Chem 781 – Part 8
NOE and through space correlation
Need for through space information
•
All 2D methods discussed so far utilized scalar couplings to establish through bond
connectivities => determination of two dimensional structure
•
The magnitude of scalar coupling could be used to determine dihedral angles and
establish configuration and conformational information.
•
For many stereo chemical problems groups more than three bonds apart have to be
related. For example to assign the methyl groups of camphor coupling constants
are not useful. Through space interaction (direct distance information) is often
needed
CH3
H3C
O
•
=> Dipolar coupling does not depend on bonds but only on proximity through
space (∼ r-3)
Review Dipolar coupling:
DAB
1
h 3 cos2   1
  A B
2
3
2
4
rAB
Depends on the nature of the nuclei (γ), the distance between them (r) and the angle
between the dipolar field and the internuclear vector (θ)
• Can be measure directly in solids, but not always in a trivial manner, as θ will
vary in powders
• Typically vanishes in solution because of 3 cos2 θ -1 term averages to zero
• Measurement of D is possible in solution when an aligning solvent is used (liquid
crystals, stretched polymenrs)
• Indirect measurement possible through effects of dipolar coupling on relaxation:
Measurement of T1 (first order) or NOE (second order effect)
1D NOE experiment – C-13
NO2
A
H
H-1
HC
HB
HD
Regular proton
Decoupled C-13
C-13
weak pulse at position H
A
B1 /2 = 10 - 30 Hz
decouple only one proton
H-1
Selectively
decoupled C-13
C-13
A
B
C
D
• decoupling (saturating) one proton at a time without affecting the other protons
can be achieved by irradiating with very low power (γB1/2π ≈ 10-30 Hz) at the
frequency of one specific hydrogen
• This results in a spectrum where only carbons close to the irradiated proton show
enhancement.
Proton-proton NOE
• In a similar manner, NOE’s can be measured between protons and can be used to
assess H-H distances.
• As the effects often are small typically the difference to a non irradiated spectrum is
typically determined.
NO2
H
A
H
C
HB
weak pulse at position H
A
B
A
B1 /2 = 10 - 30 Hz
HD
p = 2- 10 s
A
B
C
D
A
B
C
D
A
B
C
D
reference experiment (no
saturation pulse or pulse
centered outside spectral
region)
difference spectrum
A-B
NOE and relaxation
•
NOE arises from a change in population caused by relaxation. Consider a pair of
protons close in space but not necessarily coupled:
• four transitions can give rise to an
NMR signal, corresponding to
transitions involving flip of one spin
(single quantum transitions
• relaxation can occur across six
transitions, the four single quantum
transitions and the double- and zero
quantum
transitions,
with
the
transition rates (probabilities) W1, W0
and W2.

HA HB
1
A
B
W1A
W1B
A-B)
W0


A+B) A
W2
W1A
B
W1B
1

HA HB
Maximum possible NOE
•
The maximum possible NOE is given by the ratio of cross- to total relaxation:

 

W2  W0
cross relaxation
 A

W1  W1B  W0  W2 total spin lattice relaxation

1
T1
• Relaxation terms W1 and W0 unique to dipolar coupling
• W1 terms can depend on many contributions besides
dipolar coupling.
• Maximum NOE observed when dipolar coupling
dominant intercaction
Short Theory of Relaxation
Relaxation is induced by random fields caused by molecular motion:
molecular motion(frequency) • orientation dependent interaction (changing field)
Some important interactions are:
•
Anisotropy of the chemical shielding (tertiary carbons)
•
dipolar (through space) nuclear spin-spin coupling Important for protons and
protonated heteronuclei (C-H, N-H)
•
dipolar nuclear spin - electron spin coupling : important when paramagnetic
molecules are present (like oxygen)
•
quadrupolar coupling: orientation of non spherical nuclei in electric field. Only for I
> ½ nuclei, but then almost always dominant
Molecular motion:
Brownian motion for
spherical molecules:
Drot
1
kT


6 C 8r 3 solv
τc: Correlation time
R: radius of molecule
η: viscosity
As the motion is random, Drot represents an average rate of motion, with a certain
distribution of frequencies present in the ensemble of molecules determined by the
Boltzmann distribution.
Spectral Density
c
J ( ) 
1   2 c2
Gives the fraction of
molecules that are reorienting
with the frequency ω
The relaxation rates Wi will be most efficient when the tumbling at the transition
frequency reaches a maximum. One can already see that for very fast or very slow
tumbling the single quantum relaxation rate W1 at frequency ω0 will become very
inefficient
Spectral densities
J(): number of molecules at a certain frequency
(spectral density)
Drot << 0 (large molecule, low T,
high viscosity)
Drot = 0
Drot >> 0 (small molecule, high T,
low viscosity)
0
0
20
Dipolar relaxation and NOE
From a lengthy and tedious quantum mechanical deviation one can obtain
values for the relevant relaxation rates:
W1A = 3/20 DAB2 A J(ωA); W1B = 3/20 DAB2 A J(ωB)
W0 = 1/10 DAB2 A J(ωA - ωB) = 1/10 DAB2 A J(0)
for A,B both 1H
W2 = 6/10 DAB2 A J(ωA+ωB) = 6/10 DAB2 A J(2ω) for A,B both 1H
Note that the relaxation rates depend on the square of the dipolar coupling
constant, and thus are related to inter nuclear distance by rAB-6.

