Two-Dimensional (2D) NMR Methods

TWO-DIMENSIONAL (2D) NMR METHODS Practical guide explaining the fundamentals of 2D-NMR for experienced scientists as well as relevant for advanced students Two-Dimensional (2D) NMR Methods is a focused work presenting an overview of 2D-NMR concepts and techniques, including basic principles, practical applications, and how NMR pulse sequences work. Contributed to by global experts with extensive experience in the field, Two-Dimensional (2D) NMR Methods provides in-depth coverage of sample topics such as: Basics of 2D-NMR, data processing methods (Fourier and beyond), product operator formalism, basics of spin relaxation, and coherence transfer pathways Multidimensional methods (single- and multiple-quantum spectroscopy), NOESY (principles and applications), and DOSY methods Multiple acquisition strategies, anisotropic NMR in molecular analysis, ultrafast 2D methods, and multidimensional methods in bio-NMR TROSY (principles and applications), field-cycling and 2D NMR, multidimensional methods and paramagnetic NMR, and relaxation dispersion experiments This text is a highly useful resource for NMR specialists and advanced students studying NMR, along with users in research, academic and commercial laboratories that study or conduct experiments in NMR. 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