NOE Experiments

 When a proton is saturated or inverted, spatially-close protons may experience an intensity enhancement, which is termed the Nuclear Overhauser Effect (NOE). The NOE is unique among NMR methods because it does not depend upon through-bond J couplings but depends only on the spatial proximity between protons.  In other words, the strength of the NOE gives information on how close two protons are.  For small molecules, an NOE may be observed between protons that are up to 4Å apart, while the upper limit for large molecules is about 5Å.

 There are many different possible NOE experiments (NOE or ROE, steady-state or transient, 1D or 2D, etc).  The ones available on the 400 and 500 are 1D selective-NOESY, 2D-NOESY, 2D-NOESY with zero-quantum suppression, and 2D-ROESY.    Some understanding of the theory of NOE is necessary for choosing the correct experiment and for interpreting it properly.  Some of the important results from the theory are discussed below.  For a full understanding, see the excellent text Neuhaus, David, and Williamson, Michael P., The Nuclear Overhauser Effect in Structural and Conformational Analysis, 2^nd ed., WILEY-VCH, New York, 2000.

 Molecular Weight and Maximum NOE

 The maximum possible NOE depends on the molecular correlation time (or the inverse of the rate of molecular tumbling), which is in large part determined by the molecular weight and solvent viscosity.  Larger molecular weights and higher viscosities lead to larger correlation times.  The NOE is positive for small molecules (MW< 600), goes through zero for medium-sized molecules (MW range 700 – 1200), and becomes negative for large molecules (MW>1200).  (These MW ranges are approximate only.)  For medium sized molecules, the NOE may be theoretically zero.  See the figure below that is adapted from Newhaus and Williamson text. The ROESY experiment (rotating frame NOE) is preferred for medium-sized molecules since the ROE is always positive.

Time Dependence of NOE - Mixing Times

 In transient experiments, such as NOESY and ROESY, the NOE dynamically builds up and then decays due to relaxation during the mixing time, as shown below in the plot of NOE versus mixing time. The NOE, thus, goes through a maximum as function of mixing time.  The location of the maximum NOE and rate of build-up depend on the correlation time, or its proxy, the molecular weight, and the distance between protons for a particular NOE.  In general, large molecules build-up NOE quickly while small molecules build-up NOE more slowly. That is, for large molecules the point of maximum NOE is shifted to shorter mixing times.  A shorter distance between protons will also lead to faster build-up of NOE and a shift of the maximum to shorter mixing times.

 There is only one mixing time specified per NOE experiment, and it is the most important parameter for NOE experiments. For small molecules, a mixing time that maximizes the NOE is desirable, unless you intend to calculate an actual distance (see analysis section).  Generally, one is interested in a range of distances so the choice depends on molecular weight rather than a particular distance.  For large molecules, the mixing time must be kept small so that the build-up obeys the linear approximation and spin diffusion is avoided (see analysis section). The following are guidelines:

1)  small molecules 0.5 -1 sec. Start with 0.5 sec.
2)  medium size molecules 0.1 -0.5 sec.  Start with 0.25 sec.
3) large molecules 0.05 - 0.2 sec.  Start with 0.1 sec.

1D versus 2D Methods

 The choice between 2D (ROESY or NOESY) versus 1D (selective NOESY) depends on the amount of material available and the amount of information needed.  A single 2D experiment gives all NOE information simultaneously whereas 1D experiments provide NOEs  one  at a time.   In general, I recommend the 2D methods.  The minimum amount of time required (which does not depend on sample concentration but on the time necessary for experimental cycling) for 2D and 1D differ.   The minimum time for a 2D NOESY spectrum is longer.  The standard 2D NOESY often requires a minimum of 1.5 hours but the 2D NOESY with zero-quantum suppression, which uses gradients, has a minimum time of only 25 minutes. The minimum time for a single 1D selective NOESY spectrum is about 2 minutes.  Many 1D experiments, however, are usually required. If you have very little material, then signal averaging will be required anyway and the 2D version should be used.

 Spectral crowding will affect the choice of experiment.  If critical peaks to be irradiated are very close (<30 Hz) to other peaks, then the selectivity of the 1D version will not be sufficient and the 2D version will be needed.

Artifacts and Their Suppression

 Zero-quantum peaks are a common artifact in all NOESY spectra.  They occur between peaks that are J-coupled, such as ortho-protons on a ring, as can be identified by their up-down DQF-COSY type of pattern.
There is a 2D NOESY sequence that is designed to remove these zero-quantum peaks.

 In ROESY spectra, a common occurrence is TOCSY transfer between protons that are J-coupled or symmetric with respect to the center of the spectrum.  This latter artifact can be removed by proper positioning of o1p, the center of the spectrum. Finally, the cross-peak intensities have an offset dependence. See analysis section for more detail.

