Dihedral angle restraints

Fig. 6.7 Structure of d(GCGAAGC) hairpin calcU lated using the set of 99 NOEs and 37 dihedral angles restraints without (a) and with (b) inclusion of 38 residual dipolar couplings both from sugars (13) and bases (25) [82]. The ensemble a...

NMR is the experimental tool of choice to explore conformational properties, especially of flexible small molecules in solution [55-57], Interpretation of NMR-derived structural parameters in combination with molecular modeling usually offers a view of the accessible conformations to ligands. The most relevant structural parameters derived from NMR are interproton distances obtained from NOE or ROE experiments, dihedral angle restraints from 3J scalar coupling measurements and, recently, residual dipolar couplings (RDCs) [58],... 

Two conformations of EpoA in complex with tubulin have been proposed on the basis of EC [26] and NMR [76, 96] data, respectively (Fig. 11). The tubulin-bound conformation of EpoA was determined by solution NMR spectroscopy [96] before the EC structure of EpoA bound to tubulin was available. The observation that, in a 100 1 mixture with tubulin, NOE cross-peaks of EpoA have negative sign, indicated that there is a fast exchange equilibrium in solution. This offered the opportunity to measure transferred NMR experiments, that report on the bound conformation of the ligand. A total of 46 interproton distances were derived from cross-peak volumes in tr-NOE spectra. However, these distance restraints did not suffice to define a unique conformation, as several distinct structures were consistent with them. Transferred cross-correlated relaxation (Sect. 2.2.1.3) provided the additional dihedral restraints that were crucial to define the bound conformation [96, 97], One requirement to measure CH-CH dipolar and CH-CO dipolar-CSA CCR rates is that the carbon atoms involved in the interaction are labeled with 13C. The availability of a 13C-labeled sample of EpoA offered the opportunity to derive seven of these dihedral angle restraints from tr-CCR measurements (Fig. 12). 

NOE, a relaxation mechanism based upon magnetic dipole-dipole interactions of the nuclei, allows measurement of interproton distances with the basic r distance proportionality. This provides major distance restraints for strucmral calculations. Supplemented with additional data, such as original dihedral angle restraints obtained from J-coupUngs or more recent information about the orientation of the bond vectors connecting magnetically active nuclei with respect to the external magnetic field, this approach has been the foundation for NMR-based protein structure determination since its dawn in 1984 [11]. 

The energy, E, specified by this target function includes a chemical description of the protein conformation through the use of a force field, Eforcefieid- The force field potentials are generally much simpler representations of all atom force fields. The distance and dihedral angle restraints appear as weighted penalty, E nmr, terms that should be driven to zero. 

Here distance Edihedrai represent the violation energies based on the distance and dihedral angle restraints, respectively. These functions can take several forms, although a simple square well potential is commonly used. The expressions also include a summation over both upper and lower distance violations for example, Edistance = When considering upper distance re-... 

For dihedral angle restraints the functional form is similar to that of Eqs. (59) and (60). As before, the total violation, Edihedrai, is a sum over upper and lower... 

Set counter, c = 1. Perform TAD (1000 high-temperature steps followed by 3000 annealing steps) using Es as the target function. The torsion angle bounds of the current subdomain determine the dihedral angle restraint functions. In addition to the NOE-derived distance restraints, sterically based distance restraints are added to prevent van der Waals overlaps. 

A common form of nmr describes NOE-derived distance restraints and J-coupling derived dihedral angle restraints using flat-bottomed parabolic functions ... 

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