NMR for Physical and Biological Scientists Thomas C. Pochapsky and Susan Sondej Pochapsky Table of Contents


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1 Preface Symbols and fundamental constants 1. What is spectroscopy? A semiclassical description of spectroscopy Damped harmonics Quantum oscillators The spectroscopic experiment Ensembles and coherence Types of spectroscopy Practical considerations in spectroscopy Acquiring a spectrum Resolution: the problem of line width Line shape 2. Elementary aspects of nuclear magnetic resonance (NMR) Nuclear and electronic spin A quantum picture of nuclear spin The spinning top model of nuclear spin Spin state populations in ensembles Information available from NMR: 1) Nuclear shielding and chemical shift Information available from NMR: 2) Scalar coupling Information available from NMR: 3) Dipolar coupling Information available from NMR: 4) Dynamics Jcoupling time scale, decoupling experiments and exchange decoupling Interaction between nuclear spins and radiofrequency EMR: 1) RF decoupling
2 3. Elementary aspects of NMR II. Fourier Transform NMR Interaction between nuclear spins and RF: 2) a single spin in the rotating frame of reference Interaction between nuclear spins and RF: 3) An ensemble of spins in the rotating frame of reference Detection of an NMR signal Timedomain detection in the NMR experiment: the free induction decay and quadrature detection Digitization of the free induction decay Fourier transformation: timedomain FID to frequencydomain spectrum Discrete Fourier transformation Spectral phasing RF pulses and pulse phase Pulse power and offresonance effects from RF pulses Phase cycling: 1) Improved quadrature detection using CYCLOPS Factors affecting spectral quality and appearance: shimming, window functions and apodization After the fact: window functions and zero filling Linear prediction 4. Nuclear Spin Relaxation and the Nuclear Overhauser Effect Longitudinal (T1) relaxation and the sensitivity of the NMR experiment Transverse (T2) relaxation and the spinecho experiment Chemical shift and Jcoupling evolution during the spin echo Mechanisms of nuclear spin relaxation in liquids and the spectral density function Dipolar relaxation and the nuclear Overhauser effect NOE measurements, indirect NOEs and saturation transfer Heteronuclear NOE and the Solomon equation
3 Other contributions to T1 relaxation: chemical shift anisotropy, spinrotation, paramagnetic effects Quadrupolar relaxation Selective and nonselective T 1 measurement and multiexponential decay of coherence 5. Classical and Quantum Descriptions of NMR Experiments in Liquids The classical approach: the Bloch equations of motion for macroscopic magnetization Classical description of a pulsed NMR experiment A quantum mechanical description of NMR of a single spin in an isotropic liquid A quantum mechanical description of NMR of coupled spins in an isotropic liquid The timedependent nuclear spin Hamiltonian operator and solutions to the timedependent Schrödinger equation 6. Density Operator and Product Operator Descriptions of NMR Experiments in Liquids An ensemble of identical spins at equilibrium: an introduction to the density matrix formalism Expansion of the density matrix for an uncoupled spin in terms of Cartesian angular momentum operators Weakly coupled ensembles and the weak coupling approximation Singleelement operators for a two spin system Interconversion between the singleelement and Cartesian operator bases Evolution of Cartesian operators under the influence of pulses, chemical shift and Jcoupling Evolution of operators with weak Jcoupling Analysis of a simple NMR spectrum using product operators
4 7. Homonuclear Twodimensional NMR Experiments and Coherence Selection A simple twodimensional NMR experiment Coherence transfer in multidimensional NMR The COSY experiment Quadrature detection in multidimensional NMR Axial peaks Phase cycling and coherence order selection: the DQFCOSY experiment Other multiple quantum filters in COSY Multiplequantum spectroscopy Effect of π pulses on coherence Pulsed field gradients for coherence selection The gradient COSY experiment "Zeroquantum filtered COSY": NOESY and incoherent transfer Rotating frame NOEs: CAMELSPIN and ROESY Spinlocking experiments for coherence transfer: TOCSY and compositepulse decoupling 8. Heteronuclear Correlations in NMR Heteronuclear polarization transfer and the INEPT experiment Refocused INEPT Twodimensional polarization transfer: HETCOR Sensitive nucleus (inverse) detection of an insensitive nucleus: the double INEPT or HSQC experiment Multiple quantum approaches to heteronuclear correlation: DEPT and HMQC Gradient coherence selection in heteronuclear correlation NMR Phase sensitive gradient coherence selection experiments for heteronuclear correlations
5 Sensitivity enhancement in gradient coherence selection experiments 9. Building blocks for multidimensional NMR and special considerations for biological applications of NMR Polarization transfer Solvent suppression Frequency labeling periods and constant time NMR experiments Shaped and selective pulses Composite pulse decoupling and spinlocking Dealing with very large biomolecules in solution: deuteration and direct 13 C detection Interference patterns in heteronuclear relaxation: TROSY 10. NMR under anisotropic conditions: NMR in the solid state and ordered fluids Anisotropy in NMR: the chemical shift and dipolar coupling Resolving the solid state NMR spectrum: magic angle spinning (MAS) and highpower 1 H decoupling Crosspolarization for signal enhancement of dilute spins and spinspin correlations Selective reintroduction of dipolar couplings between dilute spins: rotational resonance, RFDR and REDOR Heteronuclear twodimensional techniques in solid state NMR Solid state NMR using oriented samples: PISEMA Bringing a little order to solution NMR: residual dipolar couplings and chemical shift anisotropy in ordered fluids Analysis of residual dipolar couplings
6 11. Relaxation revisited: dynamic processes and paramagnetism Time scales of molecular motion, dynamic processes and relaxation The spectral density revisited Experimental measurement of heteronuclear relaxation parameters in proteins Modelfree analysis of spin relaxation Chemical exchange and motion on slow and intermediate time scales (106 s to 101 s) Measurement of R ex Quadrupolar relaxation Hyperfine interactions and paramagnetic shifts of nuclear spins Paramagnetic relaxation of nuclear spins Relaxation and the density matrix 12. Diffusion, imaging and flow Magnetic field inhomogeneity, T 2(macro) and diffusion measurement by NMR Basic imaging concepts: Phase and frequency encoding of position in a macroscopic sample Spatially selective pulses Spatial equivalents of NMR parameters Basic 2D imaging sequences kspace Contrast and contrast agents, relaxation and flow Rapidscan MRI: echoplanar imaging and oneshot methods
7 Appendix A. Timedependent perturbations The timedependent Schrödinger equation and superposition states Hilbert space, eigenvectors and superposition of states Perturbation theory; timedependent perturbations of the Hamiltonian Semiclassical interactions between EMR and quantum oscillators using perturbation theory Appendix B. Density matrix formalism and the relaxation supermatrix A density matrix description of the 1 H, 15 N HMQC experiment RF Pulses Time evolution of the density matrix with chemical shift and coupling Semiclassical relaxation theory and the Redfield relaxation matrix
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