Isotropic tumbling

This task can be achieved by increasing the molecular size of the paramagnetic complex. In fact, by considering the paramagnetic probe as an isotropically tumbling sphere, it is expected that and molecular size (commonly assumed to increase linearly with the molecular weight) are... 

The simplest motional description is isotropic tumbling characterized by a single exponential correlation time ( ). This model has been successfully employed to interpret carbon-13 relaxation in a few cases, notably the methylene carbons in polyisobutylene among the well studied systems ( ). However, this model is unable to account for relaxation in many macromolecular systems, for instance polystyrene (6) and poly(phenylene oxide)(7,... 

ApSimon, Beierbeck, and Saunders (32) have extended this work to include a series of androstanes and cholestanes. They too find for the ring methylenes and methines that the Tx values of the former are one-half those of the latter, thus signifying mainly isotropic tumbling. 

The similarity of the 7, values for all the ring carbons in a disaccharide molecule may indicate isotropic tumbling without a preferred axis of rotation. 

For a globular protein of approximately spherical shape, the isotropic tumbling rate can be characterized by the rotational diffusional correlation time, tc, as described above. Assuming that the protein fits in a sphere of radius r, then the viscosity (rf) and temperature (T) of the sample determines rc. 

Fig. 6.2. 1H-1BN HSQC spectra of folded apomyoglobin at pH 6 (left) and unfolded apomyoglobin at pH 2 (right). Note the wide dispersion in the XH dimension in the left spectrum, and the narrow dispersion on the right. Also, the cross peaks are broader in the left spectrum, due to isotropic tumbling of the folded, globular protein. The cross peaks are narrower in the right spectrum due to rapid segmental motion of the unfolded polypeptide chain...

Figure 24.5b Relative contributions of the predominant modes of cation rotation within the tetramethylammonium dicyanamide salt across a range of temperatures. The static state decreases rapidly with increasing temperature, as does the methyl group spinning. Isotropic tumbling begins to a very small degree at 240 K and increases dramaticaiiy above 315 K. These rotational transitions are unusual for the tetramethylammonium cation.

The orientation dependence of the CSA and quadrupolar interactions are similarly affected by dynamical processes. For example, in fluids the orientation-dependence of Equations (1) and (3) is fully averaged by isotropic tumbling, because the... 

Since Peng and Wagner (1992) formulated spectral density mapping techniques which can diredly determine the spectral density fimction at severd frequencies, the isotropic tumbling or the Lipari-Szabo (1982) models may be too simplistic. Finding an acceptable spectral density function then requires an adequate motional model. The recent version of the BLOCH program by Madrid and Jardetzky (unpublished) can take any spectral density function as input and optimize the structure ensemble relative to Ihe NOE pattern. However, the basic problem of defining the correct spectral density function for each case remains. 

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