NOE Experiments



When a proton is saturated orinverted, spatially-close protons may experience an intensity enhancement, whichis termed the Nuclear Overhauser Effect (NOE). The NOE is unique among NMRmethods because it does not depend upon through-bond J couplings but dependsonly on the spatial proximity between protons.  In other words, the strength of the NOE gives information onhow close two protons are.  Forsmall molecules, an NOE may be observed between protons that are up to 4Āapart, while the upper limit for large molecules is about 5Ā.


There are many differentpossible NOE experiments (NOE or ROE, steady-state or transient, 1D or 2D,etc).  The ones available on the400 and 500 are 1D selective-NOESY, 2D-NOESY, 2D-NOESY with zero-quantumsuppression, and 2D-ROESY.   Some understanding of the theory of NOE is necessary for choosing thecorrect experiment and for interpreting it properly.  Some of the important results from the theory are discussedbelow.  For a full understanding,see the excellent text Neuhaus, David, and Williamson, Michael P., TheNuclear Overhauser Effect in Structural and Conformational Analysis, 2nd ed., WILEY-VCH, New York, 2000.



Molecular Weight andMaximum NOE


The maximum possible NOEdepends on the molecular correlation time (or the inverse of the rate ofmolecular tumbling), which is in large part determined by the molecular weightand solvent viscosity.  Largermolecular 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 NOEmay be theoretically zero.  Seethe figure below that is adapted from Newhaus and Williamson text. The ROESYexperiment (rotating frame NOE) is preferred for medium-sized molecules sincethe 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 torelaxation during the mixing time, as shown below in the plot of NOE versusmixing time. The NOE, thus, goes through a maximum as function of mixingtime.  The location of the maximumNOE and rate of build-up depend on the correlation time, or its proxy, themolecular weight, and the distance between protons for a particular NOE.  In general, large molecules build-upNOE quickly while small molecules build-up NOE more slowly. That is, for largemolecules the point of maximum NOE is shifted to shorter mixing times.  A shorter distance between protons willalso lead to faster build-up of NOE and a shift of the maximum to shortermixing times.


There is only one mixing timespecified per NOE experiment, and it is the most important parameter for NOEexperiments. For small molecules, a mixing time that maximizes the NOE isdesirable, unless you intend to calculate an actual distance (see analysissection).  Generally, one isinterested in a range of distances so the choice depends on molecular weightrather than a particular distance. For large molecules, the mixing time must be kept small so that the build-upobeys the linear approximation and spin diffusion is avoided (see analysissection). 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 - 0.2sec.  Start with 0.1 sec.


1D versus 2D Methods


The choice between 2D (ROESYor NOESY) versus 1D (selective NOESY) depends on the amount of materialavailable and the amount of information needed.  A single 2D experiment gives all NOE informationsimultaneously whereas 1D experiments provide NOEs  one  at atime.   In general, Irecommend the 2D methods.  The minimum amount of time required(which does not depend on sample concentration but on the time necessary for experimentalcycling) for 2D and 1D differ.  The minimum time for a 2D NOESY spectrum is longer.  The standard 2D NOESY often requires aminimum of 1.5 hours but the 2D NOESY with zero-quantum suppression, which usesgradients, has a minimum time of only 25 minutes. The minimum time for a single1D selective NOESY spectrum is about 2 minutes.  Many 1D experiments, however, are usually required. If youhave very little material, then signal averaging will be required anyway andthe 2D version should be used.


Spectral crowding will affectthe choice of experiment.  Ifcritical peaks to be irradiated are very close (<30 Hz) to other peaks, thenthe selectivity of the 1D version will not be sufficient and the 2D versionwill be needed.


Artifacts and Their Suppression


Zero-quantum peaks are acommon artifact in all NOESY spectra. They occur between peaks that are J-coupled, such as ortho-protons on aring, as can be identified by their up-down DQF-COSY type of pattern.

There is a 2D NOESY sequencethat is designed to remove these zero-quantum peaks.


In ROESY spectra, a commonoccurrence is TOCSY transfer between protons that are J-coupled or symmetricwith respect to the center of the spectrum.  This latter artifact can be removed by proper positioning ofo1p, the center of the spectrum. Finally, the cross-peak intensities have anoffset dependence. See analysis section for more detail.


