The Combination of Phase Information

Abstract

In the multiple isomorphous replacement method the phase information from the various heavy atom derivatives and from anomalous scattering is combined by multiplying the individual phase probability curves. If the electron density map, which results from isomorphous replacement, can be fully interpreted, the crystallographer immediately starts with model refinement and the isomorphous phase information is left behind. However, if the electron density map is inadequate for complete interpretation, map improvement (= phase refinement) should precede model refinement. Solvent flattening and the inclusion of molecular averaging are examples of map improvement techniques (Chapter 8). Another way to improve the existing model is by combining the isomorphous replacement phase information with phase information from the known part of the structure. It is clear that a general and convenient way of combining phase information from these various sources would be most useful. Such a method has been proposed by Hendrickson and Lattman (1970) and has been based on previous studies by Rossmann and Blow (1961). Hendrickson and Lattman propose an exponential form for each individual probability curve of the following type: $${p_s}(\alpha ) = {N_s}\exp \left[ {{K_S} + {A_s}\cos \alpha + B\sin \alpha + {C_s}\cos 2\alpha + {D_S}\sin 2\alpha } \right]$$ P s(α) is the probability for phase angle a derived from source s. K s and the coefficients A s B s C s and D s contain, e.g., structure factor amplitudes but not the protein phase angles α. The multiplication of the available P s (α) functions to the overall probability function P(α) is now simplified to an addition of all K s and of the coefficients A s – D s in the exponential term.