Heteronuclear dipolar couplings

Rotational-echo double-resonance (REDOR)(75,79) is a new solid-state NMR technique which is sensitive to through-space carbon-nitrogen interactions between selectively 13C and 15N-enriched sites separated by up to 5A (20-22). The parameter directly measured in a REDOR experiment is the heteronuclear dipolar coupling constant DCN, which is in itself proportional to the inverse third power of the intemuclear distance, rCN. It is this dependence on (icn)3 which accounts both for REDOR s ability to accurately measure short distances and its insensitivity to longer-range interactions. As a technique which can probe, in detail, intermolecular interactions over a distance range of 5A, REDOR is well suited to studying the distribution of small selectively-labeled molecules in polymer delivery systems. 

The PAR experiment may be described by considering two heteronuclear dipolar coupling interactions with one proton (7) in common, i.e., a Hamiltonian of the type... 

In the simplest setup, the two strong field components may be set identical to Ci = Cs = C. The relatively large CIX or CSX term averages isotropic and anisotropic chemical shift effects as well as the heteronuclear dipolar coupling interaction between 15N or 13C and H. The difference of - or the sum of - the B coefficients selects the form of the recoupled heteronuclear dipole-dipole coupling interaction, as expressed in terms of the effective Hamiltonian in the interaction frame of the rf irradiation... 

Fig. 10.22. Diagram showing the cross-polarization from protons, H, to a heteronucleus, X, such as carbons. Heteronuclear dipolar coupling enables the transfer of magnetization from H to X, such as protons to carbons. Homonuclear dipolar coupling between the abundant protons enables the redistribution of proton spin energy through spin diffusion.

The wide structural application of dipolar couplings is demonstrated by its use to validate models built by sequence homology methods. Additionally, dipolar couplings have been shown to reduce the RMSD between these models and the target structure. One example is the work reported by Chou et al., in which the RMSD of sequence homology models of the protein calmodulin, built from the structure of recoverin and parvalbumin, is reduced using heteronuclear dipolar couplings [110]. 

Composite-pulse decoupling schemes like WALTZ [36, 37], DIPSI [38], or GARP [39], which are used in solution-state NMR, have failed to offer any significant improvements in the solid state compared to CW decoupling. The residual line width in CW-decoupled spectra is dominated by a cross term between the chemical-shielding tensor of the protons and the heteronuclear dipolar-coupling tensor [40, 41]. 

Rotational-echo double resonance (REDOR), originally introduced by Gullion and Schaefer [102], is a method to recouple heteronuclear spin pairs. The sequence relies on a train of rotor-synchronized n pulses applied to the I spin to interrupt the spatial averaging of the heteronuclear dipolar coupling under MAS to give a nonvanishing dipolar Hamiltonian over a full rotor cycle (Fig. 11.8). Typically, REDOR data are collected by col-... 

Fig. 11.15 Diagram showing the relative proximity of the two ligands Glp and S3P, which form a stable ternary complex with the enzyme EPSP synthase. The distance constraints were obtained from both homonuclear and heteronuclear dipolar couplings obtained using the REDOR and DRAMA pulse sequence, together with a model showing a...

Fig. 11.16 The pulse sequence used to monitor the evolution of carboncarbon double-quantum coherence over a single rotor period in the presence of the proton-carbon heteronuclear dipolar coupling (a). The evolution of the double-quantum coherence between the Cl 4 and Cl 5 carbons in the retinal of bacteriorhodopsin in the ground state (b). The observed evolution is consistent with a C14-C15 torsion angle of 164° (reproduced with permission from Ref. [172]).

Gullion, T. and Schaefer, J. (1989) Detecbon of weak heteronuclear dipolar coupling by rotabonal-echo doubleresonance nuclear magnebc resonance. Adv. Magn. Reson., 13, 57-83. 

The heteronuclear dipolar coupling between spin species I and S is given in Eq. (2) and rewritten below in different form ... 

Key Words Heteronuclear dipolar couplings, REDOR spectroscopy, Structure, Second moments. Constant time, SIMPSON... 

In the CT-VPP-REDOR experiment (cf. Figure 3), the positions of the 7t-pulses on the /-channel which are applied at Tr/2 in conventional REDOR are changed stepwise over the complete rotor period, leading to but a partial reintroduction of the heteronuclear dipolar coupling. The resulting AS/So curve depends on the pulse position fpp according to... 

As shown in the preceding two sections, the constant time version of REDOR, CT-REDOR, may be applied as an expedient alternative to the existing REDOR versions in the presence of strong heteronuclear dipolar couplings. In these cases, only few data points are available for the data analysis, which especially in the case of multiple-spin systems renders an evaluation of the second moments impossible. The efficiency of the dipolar recoupling may be intentionally reduced either via a dislocation of the dephasing Ti-pulses from the centre of the rotor period or via an application of non-Ti-dephasing pulses. A variation of the pulse position fpp... 

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