Distance restraints

Example You could explore the possible geometries of two molecules interacting in solution and guess at initial transition structures. For example, if molecule Aundergoes nucleophilic attack on molecule B, you could impose a distance restraint between the two atoms that would form a bond, allowing the rest of the system to relax. Simulations such as these can help to explain stereochemistry or reaction kinetics and can serve as starting points for quantum mechanics calculations and optimizations. 

Figure 2 Usejaf unambiguous or ambiguous distance restraints in an optimization calculation.

Figure 5 Schematic representation of a Cartesian dynamics protocol starting from random torsion angles. The weights for non bonded (i.e., van der Waals) interactions, unambiguous distance restraints, and ambiguous distance restraints are varied independently. The covalent interactions are maintained with full weight, co.aie - for the entire protocol. Weights for other experimental terms may be varied in an analogous way. Coupling constant restraints and anisotropy restraints are usually used only in a refinement stage.

Figure 6 Steps in automated assignment. (1) Select the lowest energy structures from iteration / — 1 that are used to interpret the spectra. (2) For each peak, list all possible assignments compatible with the resonances within a frequency mnge. (3) Extract a distance for each assignment possibility from the ensemble of structures. (4) Use the distances to assign ambiguous NOEs. (5) Calibrate the peak volumes to obtain distance restraints. (6) Calculate structures based on the new restraints.

The same principal ideas are incorporated in the calculation protocols for symmetrical oUgomers as with asymmetrical systems, i.e., the weight is reduced specifically for ADRs or all distance restraints. In addition, the symmetry of the system restricts conforma-... 

To put the errors in comparative models into perspective, we list the differences among strucmres of the same protein that have been detennined experimentally (Fig. 9). The 1 A accuracy of main chain atom positions corresponds to X-ray structures defined at a low resolution of about 2.5 A and with an / -factor of about 25% [192], as well as to medium resolution NMR structures determined from 10 interproton distance restraints per residue [193]. Similarly, differences between the highly refined X-ray and NMR structures of the same protein also tend to be about 1 A [193]. Changes in the environment... 

CM Clore, AT Bifinger, M Karplus, AM Gronenborn. Application of molecular dynamics with mterproton distance restraints to 3D protein structure determination. J Mol Biol 191 523-551, 1986. 

A Aszodi, MJ Gradwell, WR Taylor. Global fold determination from a small number of distance restraints. J Mol Biol 251 308-326, 1995. 

The oldest and most widely used structural restraints in NMR spectroscopy are distance restraints derived from NOE experiments [1]. Transient NOE, 2D NOESY and ROESY spectra provide valuable information for interatomic distances up to 5 A that will be discussed in the following. 

The accuracy of obtained cross-relaxation rates and therefore the derived distance restraints is influenced by many practical aspects. A critical point is the... 

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... 

Fig. 9.4 The fixation of the Ala proton in cyclosporin A via ROE-derived distance restraints as an illustrative example for NMR structure determination. (A) The amide region of the 2D ROESY spectrum of cyclosporin A at room temperature with the cross-peaks to...

Ala 14 indicated by a box. (B) Distances to Ala 14 in the final structure indicated by dashed yellow lines as a result of the derived distance restraints. The distance to the methyl carbon is given as a representative for methyl groups. 

The next step is a careful comparison of the experimental restraints with those from the calculahons. Such a check also includes other parameters which are not directly used in the MD calculations, but can be obtained by NMR experiments. When parts of the molecule fulfill the experiments and others do not, it is an indicahon for flexibility in the part which does not meet the experimental data. To analyze such a behavior, longer MD trajectories or time- or ensemble-averaged distance restraints can be used in the calculahons. 

DG was primarily developed as a mathematical tool for obtaining spahal structures when pairwise distance information is given [118]. The DG method does not use any classical force fields. Thus, the conformational energy of a molecule is neglected and all 3D structures which are compatible with the distance restraints are presented. Nowadays, it is often used in the determination of 3D structures of small and medium-sized organic molecules. Gompared to force field-based methods, DG is a fast computational technique in order to scan the global conformational space. To get optimized structures, DG mostly has to be followed by various molecular dynamic simulation. 

The first step in the DG calculations is the generation of the holonomic distance matrix for aU pairwise atom distances of a molecule [121]. Holonomic constraints are expressed in terms of equations which restrict the atom coordinates of a molecule. For example, hydrogen atoms bound to neighboring carbon atoms have a maximum distance of 3.1 A. As a result, parts of the coordinates become interdependent and the degrees of freedom of the molecular system are confined. The acquisition of these distance restraints is based on the topology of a model structure with an arbitrary, but energetically optimized conformation. 

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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