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

International Tables for Crystallography (2006). Vol. F, ch. 14.1, p. 294   | 1 | 2 |

Section 14.1.3. The method of multiple isomorphous replacement

B. W. Matthewsa*

aInstitute of Molecular Biology, Howard Hughes Medical Institute and Department of Physics, University of Oregon, Eugene, OR 97403, USA
Correspondence e-mail:

14.1.3. The method of multiple isomorphous replacement

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The phase information provided by a second isomorph is illustrated in Fig.[link]). In theory, the three phase circles will intersect at a point and the phase ambiguity will be resolved. In practice, there will be errors in the observed amplitudes [F_{P}] and [F_{PH}] and in the heavy-atom parameters (and thus in [{\bf F}_{H}]). Also, the isomorphism may be imperfect. As a result, the intersections of the three phase circles may not coincide. Another complication arises from the fact that for reflections where [{\bf F}_{H}] is small, the circles will be essentially concentric and will not have well defined points of intersection. In other words, the phase determination will become indeterminate. The method of Blow & Crick (1959[link]) was introduced as a way to take all these factors into account. It has had an extraordinary impact, not only as a practical method for protein phase determination, but also in influencing all subsequent thinking in this area.


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(a) Harker construction for a double isomorphous replacement. [\varphi_{M}] is the `most probable' phase for [{\bf F}_{P}]. (b) Phase probability distribution corresponding to the double isomorphous replacement shown in part (a). The curve for derivative 1 is solid, that for derivative 2 is dashed, and that for the combined distribution is drawn as a dotted-and-dashed line.


Blow, D. M. & Crick, F. H. C. (1959). The treatment of errors in the isomorphous replacement method. Acta Cryst. 12, 794–802.Google Scholar

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