Lipari-Szabo model-free treatment

In the previous discussion, the electron-nucleus spin system was assumed to be rigidly held within a molecule isotropically rotating in solution. If the molecule cannot be treated as a rigid sphere, its motion is in general anisotropic, and three or five different reorientational correlation times have to be considered 79). Furthermore, it was calculated that free rotation of water protons about the metal ion-oxygen bond decreases the proton relaxation time in aqua ions of about 20% 79). A general treatment for considering the presence of internal motions faster than the reorientational correlation time of the whole molecule is the Lipari Szabo model free treatment 80). Relaxation is calculated as the sum of two terms 8J), of the type... 

Ubiquitin is a small (76 amino acids) extremely stable protein containing a broad collection of secondary structure elements including parallel and antiparallel beta strands assembled into a mixed beta sheet, alpha and 3io helices and a variety of turns (Vijay-Kumar et al., 1987 Di Stefano Wand, 1987). In previous work, we have examined the fast main chain dynamics of ubiquitin by use of 15n NMR relaxation methods (Schneider et al., 1992). These data were analyzed in terms of the so-called model free treatment of Lipari and Szabo (1982a,b). The amplitudes of motion of the backbone amide N-H vectors of the packed regions of the protein are generally highly restricted and show no apparent correlation with secondary stmcture context but do show a strong... 

Given knowledge of the covalent geometry and fundamental constants underlying relaxation, the spectral densities, J(co), remain to be defined. Here, we adopt the so-called model free treatment due to Lipari and Szabo (1982a,b) which seeks to encapsulate the unique motional character expressed in observed relaxation behavior by defining the spectral density in terms of two local parameters ... 

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