Tables for
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F, ch. 16.1, pp. 344-345   | 1 | 2 |

Section Integration with anomalous dispersion

G. M. Sheldrick,c H. A. Hauptman,b C. M. Weeks,b* R. Millerb and I. Usóna

aInstitut für Anorganisch Chemie, Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany,bHauptman–Woodward Medical Research Institute, Inc., 73 High Street, Buffalo, NY 14203-1196, USA, and cLehrstuhl für Strukturchemie, Universität Göttingen, Tammannstrasse 4, D-37077 Göttingen, Germany
Correspondence e-mail: Integration with anomalous dispersion

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In a manner analogous to the SIR case, Hauptman (1982b)[link] derived the conditional probability distribution for triplet invariants given six magnitudes [(|E_{\bf H}|, |E_{-{\bf H}}|, |E_{\bf K}|, |E_{-{\bf K}}|, |E_{{\bf H}+{\bf K}}|, |E_{-{\bf H}-{\bf K}}|)] in the presence of anomalous dispersion. It was shown that unique estimates, lying anywhere in the whole interval 0–2π, could be obtained for the triplet values. This result was unanticipated since all earlier work had led to the conclusion that a twofold ambiguity in the value of an individual phase was intrinsic to the SAS approach. Later, it was demonstrated how the probabilistic estimates led to individual phases by means of a system of SAS tangent equations (Hauptman, 1996[link]). Although the initial application of this tangent-based approach to the previously known macromomycin structure (750 non-H protein atoms plus 150 solvent molecules) was encouraging, it has not yet been applied to unknown macromolecules.

The conditional probability distributions of the quartet invariants, in both the SIR and SAS cases, have been derived based on corresponding difference structure factors rather than on the individual structure factors themselves (Kyriakidis et al., 1996[link]). Fan and his collaborators (Fan et al., 1984[link]; Fan & Gu, 1985[link]; Fan et al., 1990[link]; Sha et al., 1995[link]; Zheng et al., 1996[link]) have also extensively studied the use of direct methods in the SAS case. Applications to the known small protein avian pancreatic polypeptide at 2 Å revealed the essential features of the molecule. The direct-methods approach was used to break the phase ambiguity for core streptavidin and azurin II (proteins of moderate size) using SAS data at 3 Å. Although the direct-methods maps in these cases did not reveal the structures, the phases were good enough to serve as successful starting points for solvent flattening.


Fan, H.-F. & Gu, Y.-X. (1985). Combining direct methods with isomorphous replacement or anomalous scattering data. III. The incorporation of partial structure information. Acta Cryst. A41, 280–284.Google Scholar
Fan, H.-F., Han, F.-S. & Qian, J.-Z. (1984). Combining direct methods with isomorphous replacement or anomalous scattering data. II. The treatment of errors. Acta Cryst. A40, 495–498.Google Scholar
Fan, H.-F., Hao, Q., Gu, Y.-X., Qian, J.-Z., Zheng, C.-D. & Ke, H. (1990). Combining direct methods with isomorphous replacement or anomalous scattering data. VII. Ab initio phasing of one-wavelength anomalous scattering data from a small protein. Acta Cryst. A46, 935–939.Google Scholar
Hauptman, H. (1982b). On integrating the techniques of direct methods with anomalous dispersion. I. The theoretical basis. Acta Cryst. A38, 632–641.Google Scholar
Hauptman, H. A. (1996). The SAS maximal principle: a new approach to the phase problem. Acta Cryst. A52, 490–496.Google Scholar
Kyriakidis, C. E., Peschar, R. & Schenk, H. (1996). The estimation of four-phase structure invariants using the single difference of isomorphous structure factors. Acta Cryst. A52, 77–87.Google Scholar
Sha, B.-D., Liu, S.-P., Gu, Y.-X., Fan, H.-F., Ke, H., Yao, J.-X. & Woolfson, M. M. (1995). Direct phasing of one-wavelength anomalous-scattering data of the protein core streptavidin. Acta Cryst. D51, 342–346.Google Scholar
Zheng, X.-F., Fan, H.-F., Hao, Q., Dodd, F. E. & Hasnain, S. S. (1996). Direct method structure determination of the native azurin II protein using one-wavelength anomalous scattering data. Acta Cryst. D52, 937–941.Google Scholar

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