Heteronuclear internuclear distances

For heteronuclear dipolar relaxation, the dipole-dipole coupling between two unlike spin- nuclei / and S (e.g., 13C-H pair) separated by an internuclear distance rIS is considered. The Zeeman spin-lattice (7jz) and spin-spin (T2) relaxation times for the / spin are given, respectively, by... 

Multidimensional NMR spectra are not restricted to cases where the separate frequency axes encode signals from different nuclear types. Indeed, much of the early work on the development of 2D NMR was performed on cases where both axes involved chemipal shifts. The main value in such spectra comes from the information content in cross peaks between pairs of protons. In COSY-type spectra (COSY = Correlation SpectroscopY) cross peaks occur only between protons that are scalar coupled (i.e., within 2 or 3 bonds) to each other, whereas in NOESY (NOE Spectroscopy) spectra cross peaks occur for protons that are physically close in space (<5 A apart). A combination of these two types of 2D spectra may be used to assign the NMR signals of small proteins and provides sufficient information on internuclear distances to calculate three-dimensional structures. Figure 12.3 includes a panel showing the COSY spectrum of cyclosporin and highlights the relationships between ID H-NMR spectra and corresponding 2D homonuclear (COSY) and heteronuclear (HSQC) spectra. 

As mentioned above, the determination of atomic level structure, i.e., the backbone torsion angles for an oriented protein fiber, is possible by using both solid-state NMR method described here and specifically isotope labeling. This is basically to obtain the angle information. Another structural parameter is distance between the nuclei for atomic coordinate determination. The observation of Nuclear Overhauser Enhancements (NOEs) between hydrogen atoms is a well known technique to determine the atomic coordinates of proteins in solution [14]. In the field of solid-state NMR, REDOR (rotational echo double resonance) for detection of weak heteronuclear dipole interactions, such as those due to C and N nuclei [15, 16] or R (rotational resonance) for detection of the distance between homonuclei, are typical methods for internuclear distance determination [17,18]. The REDOR technique has been applied to structure determination of a silk fibroin model compound [19]. In general, this does not require orientation of the samples in the analysis, but selective isotope labeling between specified nuclear pairs in the samples is required which frequently becomes a problem. A review of these approaches has appeared elsewhere [16]. 

Measurement of the heteronuclear dipolar couplings defines the use of solid-state NMR spectroscopy for determination of internuclear distances. The main part of such experiments involves refocusing of the heteronuclear dipolar couplings. The REDOR experiment has been used extensively to determine the internuclear distances ( C- N, C- P... 

Temperature Dependence of Spin-Lattice Relaxation. The spin-lattice relaxation rate T ) is comprised of various contributions to the relaxation process, including homo- and heteronuclear dipolar interactions, quadrupolar interactions, chemical shift anisotropy, spin-rotation, and others (10). When the relaxation mechanism is dominated by inter- and intramolecular dipole-dipole interactions, the will increase with temperature, pass through a maximum, and decrease with increasing temperature. Since the relaxation rate is the inverse of the relaxation time, the Ti will decrease, pass through a minimum (Timin), and then increase with increasing temperature (77). The T lmin values are proportional to the internuclear distances. 

Table 9.3. Heteronuclear pairs of noble gas atoms well depths, Dm minimum-energy internuclear distances, Rta, and the sum of their van der Waals radii, rw(A) + r y(B). ...

The technique mainly applied on isotopic labeled compounds has been used in many different cases. By fitting the experimental dephasing curve of a sample of C- N labeled (10%) glycine a C- N dipolar coupling constant of 195 Hz was obtained that corresponds to a C- N internuclear distance of 2.47 A. The limit value of the heteronuclear dipolar coupling constant is around 25 Hz, then useful structure information can be obtained at distances that cannot exceed 5 A in the case of C- N and 7.5 A in the case of C- P distances. 

The introduction of and/or labels into a protein facilitates the study of dynamic properties and, in particular, localized intramolecular motions. This arises because relaxation of these nuclei is usually dominated by dipole-dipole interactions with the directly bonded proton and this relaxation is dependent upon internuclear distance (which is fixed) and the rotational correlation time, which is only uniform throughout a rigid protein. Proteins, however, usually contain regions that have greater flexibility, such as surface loops, which have different local correlation times that are reflected in heteronuclear relaxation times. 

Figure 11.15 The results of the Luliucci et al. 2006 2D heteronuclear correlation (HetCOR) study of an aged silicone engineering elastomer, Dow Corning DC745 [82]. The results show increased coupling (thus decreased internuclear distance) between polymer and silica surface. The H chemical shifts are horizontal, while the Si shift is vertical. Reproduced with permission from [82] Copyright (2006) John WUey and Sons.

Judeinstein et al have conducted direct measurement of through-space NMR interactions that provide definitive evidence for spatial proximity of different species. Dipole-dipole interactions can be measured in principle between any NMR active nuclei with heteronuclear correlation experiments in the liquid or solid state." The dipole-dipole interactions decay quickly with the internuclear distances (r ), and are difficult to evaluate for long-range distances and even more difficult when exchange, conformation, or motion phenomena are present. However, the measurement of the nuclear Overhauser method" based on the dipole-dipole-induced crossrelaxation, was proposed to successfully measure intermolecular interactions" and the formation of ion pairs." " In agreement with recent studies, the pulsed field gradient enhanced inverse HOESY (heteronuclear Overhauser enhancement spectroscopy) sequence is usually preferred because it is more sensitive for isotope pairs H- Li and also improves the digital resolution in the H crowded spectrum." ... 

The anisotropic heteronuclear dipole-dipole interaction is a function of not only the distance between two nuclei but also the orientation of the internuclear vector with respect to Bq. Therefore, the dipolar coupling values directly provide geometrical parameters that can be translated into molecular conformations. For example, H- N, C- N, and H- C dipolar couplings are commonly used to determine the relative orientations of the chemical bonds, which are converted into the conformation and/or the topology of molecules using NMR methods.5 5" ... 

In the last decades a series of homonuclear and heteronuclear recoupling experiments have been developed that combine a 2D approach with fast MAS and dipolar multiple-quantum NMR spectroscopy. In this way, the chemical shift resolution of different chemical environments allows sites of interest to be distinguished and fully identified, and then it is possible to obtain structural information since dipole-dipole couplings are sensitive to the distances between the coupled nuclei as well as to the orientation of the internuclear vector. 

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