Anomalous Scattering Data Research Articles

Direct phasing of one-wavelength anomalous-scattering data

This paper presents a brief survey of methods in ab initio phasing of one-wavelength anomalous-scattering data. In particular, the method implemented in the computer program OASIS has been tested using two new data sets from orotidine 5'-monophosphate decarboxylase (OMPDC) [Appleby et al. (2000). Proc. Natl Acad. Sci. USA. In the press] and PurE [Mathews et al. (1999). Structure, 7(11), 1395-1406]. The Se atoms were located by the small-molecule program SAPI. The electron density maps after OASIS and density modification for both structures clearly revealed the Calpha trace and, in the case of PurE, most side-chains. The test with the OMPDC data demonstrated that, by exploiting the anomalous signal at a single wavelength, direct methods can be used to determine phases at moderate ( approximately 2.5 A) macromolecular crystallographic resolution for a large-size protein (5663 non-H atoms in the asymmetric unit). The exceptionally good quality of the electron map shown in the case of PurE suggested that fully automatic model fitting is possible.

The Estimation of Four-Phase Structure Invariants Using the Single Difference of Isomorphous Structure Factors

The recently introduced approach of using the difference between isomorphous structure factors as a random variable in the derivation of joint probability distributions of isomorphous structure factors has been extended to secure the conditional joint probability distribution of the quartet phase sums present among isomorphous structure factors. It is shown for calculated data sets (native and heavy-atom derivative) of the proteins avian pancreatic polypeptide and cytochrome c that, with single-wavelength anomalous-scattering data, reliable estimates can be obtained for the quartet phase sums, even if the estimates are based on the structure-factor differences of the four quartet main-term reflections only.

Direct phasing of one-wavelength anomalous-scattering data of the protein core streptavidin.

The direct method [Fan, Hao, Gu, Qian, Zheng & Ke (1990). Acta Cryst. A46, 935-939] was used to break the phase ambiguity intrinsic to one-wavelength anomalous scattering data from a known protein of moderate size, core streptavidin, which was solved originally with three-wavelength anomalous diffraction data [Hendrickson, Pähler, Smith, Satow, Merritt & Phizackerley (1989). Proc. Natl Acad. Sci. USA, 86, 2190-2194]. Unlike that in the previous test with a small protein, the Fourier map calculated with the direct-method phases could not clearly reveal the moderate-sized protein structure. However, the phases can be improved step by step using Wang's solvent-flattening method, non-crystallographic symmetry averaging and the skeletonization method. The final electron-density map clearly shows most Calpha positions and some side chains and it is traceable without prior knowledge of the structure. It is concluded that the direct method is capable of breaking the OAS phase ambiguity of a moderate-sized protein at moderate resolution such as 3 A, while the combination of direct methods with macromolecular techniques may produce phases good enough for unknown protein structure to be traced.

Direct phasing of one-wavelength anomalous-scattering data of the protein core streptavidin

Direct phasing of one-wavelength anomalous-scattering data of the protein core streptavidin

On the application of one-wavelength anomalous scattering. IV. The absolute configuration of the anomalous scatterers.

An essential first step in most techniques for using anomalous-scattering data for phase determination is to determine the positions of the anomalous scatterers. This is usually done by use of the anomalous differences, either as input to a direct-methods procedure or to produce a Patterson map. If the arrangement of anomalous scatterers is noncentrosymmetric then it is also necessary to find their absolute configuration and a process is described for doing this based on the properties of the P(s) function [Okaya, Saito & Pepinsky (1955). Phys. Rev. 98, 1857-1858]. If the arrangement of anomalous scatterers is centrosymmetric then the problem does not occur.

Combined X-ray single-crystal and neutron powder refinement of modulated structures and application to the incommensurately modulated structure of Bi2Sr2CaCu2O8+y

A method is described for the refinement of modulated structures from a combined set of single-crystal and powder diffraction data or from powder data only. The method is especially useful when information on light atoms is to be obtained and no single crystals of suitable size for neutron diffraction are available. The program in which the method is encoded allows for differences in composition between the single-crystal and powder samples. Application to the incommensurately modulated superconductor Bi2Sr2CaCu2O8+y (2212) using powder neutron and single-crystal X-ray data confirms that the oxygen modulation in the Bi–O layer is saw-tooth-like, as observed in the preceding study based solely on X-ray data [Petricek, Gao, Lee & Coppens (1990). Phys. Rev. B, 42, 387–392], but with improved accuracy in the resulting parameters. The extra oxygen content is explicitly related to the modulation model and corresponds to 0.14–(4) per formula unit. With the refined site occupancies for the heavy atoms and the results of an anomalous-scattering study on the bismuth distribution [Coppens, Lee, Gao & Sheu (1991). J. Phys. Chem. Solids, 52, 1267–1272], a copper valency of 2.31 is obtained for the single-crystal sample. The powder value of 2.40 is somewhat less reliable as no anomalous-scattering data are available for the powder sample.

The joint probability distribution of structure factors incorporating anomalous-scattering and isomorphous-replacement data

A method to derive joint probability distributions of structure factors is presented which incorporates anomalous-scattering and isomorphous-replacement data in a unified procedure. The structure factors FH and F−H, whose magnitudes are different due to anomalous scattering, are shown to be isomorphously related. This leads to a definition of isomorphism by means of which isomorphous-replacement and anomalous-scattering data can be handled simultaneously. The definition and calculation of the general term of the joint probability distribution for isomorphous structure factors turns out to be crucial. Its analytical form leads to an algorithm by means of which any particular joint probability distribution of structure factors can be constructed. The calculation of the general term is discussed for the case of four isomorphous structure factors in P1, assuming the atoms to be independently and uniformly distributed. A main result is the construction of the probability distribution of the 64 triplet phase sums present in space group P1 amongst four isomorphous structure factors FH, four isomorphous FK and four isomorphous F−H−K. The procedure is readily generalized in the case where an arbitrary number of isomorphous structure factors are available for FH, FK and F−H−K.

The application of one-wavelength anomalous scattering. II. An analytical approach for phase determination

An analytical method has been developed by which phase estimates may be uniquely determined from one-wavelength anomalous-scattering data; the method as described can be applied to structures containing one type of anomalous scatterer. The method has been tested on two structures. The first is an Hg derivative of a small protein, avian pancreatic polypeptide (App), crystallizing in space group C2 with one molecule of 36 amino-acid residues in the asymmetric unit. The second is a Pt derivative of ribonuclease Sa (RNA), crystallizing in space group P212121 with two molecules of 96 amino-acid residues in the asymmetric unit. The phases for App give an electron density map which can easily be interpreted in terms of a model. For RNA the map is less clear but has strong similarities with the true map and could probably be interpreted. If anomalous scatterers are centrosymmetrically arranged then the analysis shows that there is a simple alternative process for calculating a map, called a Bp map, which directly shows a structural image.