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A direct-methods solution to the phase problem in the single isomorphous replacement case: theoretical basis and initial applications
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1985
Year
Numerical AnalysisCrystal StructureEngineeringMolecular BiologyDirect-methods SolutionSpectra-structure CorrelationPhase ProblemStructure DeterminationCosine InvariantsStructure ElucidationProtein X-ray CrystallographyBiophysicsBiochemistryThree-phase Structure InvariantsInverse ProblemsMolecular ModelingCrystallographyActa CrystStructural BiologyPhase RetrievalPhase EquilibriumNatural SciencesTransformation KineticsInitial ApplicationsMultiscale Modeling
The probabilistic theory of the three-phase structure invariants for a pair of isomorphous structures [Hauptman (1982). Acta Cryst. A38, 289-294] is reexamined. The analysis leads to distributions capable of estimating cosine invariants in the full range of -1 to +1. In particular, it is shown that heavy-atom substructure information can be incorporated easily into the distributions. The initial applications, using calculated diffraction data from the protein cytochrome c550, MR ≃ 14 500, and its PtCl2-4 derivative show that a remarkable increase in accuracy results from the use of the revised distributions, particularly after the incorporation of heavy-atom substructure information. Finally, it is shown that in the individual phase determinations the redundant cosine invariants play a role identical to that of the multiple isomorphous derivatives and thus provide the basis for the solution of the phase problem in the single isomorphous replacement case.