An improved method for combining isomorphous replacement and anomalous scattering diffraction data for macromolecular crystals

The coefficients for the 'best' Fourier synthesis for electron density have been shown by Blow and Crick to be the centroids of probability distributions (over the complex plane) for the structure factors. In defining probabilities for the case in which Bijvoet differences are ignored or averaged, Blow and Crick utilized simplifying assumptions not in accord with probability theory. Raiz and Andreeva defined probabilities for the same case in a theoretically correct manner. The present treatment provides somewhat better approximations for that case, and an extension to the case in which Bijvoet differences are utilized. The variances arising from experimental errors are maintained separately from those due to uncertainties in the heavy-atom parameters. The treatment is restricted here to derivatives in any one of which the scattering factors for heavy-atom anomalous scatterers have the same ratio of real and imaginary components.