Equilibrium NOE

Establishing NOEs and hence spatial proximity between protons. Suitable only for small molecules (Mr < KXX)), for which NOEs are positive. Observes steady-state or equilibrium NOEs generated from the saturation of a target. 

The clear advantages of the gradient-selected NOE experiment over the conventional steady-state NOE difference means this is becoming a popular tool in small molecule structural studies. However, there are fundamental differences between the data presented by the two experimental protocols, with steady-state experiments observing equilibrium NOEs and transient experiments observing kinetic NOEs. As a consequence, ID NOESY experiments demand a somewhat different approach to data interpretation over that currently adopted for steady-state NOE difference measurements, some of the key considerations include ... 

The interval between the second and third pulse is called the mixing time, during which the spins evolve according to the multiple-spin version of equation B 1.13.2 and equation B 1.13.3 and the NOE builds up. The final pulse converts the longitudinal magnetizations, present at the end of the mixing time, into detectable transverse components. The detection of the FID is followed by a recycle delay, during which the equilibrium... 

To understand how nOe occurs, we have to consider the following situations (a) the populations of the nucleus I prevailing at thermal equilibrium before the application of the Rf pulse on nucleus S, (b) populations immediately after the pulse is applied to nucleus S, and (c) populations after the system has had some time to respond, with either 1% or being the predominant relaxadon pathway. 

Since the equilibrium state has been disturbed, the system tries to restore equilibrium. For this it can use as the predominant relaxation pathways the double-quantum process (in fast-tumbling, smaller molecules), leading to a positive nOe, or the zero-quantum process 1% (in slower-tumbling macromolecules), leading to a negative nOe. 

The nOe difference spectrum has the advantage that it allows measurements of small nOe effects, even 1% or below. The experiment involves switching on the decoupler to allow the buildup of nOe. It is then switched off, and a w/2 pulse is applied before acquisition. The nOe is not affected much by the decoupler s being off during acquisition, since the nOes do not disappear instantaneously (the system takes several Ti seconds to return to its equilibrium state). 

If only single-quantum transitions (h, I2, S], and S ) were active as relaxation pathways, saturating S would not affect the intensity of I in other words, there will be no nOe at I due to S. This is fairly easy to understand with reference to Fig. 4.2. After saturation of S, the fMjpula-tion difference between levels 1 and 3 and that between levels 2 and 4 will be the same as at thermal equilibrium. At this point or relaxation processes act as the predominant relaxation pathways to restore somewhat the equilibrium population difference between levels 2 and 3 and between levels 1 and 4 leading to a negative or positive nOe respectively. 

Transient nOe represents the rate of nOe buildup. The nOe effect (so-called equilibrium value) itself depends only on the competing balance between various complex relaxation pathways. But the initial rate at which the nOe grows (so-called transient nOe) depends only on the rate of cross-relaxation t, between the relevant dipolarly coupled nuclei, which in turn depends on their internuclear distance (r). 

Three-spin effects arise when the nonequilibrium population of an enhanced spin itself acts to disturb the equilibrium of other spins nearby. For example, in a three-spin system, saturation of spin A alters the population of spin B from its equilibrium value by cross-relaxation with A. This change in turn disturbs the whole balance of relaxation at B, including its cross-relaxation with C, so that its population disturbance is ultimately transmitted also to C. This is the basic mechanism of indirect nOe, or the three-spin effect. 

If all nuclei are assigned and the spectral parameters for the conformational analysis are extracted, a conformation is calculated - usually by distance geometry (DG) or restrained molecular dynamics calculations (rMD). A test for the quality of the conformation, obtained using the experimental restraints, is its stability in a free MD run, i.e. an MD without experimental restraints. In this case, explicit solvents have to be used in the MD calculation. An indication of more than one conformation in fast equilibrium can be found if only parts of the final structure are in agreement with experimental data [3]. Relaxation data and heteronuclear NOEs can also be used to elucidate internal dynamics, but this is beyond the scope of this article. 

