1. Relaxation Time Phenomenon & Application
NMR Spectroscopy
Relaxation Time
Phenomenon & Application

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

3. magnetization vector's trajectory
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.

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

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

11. T1 relaxation

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

13. Spin-spin relaxation (Transverse) T2
T2 represents 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

14. 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)

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

16. Spin-spin relaxation (Transverse) T2

17. Spin-Echo Experiment

18. Spin-Echo experiment

19. MXY =MXYo e-t/T2

20. Carr-Purcell-Meiboom-Gill sequence

21. 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 T2 relaxation such that T2 becomes shorter than T1.

23. 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

24. 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)

25. Application

27. Characterizing Protein Dynamics: Parameters/Timescales
Relaxation

28. 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

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