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**Relaxation Time Phenomenon & Application**

NMR Spectroscopy Relaxation Time Phenomenon & Application

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**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!

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**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.

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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.

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**Relaxation time – Bloch Equation**

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**Relaxation time – Bloch equation**

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**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

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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.

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**Longitudinal Relaxation time T1**

Inversion-Recovery Experiment 180y (or x) 90y tD

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T1 relaxation

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**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

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**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

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**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)

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**Spin-spin relaxation (Transverse) T2**

90y 180y (or x) tD tD signal width at half-height (line-width )= (pi * T2)-1

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**Spin-spin relaxation (Transverse) T2**

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Spin-Echo Experiment

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Spin-Echo experiment

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MXY =MXYo e-t/T2

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**Carr-Purcell-Meiboom-Gill sequence**

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**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.

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**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

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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: 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 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

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**Linewidth is Dependent on MW**

A B Small (Fast) Big (Slow) 1H 15N Linewidth determined by size of particle Fragments have narrower linewidths

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