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NMR Spectroscopy

NMR Spectroscopy. Relaxation Time Phenomenon & Application. Relaxation- Return to Equilibrium. t. t. x,y plane. z axis. Longitudinal. Transverse. 0. 0. 1. 1. t. t. 2. 2. E -t/ T 2. 1- e -t/ T 1. 8. 8. Transverse always faster!. Relaxation.

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NMR Spectroscopy

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  1. NMR Spectroscopy Relaxation Time Phenomenon & Application

  2. Relaxation- Return to Equilibrium t t x,y plane z axis Longitudinal Transverse 0 0 1 1 t t 2 2 E-t/T2 1-e-t/T1 8 8 Transverse always faster!

  3. Relaxation magnetization vector's trajectory The initial vector, Mo, evolves under the effects of T1 & T2 relaxation and from the influence of an applied rf-field. Here, the magnetization vector M(t) precesses about an effective field axis at a frequency determined by its offset. It's ends up at a "steady state" position as depicted in the lower plot of x- and y- magnetizations. http://gamma.magnet.fsu.edu/info/tour/bloch/index.html

  4. Relaxation The T2 relaxation causes the horizontal (xy) magnetisation to decay. T1 relaxation re-establishes the z-magnetisation. Note that T1 relaxation is often slower than T2 relaxation.

  5. Relaxation time – Bloch Equation • Bloch Equation

  6. Relaxation time – Bloch equation

  7. Spin-lattice Relaxation time (Longitudinal) T1 Relaxation mechanisms: 1. Dipole-Dipole interaction "through space" 2. Electric Quadrupolar Relaxation 3. Paramagnetic Relaxation 4. Scalar Relaxation 5. Chemical Shift Anisotropy Relaxation 6. Spin Rotation

  8. Relaxation • Spin-lattice relaxation converts the excess energy into translational, rotational, and vibrational energy of the surrounding atoms and molecules (the lattice). • Spin-spin relaxation transfers the excess energy to other magnetic nuclei in the sample.

  9. Longitudinal Relaxation time T1 Inversion-Recovery Experiment 180y (or x) 90y tD

  10. T1 relaxation

  11. Interaction Range of interaction (Hz) relevant parameters Dipolar coupling 104 - 105 - abundance of magnetically active nuclei- size of the magnetogyric ratio Quadrupolar coupling 106 - 109 - size of quadrupolar coupling constant- electric field gradient at the nucleus Paramagnetic 107 -108 concentration of paramagnetic impurities Scalar coupling 10 - 103 size of the scalar coupling constants Chemical Shift Anisotropy (CSA) 10 - 104 - size of the chemical shift anisotropy- symmetry at the nuclear site 6- Spin rotation

  12. Spin-spin relaxation (Transverse) T2 • T2represents the lifetime of the signal in the transverse plane (XY plane) • T2 is the relaxation time that is responsible for the line width. line width at half-height=1/T2

  13. Spin-spin relaxation (Transverse) T2 Two factors contribute to the decay of transverse magnetization. • molecular interactions ( lead to a pure pure T2 molecular effect) • variations in Bo ( lead to an inhomogeneous T2 effect)

  14. Spin-spin relaxation (Transverse) T2 • signal width at half-height (line-width )= (pi * T2)-1 90y 180y (or x) tD tD

  15. Spin-spin relaxation (Transverse) T2

  16. Spin-Echo Experiment

  17. Spin-Echo experiment

  18. MXY =MXYo e-t/T2

  19. Carr-Purcell-Meiboom-Gill sequence

  20. T1 and T2 • In non-viscous liquids, usually T2= T1. • But some process like scalar coupling with quadrupolar nuclei, chemical exchange, interaction with a paramagnetic center, can accelerate the T2relaxation such that T2becomes shorter than T1.

  21. Relaxation and correlation time For peptides in aqueous solutions the dipole-dipole spin-lattice and spin-spin relaxation process are mainly mediated by other nearby protons

  22. Why The Interest In Dynamics? • Function requires motion/kinetic energy • Entropic contributions to binding events • Protein Folding/Unfolding • Uncertainty in NMR and crystal structures • Effect on NMR experiments-spin relaxation is dependent on rate of motions  know dynamics to predict outcomes and design new experiments • Quantum mechanics/prediction (masochism)

  23. Application

  24. Characterizing Protein Dynamics: Parameters/Timescales Relaxation

  25. NMR Parameters That Report On Dynamics of Molecules • Number of signals per atom: multiple signals for slow exchange between conformational states • Linewidths: narrow = faster motion, wide = slower; dependent on MW and conformational states • Exchange of NH with solvent:requires local and/or global unfolding events  slow timescales • Heteronuclear relaxation measurements • R1 (1/T1) spin-lattice- reports on fast motions • R2 (1/T2) spin-spin- reports on fast & slow • Heteronuclear NOE- reports on fast & some slow

  26. B A B A Big (Slow) Small (Fast) 15N 15N 15N 1H 1H 1H Linewidth is Dependent on MW • Linewidth determined by size of particle • Fragments have narrower linewidths

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