Spin-1/2 Systems: Dipolar and CSA Relaxation
4.3.1 Longitudinal Relaxation in a Two-spin System
4.3.2 Transverse Relaxation in a Two-spin System
4.3.3 Double-quantum Relaxation
4.3.4 Relaxation in Larger Spin Systems
4.4 Other Relaxation Mechanisms
4.4.1 Quadrupolar Relaxation
4.4.2 Scalar Relaxation
4.5 Concluding Remarks
References
5 Coherence Transfer Pathways
5.1 Coherence Transfer Pathways: What and Why?
5.2 Principles of Coherence Selection
5.2.1 Precession of a coherence about the z-component of a magnetic field
5.2.2 Effect of changing the phase of a radiofrequency pulse that converts one coherence order term into another
5.3 Coherence Transfer Pathway Selection by Phase Cycling
5.3.1 CYCLOPS
5.3.2 EXORCYCLE
5.4 Cogwheel Phase Cycling
5.5 Coherence Transfer Pathway Selection by Pulsed-field Gradients
5.6 Comparison Between Phase Cycling and Pulsed-field Gradients
5.7 CTP Selection in Heteronuclear Spin Systems
5.8 Additional Approaches to Coherence Selection
References
6 Nuclear Overhauser Effect Spectroscopy
6.1 Introduction
6.2 Nuclear Overhauser Effect
6.2.1 Qualitative Picture
6.2.2 NOE: Quantitative Picture
6.2.3 NOE and Distance Dependence: Many-spin System
6.2.4 NOE Comparison and Distance Elucidation
6.2.5 Indirect NOE Effects
6.3 Measurement of NOE
6.4 Heteronuclear NOE
6.5 NOE Kinetics
6.5.1 Initial-Rate Approximation
6.6 Nuclear Overhauser Effect Spectroscopy, NOESY
6.6.1 NOESY Pulse Scheme
6.6.2 NOESY Theory
6.7 Rotating-frame NOE, ROE
6.8 Relative Signs of Cross Peaks
6.9 Generalised Solomon’s Equation
6.10 NOESY and ROESY: Practical Considerations and Experimental Spectra
6.11 Conclusions
Acknowledgments
References
7 DOSY Methods for Studying Non-equilibrium Molecular and Ionic Systems
7.1 Introduction
7.2 Spatial Spin “Encoding” Using Magnetic Field Gradient
7.3 Formation of NMR Signal and Spin Echo in the Presence of Field Gradient
7.4 NMR of Liquids in An Electric Field: Electrophoretic NMR
7.4.1 Measurement of Drift Velocities
7.4.2 Technical Development
7.4.3 Application Areas: From Dilute to Concentrated Electrolytes
7.4.4 Methods of Transformation and Processing: MOSY
7.4.5 Is eNMR a non-equilibrium experiment or a steady-state experiment?
7.5 Ultrafast Diffusion Measurements
7.6 Ultrafast Diffusion Exchange Spectroscopy
References
8 Multiple Acquisition Strategies
8.1 Introduction
8.2 Types of Multiple Acquisition Experiments
8.3 Utilization of Forgotten Spin Operators
8.4 Application of Multiple Acquisition Techniques
8.4.1 Solution NMR Spectroscopy
8.4.2 Solid-State NMR Spectroscopy
8.5 Modularity of Multiple Detection Schemes and Other Novel Approaches
8.6 Future of Multiple Acquisition Detection
Acknowledgments
References
9 Anisotropic One-dimensional/Two-dimensional NMR in Molecular Analysis
9.1 Introduction
9.2 Advantages of Oriented Solvents
9.2.1 Description of Orientational Order Parameters
9.2.2 The GDO Concept
9.3 Description of Useful Anisotropic NMR Parameters
9.3.1 Residual Dipolar Coupling (RDC)
9.3.2 Residual Chemical-shift Anisotropy (RCSA)
9.3.3 Residual Quadrupolar Coupling (RQC)
9.3.4 Spectral Consequences of Enantiodiscrimination
9.4 Adapted 2D NMR Tools
9.4.1 Spin-1/2 Based 2D Experiments
9.4.2 Spin-1 Based 2D Experiments
9.5 Examples of Polymeric Liquid Crystals
9.5.1 Polypeptide or Polyacetylene-based Systems
9.5.2 Compressed and Stretched Gels
9.5.3 Polynucleotide-based Chiral Oriented Media
9.5.4 Some Practical Aspects of Polymer-based LLCs Preparation
9.6 Contribution to the Analysis of Chiral and Prochiral Molecules
9.6.1 Analysis and Enantiopurity Determination of Chiral Mixtures
9.6.2 Discrimination of Enantiotopic Elements in Prochiral Structures
9.6.3 Dynamic Analysis by 2H NMR
9.7 Structural Value of Anisotropic NMR Parameters
9.7.1 From the Molecular Constitution to Configuration of Complex Molecules
9.7.2 Contribution of Spin-1/2 NMR
9.7.3 Configuration Determination Using Spin-1 NMR Analysis
9.7.4 Determining the Absolute Configuration of Monostereogenic Chiral Molecules
9.8 Conformational Analysis in Oriented Solvents
9.9 Anisotropic 2H 2D NMR Applied to Molecular Isotope Analysis
9.9.1 The Natural (2H/1H) Isotope Fractionation: Principle
9.9.2 Case of Prochiral Molecules: The Fatty Acid Family
9.9.3 New Tools for Fighting Against Counterfeiting
9.10 Anisotropic NMR in Molecular Analysis: What You Should Keep in Mind
References
10 Ultrafast 2D methods
10.1 Introduction
10.2 UF 2D NMR Principles: Entangling the Space and the Time
