Lipari-Szabo

The largest correlation times, and thus the slowest reorientational motion, were shown by the three C- Fl vectors of the aromatic ring, with values of between approximately 60 and 70 ps at 357 K, values expected for viscous liquids like ionic liquids. The activation energies are also in the typical range for viscous liquids. As can be seen from Table 4.5-1, the best fit was obtained for a combination of the Cole-Davidson with the Lipari-Szabo spectral density, with a distribution parame-... 

The Lipari-Szabo approach has been essentially used in the study of large biomolecules,21-24,28 less often for the medium size molecules as will be discussed in Section 6. 

Attempts to interpret the corresponding build-up curves according to the Lipari-Szabo approach lead to inconsistent results (for instance, order parameters greater than unity). This indicates that these remote correlations are probably not of infra-molecular origin but would rather arise from znfer-molecular dipolar interactions which could become significant when some contacts exist between neighbouring aliphatic chains. This... 

A.4. Rotational dynamics application of the Lipari-Szabo approach to describe internal flexibility of macromolecular chelates... 

While the assumption of an isotropic rotational motion is reasonable for low molecular weight chelates, macromolecules have anisotropic rotation involving internal motions. In the Lipari-Szabo approach, two kinds of motion are assumed to affect relaxation a rapid, local motion, which lies in the extreme narrowing limit and a slower, global motion (86,87). Provided they are statistically independent and the global motion is isotropic, the reduced spectral density function can be written as ... 

The Lipari-Szabo approach was used to understand the cause of the pH-dependent relaxivities of PAMAM-type dendrimeric Gdm complexes (74). Three different generations (5,7,9) of PAMAM dendrimers loaded with the [Gd(EPTPA)(H20)]2 chelate via a benzyl-thiourea linkage have been investigated (Scheme 8). The relaxivities show a strong and reversible pH dependency for all three dendrimer complexes,... 

We should note that the use of the Lipari-Szabo analysis implies that relaxation data are available at multiple magnetic fields. It provides a phenomenological description of the rotational motion that can be very useful for comparing systems with similar structure. Nevertheless, one should be aware of the limits of this approach and avoid direct comparison of local or global rotational correlation times for structurally very different compounds. 

Parameters Obtained for the Macromolecular Gdm Complexes by Fitting the H NMRD Data with the Use of the Lipari-Szabo Approach (90)... 

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... 

In addition, Nicolle et al. (Ill) have shown that the mobility of the embedded Gd-complex can be described by two rotational correlation times using the Lipari-Szabo analysis, i.e., a correlation time describing the overall rotational mobility of the micelle and a correlation time for the internal mobility of the Gd-complex inside the micellar structure. 

Internal Flexibility of Macromolecular Gd(lll) Complexes. The Lipari-Szabo Approach... 

Unlike for globular proteins, internal motions of IDPs can hardly be interpreted within the framework of the Lipari-Szabo model-free formalism. IDPs are dominated by segmental motions with low or negligible cooperativity between... 

In some polymers such segmental motions can be important, whereas in others (e.g., proteins) the overall skeleton is rigid, but there are rapid internal motions of moieties relative to the skeleton. In this case, relaxation and NOE data are often analyzed by the Lipari-Szabo formalism,96 which yields values for an overall correlation time rM, a correlation time for fast motions re, and a generalized order parameter S (see Eq. 7.16), which describes the amplitudes of the internal motions. 

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. 

The interpretation of relaxation data is most often performed either with reduced spectral density or the Lipari-Szabo approach. The first is easy to implement as the values of spectral density at discrete frequencies are derived from a linear combinations of relaxation rates, but it does not provide any insight into a physical model of the motion. The second approach provides parameters that are related to the model of the internal motion, but the data analysis requires non-linear optimisation and a selection of a suitable model. A graphical way to relate the two approaches is described by Andrec et al Comparison of calculated parametric curves correlating 7h and Jn values for different Lipari-Szabo models of the internal motion with the experimental values provides a range of parameter values compatible with the data and allows to select a suitable model. The method is particularly useful at the initial stage of the data analysis. 

Canet et al found that the standard Lipari-Szabo approach was inadequate for the analysis of multifield N relaxation parameters of a 86 residue protein even when the extended model or anisotropy of the overall motion were introduced. To remedy the situation they used the correlation function in... 

Experimental methods, theory, analysis, protein applications Systematic up to 10% N T2 overestimation in 180° CPMG train Evaluation of Lipari-Szabo parameters without non-linear fit... 

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