Cross-correlation effects

General base catalysis of the reaction of a nucleophile (HNu) is kinetically equivalent to general acid catalysis of the reaction of the deprotonated nucleophile (Nu ). A distinction can be made employing cross-correlation effects where the value of the Bronsted a is measured as a function of another parameter such as the nucleophilicity of the attacking nucleophile. 

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The cross-correlation effects between the DD and CSA interactions also influence the transverse relaxation and lead to the phenomenon known as differential line broadening in a doublet [40], cf Figure Bl.13.8. There is a recent experiment, designed for protein studies, that I wish to mention at tire end of this section. It has been proposed by Pervushin etal [4T], is called TROSY (transverse relaxation optimized spectroscopy) and... 

The relaxation data for the anomeric protons of the polysaccharides (see Table II) lack utility, inasmuch as the / ,(ns) values are identical within experimental error. Obviously, the distribution of correlation times associated with backbone and side-chain motions, complex patterns of intramolecular interaction, and significant cross-relaxation and cross-correlation effects dramatically lessen the diagnostic potential of these relaxation rates. 

Cross-correlation effects between 15N CSA and 1H-15N dipolar interactions [10] will result in different relaxation rates for the two components of the 15N spin doublet, which could significantly complicate the analysis of the resulting bi-exponential decay of the decoupled signal in T, or T2 experiments. To avoid this problem, 180° 1H pulses are applied during the 15N relaxation period [3, 4], which effectively averages the relaxation rates for the two components of the 15N spin doublet... 

In addition, cross-correlation effects between 15N CSA and 1H-15N dipolar interaction could be measured, see e.g. Refs. [24-26] ... 

Fig. 4. Pulse sequences for determining spin-spin relaxation time constants. Thin bars represent 7t/2 pulses and thick bars represent tt pulses, (a) the CPMG sequence, (b) the spin-lock sequence used for determining T p and (c) a two-dimensional proton-detected INEPT-enhanced CPMG. T is the waiting period between individual scans. The pulse train during the T period is used for suppression of cross-correlation effects, and the delay S is set to < (1/2)J. The delay A in (c) is set to (1/4)Jih and A is set to (1/4)Jih to maximize the intensity of IH heteronuclei and to (1 /8) Jm to maximize the intensity of IH2 spins. The phase cycling in (c) is as follows i = y,—y 2 = 2 x),2 —x), i = 8(x), 8(—x) Acq = x, 2(—x), x, —x, 2(x), —x, —x, 2(x), —x,x, 2(—x), x. The onedimensional version the proton-detected experiment can be obtained by omitting the ti delay.

For a spin-1/2 nucleus, such as carbon-13, the relaxation is often dominated by the dipole-dipole interaction with directly bonded proton(s). As mentioned in the theory section, the longitudinal relaxation in such a system deviates in general from the simple description based on Bloch equations. The complication - the transfer of magnetization from one spin to another - is usually referred to as cross-relaxation. The cross-relaxation process is conveniently described within the framework of the extended Solomon equations. If cross-correlation effects can be neglected or suitably eliminated, the longitudinal dipole-dipole relaxation of two coupled spins, such... 

In the case of T measurements we have mentioned that cross relaxation provides multiexponential magnetization recovery (Sections 1.7.4 and 7.2.2). A far less known analogy may occur in the linewidths, as already discussed (Section 8.8) when two protons are dipole-dipole coupled and cross correlation occurs between Curie relaxation and proton-proton dipolar relaxation. In this case, we are in the presence of two overlapping signal components with different linewidths, i.e. of biexponentiality in T2 [35], Pulse sequences are available to remove the effects of cross correlation [36]. Such effects are common in paramagnetic metalloproteins where Curie relaxation is usually relevant (in principle, such cross correlation effects can be operative also in the case of 7i, although only to the extent that Curie relaxation on T is effective). 

The exploitation of cross-correlation effects in high magnetic fields has introduced a new form of NMR spectroscopy called transverse relaxation-optimised spectroscopy or TROSY. The cross-correlation of the optimised dipole-dipole (DD) and chemical shift anisotropy (CSA) relaxation mechanisms leads to differential transverse relaxation rates for the two components of the l5N- H doublet in undecoupled spectra of l5N-labelled proteins. For one component, DD and CSA relaxation constructively add to produce very efficient relaxation, leading to a broad line, whereas for the other component, the two relaxation mechanisms constructively interfere, leading to a narrow line when the two mechanisms are nearly equal. There is no optimum field where DD and CSA relaxation are equal for all amide bonds, because DD relaxation between the amide protons and other nearby protons differs for each residue.72 Clearly, the overall effectiveness of TROSY is optimized when the non-exchangeable protons in the macromolecule... 

Kupriyanov studied relaxation of spin 1/2 in the scalar coupled spin system AMX with quadrupolar nuclei in the presence of cross correlation effects. Khaneja et a/. presented optimal control of spin dynamics in the presence of relaxation. Eykyn et a/. studied selective cross-polarization in solution state NMR of scalar coupled spin 1/2 and quadrupolar nuclei. Tokatli applied the product operator theory to spin 5/2 nuclei. Mahesh et a/. used strongly coupled spins for quantum information processing. Luy and Glaser " inves-... 

Dipolar Couplings and Distance Information. - The nuclear Overhauser effect (NOE) arises from dipolar interactions between magnetic moments associated with nuclear spins and it has become a powerful tool to extract relevant pieces of structural information about small molecules, as well as in molecules of biological interest. As a consequence, accurate NOE measurement is a very crucial issue. Walker et presented a comparison between direct and a new inverse HOESY experiment aimed at the detection of heteronuclear NOE between H and which is particularly well suited for symmetric compounds. It transpires that directly detected data are more suitable for quantitative assessment even if they suffer from lower sensitivity, whereas inverse detection is quite appropriate for a quick and quahtative assessment. In the latter experiment, unwanted cross-correlation effects may hide valuable NOE data (cross-relaxation), this drawback can be circumvented by a slight modification of the pulse sequence. 

NMR relaxation data depend on dipolar ( N and C) and quadrupolar ( H) interactions on chemical shift anisotropy and cross-correlation effects. It is well known that the NMR relaxations can be written as functions of the spectral densities of the magnetic interactions, and this is the intersecting point between macroscopic and microscopic descriptions The spectral densities are calculated within the theoretical framework describing the dynamics of the system. 

Bendall, M. R. and Pegg, D. T. Identification of isolated methyl groups by detection of cross-correlation effects using polarization transfer. J. Magn. Reson. 53 40-48, 1983. 

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