Rigid domains in proteins: an algorithmic approach to their identification

A rigid domain, defined here as a tertiary structure common to two or more different protein conformations, can be identified numerically from atomic coordinates by finding sets of residues, one in each conformation, such that the distance between any two residues within the set belonging to one conformation is the same as the distance between the two structurally equivalent residues within the set belonging to any other conformation. The distance between two residues is taken to be the distance between their respective alpha carbon atoms. With the methods of this paper we have found in the deoxy and oxy conformations of the human hemoglobin alpha 1 beta 1 dimer a rigid domain closely related to that previously identified by Baldwin and Chothia (J. Mol. Biol. 129: 175-220, 1979). We provide two algorithms, both using the difference-distance matrix, with which to search for rigid domains directly from atomic coordinates. The first finds all rigid domains in a protein but has storage and processing demands that become prohibitively large with increasing protein size. The second, although not necessarily finding every rigid domain, is computationally tractable for proteins of any size. Because of its efficiency we are able to search protein conformations recursively for groups of non-intersecting domains. Different protein conformations, when aligned by superimposing their respective domain structures, can be examined for structural differences in regions complementing a rigid domain.