PROTEIN NMR SPECTROSCOPY

Transcription

1 List of Figures List of Tables xvii xxvi 1. NMR SPECTROSCOPY Introduction to NMR Spectroscopy One Dimensional NMR Spectroscopy Classical Description of NMR Spectroscopy Nuclear Spin Transitions Detection of Nuclear Spin Transitions Continuous Wave NMR Pulsed NMR Summary of the Process of Acquiring a One Dimensional Spectrum Phenomenological Description of Relaxation Relaxation and the Evolution of Magnetization Chemical Shielding Characteristic 1 H, 13 C and 15 N Chemical Shifts Effect of Electronic Structure on Chemical Shifts Ring Current Effects Effects of Local Environment on Chemical Shifts Use of Chemical Shifts in Resonance Assignments Chemical Shift Dispersion & Multi-dimensional NMR Exercises Solutions PRACTICAL ASPECTS OF ACQUIRING NMR SPECTRA Components of an NMR Spectrometer Magnet 29

2 vi PROTEIN NMR SPECTROSCOPY Computer Probe Pre-amplifier Module The Field-frequency Lock Shim System Transmitter & Pulse Generation Receiver Acquiring a Spectrum Sample Preparation Beginning the Experiment Temperature Measurement Shimming Tuning and Matching the Probe Adjusting the Transmitter Calibration of the 90 Pulse Length Setting the Sweepwidth: Dwell Times and Filters Setting the Receiver Gain Spectral Resolution and Acquisition Time of the FID Experimental 1D-pulse Sequence: Pulse and Receiver Phase Phase Cycle Phase Cycle and Artifact Suppression Exercises Solutions INTRODUCTION TO SIGNAL PROCESSING Removal of DC Offset Increasing Resolution by Extending the FID Increasing Resolution by Zero-filling Increasing Resolution by Linear Prediction (LP) Removal of Truncation Artifacts: Apodization Effect of Apodization on Resolution and Noise Using LP & Apodization to Increase Resolution Solvent Suppression Spectral Artifacts Due to Intensity Errors Errors from the Digital Fourier Transform Effect of Distorted and Missing Points Delayed Acquisition Phasing of the Spectrum 82

3 vii Origin of Phase Shifts Applying Phase Corrections Chemical Shift Referencing Exercises Solutions QUANTUM MECHANICAL DESCRIPTION OF NMR Schrödinger Equation Vector Spaces and Properties of Wavefunctions Particle in a Box Expectation Values Dirac Notation Wavefunctions in Dirac Notation Scalar Product in Dirac Notation Operators in Dirac Notation Expectation Values in Dirac Notation Hermitian Operators Determining Eigenvalues Additional Properties of Operators Commuting Observables Time Evolution of Observables Trace of an Operator Exponential Operator Unitary Operators Exponential Hermitian Operators Hamiltonian and Angular Momentum Operators for a Spin-1/2 Particle Rotations Rotation Groups Rotation Operators Rotations of Wave Functions and Operators Exercises Solutions QUANTUM MECHANICAL DESCRIPTION OF A ONE PULSE EXPERIMENT Preparation: Evolution of the System Under B o Excitation: Effect of Application of B The Resonance Condition 118

4 viii PROTEIN NMR SPECTROSCOPY 5.3 Detection: Evolution of the System Under B o THE DENSITY MATRIX & PRODUCT OPERATORS Introduction to the Density Matrix Calculation of Expectation Values From ρ Density Matrix for a Statistical Mixture One-pulse Experiment: Density Matrix Description Effect of Pulses on the Density matrix Product Operators Transformation Properties of Product Operators Description of the One-pulse Experiment Evaluation of Composite Pulses Exercises Solutions SCALAR COUPLING Introduction to Scalar Coupling Basis of Scalar Coupling Coupling to Multiple Spins Quantum Mechanical Description Analysis of an AX System Analysis of an AB System Decoupling Experimental Implementation of Decoupling Decoupling Methods Performance of Decoupling Schemes Exercises Solutions COUPLED SPINS: DENSITY MATRIX AND PRODUCT OPERATOR FORMALISM Density Matrix for Two Coupled Spins Product Operator Representation of the Density Matrix Detectable Elements of ρ Density Matrix Treatment of a One-pulse Experiment Manipulation of Two-spin Product Operators Transformations of Two-spin Product Operators Product Operator Treatment of a One-pulse Experiment 165

