Guide to NOE Experiments

reference "The Nuclear Overhauser Effect in Structural and Conformational Analysis" by Neuhaus & Williamson.

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There are 3 types of experiment for measuring NOE's (see diagrams) :

  1. Steady State - a single resonance is saturated at low power for approximately five times T1 before acquiring the FID.
  2. Truncated driven NOE (TOE) - as above, but saturated for various shorter times so the buildup of NOE can be observed.
  3. Transient NOE

cyclenoe gnoe noesy


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.

energy level diagram 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.

percent NOE enhancements

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.

NOE buildup rates

Why NOE's cannot be used as a measure of internuclear distance.

  1. 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.
  2. 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.
  3. Different types of experiment (such as cyclenoe and gnoe) give different NOE enhancements, so the percentage enhancements cannot be compared between experiments.
  4. Different mixing times and different spin-lattice relaxation times affect the amount of NOE enhancement.
  5. Other relaxation mechanisms such as disolved oxygen, or highly deuterated solvents such as DMSO-d6, benzene-d6 or acetone-d6 reduce the NOE.
  6. 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.

basic gnoe experiment

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.

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