title: On integrating the techniques of direct methods and SIRAS: the probabilistic theory of doublets and its applications.
abstract: The mathematical formalism of direct methods is here applied to the SIRAS (single-isomorphous replacement combined with anomalous scattering) case. Specifically, the joint probability distribution of three structure factors, which plays the central role in the probabilistic theory of the two-phase structure invariants (doublets), is derived. This distribution leads directly to the conditional probability distribution of the two-phase structure invariants, given the values of selected sets of magnitudes. Furthermore, a probabilistic formula for estimating individual phases of the derivative structure is derived, provided that the heavy-atom substructure is assumed to be known. The formulas were tested for experimental SIRAS data and results are reported.
authors.affiliation: Hauptman-Woodward Medical Research Institute and Department of Structural Biology, School of Medicine and Biomedical Sciences, State University of New York at Buffalo, 73 High Street, 14203, USA. xu@hwi.buffalo.edu
authors.forename: Hongliang
authors.initials: H
authors.lastname: Xu
authors.forename: Herbert A
authors.initials: HA
authors.lastname: Hauptman
mesh_terms: D000115:Acetylesterase / Q000737:chemistry; D043383:Adenosylhomocysteinase; D018360:Crystallography, X-Ray; D006867:Hydrolases / Q000737:chemistry; D008956:Models, Chemical; D011336:Probability; D011506:Proteins / Q000737:chemistry*; D012542:Scattering, Radiation
chemical_list: D011506:Proteins; D006867:Hydrolases; D000115:Acetylesterase; C081851:acetylxylan esterase; D043383:Adenosylhomocysteinase