Now if S is strongly irradiated, then it is saturated and S is no longer at its Boltzmann equilibrium. Therefore it cannot maintain the Boltzmann equilibrium of spins 7, and the intensity of the 7 signal is changed. Equalizing S populations produces a proportional change in 7 populations such that equation 3.41 can be written in which r IS is called the nuclear Overhauser enhancement (NOE) factor. 

The steady-state heteronuclear 15N 1H NOEs are determined as a ratio of cross-peak intensities in two experiments, with and without presaturation of amide 1H nuclear spins, usually referred to as NOE and NONOE experiments, respectively. Magnetization exchange between amide protons and water protons could affect the equilibrium 1H magnetization in the NONOE experiment, and thereby increase the measured NOE values. 

The effect could be considerable for solvent-exposed parts of the backbone and could render the NOE values inaccurate. These systematic errors could be minimized by using water flip-back pulses in order to avoid saturation of H20 magnetization [11]. The NOE data are generally more susceptible to errors than Ri and R2 because (i) the NOE experiments start with the equilibrium 15N magnetization that is 10 fold lower than that of (XH) in the Hi and R2 experiments, hence relatively low sensitivity, and (ii) the NOE values are derived from only two sets of measurements, whereas R1 and R2 data are obtained from fitting multiple sets of data the latter is expected to result in a more efficient averaging of experimental errors. 

In the isotope edited/ filtered spectra of a protein-ligand complex, the species actually observed is generally the complex itself. This is an important difference from transferred NOE or saturation difference techniques, where the existence of an equilibrium between free and bound species - and a certain rate of exchange between them - is essential (Chapts. 13 and 16). The general conditions for isotope filtering/editing are therefore identical to those required for standard protein NMR sample concentrations are usually limited by availability and solubility of the components to the order of 1 mM. Considerably lower concentrations will reduce the sensitivity of the experiments to unacceptable levels,... 

Nuclear Overhauser enhancement spectroscopy ( H- H NOESY and NOE) experiments show only the TTC isomer in equilibrium with the TTT isomer for 6,8-dinitro-BIPS [36,55] and 6-nitro,8-bromo-BIPS. The TTC form dominates the equilibrium. Spectral broadening for several proton resonances in the spectra of 6,8-dinitro-BIPS and 6-nitro,8-bromo-BIPS indicate a rapid exchange between these two isomeric forms. The activation energy for this isomerisation is reported to be 43.6 kJ mol and the energy difference between the the TTC and TTT forms is 4.6 kJ mol [55]. 

Two independent NOE experiments on NOSH merocyanine [88,98] show that the TTC isomer is the most stable form in solution, but one of these studies also reported that the CTC isomer is also present in equilibrium [88]. These two isomeric forms are in rapid exchange on the H-NMR time scale, as we see only... 

Abe and co-workers [89] worked on the spiro-oxazine system NOSI6 shown in Scheme 13 and found markedly different ring-closure kinetics. Note that in the case of Abe and co-workers compound NOSI6, there are no unfavorable interactions between the proton on the naphthalene and the methine proton in either the TTT and CTT forms. In fact, TTT and CTT should be the most planar forms. Compare that to the case of the NOSH merocyanine, which was studied using H-NOE and found to be an equilibrium mixture of TTC and CTC [88]. Ring closure would clearly be a more favorable series of rotations to form the closed-form geometry for CTC and TTC than it would be for CTT and TTT. 

In the systems that I have examined, I can satisfy the dynamic requirements with a ten second pulse delay. The longest methyl T] may be 3 seconds. In general, the longer the side chain, the longer will be the methyl Tj. We will hear more about this subject later on. We need not be too concerned about NOE factors because they are usually full under the experimental conditions (T = 120-130°C) used for polymer quantitative measurements. The Tj problem can be handled, even under non-equilibrium conditions, by utilizing resonances from the same types of carbon atoms in a quantitative treatment. Such an approach can sometimes lead to more efficient quantitative NMR measurements. Adequate pulse spaclngs will have to be used whenever one wishes to utilize all of the observed resonances. Quantitative measurements in branched polyethylenes are very desirable because this is one of the best applications of analytical polymer C-13 NMR. 

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