Macromolecular Structure and Function

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Macromolecular Structure and Function
Structure and Dynamics by NMR John Gross, Oct 19
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Macromolecules are Dynamic
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Time Scales of Macromolecular Transitions
Vibrations
Librations
Sidechain Rotation
Allostery Domain Motions Helix-Helix Motions
Breathing Modes
-15
Log (timescale in seconds)
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Nuclear Spins Microscopic Bar Magnets
N
S

Bar Magnet
Magnetic Moment
Protein Fragment
Magnetic moment
Angular Momentum
The proportionality constant g strength of bar
magnet
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Spin Precession
Magnetic Field, Bo
Precession frequency gB0wo
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Driving Forces for Precession
Precessional Orbits
Gravity
Applied magnetic field,B0
Spinning Top
Spinning Nucleus
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Equation of Motion
Based on magnetic torque
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Nuclear Spins Report Local Environment
Btotal
Blocal
Bapplied

determines precession
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Detection of Spin Precession
Z
Y
X
Detector measures magnetic field on x-axis
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Net Magnetization
No Transverse Magnetization at equilibrium
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Magnetic Energy
N
m
E -mzBz
S
Static Magnetic Field Oriented Along Z-Axis
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Energy States (spin-1/2 nucleus)
Energy
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Net Magnetization along Z Axis
Z
Z
Y
Y
X
X
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Equation of Motion for Magnetization
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Summary
Nuclear Spins precess in magnetic field.
Frequency of precession depends on sum of local
and applied field Need transverse magnetization
to detect precession Random orientations of
transverse magnetization cancel out at
equilibrium Magnetization polarized along
direction of applied field (z-axis)
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Solution I apply second field along y Axis
Z
Y
B1
X
Bo
If B1 gtgt Bo, Mz would rotate about B1. Leave
B1 on until X axis reached ----gt transverse
magnetization Approach is not practical.
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Magnetic Resonance
Z
Y
1/n0
B1
X
Bo
Turn B1 on and off with a frequency matching
the precessional frequency
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Resonance
Ensemble of Nuclear Spins
Resonant RF Field
Random Phase Phase Synchronization No NMR
Signal NMR Signal!
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Magnetic Resonance
Z
Y
1/n0
B1
X
Bo
Turn B1 on and off with a frequency matching
the precessional frequency
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Resonance and the Rotating Frame
Bo
Bo - w/g
wo
wo
- w
w
Lab Frame
Rotating Frame
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90 Degree Pulse On Resonance
Z
Y
X
Net magnetization rotated into transverse
plane Rotates due to static and local fields
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Resonance
Ensemble of Nuclear Spins
Resonant RF Field
Random Phase Phase Synchronization No NMR
Signal NMR Signal!
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FID
Oscillation of Transverse Magnetic Field Induces
a Measureable Current the Free Induction Decay
Fourier transform of time domain signal
generates frequency domain spectrum
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NMR Signal of One Pulse-Acquire Experiment
Re S(t)
dt accumulated phase of magnetization in
transverse plane Relaxation term decreases
amplitude over time
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The Fourier Transform
For
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The NMR Spectrum
Absorptive
Re S(n)
0
Dispersive
Im S(n)
0
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Properties of the FT
FTf(t)g(t)FTf(t)FTg(t) (superposition
principle) If f(t) is even, then FTf(t)f(v)
is even If f(t) is odd, then FTf(t)f(v) is
odd
Linear Operation
Parity conserving
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Convolution Theorem
Convolution of f and g is defined as
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Phase Encoding
90y
Re s(t)
1/d
90y
d Resonance Offset