 If protons are undergoing chemical exchange, corresponding cross peaks occur in all NOE and ROE experiments.  In fact, chemical exchange can be studied with these same NOE methods and are then termed EXESY experiments.

 In 1D selective NOESY experiments, there are several types of possible artifacts: zero-quantum (up-down) peaks as well as the unsuppressed residual from very intense singlets.   Moreover, the experiment uses selective pulses and their proper calibration is required for optimal results and suppression of artifacts.

Choice of Experiment – a Prescription

 Small molecules (MW < 600)

 The usual choice is 2D NOESY with zero-quantum suppression.  Exceptions would be if you have a very concentrated sample and you are only interested in one or two NOEs and the peaks to be irradiated are well-separated; then choose the 1D selective NOESY.  ROESY has only disadvantages for small molecules.

 Medium sized molecules (700 < MW < 1200)

 ROESY is preferred. 

 Large Molecules (MW > 1200)

 The choice here is more complicated.  The usual choice is 2D NOESY but 2D ROESY has advantages.  ROESY suffers less from spin diffusion and the resulting interpretation errors.  However, ROESY is less sensitive for large molecules and has other disadvantages such as TOCSY artifacts. See analysis section.

Sample Considerations:

 Preparation: Removing Dissolved Oxygen

 Dissolved oxygen or other paramagnetic species such as Cu²⁺ can reduce or completely quench the NOE.  For small molecules, it is extremely important to remove dissolved oxygen.  For   large molecules, the removal of oxygen is not critical.   Removal of oxygen must be done by the freeze-pump-thaw method.  Simply bubbling argon through the sample is not sufficient.   The following describes the freeze-pump-thaw procedure:

1) freeze the sample in liquid nitrogen or CO2/acetone.
2) evacuate the space above the solution.
3) turn off vacuum but keep sample isolated and allow to thaw.   As it thaws, bubbling should be noticed.
4) repeat several times (3-4 times).
5) backfill with N2.
When finished, the sample should, of course, be sealed in some manner.  Tubes with attached stopcocks are available.

 Sample size and tube options

When sample quantity is very limited, it is advantageous to limit the amount of solvent in which it is dissolved.  If a normal 5mm tube is used, however, this cannot be less than about 500mL without causing serious lineshape problems (shimming problems) and the attendant loss of signal-to-noise.   There are special tubes made by Shigemi, however, that can be used to restrict the active volume and, hence, reduce the amount of solvent without causing lineshape problems. Shigemi tubes are available from Aldrich.

 
ANALYSIS – peak identification

 Relative Phase of Cross Peaks

 The phase of  ROE, NOE and chemical exchange cross peaks can be different and are summarized in the figure below. In this figure, it is assumed that protons A and B have an NOE or ROE while protons C and D are undergoing chemical exchange.  Note that the phase behavior differs for large and small molecules. For small molecules, the diagonal peaks and NOE cross peaks have opposite phase. If the diagonal is negative, then NOE cross peaks will be positive.  For large molecules, the diagonal and the NOE cross peaks have the same phase.   The phase of the cross peaks, then, indicates whether the molecule is in the large or small molecule region, which has important implications for quantitation, as discussed below.  Note that this phase behavior is due to the positive/negative nature of NOE described at the beginning of this handout.

 Cross peaks due to chemical exchange, if it is occurring, have the same phase as the diagonal for both small and large molecules in both ROESY and NOESY.

 In ROESY, the diagonal peaks and ROE cross peaks have opposite phase for all molecules since the ROE is always positive.  TOCSY cross peaks are the major artifact in ROESY spectra.  TOCSY peaks have the same phase as the diagonal, and are thus similar to exchange peaks.  TOCSY occurs between spins that are J coupled and that are relatively close in chemical shift.  It also occurs for peaks that are symmetric about o1p.  A possible complication is the relay of ROE through TOCSY resulting in false ROESY cross peaks. For example, geminal methylene peaks often show TOCSY cross peaks.  Assume there is a third proton that should have an ROE to only one of the geminal protons but not its partner.  TOCSY can transfer the ROE to its partner and it may appear as if the third proton has an ROE to both geminal protons.

Spin Diffusion

When analyzing NOESY spectra, one must understand the consequences of spin diffusion.   Spin diffusion occurs primarily for large molecules and for long mixing times outside the “linear approximation”.   In NOESY spectra, spin diffusion can lead to misleading cross peaks and incorrect distances.  In this section, I describe the presence of extra, misleading cross peaks and in the quantitation section, I discuss incorrect distances. Assume there are four protons A, B, and E and F and that A and B, B and E, and E and F are close.  That is, you expect NOEs between those three pairs, as shown in the figure below.  These expected cross peaks between protons that are close are termed direct contributions.  When spin diffusion is present, indirect contributions will also be present and a cross peak between A and C will likely be present.  In spin diffusion, the magnetization follows a path from A to B and then from B to C but appears to be directly from A to C. In NOESY spectra of large molecules, the phase of these indirect peaks is the same as for direct contributions and the resulting cross peaks are impossible to distinguish at a single mixing time. The appearance of the A to C cross peak could lead you to erroneously conclude that protons A and C are close.

