The molecular replacement method. II. The translation function problem; a new translation function

Abstract

A new translation function, a generalization of the translation function introduced by Rossmann, Blow, Harding, and Coller, is defined. Peaks of this new translation function are related to the orientation and point group of and translation vectors between molecules in a crystal. A method is formulated to determine all peaks of this new translation function corresponding to a given crystal. The applicability of this method is shown in the analysis of translation function data to determine the translation vectors between molecules, and to determine the point group of the molecules when the solution of the rotation function problem is not unique. This new translation function has an advantage over the translation function introduced by Rossmann and co-workers, in that it may contain peaks which are not streaked. It is proposed that this new translation function be used in the structure determination of bovine liver catalase. For trigonal crystalline bovine liver catalase it is shown how this new translation function can be used to determine the point group of and the translation vectors between the catalase molecules.