Integration with isomorphous replacement

Sheldrick, G. M.; Hauptman, H. A.; Weeks, C. M.; Miller, R.; Usón, I.

doi:10.1107/97809553602060000689

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

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

Section 16.1.9.1. Integration with isomorphous replacement

G. M. Sheldrick,^c H. A. Hauptman,^b C. M. Weeks,^b ^* R. Miller^b and I. Usón^a

^a Institut 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: weeks@orion.hwi.buffalo.edu

16.1.9.1. Integration with isomorphous replacement

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The integration of traditional direct methods with isomorphous replacement was initiated by Hauptman (1982a), who studied the conditional probability distribution of triplet invariants comprised jointly of native and derivative phases assuming as known the six magnitudes associated with reciprocal-lattice vectors H, K and $[-{\bf H}-{\bf K}]$ . It was shown that many triplets, whose true values were near either 0 or π, could be identified and reliably estimated. Later it was shown that cosine estimates could be obtained anywhere in the range −1 to +1 (Fortier et al., 1985). In a series of six recent papers, Giacovazzo and collaborators utilized a combined direct-methods/isomorphous-replacement approach, with limited success, to devise procedures for the ab initio solution of the phase problem for macromolecules (Giacovazzo, Siliqi & Ralph, 1994; Giacovazzo, Siliqi & Spagna, 1994; Giacovazzo, Siliqi & Zanotti, 1995; Giacovazzo & Platas, 1995; Giacovazzo, Siliqi & Platas, 1995; Giacovazzo et al., 1996). Their methods depend only on diffraction data for a pair of isomorphous structures and do not require any prior structural knowledge. Hu & Liu (1997) have generalized the earlier work to obtain the conditional distribution of the general (n-phase) structure invariant when diffraction data are available for any number (m) of isomorphous structures. Finally, it has been shown that, provided the heavy-atom substructure is known, Hauptman's triplet distribution leads to unique values for the triplets and the individual phases (Langs et al., 1995).

References

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International Tables for Crystallography (2006). Vol. F. ch. 16.1, p. 344