Transcript Center for Structural Biology

Nuclei With Spin Align in
Magnetic Fields
Efficiency factornucleus
Ho
Alignment
parallel
anti-parallel
Energy
DE = h g Ho
Constants
Strength of
magnet
Resonance: energy match causes transitions
Resonance: Perturb Equilibrium
p
Ho
DE
1. equilibrium
Efficiency factornucleus
ap
H1
hn = DE
DE = h g Ho
2. pump in energy
Constants
p
ap
3. non-equilibrium
Strength of
magnet
Return to Equilibrium (Relax):
Read Out Signals
p
DE
3. Non-equilibrium
ap
hn = DE
4. release energy (detect)
p
5. equilibrium
ap
Magnetic Resonance Sensitivity
Sensitivity f (population difference)
Np
= e-DE/kT
S ~ DN =
Nap
DE is small
At room temp., DN ~ 1:105
Intrinsically low sensitivity!
Efficiency factornucleus
DE = h g Ho
Constants
Strength of
magnet
Increase sensitivity by increasing magnetic field strength
Intrinsic Sensitivity
Nucleus
g
% Natural
Abundance
Relative
Sensitivity
1H
2.7 x 108
99.98
13C
6.7 x 107
1.11
0.004
15N
-2.7 x 107
0.36
0.0004
31P
1.1 x 108
100.
0.5
e-
1.8 x 1011
100.
>600
1.0
The Classical Treatment:
Nuclear Spin Angular Momentum
Two spins
All spins
 Sum
Ho
parallel
anti-parallel
Torque + int. motion = precession
Precession around Z axis
Larmor frequency:  = g H0
excess
facing
down
Bulk
Magnetization
Effect Of An RF Pulse
RFy
RFy
t
=
Only the
excess
spins
 = g H0
phase
coherence
Ax
t
f

NMR frequency
Fourier
Transform
Variation of signal
at X axis vs. time
The Power of Fourier Transform
t
90ºx RF pulse
+
1 = g H0
2 = g H0
A
t
f
2 1
Fourier
Transform
NMR frequency domain
NMR time domain
 Spectrum of frequencies
 Variation in amplitude vs time
Relaxation- Return to Equilibrium
t
t
x,y plane
Transverse
0
Longitudinal
1
1
t
t
2
2
8
E-t/T2
1-e-t/T1
Transverse always faster!
8
0
z axis
Longitudinal (T1) Relaxation
MECHANISM
Molecular motions cause the nuclear magnets to
fluctuate relative to a fixed point in space
Fluctuating magnetic fields promote spins to flip
between states
Over time, spin flips cause a return to equilibrium
dMz/dt = Meq – Mz/T1
t
Mz(t) = Meq (1-e-t/T1)
Mz(t)  Meq
Transverse (T2) Relaxation
MECHANISM
Magnetic field is not homogenous to an infinite
degree
Each spin comprising the bulk magnetization will
feel a slightly different field
Over time, the spin fan out (lose coherence)
t
time
dMx,y/dt = Mx,y/T2
Linewidth
The Pulse FT NMR Experiment
90º pulse
Experiment
(t)
equilibration
detection of signals
Fourier
Transform
Data
Analysis
Time domain (t)
NMR Spectrum
Chemical Shift & Linewidth
Chemical shift: intrinsic frequency
Linewidth: relaxation (MW)
Preparation of Magnetization
Building Towards 2D NMR
E
t1
Equilib.
Detect
If E is sufficiently long,
full peak intensity
90º pulse
E-d
t1
Detect
If E is too short,
intensity is reduced
90º pulse
What if we caused the peak intensity to vary at a
rate equal to the precession freqeuncy?
Frequency Labeling
Systematically Alter The Equilibrium
0
t1
I
t
D
t1
2D
t1
3D
t1
0 D
3D
5D
FT
FT the variation in intensity and get Larmor frequency!
Indirect Detection 2D NMR
F2
t1
t2
F1
1) Add pulse to frequency label during t1
2) Introduce mixing period before t2
mix
t1
t2
The Mixing Process- Uses Coupling
Through
Space
Through
Bonds
2D NMR: Coupling is the Key
2D detect signals twice
(before/after coupling)
90º pulse
t1
Same as 1D
experiment
Mixing causes an
exchange between
spins that are
coupled
2D NMR Pulse Sequence
t2
t1
t2
The 2D NMR Spectrum
Pulse Sequence
t1
t2
Spectrum
Before mixing
Coupled spins
give rise to
crosspeaks
After mixing
Multi-Dimensional NMR:
Built on the 2D Principle
3D- detect signals 3 times
90º pulse
(t3)
t1
Same as 1D
experiment
t2
t3
3D NMR Pulse Sequence
Experiments are composites