5 ix 9. TWO DIMENSIONAL HOMONUCLEAR J-CORRELATED SPECTROSCOPY Multi-dimensional Experiments Elements of Multi-dimensional NMR Experiments Generation of Multi-dimensional NMR Spectra Homonuclear J-correlated Spectra COSY Experiment Double Quantum Filtered COSY (DQF-COSY) Product Operator Treatment of the DQF-COSY Experiment Effect of Passive Coupling on COSY Crosspeaks Scalar Correlation by Isotropic Mixing: TOCSY Analysis of TOCSY Pulse Sequence Isotropic Mixing Schemes Time Dependence of Magnetization Transfer by Isotropic Mixing Exercises Solutions TWO DIMENSIONAL HETERONUCLEAR J-CORRELATED SPECTROSCOPY Introduction Two Dimensional Heteronuclear NMR Experiments HMQC Experiment HSQC Experiment Refocused-HSQC Experiment Comparison of HMQC, HSQC, and Refocused-HSQC Experiments Sensitivity in 2D-Heteronuclear Experiments Behavior of XH 2 Systems in HSQC-type Experiments COHERENCE EDITING: PULSED-FIELD GRADIENTS AND PHASE CYCLING Principals of Coherence Selection Spherical Basis Set Coherence Changes in NMR Experiments Coherence Pathways Phase Encoding With Pulsed-Field Gradients Gradient Coils 218

6 x PROTEIN NMR SPECTROSCOPY Effect of Coherence Levels on Gradient Induced Phase Changes Coherence Selection by Gradients in Heteronuclear NMR Experiments Coherence Selection Using Phase Cycling Coherence Changes Induced by RF-Pulses Selection of Coherence Pathways Phase Cycling in the HMQC Pulse Sequence Exercises Solutions QUADRATURE DETECTION IN MULTI-DIMENSIONAL NMR SPECTROSCOPY Quadrature Detection Using TPPI Hypercomplex Method of Quadrature Detection States-TPPI - Removal of Axial Peaks Sensitivity Enhancement Echo-AntiEcho Quadrature Detection: N-P Selection Absorption Mode Lineshapes with N-P Selection RESONANCE ASSIGNMENTS: HOMONUCLEAR METHODS Overview of the Assignment Process Homonuclear Methods of Assignment N Separated Homonuclear Techniques D 15 N HSQC Experiment D 15 N Separated TOCSY Experiment The HNHA Experiment - Identifying H α Protons The HNHB Experiment- Identifying H β Protons Establishing Spin-system Connectivities with Dipolar Coupling Exercises Solutions RESONANCE ASSIGNMENTS: HETERONUCLEAR METHODS Mainchain Assignments Strategy Methods for Mainchain Assignments Description of Triple-resonance Experiments HNCO Experiment HNCA Experiment Selective Excitation and Decoupling of 13 C 294

7 xi Selective 90 Pulses Selective 180 Pulses Selective Decoupling: SEDUCE Frequency Shifted Pulses Sidechain Assignments Triple-resonance Methods for Sidechain Assignments The HCCH Experiment Exercises Solutions PRACTICAL ASPECTS OF N-DIMENSIONAL DATA ACQUISITION AND PROCESSING Sample Preparation NMR Sample Tubes Sample Requirements Solvent Considerations - Water Suppression Amide Exchange Rates Solvent Suppression Instrument Configuration Probe Tuning Calibration of Pulses Proton Pulses Heteronuclear Pulses T 1,T 2 and Experimental Parameters Fundamentals of Nuclear Spin Relaxation Effect of Molecular Weight and Magnetic Field Strength on T 1 and T Effect of Temperature on T Relaxation Interference: TROSY Determination of T 1 and T Acquisition of Multi-Dimensional Spectra Setting Polarization Transfer Delays Defining the Directly Detected Dimension: t Defining Indirectly Detected Dimensions Processing 3-Dimensional Data Data Structure Defining the Spectral Matrix Data Processing Processing the Directly Detected Domain 348

