An application of vector space search methods to the Patterson function of myoglobin

By searching the 1.5 Å Patterson function of myoglobin (space group P2₁) with intragroup vector sets characteristic of the heme group and of the main chain of a 4- or 5-turn α-helix, it is shown that it is possible to determine the orientation of the heme, and the axial directions of the prominent helices A, B, E, G, and H. Additional searches performed with helices A, G, and H correctly reveal the true orientations about the helical axes. Translation searches with intergroup vectors, similarly yield the correct positions of the heme and helices A, G, and H relative to a 21 axis. The relative y coordinates (along 2₁) of the heme group and a helix can be unambiguously found by a search using vectors from the heme Fe atoms to the correctly oriented helix. Several image-seeking functions are explored by varying the selection and weighting of the search vectors. The best results are obtained with an image-seeking function defined as a weighted average over a selected subset of search vectors. The selection is made for each setting of the vector set, and is based on the value of the Patterson function at each search vector in relation to the distribution of values in the entire Patterson function.