Guide to NOE Experiments
reference "The Nuclear Overhauser Effect in Structural and
Conformational Analysis" by Neuhaus & Williamson.
Notes:
- You should de-gas your sample using the freeze-pump-thaw technique
before running an NOE experiment.
- As described later in these notes, the Nuclear Overhauser
Enhancement is small for molecules with molecular weights of around 2000
Daltons. For molecules like this, a ROESY experiment
(not described on this page) is advisable.
- Although ROESY has the advantage compared to NOESY that enhancements
for molecules of all weights are positive, and therefore there is no
molecular weight at which ROEs are nearly zero, ROESY has the disadvantage
that TOCSY artifact peaks can occur. This problem does not arise in a NOESY.
(Note however that ROESY artifacts do not occur in TOCSY spectra).
- NOE type experiments can also be used to measure chemical exchange.
However if you are trying to measure NOEs in a molecule that is
undergoing exchange, it is possible to confuse exchange with
negative NOEs.
- NOEs are affected by molecular tumbling, and can therefore increase at
low temperatures.
- Since it is usual to acquire 256 or more increments in a 2D NOESY,
the 1 dimensional experiments take less time to run. However, to run
a 1D experiment it is necessary to selectively saturate or pulse a
single resonance - something that is only possible if the resonances
to be saturated do not overlap with other resonances. When submitting
a sample for a 1D NOE experiment, it is a good idea to provide a
previously obtained spectrum with the resonances you wish to saturate
marked.
- Gradient NOE experiments do not give as large an NOE enhancement as
steady state experiments. Their advantage over steady state experiments
arises from the fact that gradient NOE experiments are not difference
experiments. The absence of subtraction artifacts means that much smaller
NOEs can be reliably measured in gradient experiments.
There are 3 types of experiment for measuring NOE's (see diagrams) :
- Steady State - a single resonance is saturated at low power for
approximately five times T1 before acquiring the FID.
- Truncated driven NOE (TOE) - as above, but saturated for various shorter
times so the buildup of NOE can be observed.
- Transient NOE
- 1D - a single resonance is selectively inverted.
- 2D - all resonances are frequency labeled by a 90 degree pulse
and a variable delay.
Theory
Consider two spins I and S, where I is the spin whose resonance is measured
and S is the spin whose resonance is saturated. The spins are close enough
to have a dipole-dipole coupling (i.e. a through-space interaction) but
there is no spin-spin coupling (i.e. scalar coupling - the coupling that
causes multiplets in an NMR spectrum).
The NOE enhancement fI{S} is defined as the fractional change
in the intensity of I on saturating S:
fI{S} = (I - I0)/I0
where I0 is the equilibrium intensity of I.
In the energy level diagram for a 2 spin system, it is the transitions
that involve a simultaneous flip of both spins (cross - relaxation) that
cause NOE enhancements. If the W2 transition occurs after spin
S has been
saturated, it gives a positive NOE of the I signal. Similarly a W0
transition gives a negative NOE. W0 is a zero quantum transition
whose frequency is simply the difference in chemical shift between the 2
signals (zero up to a few kHz). W2 is a double quantum transition
whose frequency is the sum of the chemical shifts of the 2 signals. In a
500 MHz spectrometer this frequency is 500 MHz + 500 MHz = 109 Hz.
A transition corresponding to a given frequency is promoted by
molecular motion at the same frequency. Small molecules in non-viscous
solvents tumble at rates around 1011 Hz, while larger molecules
such as proteins tumble at rates around 107 Hz. For small
molecules, W2 will be greater than W0 and NOE
enhancements will be positive. For larger molecules W0 will
become greater than W2 and NOE enhancements will be negative.
When dealing with isotropic molecular tumbling, the correlation time
tauc is the time taken for the molecule to rotate by roughly
1 radian about any axis. A very approximate estimate is
tauc = 10-12WM where WM
is the molecular mass in Daltons.
As well as the tumbling rate and the distance between nuclei, the
size of the NOE also depends on the number of available relaxation
pathways. In the diagram below, nucleus B is saturated, and the
effects on nuclei A, C and D are observed. One would expect nucleus A to
show the largest NOE since it is closest to nucleus B (the relative
distances are shown as A to B = 1, B to C and C to D = 2). However a
further reason for its large NOE is that nucleus A depends mainly on
nucleus B for cross-relaxation. Nucleus C is relaxed by nucleus D as
well as B, so it shows a smaller NOE. Nucleus D has an indirect NOE
from nucleus B. Indirect effects usually give rise to negative
NOEs. (See Neuhaus and Williamson for more details). Note that as the
tumbling rate decreases (i.e. omega tau C increases) all other
parameters become irrelevant and the NOEs tend towards -100%. The
notation fA{B} means the NOE enhancement of spin A when
spin B is saturated.