10.2.1 Spatial Encoding
10.2.2 Reading Out the Spatially Encoded Signal
10.2.3 ProcessingWorkflow in UF Experiments
10.3 Specific Features of UF 2D NMR
10.3.1 Line-shape of the Signal
10.3.2 Resolution and Spectral Width
10.3.3 Sensitivity Considerations
10.4 Advanced UF Methods
10.4.1 Improving the Sensitivity
10.4.2 Improving Spectral Width and Resolution
10.5 UF 2D NMR: A Versatile Approach
10.5.1 Accelerating 2D NMR Spectroscopy Experiments
10.5.2 Accelerating Dynamic Experiments (UF pseudo-2D)
10.6 Overview of UF 2D NMR Applications
10.6.1 Reaction Monitoring
10.6.2 Single-scan 2D Experiments on Hyperpolarized Substrates
10.6.3 Quantitative UF 2D NMR
10.6.4 UF 2D NMR in Oriented Media
10.6.5 UF 2D NMR in Spatial Inhomogeneous Fields
10.7 Conclusion
References
11 Multi-dimensional Methods in Biological NMR
11.1 Introduction
11.2 Experimental Approaches
11.2.1 NMR Spectroscopic Information on Structural Features
11.2.2 Spectroscopic Information on Dynamical Features
11.2.3 NMR Spectroscopic Information Obtained from Interaction Studies
11.2.4 Quench Flow Methodology in Combination with NMR – Hydrogen-to-deuterium Exchange
11.2.5 Expanding Multi-dimensional NMR Spectroscopy from in vitro to in vivo Applications
11.2.6 Multi-Dimensional NMR Spectroscopy as an Integrated Approach in Structural Biology
11.3 Case Studies
11.3.1 Determining Thermodynamic Stability of Biomolecules at Atomic Resolution
11.3.2 Exotic Heteronuclear NMR Spectroscopy Correlating 31P with 13C
11.3.3 Following Biomolecular Dynamics by Homonuclear and Heteronuclear ZZ Exchange
11.3.4 Probing Structural Features by Solvent PREs
11.3.5 Discerning Protein Dynamics by Probing Fast Amide Proton Exchange
11.3.6 Integrated Approaches Utilizing Structural Information from NMR Spectroscopy
11.3.7 Multi-dimensional NMR Spectroscopy on ex vivo Samples
References
12 TROSY: Principles and Applications
12.1 Introduction
12.2 The Principles of TROSY
12.2.1 The Physical Picture of TROSY
12.2.2 Theory of TROSY
12.3 Practical Aspects of TROSY
12.3.1 Field Strength Dependence of TROSY for 1H–15N Groups
12.3.2 Peak Pattern of 1H-15N TROSY Spectrum
12.4 Applications of TROSY
12.4.1 Two-Dimensional [1H,15N]-TROSY
12.4.2 [1H,15N]-TROSY for Backbone Resonance Assignments in Large Proteins
12.4.3 [1H,15N]-TROSY for Assignment of Protein Side-chain Resonances
12.4.4 Application of [1H,15N]-TROSY for RDC Measurements
12.4.5 [1H,15N]-TROSY-based NOESY Experiments
12.4.6 Studies of Dynamic Processes Using the [1H,15N]-TROSY Concept
12.5 Transverse Relaxation-optimization in the Polarization Transfers
12.6 15N Direct Detected TROSY
12.7 [1H,13C]-TROSY Correlation Experiments
12.7.1 Methyl-TROSY NMR
12.8 Applications to Nucleic Acids
12.9 Intermolecular Interactions and Drug Design
12.10 Conclusion
12.A Appendix
Acknowledgments
References
13 Two-Dimensional Methods and Zero- to Ultralow-Field (ZULF) NMR
13.1 Introduction and Motivation
13.2 Early Work
13.3 Two-dimensional NMR Measured at Zero Magnetic Field
13.4 Nuclear Magnetic Resonance at Millitesla Fields Using a Zero-Field Spectrometer
13.5 Field Cycling NMR and Correlation Spectroscopy
13.6 ZERO-Field - High-Field Comparison
13.7 Conclusion and Outlook
Acknowledgments
References
14 Multidimensional Methods and Paramagnetic NMR
14.1 Introduction
14.2 NMR Methods for Paramagnetic Systems in Solution
14.2.1 Homonuclear Correlations
14.2.2 Heteronuclear Correlations
14.2.3 Long-Range Paramagnetic Effects
14.2.4 Heteronuclear Detection Strategies
14.3 NMR Methods for Paramagnetic Systems in Solids
14.3.1 Adiabatic Pulses
14.3.2 Homonuclear Correlations
14.3.3 Heteronuclear Correlations
14.3.4 Long-Range Paramagnetic Effects
14.3.5 Separation of Shift and Shift-anisotropy Interactions
14.3.6 Separation of Shift-anisotropy and Quadrupolar Interactions
Acknowledgments
References
15 Chemical Exchange
15.1 Introduction
15.2 Bloch-McConnell Equations
15.2.1 Slow Exchange
15.2.2 Fast Exchange
15.2.3 Dependence of the Linewidth On Magnetic Field Strength
15.2.4 Exchange in the Absence of Chemical-Shift Differences
15.2.5 Multi-State Exchange
15.3 Studying Exchange Between Visible States
15.3.1 Lineshape Analysis
15.3.2 ZZ-Exchange Experiment
15.4 Studying Exchange Between a Visible State and Invisible State(s)
15.4.1 CPMG Experiments
15.4.2 CEST and DEST Experiments
15.4.3 R1ρ Relaxation Dispersion Experiment
15.5 Summary
Acknowledgments
References
Appendix A Proton-Detected Heteronuclear and Multidimensional NMR
Index
EULA