t
Re s(t)
dt 90º
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Vector Picture
z
z
t
y
y
x
2pdt
x
During t delay, magnetization evolves due to
Chemical Shift frequency d determined by
resonance offset.
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NMR Signal After Phase Encoding Delay t
t 0, d gt0
2pt d p
0
Phase and amplitude of detected signal depends on
prior history!
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Multiple spins Phase Encode Experiment
z
z
t
y
y
dt
x
x
d 0
d gt 0
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Spectrum After t Delay for Multiple Spins
Re S(n)
0
Blue Spin is on resonance (d0)and relaxes
fast Red Spin is off resonance (d) and relaxes
slow
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The Spin Echo
90y
t
t
t
x
x
-f
Echo Forms After 2t
f2ptd
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Spin Echo Spectra at Variable t Delay
Re S(n)
t40 ms
t20 ms
t0
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Extracting R2 from Spin-Echo Data
I(t)
t
This can be thought of as a type of 2D NMR
Experiment
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Main Points
NMR signal of a spin depends on its
history Spin Echo neatly separates chemical
shift evolution from relaxation Formally, we say
the spin-echo refocuses the chemical shift
evolution during the 2t delay. In effect, it
appears that there is no evolution during the
delay preceding acquisition.
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The Inversion Recovery Experiment
90y
t
t
Note lack of CS evolution during delay
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Physical Picture of Inversion Pulse (the 180)
After 180
Before 180 _at_EQ
Energy
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Inversion Recovery Data
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Analysis of Inversion Recovery Data
Mzeq
Mz Mzeq ( 1 -2 e-tR1 )
Mz(t)
-Mzeq
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The J Coupling
Consider two spin-1/2 nuclei (ie, 1H and 15N)
1H
Augments local field
e-
15N
Diminishes local field
Effect transmitted through electrons in
intervening bonds
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J Coupling Dynamics
z
z
t
y
y
x
x
Components rotate faster or slower than rotating
frame by - J/2
(After 90y pulse)
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J Coupling Signal
90y
z
y
1/J
x
Im S(t) 0 for pure J evolution since
projections of counter-rotating fields cancel
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Spectrum with J coupling
1JNH
90 Hz
0
15N Detected Spectrum
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Energy Level Picture
0
10
1
11
1H 90 pls
10
10
11
11
HN
HN
Amplitude of signal proportional to equilibrium
population difference across transitions
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1H Versus 15N Detection
0
1H 90 pls
1JNH
1.0
1
10
1H Spectrum
15N 90 pls
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1.0
1JNH
HN
15N Spectrum
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Combined Chemical Shift and J-Evolution
S(t) exp(-i2pdt)cos(pJt)
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Spectrum of Combined Chemical Shift and J
Evolution
J
0
d
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How to calculate spectrum from joint CS and J
evolution
J
FTf(t)
FTg(t)

J/2
W
-J/2
W
d is Kronecker delta function
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Spin-Echo Part II
90y
t
t
t
JXH only
J Coupling Refocused
J CS
J Coupling Chemical Shift Refocused
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Spin Echo Application of 180 to remote spin
90y
t
t
Local field on 1H due to J Coupling averages to
zero over 2t
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Spin Echo with 180º Pulse on Remote Spin
90y
1H
t
t
t
15N
J Coupling Refocused Chemical Shift unperturbed!
2pdt
4pdt
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Heteronuclear Decoupling
1H
t
With decoupling
0
d
15N
Without decoupling
e
e
e
e
e
0
Decoupling train of spin-echos removes effect
of J coupling
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Spin Echo with simultaneous 180 degree pulses
90y
t
t
t
J Coupling unaffected, Chemical Shift refocused!
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Spin-Echo Modules The Building Blocks of Modern
nD NMR
1H
t
t
Refocus 1H CS JNH
1H
t
t
15N
1H CS Active Refocus JNH
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HSQC
y
1H
D
D
t2
15N
t1/2
t1/2
DEC
j
f
e
g
h
i
a
b
c
d
Bodenhausen Ruben
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HSQC
1H
15N
a
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INEPT
D1/4JNH
y
1H
D
D
a
b
c
d
15N
Hz HzNa HzNb
b)
Hx ( HxNa HxNb)
HyNz HyNa - HyNb
HzNa - HzNb HzNz
Morris Freeman
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INEPT inverts population over one transition
0
10
1
1
HzNb
10
0
HzNa
11
11
INEPT
HN
HN
Hz HzNa HzNb
HzNa - HzNb HzNz
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Effect of INEPT
y
90y
1H
D
D
15N
15N
FT
FT
0
0
15N Detected Spectrum
Ten-fold Enhancement in Sensitivity due to
Polarization Transfer
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15N Chemical Shift Evolution
y
1H
D
D
t2
15N
t1/2
t1/2
DEC
g
h
i
j
f
e
g)
f)
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Reverse INEPT
y
1H
D
D
t2
15N
t1/2
t1/2
DEC
g
h
i
j
f
e
cos(2pdNt1)xHy(Na-Nb)
g)
h)
i)
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Detection
y
1H
D
D
t2
15N
t1/2
t1/2
DEC
g
h
i
j
f
e
t2
j)
2pdHt2
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HSQC Signal
y
1H
D
D
t2
15N
t1/2
t1/2
DEC
j
f
e
g
h
i
a
b
c
d
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2D Time-Domain Data
t1
t2
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2D Fourier Transform FT Direct Dimension
FT Direct Dimension
Re S(t1,?2) is absorptive. But
unable to discriminate sign of dN
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Obtaining the Sine Component
y
1H
D
D
t2
y
15N
t1/2
t1/2
DEC
g
h
i
j
f
e
g)
e)
f)
2pdNt1
States, Ruben, Haberkorn
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After Obtaining Im Part of Indirect Dimension .
. .
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Combining 2D Data
Problem both Real and Imaginary components
of Spectrum have dispersive character!
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Solution swap Re of Ss with Im of Sc prior to
second FT
Sc
Ss
Swap
FT
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The HSQC Spectrum
N
HN