The table below shows the maximum theoretical NOE enhancements for
different experiments and molecule sizes.
Maximum Enhancement
|
steady state
|
1D transient
|
2D NOESY
|
small molecules
|
50%
|
38.5%
|
19.2%
|
large molecules
|
-100%
|
-100%
|
-100%
|
NOE Buildup Rates
In transient experiments there are two competing processes
occurring during the delay tau (or taum). One is cross -
relaxation from the perturbed spins which causes NOE enhancements.
The other is spin - lattice relaxation which restores all intensities
to their equilibrium values (thus destroying NOE).
The initial buildup rate in a 1D transient NOE experiment
is twice the rate for NOESY and TOE because the spin S is selectively
inverted rather than all spins being flipped through 90° (NOESY)
or being saturated (TOE).
The subsequent decay of NOE enhancements in transient experiments
depends on the spin - lattice relaxation time T1. In steady state and
TOE experiments spin S is saturated continuously, making the relaxation
rate irrelevant. Because of differing buildup and decay rates, the actual
NOE enhancement can vary greatly, depending on T1 and the choice of tau.
Under some conditions the transient enhancement can be greater than
the steady state enhancement.
Why NOE's cannot be used as a measure of internuclear distance.
- Spin diffusion. In large molecules the population disturbance,
initially present only in the nucleus being saturated, spreads out
through the molecule by cross-relaxation until at steady state, every
spin is affected.
- Although spin diffusion is much less important in the positive NOE
regime (i.e. small molecules) indirect NOEs can still alter
the observed enhancement. Note however that indirect NOEs build up
more slowly than direct NOEs, so their effect is reduced if the
mixing time is small (around 0.1 second in transient NOE experiments)
or the saturation time (in TOEs) is short.
- Different types of experiment (such as cyclenoe and gnoe) give
different NOE enhancements, so the percentage enhancements cannot
be compared between experiments.
- Different mixing times and different spin-lattice relaxation times
affect the amount of NOE enhancement.
- Other relaxation mechanisms such as disolved oxygen, or highly
deuterated solvents such as DMSO-d6, benzene-d6 or acetone-d6
reduce the NOE.
- If the molecule is not rigid, internuclear distances will appear
less than their true value.
However for many applications the numerical value of an enhancement is
not vital in reaching a structural conclusion. The appearance of an
enhancement at one resonance rather than another is often sufficient.
Alternatively, enhancements can be categorised as strong, medium or weak.
If internuclear distances are required, a series of NOE experiments should
be performed to measure the rate of buildup of the NOE, rather than
its percentage enhancement for a single experiment.
The Gradient NOE Experiment
In the basic experiment (ref JACS 116 6037) the only
magnetisation which is refocused by the final gradient is that which was
defocused by the first gradient. Thus the only resonances observed are those
which arise from the spin which was excited by the selective 90° pulse
and from spins to which magnetisation has been transferred by
cross-relaxation.
The use of gradients results in the refocusing of just one out of two
possible coherence transfer pathways, leading to a reduction in the signal
intensity by a factor of 2. In addition, compared to the 1D transient
experiment, the initial buildup rate of the NOE in the gradient experiment
is reduced by a factor of 2 (because a 90° selective pulse is used
instead of a 180° pulse). However the gradient experiment records the
NOE spectrum directly so that no reference spectrum is needed (i.e. this is
not a difference experiment). Thus the net signal to noise is half the
transient experiment. (The percentage NOEs are the same as NOESY).
Because this is not a difference experiment it produces no cancellation
artifacts, and it is therefore possible to reliably detect much smaller
NOEs than is possible with the steady state technique.
Excitation Sculpting. (ref. JACS 117 4199).
This is used in the NOE1D experiment on the Inova 500.
The heart of this method is the double pulsed field gradient spin echo
(DPFGSE) sequence
G1 - S - G1 - G2 - S - G2 - where
S is any sequence of RF pulses of any kind, and G1
and G2 are pulsed field gradients. When used for NOE
measurement we obtain a theoretical factor of 2 in signal (compared to
the previous experiment) by not discarding one coherence transfer
pathway. There is also a large taum dependent gain in
sensitivity attributed to diffusion losses in GOESY.
It is
possible to quote the percentage enhancement in this experiment, but
remember that the value of the enhancement depends on the mixing time
used. Also if some nuclei in a molecule have shorter T1s than the
others, they will appear to have a lower NOE enhancement because the
NOE will be further down the "decay" part of the curve at the end of
the mixing time.