Search

Ab initio and non-ab initio phasing methods are often unable to provide phases of sufficient quality to allow the molecular interpretation of the resulting electron-density maps. Phase extension and refinement is therefore a necessary step: its success or failure can make the difference between solution and nonsolution of the crystal structure. Today phase refinement is trusted to electron-density modification (EDM) techniques, and in practice to dual-space methods which try, via suitable constraints in direct and in reciprocal space, to generate higher quality electron-density maps. The most popular EDM approaches, denoted here as mainstream methods, are usually part of packages which assist crystallographers in all of the structure-solution steps from initial phasing to the point where the molecular model perfectly fits the known features of protein chemistry. Other phase-refinement approaches that are based on different sources of information, denoted here as out-of-mainstream methods, are not frequently employed. This paper aims to show that mainstream and out-of-mainstream methods may be combined and may lead to dramatic advances in the present state of the art. The statement is confirmed by experimental tests using molecular-replacement, SAD-MAD and ab initio techniques.

The efficient multipurpose figure of merit MPF has been defined and characterized. It may be very helpful in phasing procedures. Indeed, it might be used for establishing the centric or acentric nature of an unknown structure, for identifying the presence of some pseudotranslational symmetry, for recognizing the correct solution in multisolution approaches and for estimating the quality of structure models as they become available during the phasing process. Thus, phase improvement or deterioration may be monitored and useless models may be discarded to save computing time. It is also shown that MPF may be applied in different phasing approaches, no matter if ab initio or non ab initio.

The joint probability distribution function method is applied to multiple-wavelength anomalous dispersion (MAD) powder data. The distributions are calculated by assuming prior knowledge of the scattering intensities at two wavelengths and of the anomalous-scatterer substructure. The method leads to formulas estimating the full structure phases and their reliability. The procedure has been applied to two structures, one unknown and one known; the second was used as a control for the phasing procedure. In spite of the unavoidable peak overlapping in the diffraction pattern, the formulas proved to be very effective. Combined with a new algorithm for phase extension, they enabled the solution of both crystal structures.

Two algorithms are described for limiting data resolution and for predicting the most informative wavelength combinations in MAD techniques. Both have been successfully tested using experimental data from a large set of test structures.