Section 25.2.1.6. Parameter refinement

With this option, one minimizes for isomorphous-replacement data or for anomalous-scattering data with respect to the desired parameters. Typically, the weights are taken as the reciprocal of the `standard error' (expected lack of closure) or its square. The summations are taken over all reflections for which the protein phase is thought to be reasonably valid, usually implied by a figure of merit of 0.4 or higher. The protein phase estimate usually comes from the centroid of the appropriate combined phase probability distribution given by equation (25.2.1.10); however, one has the option of including all data sets when combining the distributions, or including all except that for the derivative being refined. Once new heavy-atom and scaling parameters are obtained, new individual SIR or SAS phase probability distributions are computed and combined to provide new protein phases, and these phases are used to update the standard error estimates as described earlier. Then the individual distributions are recomputed once more using the new standard error estimates, and these distributions are combined again to give new protein phase estimates. The process is then iterated using the new phases and new heavy-atom parameters to start another round of refinement. After several iterations, the heavy-atom parameters, standard error estimates and protein phase estimates converge to their final values.

This variation, also available in PHASIT, is similar to the classical phase refinement described above, except that instead of using only a single value for the protein phase φ during the calculation of , all possible values are considered, with each contribution weighted by the corresponding protein phase probability (Otwinowski, 1991). One minimizes with respect to the desired parameters for isomorphous-replacement data, where is the protein phase probability and the inner summation is over all allowed protein phase values, stepped in intervals of 5° (or 180° for centric reflections). For anomalous-scattering data, a similar modification is made to equation (25.2.1.14). The weights may be as in the classical phase refinement case or unity. Since each contribution is weighted by its phase probability regardless, there is no need to use a high figure-of-merit cutoff, as was done earlier. In fact, very good results are usually obtained using unit weights for (that is, only the probability weighting) and a figure-of-merit cutoff of around 0.2 for inclusion of reflections in the summations. This variation has been found to increase stability in the refinement and works considerably better than conventional phase refinement when the phase probability distributions are strongly multimodal. Parameter refinement and phasing iterations proceed as described earlier. The combination of probability weighting during refinement with probability weighting during standard error estimation enables the key features of maximum-likelihood refinement to be carried out, although only approximately.

When using either the conventional phase refinement or approximate-likelihood methods, protein phase estimates are required. In the former case, only a single value is used, whereas in the latter, information about all possibilities is provided by way of the phase probability distribution. Normally, this information comes from a prior phasing calculation; thus, the estimates are typically SIR, SAS, MIR etc. phases. However, in PHASIT, an option allows one to read in the protein phase information from an external source. This enables parameter refinement (by either conventional or approximate-likelihood methods) using protein phase estimates that are improvements over the initial ones. For example, one could get the best phases by one of the previously described methods, but then improve them by density-modification procedures, such as solvent flattening or negative-density truncation and/or NC symmetry averaging. Using these improved phases in the calculation of when refining should then lead to more accurate heavy-atom and scaling parameters, which in turn will produce still better protein phases. These new protein phases can either be treated as final and used to produce an electron-density map for interpretation, or be used to initiate another round of phase improvement by density modification. There are several cases where this type of refinement has been beneficial, and it is particularly useful for the refinement of derivative-to-native scaling parameters.

Although GREF can be used to refine individual heavy-atom or anomalous-scatterer parameters against isomorphous or anomalous structure-factor difference magnitudes, it is actually a group refinement program. Thus, all entities to be refined are treated as rigid bodies such that only group orientations, positions, scaling and temperature parameters can be refined. The groups, however, can be defined arbitrarily. For individual heavy-atom sites, they are simply defined as single atom `groups', and no orientation parameters are selected for refinement. This enables the program to serve two additional roles. In the case where the heavy-atom reagent is known to contain a rigid group, it can be properly treated. Also, if one chooses the target values to be native structure-factor amplitudes instead of difference magnitudes and inputs an entire protein molecule or domain, then conventional rigid-body or segmented rigid-body refinement can be carried out. The output consists of the refined parameters and a Fourier-coefficient file suitable for map or phase combination calculations.