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The analysis of X-ray diffraction intensities is complicated by the anisotropy of anomalous scattering (AAS) that can occur due to resonance associated with transitions between core electrons and valence molecular orbitals. Substantial AAS has been observed directly in diffraction data near the K edge of selenium in selenolanthionine [Templeton & Templeton (1988). Acta Cryst. A44, 1045-1051] and in pleiochroism of X-ray absorption in selenobiotinyl streptavidin [Hendrickson, Pähler, Smith, Satow, Merritt & Phizackerley (1989). Proc. Natl Acad. Sci. USA, 86, 2190-2194]. The impact of AAS on the multiple-wavelength anomalous diffraction (MAD) method for phase determination is of particular interest in the context of this chemical state of selenium in the light of a general method that has been developed to incorporate selenomethionine into proteins for use in MAD phasing [Hendrickson, Horton & LeMaster (1990). EMBO J. 9, 1665-1672]. The first step of the MAD phasing method necessarily assumes that the anomalous-scattering factors are isotropic and our first aim here is to evaluate the effect of this approximation on initially determined phases. To obtain ultimate phases free from the effects of anisotropy, a least-squares procedure has been written in which global parameters (i.e. pertaining to the whole data set) are refined simultaneously with local parameters (i.e. pertaining to a given node h). The AAS is taken explicitly into account by considering f' and f” as tensors instead of scalars [Templeton & Templeton (1982). Acta Cryst. A38, 62-67], and the components of the f' and f'' tensors are among the refinable global parameters. The effectiveness of this procedure is tested with data simulated from the refined atomic model of selenobiotinyl streptavidin. The application of this procedure to actual Photon Factory measurements is also described. The results show that AAS does not cripple the MAD method, and that phases uncorrupted by these effects can be recovered.
