Angle Restraints

Well before homonudear coupling constants could be measured in proteins, Karplus71 72 proposed the relationship between the coupling constant J and the dihedral angle between vicinal protons 0  

Given restraints on dihedral angles, a penalty function Vd r(0), weighted by an arbitrary force constant /Cdlr, was first constructed by analogy with torsional angle potentials in molecular force fields42  

There is probably no reason to favor either of the forms given in Eqs. [20] and [21], but an improvement has been suggested by Kim and Prestegard.77 As was the reasoning with distance restraint terms, one should not base a penalty function on a derived quantity, the dihedral angle 0. Instead, one should use an expression of the form 

Historically, the field of molecular dynamics (MD) evolved as a means of simulating the behavior of molecules in an attempt to reproduce and, hopefully, to predict structural, dynamic, and thermodynamic properties of molecules.78-80 In recent years, however, it has become popular as a means for refining molecular structures with respect to experimental data.81 This relies on the fact that if any system is simulated, it will tend to run downhill energetically 

Conceptually, the MD algorithm is simple. One starts with Newton s equations of motion relating force (F), and mass (m), and acceleration (a ) 

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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...

Methods for the Measurement of Angle Restraints Application to Biomacromolecules... 

Using 18 trNOE-derived distance restraints and 13 trCCR-derived backbone torsion angle restraints, structure calculations using distance geometry and simulated annealing [48] resulted in a well-defined structure of the IKK/1-derived peptide bound to NEMO. The backbone structure is displayed in Fig. 7B and is compared with the result of the calculation carried out using the trNOE-derived distance restraints alone. It is obvious from Eig. 7 that only the combination of the trNOE- and trCCR-derived restraints results in the structure elucidation of the bound conformation of this peptide. 

Fig. 7 Solution of structure calculations of the NBD-peptide bound to NEMO. A Only trNOE-derived distance restraints were used in the calculation. The structure is not defined by the distance restraints alone. B trNOE-derived distance restraints and trCCR-derived torsion angle restraints were combined. These restraints complement each other and are sufficient to define the NEMO-bound conformation of the IKK/8-derived peptide. In both cases ten solutions were superimposed...

Introduce bond angle restraints where required. 

The structural modeling of PG and PLV with the anti-parallel p-sheet form is carried out by the hybrid distance geometry-dynamic simulated annealing method115 as contained in the X-PLOR 3.1 program.116 For structural calculations, the proton-proton distance restraints and the torsion angle restraints ( =—139° and v /=135°) are derived from reference data by Wiithrich et al.ni Hydrogen-bond distance restraints are used for the N and atoms (2.7-3.3 A) in the secondary structure.118 120 The reference data of intra- and intermolecular proton-proton distances are shown in Fig. 19. 

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). 

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