In order to determine what values of rotational and translational parameters will best allow a large fragment of a protein molecule to explain the diffraction from another protein, a correlation function between Fo and Fc must be defined. Various such correlation functions are discussed; the scalar product 2 2S_Fo(h)Fc(h) is recommended for establishing the rotation, but the residual is better for the translation.It is shown that the calculation of the latter is not computationally impracticable. A large fragment of the hen-egg-white lysozyme molecule was used as a model for human lysozyme; rotational and translational searches were successful, and the unrefined residual was 49 %. Wilson's distribution functions are shown to apply to lysozyme surprisingly well. One consequence of this is that the results of Parthasarathy & Parthasarathi [Acta Cryst. (1972). A28, 426-432] may be used to derive a value of the average error in the coordinates.

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Methods suitable for completing and refining a protein structure are investigated both theoretically and with human and hen lysozymes as an example. Sim (or Woolfson) weighting and the ~-synthesis are compared with unweighted maps, and while the former is an improvement over unweighted maps, the ~-synthesis is less clearly an improvement. Both WFo exp (i~c) and difference maps were found to be useful, and a comparison between the isomorphous replacement map of human lysozyme and our maps based on hen lysozyme was encouraging.

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