Time-averaged distance restraints

The first step in implementing this model is to define f(t) suitable for use in a penalty function. Naively, one could write 

this could be cast into a form suitable for averaging over a molecular 

In practice, however, Eq. [14] would not be suitable for an energy term because the rate of change of f(t) would depend on how long the averaging had been 

Finally, the derivative of Eq. [15] has fourth-power terms with respect to r(t)/r(t), so it was not used to define an energy term as such. Instead, a force was defined in terms of f(t)  

One drawback of this method is that it requires the use of an extra parameter, t, the time constant for the decay of the memory function. In practice, this should not be a problem as long as t is longer than the period of the longest motions which are important for NOE averaging. A limitation of the method is that, in contrast to the two-state model of Scarsdale et al.,47 the procedure can only average over conformations that can interchange during the short time of a molecular dynamics simulation. 

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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. 

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. 

A. E. Torda, R. M. Sheek, and W. F. van Gunsteren, Time-averaged nuclear overhauser effect distance restraints applied to tendamistat, J. Mol. Biol., 214 (1990), 23. 

Time-averaged restraints may be able to overcome this problem [Torda et al. 1990]. Rather than using the instantaneous value of a distance in the restraint function, the time-averaged restraint method uses a value that is averaged over time. The simple harmonic error function then becomes ... 

Torda A E, R M Scheek and W F van Gunsteren 1990 Time-averaged Nuclear Overhauser Effect Distance Restraints Applied to Tendamistat. Journal of Molecular Biology 214 223-235. 

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