International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 12.2, pp. 258-259
Section 12.2.4.1. Treatment of errors
a
Institut für Pharmazeutische Chemie der Philipps-Universität Marburg, Marbacher Weg 6, D-35032 Marburg, Germany, and bMax-Planck-Institut für Biochemie, 82152 Martinsried, Germany |
Until now, we have dealt with cases involving perfect data. Although this ideal may now be attainable using MAD techniques, this is not necessarily the usual laboratory situation. In the first place, it is necessary to scale the derivative data to the native . One of the most common scaling procedures is based on the expected statistical dependence of intensity on resolution (Wilson, 1949). This may not be particularly accurate when only low-resolution data are available, in which case a scaling through equating the Patterson origin peaks of native and derivative sets may provide better results (Rogers, 1965).
A model to account for errors in the data, determination of heavy-atom positions etc. was proposed by Blow & Crick (1959), in which all errors are associated with (Fig. 12.2.4.1); a more detailed treatment has been provided by Terwilliger & Eisenberg (1987). Owing to errors, the triangle formed by , and fails to close. The lack of closure error ɛ is a function of the calculated phase angle : Once an initial set of heavy-atom positions has been found, it is necessary to refine their parameters (x, y, z, occupancy and thermal parameters). This can be achieved through the minimization of where E is the estimated error (Rossmann, 1960; Terwilliger & Eisenberg, 1983). This procedure is safest for noncentrosymmetric reflections (φ restricted to 0 or π) if enough are present. Phase refinement is generally monitored by three factors: for noncentrosymmetric reflections only; acceptable values are between 0.4 and 0.6; which is useful for monitoring convergence; and the which should be greater than 1 (if less than 1, then the phase triangle cannot be closed via ).
The resulting phase probability is given by The phases have a minimum error when the best phase , i.e. the centroid of the phase distribution, is used instead of the most probable phase. The quality of the phases is indicated by the figure of merit m, where A value of 1 for m indicates no phase error, a value of 0.5 represents a phase error of about 60°, while a value of 0 means that all phases are equally probable.
The best Fourier is calculated from where the electron density should have minimal errors.
References
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