Stereochemical restraint refinement

In the case of ITPP, Ferro and BrCickner (28) showed that unrestrained minimization of the total energy for a microcrystal corresponding to unstretched fibers yields a structure in very close agreement to the crystallographically refined one. This was in contrast to the earlier results with less accurate calculations. Furthermore, their calculations, which used slightly modified MM2 potentials and a modest restraint on the cartesian coordinates, provided a stereochemically acceptable model that reproduces the powder diffraction profile as accurately as the least-squares fitted model. 

Model building is an interpretation of the currently available electron density. Refinement is the adjustment of the built model to fit better to the experimental data. A crucial point here is that a density map computed from the refined model is generally better than the map obtained from the same model before the refinement. This then allows for an even better model to be built. Thus, refinement is needed to improve the outcome of model building by generating a better electron density map and model building is needed to provide a model in the first place and to provide stereochemical restraints for the subsequent refinement to proceed smoothly. This viewpoint merges these two steps into one model optimization process. 

Figure 11.3 Parallel-eye stereoscopic image of a model of the complete VS ribozyme (Lipfert et al., 2008). The model was constructed by connecting previously defined helical sections of a low-resolution model fitting the density map shown in Fig 11.2. Energy-minimization refinement against the standard stereochemical restraints was used to regularize and refine the structure. The scissile phosphate is shown as a sphere, and the probable active site components A756 and G638 are annotated.

Subsequently, the baboon a-lactalbumin structure was refined at 1.7-A resolution by Acharya et al. (1989). Using the structure of domestic hen egg white lysozyme as the starting model, preliminary refinement was made using heavily constrained least-squares minimization in reciprocal space. Further refinement was made using stereochemical restraints at 1.7-A resolution to a conventional crystallographic residual of 0.22 for 1141 protein atoms. 

R.B. Von Dreele, Combined Rietveld and stereochemical restraint refinement of a protein crystal structure, J. Appl. Cryst. 32, 1084 (1999). 

For the minimization function in a Rietveld refinement including stereochemical restraints, the terms are Y - powder pattern, a - bond angles. 

Unlike the rigid body formulation, the use of restraints does not result in a reduction in the number of parameters used to describe a crystal structure, but it includes additional stereochemical information to augment the suite of diffraction observations i.e. the powder pattern), thus permitting a full refinement of the structure. 

Figure 9.10 Result of final stereochemical restraint refinement of the complex Fe[OP(C6H5)3]4Cl2[FeCl4]. Observed profile is indicated by ( + ), calcu lated and difference curves are shown and refiection positions are marked as ( ).

The crystal structures of proteins represent an extreme in the number of atom positions needed to describe them compared to those structures more commonly studied by powder diffraction. For example, the well-known tetragonal crystal structure of hen egg white lysozyme has 1001 nonhydrogen atoms within the protein molecule another 100 or so water molecules and salt ions are also present. This gives over 3000 atomic x,j,z coordinates. Nonetheless, a Rietveld refinement of these structures from powder diffraction data can be performed by extending the suite of restraints to include all stereochemical features that show characteristic values.The suite of restraints given in Equation (24) is then ... 

The relative weights for the X-ray observations and the restraints may be adjusted. In the early stages of refinement, the weights for the restraints might be relatively high in order to achieve a stereochemically sensible model. Gross errors in the structure can be detected by difference Fourier syntheses (section 2(h)). As the refinement progresses, the restraints may be relaxed. The final R value depends upon resolution and the restraints, and it is important that both values are quoted so that the stereochemical reasonableness of the structure can be assessed. 

Similar to the use of stereochemical restraints to stabilize the refinement of atomic coordinates, anisotropic displacement parameters need to be restrained to keep them physically reasonable. The restraints implemented in SHELXL are described in... 

Campbell, P.J.S. and S. Amott. 1978. LAIS A linked-atom least-squares reciprocal-space refinement system incorporating stereochemical restraints to supplement sparse diffraction. Acta Crystallographica. Section A 34 3-11. 

---