Restraints, in structure calculations

One important application of RDC measurements is the structural refinement of biomolecules that consist of several domains that are connected by more or less flexible linkers. Because of the flexibility of the linker and the distance between domains, J-couplings and NOE restraints will frequently not be sufficient for correct determination of the relative domain orientation. The addition of RDC restraints in structure calculation not only refines the biomolecular structure but also allows the relationship between structure and function to be studied. Interactions with other biomolecules and ligand binding may induce an intramolecular rearrangement of the relative orientation of domains that is detectable through RDC measurements (21, 22). 

Considering all potential experimental and systematic errors of NOE/ROE crosspeak intensities, it is remarkable how robust the derived distance restraints still are. The reason Ues in the dependence of the cross-relaxation rate even if a cross-peak intensity is determined wrongly by a factor 2, the resulting distance restraint is only affected by the factor 1.12, which usually lies within the error range of distance restraints used in structure calculations. It should be further noted that the quaUty of a resulting structure is not so much determined by the... 

The full potenhal of RDCs, however, can be seen by the incorporation of RDC data in structure calculations. Several programs hke XPLOR-NIH, DISCOVER or GROM ACS allow the incorporation of RDCs as angular or combined angular and distance dependent restraints. Several studies on sugars have been reported (see, e.g. Ref [43] and references therein) and Fig. 9.8 shows the comparison of three structural models for the backbone of the cyclic undecapeptide cyclosporin A, derived from X-ray crystahography, ROE data in CDCI3 as the solvent, and RDCs and ROEs obtained in a PDMS/CDCfi stretched gel [22]. Due to the sensitivity to... 

The nondegenerate geminal pairs are usually named according to their chemical shifts (e.g., downfield of ft ) rather than their stereochemical relationships (pro-R and pro-S). In structure calculations, this usually is dealt with by creating a pseudo-atom right between the pro-R and pro-S positions in 3D space. The NOE restraints are applied to the pseudoatom and not to the real atoms, and the distance limit is increased a bit to account for the ambiguity (we do not really know which restraint applies to which of the two positions in space). Similarly, a pseudoatom is created at the center of the three equivalent protons of a CH3 group, and the distance restraint is applied to the pseudoatom. 

The /r dependence of p causes the buildup rate to fall off very rapidly with internuclear distance, with the result that NOEs are short-range interactions that are typically not observed between protons separated by more than 5.5 A (but see below). Nevertheless, this provides extremely valuable structural information since spatially proximal protons will yield a crosspeak in NOESY spectra regardless of how distal they are in the amino acid sequence. Since several thousand NOEs will be observed for even a protein of modest size, NOEs provide the most important structural restraints for structure calculations. But first they need to be assigned to specific proton pairs, quantified, and converted into distance information. 

Second, undesired TOCSY peaks appear because some nuclei that are spin coupled experience similar fields during the application of the spin-lock and fulfil the Hartmann-Hahn condition. Since the TOCSY peaks are phase shifted by 180° with respect to the ROESY peaks, they can easily be recognized. However, the superposition of contributions from direct and indirect transfer results in a decrease of cross peak intensity and therefore in distances which are too long. When only lower boundaries are used as restraints in MD calculations this would lead to lower restraints and a less well-defined structure but would not induce wrong results. In addition, different internal correlation times, such as the above-mentioned different flexibility of the molecule have a smaller influence in ROESY than in NOESY spectra. 

Structure calculation algorithms in general assume that the experimental list of restraints is completely free of errors. This is usually true only in the final stages of a structure calculation, when all errors (e.g., in the assignment of chemical shifts or NOEs) have been identified, often in a laborious iterative process. Many effects can produce inconsistent or incorrect restraints, e.g., artifact peaks, imprecise peak positions, and insufficient error bounds to correct for spin diffusion. 

If all nuclei are assigned and the spectral parameters for the conformational analysis are extracted, a conformation is calculated - usually by distance geometry (DG) or restrained molecular dynamics calculations (rMD). A test for the quality of the conformation, obtained using the experimental restraints, is its stability in a free MD run, i.e. an MD without experimental restraints. In this case, explicit solvents have to be used in the MD calculation. An indication of more than one conformation in fast equilibrium can be found if only parts of the final structure are in agreement with experimental data [3]. Relaxation data and heteronuclear NOEs can also be used to elucidate internal dynamics, but this is beyond the scope of this article. 

As it was mentioned in Section 9.4.1, 3D structures generated by DG have to be optimized. For this purpose, MD is a well-suited tool. In addition, MD structure calculations can also be performed if no coarse structural model exists. In both cases, pairwise atom distances obtained from NMR measurements are directly used in the MD computations in order to restrain the degrees of motional freedom of defined atoms (rMD Section 9.4.2.4). To make sure that a calculated molecular conformation is rehable, the time-averaged 3D structure must be stable in a free MD run (fMD Sechon 9.4.2.5J where the distance restraints are removed and the molecule is surrounded by expMcit solvent which was also used in the NMR measurement Before both procedures are described in detail the general preparation of an MD run (Section 9.4.2.1), simulations in vacuo (Section 9.4.2.2) and the handling of distance restraints in a MD calculation (Section 9.4.2.3) are treated. Finally, a short overview of the SA technique as a special M D method is given in Sechon 9.4.2.6. 

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