max
AB
5     4 

10  23   4 
2 2
0 c
2 2
o c
4 4
0 c
4 4
0 c
Maximum NOE for a homonuclear spin system
NOE versus τc
Lets consider some extreme cases:
very small molecules:
Drot >> ω0 or τc ω0 << 1: ηABmax = + ½
very large molecules or viscous solutions:
Drot << ω0 or τ c ω0 >> 1: ηABmax = -1
somewhere in between there will be a case with
ηABmax = 0 !!!
• The above leads to the apparently ridiculous result that the NOE does not
depend on the distance A-B anymore. But note that we were talking of
maximum NOE after achieving a steady state, considering an isolated pair
of protons.
• For an isolated two spin system it is not the NOE itself that depends on the
distance, but the rate at which the NOE is generated, σ = W2 - W0.
Therefore measurement of NOE buildup will be a more appropriate
experiment in most cases.
• If there where only two protons in the universe, irradiating one would
always eventually result in the same NOE no matter what the distance. But
if they are 1 light years apart it will take the age of the universe to build up
that NOE
• Usually more than two isolates spins are present and it is the competing
effect of different dipolar couplings which will lead to different NOE
values
Example linear four spin system
0.8 %
49.2%
44.3 %
A
4
B
2
45%
C
1
D
49 %
0.7 %
The maximum steady state NOE will be determined by the competition of
relaxation pathways between different pairs of nuclei.
• steady state NOE can be deceiving for isolated protons
• The strength of the NOE will not be symmetrical.
• In practice that means that more than one NOE should be considered before
interpreting any result.
Measuring Transient NOE

sel
a
1

H

2
b
c
2
sel


2
1
H
2

x
x,-x
x + -
Gradient
a) Basic transient 1D-NOE difference experiment involving a selective 180⁰
pulse.
b) Pulsed Field Gradient Spin Echo 1D NOE experiment
c) NOE buildup curve for a linear four spin system. For short mixing times (<200
ms) the NOE is roughly linear with the cross relaxation rate σ
Two dimensional NOESY
x,-x,x,-x
x
x,x,-x,-x
τ
t1
acquisition(x,-x,-x,x)
• The Sequence is identical to DQF COSY with a mixing time τ added.
• A different phase cycle is employed selecting the z-magnetization present
after the second 90̊ pulse (term I in the description of the COSY experiment
90x
IzA
ΩAt 1
90x(select z)
-IzA cos(ΩA t 1)
Two Dimensional NOESY (II)
• During the mixing time τ cross relaxation and chemical exchange with spin
B can take place with the rates σAB and kAB , respectively.
•
Both processes will create z-magnetization of spin B modulated with the
chemical shift of spin A during t1
NOE(W2-W0) τ,
exchange(kAB) τ
σAB







-IzA cos(ΩA t 1)(1-1/T1τm) + (W2-W0-kAB)τm IzBcos(ΩA t1)




























 


































