Spin-diffusion limit

For macromolecules (or small molecules in viscous solvents at a low temperature) in a high magnetic field, wqTc 3> 1. At this spin-diffusion limit the rotating-frame cross-relaxation rate is twice as fast as in the laboratory frame, and the rates are of the opposite sign, 5 = —1/2 (fig. 1, top). 

Figure 8.8. The variation in the maximum theoretical homonuclear steady-state NOE in a two-spin system as a function of molecular tumbling rates (defined by the dimensionless parameter cOoTc). The region of fast motion is the extreme narrowing limit and that of slow motion is the spin-diffusion limit.

The maximum possible negative NOE in a homonuclear system is —100%. Between the extreme narrowing and spin diffusion limits, lies the difficult region in which NOEs can become zero (when cooTc 1) or at least rather weak, often demanding a change in experimental conditions or the use of rotating-frame NOE measurements. 

Kramer and Glaser analysed the transfer efficiency of cross-relaxation compensated (Clean) TOCSY sequences for applications to residual dipolar couplings. Surprisingly most conventional Clean TOCSY sequences are very inefficient for dipolar transfer. It is shown theoretically, that this is a general property of all phase-alternating mixing sequences, i.e., for such sequences the suppression of cross-relaxation excludes dipolar transfer in the spin-diffusion limit. A new family of clean dipolar TOCSY sequences is derived which provides excellent transfer efficiencies for a broad range of offset frequencies. 

At 500 MHz, moderate-sized (more than six residues) oligosaccharides lie within the spin-diffusion limit. However, for smaller molecules, as the value of the function (OqT (where (Oq is the Larmor frequency of protons, and is the correlation time of the molecule) approaches 1 then the value of the NOE tends towards 0. Cross-peak intensities of NOESY spectra of smaller oligosaccharides (2-5 residues) may thus become too small to measure accurately. In such cases, the rotating frame Overhauser effect spectroscopy (ROESY, originally referred to as CAMELSPIN) experiment is commonly used to measure NOE values. To reduce the appearance of HOHAHA-like cross-peaks, a low power spin-lock field should be used, and the transmitter carrier offset to the low-field end of spectrum. The offset dependency of cross-peak intensities should also be removed by 90° pulses at either end of spin-lock period. 

---