On the estimation of the locations of subunits within macromolecular aggregates from neutron interference data

Neutron interference methods are currently being used to determine the positions of the centers of mass of subunits in macromolecular aggregates, e.g. Langer, Engelman & Moore [J. Mol. Biol. (1978). 119, 463-485] and May et al. [Fourth International Conference on Small-Angle Scattering of X-rays and Neutrons, Gatlinberg, Tennessee, 1977. Abstract F-2. Unpublished]. Subunit positions are found by triangulation from distances estimated from data sets which relate subunits pairwise. A serious limitation of the method as it has been applied so far is that only an approximate value for the distance between a pair of subunits can be obtained from its corresponding data. The errors in distances which result from these approximations lead in turn to inaccuracies in subunit positions. This paper presents a method for analyzing the whole set of data obtained for a structure which eliminates the need for approximating distances from individual data sets and leads, therefore, to unbiased estimates of subunit locations. This method of analysis also yields information about subunit radius of gyration in situ.