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NMR Spectroscopy Relaxation Time Phenomenon & Application.

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Presentation on theme: "NMR Spectroscopy Relaxation Time Phenomenon & Application."— Presentation transcript:

1 NMR Spectroscopy Relaxation Time Phenomenon & Application

2 Relaxation- Return to Equilibrium t z axisx,y plane t E -t/T 2 t 1-e -t/T 1 t Longitudinal Transverse Transverse always faster!

3 magnetization vector's trajectory The initial vector, M o, evolves under the effects of T 1 & T 2 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. ch/index.html Relaxation

4 The T 2 relaxation causes the horizontal (xy) magnetisation to decay. T 1 relaxation re-establishes the z-magnetisation. Note that T 1 relaxation is often slower than T 2 relaxation. Relaxation

5 Relaxation time – Bloch Equation  Bloch Equation

6 Relaxation time – Bloch equation

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

8 Relaxation  Spin-lattice 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  Spin-spin relaxation transfers the excess energy to other magnetic nuclei in the sample.

9 Longitudinal Relaxation time T 1 Inversion-Recovery Experiment 180 y (or x) 90 y tDtD

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11 T 1 relaxation

12 Interaction 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) T 2  T 2 represents the lifetime of the signal in the transverse plane (XY plane)  T 2 is the relaxation time that is responsible for the line width. line width at half-height=1/T 2

14 Spin-spin relaxation (Transverse) T 2 Two factors contribute to the decay of transverse magnetization.  molecular interactions ( lead to a pure pure T 2 molecular effect)  variations in B o ( lead to an inhomogeneous T 2 effect)

15 Spin-spin relaxation (Transverse) T 2  signal width at half-height (line-width )= (pi * T 2 ) y (or x) 90 y tDtD tDtD

16 Spin-spin relaxation (Transverse) T 2

17 Spin-Echo Experiment

18 Spin-Echo experiment

19 M XY =M XYo e -t/T2

20 Carr-Purcell-Meiboom-Gill sequence

21 T 1 and T 2  In non-viscous liquids, usually T 2 = T 1.  But some process like scalar coupling with quadrupolar nuclei, chemical exchange, interaction with a paramagnetic center, can accelerate the T 2 relaxation such that T 2 becomes shorter than T 1.

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

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

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27 Characterizing Protein Dynamics : 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  R 1 (1/T 1 ) spin-lattice- reports on fast motions  R 2 (1/T 2 ) spin-spin- reports on fast & slow  Heteronuclear NOE- reports on fast & some slow

29 Linewidth is Dependent on MW A B A B 1H1H 1H1H 15 N 1H1H  Linewidth determined by size of particle  Fragments have narrower linewidths Small (Fast) Big (Slow)

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