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NMR Spectroscopy Relaxation Time Phenomenon & Application

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Relaxation- Return to Equilibrium t z axisx,y plane 0 1 2 t 0 1 2 8 8 E -t/T 2 t 1-e -t/T 1 t Longitudinal Transverse Transverse always faster!

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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. http://gamma.magnet.fsu.edu/info/tour/blo ch/index.html Relaxation

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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

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Relaxation time – Bloch Equation Bloch Equation

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Relaxation time – Bloch equation

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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

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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.

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

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T 1 relaxation

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Interaction Range of interaction (Hz) relevant parameters Dipolar coupling10 4 - 10 5 - abundance of magnetically active nuclei - size of the magnetogyric ratio Quadrupolar coupling10 6 - 10 9 - size of quadrupolar coupling constant - electric field gradient at the nucleus Paramagnetic10 7 -10 8 concentration of paramagnetic impurities Scalar coupling10 - 10 3 size of the scalar coupling constants Chemical Shift Anisotropy (CSA) 10 - 10 4 - size of the chemical shift anisotropy - symmetry at the nuclear site 6- Spin rotation

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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

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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)

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Spin-spin relaxation (Transverse) T 2 signal width at half-height (line-width )= (pi * T 2 ) -1 180 y (or x) 90 y tDtD tDtD

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Spin-spin relaxation (Transverse) T 2

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Spin-Echo Experiment

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Spin-Echo experiment

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M XY =M XYo e -t/T2

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Carr-Purcell-Meiboom-Gill sequence

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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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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

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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)

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Application

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Characterizing Protein Dynamics : Characterizing Protein Dynamics : Parameters/Timescales Relaxation

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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

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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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