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Novelties Associated with a biodynamical interpretation of nuclear spin relaxation Werbelow, Lawrence Glen

Abstract

Employing the semiclassical form of the density operator theory of dynamic processes, the transient nuclear spin behavior is analyzed for a range of motional parameters of significance for biological interpretations of nuclear magnetic relaxation data. Only relaxation which results solely from the reorientational modulation of the various spin couplings is considered. The bath correlation functions which enter into the theory are assumed to be completely characterized by two unique motional constants (a dynamic symmetric top approximation). The effects of slow, anisotropic modulation of spin-spin and spin-molecule interactions on T₁, T₂, T₁ ratios, T₂ ratios, and Overhauser enhancements are discussed. It is rationalized that in general, any parameter dependent upon the spectral density at zero frequency is independent of the magnitude of the asymmetry in the motion. Likewise, parameters independent of the near-zero frequency spectral component often are sensitive solely to the magnitude of the motional asymmetry. These considerations are extended to multispin systems and spin systems where nuclear magnetic relaxation proceeds by competing interactions characterized by nonvanishing interference or cross-correlation functions. In general, one cannot define unambigiously a unique T₁ or T₂ in such a case as the predicted decay is multi-(non)exponential. The spin behavior in such a situation is thoroughly analyzed and many intriguing predictions are presented. It is seen that the failure of a white spectral density approximation or a single exponential decay of the molecular correlation function often leads to predictions of extreme nonexponentiality of the magnetization decay. While the results of these calculations are of general interest, they are especially pertinent for those concerned with biological applications of NMR. Finally, the initial concepts are extended to a discussion of the potentially powerful Perturbed Angular Correlation experiment where it is shown that the coincidence counting rate will in general be influenced by anisotropic modulation of the quadrupolar perturbation. It is emphasized that a conventional interpretation of relaxation data is impregnated with hidden, "extreme-narrowed", reasoning. Extensive figures are provided which not only facilitate experimental application of the calculations, but also provide striking evidence for the caution which must be exercised in any biodynamical interpretation of nuclear spin relaxation.

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