NMR%20Spectroscopy

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NMR Spectroscopy

• Relaxation Time
• Phenomenon Application

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Relaxation- Return to Equilibrium
t
t
z axis
x,y plane
Longitudinal
Transverse
0
0
1
1
t
t
2
2
E-t/T2
1-e-t/T1
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Transverse always faster!
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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.
http//gamma.magnet.fsu.edu/info/tour/bloch/index.
html
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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

• 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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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-height1/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
180y (or x)
90y
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

• Linewidth determined by size of particle
• Fragments have narrower linewidths

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