Lipari-Szabo model

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... 

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... 

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. 

Andrec M, Montelione GT, Levy RM (1999) Estimation of dynamic parameters from NMR relaxation data using the Lipari-Szabo model-free approach and Bayesian statistical methods. J Magn Reson 139 408 21... 

Back to high-resolution NMR, Andrec etal used Bayesian techniques to attribute probabilities to dynamic parameters using relaxation data in a Lipari-Szabo model-free approach. The following year, the same group- discussed the contributions of rotational diffusion anisotropy and estimated them using Bayesian methods. The importance of such measurement is highlighted in order to avoid misinterpretation of relaxation data contributing to bias molecular motion parameters. 

The most common way of dealing with non-rigid (macro) molecular systems is the model free analysis proposed by Lipari and Szabo and even earlier, in a slightly different formulation, by Wennerstrom et al. The Lipari-Szabo model assumes uncorrelated internal and global motions. The spectral densities are expressed in terms of a global and a local correlation time and a generalized order parameter, measuring the... 

Several authors reported investigations of protein dynamics on the pico- and nano-second time scales. A standard approach to the protein backbone dynamics in this range is to measure N Ti, and NOE and to interpret the data using the Lipari-Szabo model-free approach, while or relaxation measurements provide information on the side-chain motions. The Lipari-Szabo order parameters can also be derived from MD simulations. Some authors compared the experimentally derived with the MD-derived counterparts. Smith and co-workers reported a study of this kind for the backbone of lysozyme from a bacteriophage and... 

Sharp and coworkers have studied protein motion using the Lipari-Szabo model-free squared generalized methyl axis order parameter technique connected with Bayesian statistics and by combining NMR and MD simulations with the focus on the motion of the methyl groups in seven different proteins and conformational entropy. With new better optimized force fields the accuracy of the computed order parameters has increased markedly and as a result from the study a three-class model is proposed. This study promotes the dynamical view of proteins obtained in a multidimensional-NMR/MD approach. 

These measurements have been interpreted by the Lipari-Szabo model-free approach, in which molecular motion is separated into overall and internal motions, related to the overall and internal correlation times Xq and r, ... 

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