Transcript NMR Spectroscopy

NMR Spectroscopy
Relaxation Time
Phenomenon & Application
Relaxation- Return to Equilibrium
t
t
x,y plane
Transverse
Longitudinal
1
1
t
t
2
2
-t/T2
E
8
0
-t/T1
1-e
Transverse always faster!
8
0
z axis
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- http://gamma.magnet.fsu.edu/info/tour/blo
and y- magnetizations.
ch/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 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 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.
Longitudinal Relaxation time T1
Inversion-Recovery Experiment
180y (or x)
90y
tD
T1 relaxation
Interaction
Dipolar coupling
Range of
relevant parameters
interaction (Hz)
104 - 105
Quadrupolar coupling
106 - 109
Paramagnetic
107 -108
Scalar coupling
10 - 103
Chemical Shift
Anisotropy (CSA)
6- Spin rotation
10 - 104
- abundance of magnetically
active nuclei
- size of the magnetogyric ratio
- size of quadrupolar coupling
constant
- electric field gradient at the
nucleus
concentration of paramagnetic
impurities
size of the scalar coupling
constants
- size of the chemical shift
anisotropy
- symmetry at the nuclear site
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
90y
180y (or x)
tD
tD
 signal width at half-height (line-width )= (pi * T2)-1
Spin-spin relaxation (Transverse) T2
Spin-Echo Experiment
Spin-Echo experiment
MXY =MXYo
-t/T2
e
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.
Relaxation and correlation time
For peptides in aqueous solutions the dipole-dipole spin-lattice and spinspin relaxation process are mainly mediated by other nearby protons
1
T1


2 
1
4

II  1 c 

6
2 2
2 2
5 r
1    c 1  4  c 
1
T2


1 
5
2



I
I

1

3



c
6
2 2
2 2
5 r
 1    c 1  4  c 
4 2
4 2
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)
Application
Characterizing Protein Dynamics:
Parameters/Timescales
Relaxation
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
Linewidth is Dependent on MW
A
B
A
B
Big
Small
(Slow) (Fast)
15N
Linewidth
determined by
size of particle
15N
15N
Fragments
have narrower
linewidths
1H
1H
1H