 ROESY spectra suffer much less from spin diffusion; the phase of indirect contributions may be different from direct contributions and allows their easy identification.  The phase of indirect contributions alternates with number of steps of transfer.  That is, the phase of 2-step indirect contributions is opposite to direct contributions, while that of 3-step indirect contributions is the same as direct contributions. 3-step contributions are rare, however.  (see Bax, J. Magn. Res. 70, 327-331 (1986))

Analysis – Quantitative Distance Determination

 For organic molecules, it is generally sufficient to classify NOE peak intensities as strong, medium, and weak and make qualitative deductions about relative distances.   If an actual distance is needed, one may use the well-known approach in which the NOE is inversely proportional to the distance to the 6^th  power, i.e.,

r_ij= r_ref (a_ref/a_ij)^1/6

 where a_ij is the NOE cross-peak volume and r_ij is the interproton distance of the the two protons i and j.    Given a known distance between two protons (r_ref) and its NOE volume (a_ref), a distance can calculated from another NOE volume. 

 For this relation to be valid, a strict experimental protocol must followed.   First, the mixing time must be relatively short so that the linear approximation is valid and spin diffusion is avoided. For small molecules, the mixing time must be less than several hundred milliseconds.  For large molecules, there may be no practical value for a mixing time that completely avoids spin diffusion but, in general, the mixing time must be less than 100 msec.  Whether spin diffusion leads to an apparent increase or decrease in distance depends on the details of the molecular geometry. Linear geometries lead to shorter apparent distances while non-linear geometries may lead to longer  distances (See Neuhaus and Williamson p117-122) To help ensure that the mixing time is within the linear region, a build-up curve is performed. A build-up curve is a series of NOE spectra taken at different mixing times.  If one is within the linear region, then the NOE will linearly increase with mixing time.   A second requirement for quantitative work is that the relaxation delay must be long enough to allow reasonable recovery of the magnetization between scans.  The normal time of 2 sec for D1 is not sufficient and one must increase this. The proper D1 should be at least 3 times T₁. A T₁ determination may be necessary.

Effect of Conformational Mobility

 The purpose of running a NOESY is often to determine conformation by establishing a distance between two protons.  When more than one conformation is present, however, the NOE may give misleading distances.  If the conformations are being averaged over the time scale of the experiment (the mixing time) the NOE will not reflect the average distance between the protons but rather the average of the inverse sixth power of the distance.  Since

the effective distance for NOE is less than the average distance, r_eff < r_ave. and the effective distance is weighted towards that of  the “closest approach”.  For example, assume there are two conformations A and B and that the A conformation is 10% populated.  If the protons are 0.2 nm apart in conformation A and 0.6 nm apart in conformation B, then the effective distance is 0.293 nm which is much closer than the 0.6 nm separation that is present in the dominant conformer.  This is summarized in the table below. Thus, in such cases the NOE will reflect the conformation where the protons are closer.

 ROESY – Quantitative Distance Determination

In addition to the above considerations for NOESY, the ROESY has additional complications.   The cross peak intensities have an offset dependence relative to the transmitter center, o1p.  Cross-peaks are less intense the further they are from the center, regardless of spatial distance. For example, assuming o1p is 5 ppm, then a cross-peak between protons at 1 and 2 ppm will have lower intensity than between protons at 4 and 5 ppm, even if they have the same interproton distance.   This dependence is well characterized and can be corrected in the following way (see Ammalahti, et al.. J. Magn. Res. A, 122, 230-232 (1996)).  Distances are calculated from corrected intensities:

 r_ij= r_ref (a_refc_ref/a_ijc_ij)^1/6

 where

 c_ij= 1/(sin²q_isin²q_j)

 and

 tanq_I = gB₁/(w_I -w₀)

 where (w_I -w₀) is the difference between the chemical shift of the peak (in Hz) and o1p (in Hz) and gB₁ is the spin lock power (which is about 2500 Hz in our case).  Volume corrections of up to a factor of 4, in far off-resonance cases, may be required.

 An additional complication with quantitation of ROESY spectra is that TOCSY transfer may occur and cancel or partially cancel ROESY cross peaks.  This obviously has deleterious effects on distance determination.  This is a particular problem for the reference ROE for which a J-coupled methylene pair is often chosen.    See John Decatur for advice if detailed distance information is needed.