If protons are undergoingchemical exchange, corresponding cross peaks occur in all NOE and ROEexperiments.  In fact, chemicalexchange can be studied with these same NOE methods and are then termed EXESYexperiments.


In 1D selective NOESYexperiments, there are several types of possible artifacts: zero-quantum(up-down) peaks as well as the unsuppressed residual from very intensesinglets.   Moreover, theexperiment uses selective pulses and their proper calibration is required foroptimal results and suppression of artifacts.


Choice of Experiment– a Prescription


Small molecules (MW < 600)


Theusual choice is 2D NOESY with zero-quantum suppression.  Exceptions would be if you have a veryconcentrated sample and you are only interested in one or two NOEs and thepeaks to be irradiated are well-separated; then choose the 1D selectiveNOESY.  ROESY has onlydisadvantages for small molecules.


Medium sized molecules (700< MW < 1200)


ROESYis preferred. 


Large Molecules (MW >1200)


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


Sample Considerations:

Preparation:Removing Dissolved Oxygen


Dissolved oxygen or otherparamagnetic species such as Cu2+ can reduce or completely quenchthe NOE.  For small molecules, it is extremelyimportant to remove dissolved oxygen. For   large molecules,the removal of oxygen is not critical.   Removal of oxygen must be done by the freeze-pump-thawmethod.  Simply bubbling argonthrough the sample is not sufficient.   The following describes the freeze-pump-thawprocedure:

1) freeze the sample inliquid nitrogen or CO2/acetone.

2) evacuate the space abovethe solution.

3) turn off vacuum but keepsample isolated and allow to thaw.  As it thaws, bubbling should be noticed.

4) repeat several times (3-4times).

5) backfill with N2.

When finished, the sampleshould, of course, be sealed in some manner.  Tubes with attached stopcocks are available.


Sample size and tube options


When sample quantity is verylimited, it is advantageous to limit the amount of solvent in which it isdissolved.  If a normal 5mm tube isused, however, this cannot be less than about 500mL without causing serious lineshape problems (shimmingproblems) and the attendant loss of signal-to-noise.   There are special tubes made by Shigemi, however, thatcan be used to restrict the active volume and, hence, reduce the amount ofsolvent without causing lineshape problems. Shigemi tubes are available fromAldrich.



ANALYSIS – peakidentification


Relative Phase of Cross Peaks


Thephase of  ROE, NOE and chemicalexchange 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 whileprotons C and D are undergoing chemical exchange.  Note that the phase behavior differs for large and smallmolecules. For small molecules, the diagonal peaks and NOE cross peaks haveopposite phase. If the diagonal is negative, then NOE cross peaks will bepositive.  For large molecules, thediagonal and the NOE cross peaks have the same phase.   The phase of the cross peaks, then, indicates whetherthe molecule is in the large or small molecule region, which has importantimplications for quantitation, as discussed below.  Note that this phase behavior is due to thepositive/negative nature of NOE described at the beginning of this handout.


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


InROESY, the diagonal peaks and ROE cross peaks have opposite phase for allmolecules since the ROE is always positive.  TOCSY cross peaks are the major artifact in ROESYspectra.  TOCSY peaks have the samephase as the diagonal, and are thus similar to exchange peaks.  TOCSY occurs between spins that are Jcoupled and that are relatively close in chemical shift.  It also occurs for peaks that aresymmetric about o1p.  A possiblecomplication is the relay of ROE through TOCSY resulting in false ROESY crosspeaks. For example, geminal methylene peaks often show TOCSY cross peaks.  Assume there is a third proton thatshould have an ROE to only one of the geminal protons but not its partner.  TOCSY can transfer the ROE to itspartner and it may appear as if the third proton has an ROE to both geminalprotons.





