Macromolecular refinement is an iterative process. Each step consists of an automated optimization of the model, followed by the detailed examination of the remaining discrepancies between the model and the data: the electron-density map and ideal stereochemical restraints. TNT performs the optimization and provides information that the graphics program can display. After manual corrections have been applied to the model, it is returned to the optimizer.
The first time the model is ``exposed'' to refinement is the most difficult. The parameters of the model may fail to reach their optimum values because the errors in the model may be so large or of such a character that the automated procedures fail. To detect and correct these errors, one must anticipate the sort of error that might be found in a model. The following points are relevant to all refinement programs.
There are basically three sources for the sort of model one would use to begin refinement -- multiple isomorphous replacement (m.i.r.) phasing followed by model building, molecular replacement with the model of a similar molecule in another crystal, or molecular substitution (use of a model from an isomorphous crystal form with a small modification in the molecule, as with mutant or inhibitor structures). The nature and magnitude of starting errors in a model depends on which of these methods was employed.
A model built from a m.i.r. map typically will contain some errors as large as an Ångstrom or two, many side chains may be built in the wrong rotomer, and there may be chain-tracing errors. While these are usually the worst starting models, the automated refinement programs will operate quite well. In spite of their inability to correct the latter two kinds of errors, positional errors of up to three Ångstroms can be corrected and the majority of smaller errors also will be reduced.
The refinement programs work well with these models because the models' errors match the assumptions built into the programs. Most refinement programs presume that the error in one parameter is unrelated to the errors in the other parameters in the model (i.e. the off-diagonal elements of the normal matrix are ignored.). In a m.i.r. model the errors in the positions of two atoms are uncorrelated if the atoms are greater than about five Ångstroms apart. A good m.i.r. model can be subjected to individual-atom refinement using the highest resolution data available.
The errors in a molecular-replacement model are correlated. One expects that significant rigid-body shifts will be required for the entire molecule, and then for individual domains with respect to each other. Often it will be difficult to see in a difference map that these shifts are needed, and since all refinement packages basically attempt to flatten the difference map, the automated programs will not identify the problem either. If individual-atom refinement is performed, the R value typically will drop to between 35% and 25% and fail to improve further.
Since there is no indicator of correlated errors, they must always be presumed to exist. For every molecular-replacement model, rigid-body refinement should be performed. Each molecule in the model must be defined as a rigid group and refined. Then each molecule must be split into domains and refined again. If the molecule has parts that might be expected to be variable, then they should be refined as rigid groups too.
One performs rigid-body refinement to encourage large shifts of large objects. Only the low-resolution diffraction data should be used. A resolution cutoff of 5Å is recommended. Once the rigid-body refinement is complete, the model can be refined with individual atoms to the highest resolution data available.
Refinement of models derived from the third source, molecular substitution, can prove difficult simply because the seriousness of the errors are underestimated. One expects that the starting model will be quite accurate because the changes in the molecule are so slight. However these models often are subject to the same invisible problems as those of molecular-replacement models.
For example, cell constants may change from crystal to crystal. A subtle consequence of such a change is that if the model happens to be built into an asymmetric unit far from the origin of the unit cell, a significant translation of the entire molecule will be required. This error will be difficult to correct with individual atom refinement -- rigid-body refinement is needed. Rigid-body refinement is also required when the domains of the molecule move in response to the structural modification.
Even though the R value of the starting model may be low and the errors are expected to be quite small, these models must be treated with the same skepticism as molecular-replacement models.