Structural ensembles, determination from

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

Molecular modeling is an indispensable tool in the determination of macromolecular structures from NMR data and in the interpretation of the data. Thus, state-of-the-art molecular dynamics simulations can reproduce relaxation data well [9,96] and supply a model of the motion in atomic detail. Qualitative aspects of correlated backbone motions can be understood from NMR structure ensembles [63]. Additional data, in particular residual dipolar couplings, improve the precision and accuracy of NMR structures qualitatively [12]. 

The structure of a molecule is given by the three-dimensional distribution of atomic cores and valence electrons. This structure has been elucidated for many molecules with the use of X-ray or electron diffraction data. Chemical properties of molecules are observed under conditions which permit internal motions. Such observations yield views which may differ markedly as a function of time. Thus, observable properties are determined from equilibrated ensembles of species differing in geometry and energy. 

Recently, Lindorff-Larsen el al.uo included the order parameter (S 2) in the target function, and refined an ubiquitin X-ray structure by restrained molecular dynamics (Section 6.4) to obtain an NMR structure ensemble (Section 6.5) from the trajectories. They simulated the values of RDCs (Section 9.1) and side chain scalar coupling from the calculated ensemble to confirm that the method can determine the protein three-dimensional structure and dynamic structure simultaneously. The simulated values were in good agreement with the corresponding measurement data. The simulation accuracy was improved from the preliminary calculated structure without the order parameters. The approach is typically important, because they tried to link the ensemble with a dynamic structure directly. 

Determination of Structural Ensembles from NMR Data Conformational Sampling and Probability Assessment... 

A method called PARSE (Probability Assessment via Relaxation rates of a Structural Ensemble) is described for determination of ensembles of structures from NMR data. The problem is approached in two separate steps (1) generation of a pool of potential conformers, and (2) determination of the conformers probabilities which best account for the experimental data. The probabilities are calculated by a global constrained optimization of a quadratic objective function measuring the agreement between observed NMR parameters and those calculated for the ensemble. The performance of the method is tested on synthetic data sets simulated for various structural ensembles of the complementary dinucleotide d(CA) d(TG). 

Fig. 9 An ensemble of ten superimposed low-energy structures of a ribbonforming peptoid hexamer as determined by NMR spectroscopy, depicted with (a) and without (b) the side chains that induce this secondary structure motif. Reproduced from [87], with permission Wiley-VCH...

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