Spin Diffusion


When analyzing NOESY spectra,one must understand the consequences of spin diffusion.   Spin diffusion occursprimarily for large molecules and for long mixing times outside the “linearapproximation”.   In NOESYspectra, spin diffusion can lead to misleading cross peaks and incorrectdistances.  In this section, Idescribe the presence of extra, misleading cross peaks and in the quantitationsection, I discuss incorrect distances. Assume there are four protons A, B, andE and F and that A and B, B and E, and E and F are close.  That is, you expect NOEs between thosethree pairs, as shown in the figure below.  These expected cross peaks between protons that are closeare termed direct contributions. When spin diffusion is present, indirect contributions will also bepresent and a cross peak between A and C will likely be present.  In spin diffusion, the magnetizationfollows a path from A to B and then from B to C but appears to be directly fromA to C. In NOESY spectra of large molecules, the phase of these indirect peaksis the same as for direct contributions and the resulting cross peaks areimpossible to distinguish at a single mixing time. The appearance of the A to Ccross peak could lead you to erroneously conclude that protons A and C areclose.


ROESY spectra suffer muchless from spin diffusion; the phase of indirect contributions may be differentfrom direct contributions and allows their easy identification.  The phase of indirect contributionsalternates with number of steps of transfer.  That is, the phase of 2-step indirect contributions isopposite to direct contributions, while that of 3-step indirect contributionsis 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 isgenerally sufficient to classify NOE peak intensities as strong, medium, andweak 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 proportionalto the distance to the 6th power, i.e.,


rij= rref (aref/aij)1/6


where aij is the NOE cross-peak volume and rijis the interproton distance of the the two protons i and j.    Given a known distancebetween two protons (rref) and its NOE volume (aref), a distancecan calculated from another NOE volume. 


For this relation to bevalid, a strict experimental protocol must followed.   First, the mixing time must be relatively short sothat the linear approximation is valid and spin diffusion is avoided. For smallmolecules, the mixing time must be less than several hundred milliseconds.  For large molecules, there may be nopractical value for a mixing time that completely avoids spin diffusion but, ingeneral, the mixing time must be less than 100 msec.  Whether spin diffusion leads to an apparent increase ordecrease in distance depends on the details of the molecular geometry. Lineargeometries lead to shorter apparent distances while non-linear geometries maylead to longer  distances (SeeNeuhaus and Williamson p117-122) To help ensure that the mixing time is withinthe linear region, a build-up curve is performed. A build-up curve is a seriesof NOE spectra taken at different mixing times.  If one is within the linear region, then the NOE willlinearly increase with mixing time.  A second requirement for quantitative work is that the relaxationdelay must be long enough to allow reasonable recovery of the magnetizationbetween scans.  The normal time of2 sec for D1 is not sufficient and one must increase this. The proper D1should be at least 3 times T1. A T1 determination may benecessary.


Effect ofConformational Mobility


The purpose of running aNOESY is often to determine conformation by establishing a distance between twoprotons.  When more than oneconformation is present, however, the NOE may give misleading distances.  If the conformations are being averagedover the time scale of the experiment (the mixing time) the NOE will notreflect the average distance between the protons but rather the average of theinverse sixth power of the distance. Since



the effective distance forNOE is less than the average distance, reff < rave.and the effective distance is weighted towards that of  the “closest approach”.  For example, assume there are twoconformations A and B and that the A conformation is 10% populated.  If the protons are 0.2 nm apart inconformation A and 0.6 nm apart in conformation B, then the effective distanceis 0.293 nm which is much closer than the 0.6 nm separation that is present inthe dominant conformer.  This issummarized in the table below. Thus, in such cases the NOE will reflect theconformation where the protons are closer.




ROESYQuantitativeDistance Determination


In addition to the aboveconsiderations for NOESY, the ROESY has additional complications.   The cross peak intensities havean offset dependence relative to the transmitter center, o1p.  Cross-peaks are less intense thefurther 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 willhave lower intensity than between protons at 4 and 5 ppm, even if they have thesame interproton distance.  This dependence is well characterized and can be corrected in thefollowing way (see Ammalahti, et al.. J. Magn. Res. A, 122, 230-232(1996)).  Distances are calculatedfrom corrected intensities:


rij= rref (arefcref/aijcij)1/6




cij= 1/(sin2qisin2qj)




tanqI = gB1/(wI -w0)


where (wI -w0) is the difference between the chemicalshift of the peak (in Hz) and o1p (in Hz) and gB1 is the spin lock power (which is about2500 Hz in our case).  Volumecorrections of up to a factor of 4, in far off-resonance cases, may be required.


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