Crystallographic relationship between human and hen-egg lysozymes. I. Methods for the establishment of molecular orientational and positional parameters

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 F_o and F_c must be defined. Various such correlation functions are discussed; the scalar product ΣF_o²(h)F_c²(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.