NMR Spectroscopy

Relaxation Time

Phenomenon & Application

Relaxation- Return to EquilibriumRelaxation- Return to Equilibrium

t

z axisx,y plane

0

1

2

t

0

1

2

8 8

E-t/T2

t

1-e-t/T1

t

LongitudinalTransverse

Transverse always faster!

magnetization vector's magnetization vector's trajectorytrajectory

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

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.

Relaxation

Relaxation time – Bloch Equation

Bloch Equation

Relaxation time – Bloch equation

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

Relaxation

Spin-lattice relaxationSpin-lattice relaxation converts the excess energy into translational, rotational, and vibrational energy of the surrounding atoms and molecules (the lattice).

Spin-spin relaxationSpin-spin relaxation transfers the excess energy to other magnetic nuclei in the sample.

Longitudinal Relaxation time T1

Inversion-Recovery ExperimentInversion-Recovery Experiment

180y (or x) 90y

tD

T1[1].swf

T1 relaxation

InteractionRange 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

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

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)

Spin-spin relaxation (Transverse) T2

signal width at half-height (line-width )= (pi * T2)-1

180y (or x)90y

tD tD

Spin-spin relaxation (Transverse) T2

Spin-Echo Experiment

Spin-Echo experiment

MXY =MXYo e-t/T2

Carr-Purcell-Meiboom-Gill sequence

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.

22226

241

2

22226

241

1

41

2

1

531II

5

1

41

4

1

11II

5

2

ccc

ccc

rT

rT

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

Why The Interest In Why The Interest In Dynamics? 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)

Application

Characterizing Protein DynamicsCharacterizing Protein Dynamics: : Parameters/Timescales

Relaxation

NMR Parameters That Report On NMR Parameters That Report On Dynamics of MoleculesDynamics 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

Linewidth is Dependent on MW

A B A B

1H

1H

15N

15N

1H

15N

Linewidth determined by size of particle

Fragments have narrower linewidths

Small(Fast)

Big(Slow)