A translation function combining packing and diffraction information: an application to lysozyme (high-temperature form)

A new translation function T(t) is defined, whose main peak is expected to give directly the absolute position t = t₀ of a known molecular configuration (the isostructural model) of known orientation in an unknown crystal structure. T(t) combines all required information: crystal symmetry, molecular steric properties of the model and experimental data (observed structure factors F_o) leading to more reliable results: T(t) = TO(t)/O(t), where TO(t) measures the degree of agreement between F_o and F_c(t), while O(t) is a function measuring intermolecular overlap. TO and O can both be computed efficiently by the possibility of their expansion in Fourier series, and the use of FFT. A theoretical study followed by application to a simple synthetic structure cast light upon ambiguities and failures [e.g. Bott & Sarma (1976). J. Mol. Biol. 106, 1037-1046] encountered in using translation functions previously described [e.g. Crowther & Blow (1967). Acta Cryst. 23, 544-548]. The crystal structure of the high-temperature form of hen-egg-white lysozyme was determined at 6 Å resolution by the application of this fast translation function and compared with the equivalent structure obtained by the isomorphous replacement method.