8 xii PROTEIN NMR SPECTROSCOPY Variation in Processing Useful Manipulations of the Free Induction Decay DIPOLAR COUPLING Introduction Energy of Interaction Effect of Isotropic Tumbling on Dipolar Coupling Effect of Anisotropic Tumbling Measurement of Inter-proton Distances NOESY Experiment Crosspeak Intensity in the NOESY Experiment Effect of Molecular Weight on the Intensity of NOESY Crosspeaks Experimental Determination of Inter-proton Distances Residual Dipolar Coupling (RDC) Generating Partial Alignment of Macromolecules Theory of Dipolar Coupling Measurement of Residual Dipolar Couplings Estimation of the Alignment Tensor PROTEIN STRUCTURE DETERMINATION Energy Functions Experimental Data Covalent and Non-covalent Interactions Energy Minimization and Simulated Annealing Energy Minimization Simulated Annealing Generation of Starting Structures Random Coordinates Distance Geometry Refinement Illustrative Example of Protein Structure Determination EXCHANGE PROCESSES Introduction Chemical Exchange General Theory of Chemical Exchange Fast Exchange Limit Slow Exchange Limit Intermediate Time Scales Measurement of Chemical Exchange 411

9 xiii Very Slow Exchange:k ex << ν Slow Exchange: k ex < ν Slow to Intermediate Exchange: k ex ν Fast Exchange: k ex > ν Measurement of Exchange Using CPMG Methods Distinguishing Fast from Slow Exchange Effect of Temperature Magnetic Field Dependence Ligand Binding Kinetics Slow Exchange Intermediate Exchange Fast Exchange Exercises Solutions NUCLEAR SPIN RELAXATION AND MOLECULAR DYNAMICS Introduction Relaxation of Excited States Time Dependent Field Fluctuations Chemical Shift Anisotropy Dipolar Coupling Frequency Components from Molecular Rotation Spin-lattice (T 1 ) and Spin-spin (T 2 ) Relaxation Spin-lattice Relaxation Spin-lattice Relaxation of Like Spins Spin-lattice Relaxation of Unlike Spins Spin-spin Relaxation Heteronuclear NOE Motion and the Spectral Density Function Random Isotropic Motion Anisotropic Motion - Non-spherical Protein Constrained Internal Motion Combining Internal and External Motion Effect of Internal Motion on Relaxation Anisotropic Rotational Diffusion Measurement and Analysis of Relaxation Data Pulse Sequences Measuring Heteronuclear T 1 457

10 xiv PROTEIN NMR SPECTROSCOPY Measuring Heteronuclear T Data Analysis and Model Fitting Defining Rotational Diffusion Determining Internal Rotation Systematic Errors in Model Fitting Statistical Tests χ 2 Test for Goodness-of-fit Test for Inclusion of Additional Parameters Alternative Methods of Model Selection Error Propagation Exercises Solutions 474 Appendices 475 A Fourier Transforms 475 A.1 Fourier Series 475 A.2 Non-periodic Functions - The Fourier Transform 476 A.2.1 Examples of Fourier Transforms 477 A.2.2 Linearity 481 A.2.3 Convolutions: Fourier Transform of Products of Two Functions 481 B Complex Variables, Scalars, Vectors, and Tensors 485 B.1 Complex Numbers 485 B.2 Representation of Signals with Complex Numbers 486 B.3 Scalars, Vectors, and Tensors 487 B.3.1 Scalars 487 B.3.2 Vectors 487 B.3.3 Tensors 488 C Solving Simultaneous Differential Equations: Laplace Transforms 491 C.1 Laplace Transforms 491 C.1.1 Example Calculation 492 C.1.2 Application to Chemical Exchange 493 C.1.3 Application to Spin-lattice Relaxation 494 C.1.4 Spin-lattice Relaxation of Two Different Spins 495 D Building Blocks of Pulse Sequences 497 D.1 Product operators 497 D.1.1 Pulses 497 D.1.2 Evolution by J-coupling 497 D.1.3 Evolution by Chemical Shift 498

11 xv D.2 Common Elements of Pulse Sequences 498 D.2.1 INEPT Polarization Transfer 498 D.2.2 HMQC Polarization Transfer 499 D.2.3 Constant Time Evolution 499 D.2.4 Constant Time Evolution with J-coupling 500 D.2.5 Sequential Chemical Shift & J-coupling Evolution 501 D.2.6 Semi-constant Time Evolution of Chemical Shift & J-Coupling 501 References 505 Index 519