Diagonal peak
cross peak
z
z
z
t1
90
y
y
x
x
z
z
z
NOE(W2) 
90x
90x
y
x
N
or OE
ex (W
ch 0 )
an 
ge
(k
AB
y
y
x
x
z
z
)
90x
y
x
y
x
Result of 2D NOESY experiment:
case I: σAB dominated by W0 (large molecules) OR chemical exchange:
negative σAB
=> Diagonal and cross peak have the same sign (both normally
phased positive, negative NOE gives positive cross peaks)
case II: σAB dominated by W2 (small molecules): positive σAB
=> Diagonal and cross peak have opposite sign. Phase correction
typically makes diagonal positive and cross peaks negative,
positive NOE gives negative cross peaks)
Properties of 2D NOESY spectrum
• Cross peaks between protons which are in close spatial proximity
• For short enough mixing times (small molecules 400 -800 ms, large
molecules 100-200 ms) the cross peak intensity is proportional to the cross
relaxation rate and thus to rab-6.
• Correlation time τC t is usually not known. Therefore only relative
distances can be determined. Usually known fixed distances can be used
for calibration (geminal CH2, aromatic CH=CH, ...)
• For small molecules NOE and chemical exchange will give cross peaks of
opposite sign and can be distinguished.
• As sequence is identical to DQF-COSY, coupling can cause artefacts in
spectrum. These will be anti-phase in nature
Limitation of NOESY experiment:
• If the molecular weight is around 1000 g mol-1 Drot is of the order of the
lamor frequency and W0 and W2 become very similar or equal.
• NOE’s will be very weak or zero no matter how close the distance (5 +
ω02τc2-4ω04τc4 = 0). NOESY experiments will fail in that case.
Principle of ROESY experiment
The zero NOE point is given by ω0τc = and thus depends both on
ω0 and τc
For a given molecule both parameters can be varied to reach a
region where NOE ≠0:
• One can vary τc by changing temperature or solvent (viscosity).
This option is often limited due to sample considerations
• change ω0: Using a different magnetic B0 field. On first sight, this
option appears even more limited in practice as extremely weak
magnets would give poor sensitivity and resolution.
• However, relaxation taking place during a spin lock depends only on
the effective field, which is the applied B1 field, which is much
weaker than the static B0 field.
ROESY Experiment
x
y
t1
acquisition
Spin lock pulse
ωeff = ω 1SL = γHB1
typically 3-5 kHz
Drot >> ω eff (or τc • ω eff << 1) will be always be fulfilled and
ROE’s will always be positive.
• ROE’s will be observable for molecules where NOESY
gives no signal
• For large molecules (or low temperature) ROE peaks and
exchange peaks will have opposite sign and can be
distinguished (as ROE will always be dominated by W2)
ROESY vs. TOCSY
The ROESY experiment utilizes the same pulse sequence as the
TOCSY experiment. The only difference are the strength and length of
the spin lock pulse:
• TOCSY: γB1/2π 10 kHz, τPSL = 15 - 80 ms, pulse is too short for
effective ROESY
• ROESY: γ B1/2 π 1.5 kHz, τ PSL = 400 ms, field is too weak for
effective TOCSY
• sign of TOCSY peaks is always same as diagonal (positive), for
ROESY peaks it is opposite to diagonal (negative)
• TOCSY spectrum spectra can exhibit weak ROESY peaks, an
ROESY spectra can exhibit weak TOSY peaks.
Assignment of methyl groups in
camphor
8
CH3
9
CH3
H
H
O
H
4
CH3
10
5
H
7
6
H
H
H
• CH3(8) is on the side of
the C=O group
• CH3(9) on the opposite
side of the molecule
• Assignment of diastereo
topic protons 4, 6, 7
NOE and conformational analysis
NOE’s can be used to supplement coupling constants in the measurement of
dihedral angles.
Particularly useful for identifying staggered conformations
Example side-chain angle in proteins/peptides
-
CO
NH
>
HMBC
2CO>3CO
CO
NH
<
2CO~3CO,
weak
CO
NH
~
2CO<3CO
Secondary structure in proteins
H
N
N
H i-H
i+1
H

N
i


H -N-C -H = -117
o
(  )
o
N
i
-Hi+3



H -N-C -H = -199
o
( = -139 )
o
-HNi+1
Structure determination of
Macromolecules
Assignment
J

6
NOE/ROE ~ 1/r
(NOESY,ROESY)
J coupling
(E.COSY,DQ/ZQ,FIDS, quant. J)
Distance Restraints
Dihedral Restraints
Structure Calculation
(Simulated Annealing, Distance Geometry,
Molecular Dynamics)
3D -Structure
Example: Metallothionein beta-N
domain: 33 residues
Example Metallothionein
• Using NOEs, H-H coupling
constants and H-Cd couplings
• Calculate many structures starting
from different random starting
points
• Keep 30 lowest energy structures
Some special considerations when
working with biological macromolecules
• molecular weight is 5000 - 30000 g/mol:
• short T2 => broad lines
• Experiments utilizing multiple steps of one-bond correlations work better than those
utilizing long range couplings. In-phase transfer preferred over antiphase transfer
(TOCSY vs. COSY)
• heavy overlap of lines due to complexity of molecule => highest magnetic field
possible should be used, two dimensional experiments reach their limits
• usually computer software needed to keep track of assignment data
• Often more than two dimensions are needed to resolve all signals.
•
Proteins can be produced using expression media, and enrichment with 13C and/or
15N which will allow experiments not possible with natural abundance samples
Two dimensional NMR often insufficient
CaM/C21W HN-HSQC
Three – or more dimensional NMR
necessary
1
H [ppm]
2.0
10
9
8
7
6
5
4
3
2
1
0
ppm
w
11
w (15N
)
4.0
1(
H)
5.0
4.0
3.0
1
1D
2.0
1.0
w (1H)
H [ppm]
2D
3D
Example HNCO
3D NMR for separating NOE peaks
Slice of 3D NOESY-HSQC
2D NOESY
1
13
H [ppm]
C = 20.3 ppm
I74 H(CH3)
1
0.0
H [ppm]
V68 H
V15 H
P67 H
K42 H’
L29 H
V93 H
A85 H
D53 H’
L82 H
2.0
2.0
V68 H
V56 H
V93 H
Y23 H ’
Y76 H’
L82 H
Y76 H
Y23 H
S90 H’
4.0
S88 H
V56 H
V93 H
S90 H
S86 H
A85 H
4.0
3.0
1
H [ppm]
2.0
N79 H
V68 H
V93 H’ V15 H’
V68 H’
V56 H’
5.0
4.0
P26 H
1.0
1.2
1
0.8
H [ppm]
0.6
Example Calmodulin
• 148 Amino acids
• 3 D experiments
necessary
• Takes many months to
complete assignment
and structure
determination