A rigid domain, defined here as a tertiary structure common to two or
more different protein conformations, can be identified numerically fr
om atomic coordinates by finding sets of residues, one in each conform
ation, 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 o
ther conformation. The distance between two residues is taken to be th
e distance between their respective alpha carbon atoms. With the metho
ds of this paper we have found in the deoxy and oxy conformations of t
he human hemoglobin alpha(1) beta(1) dimer a rigid domain closely rela
ted to that previously identified by Baldwin and Chothia (J. Mol. Biol
. 129: 175-220, 1979). We provide two algorithms, both using the diffe
rence-distance matrix, with which to search for rigid domains directly
from atomic coordinates. The first finds all rigid domains in a prote
in but has storage and processing demands that become prohibitively la
rge 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. Diff
erent protein conformations, when aligned by superimposing their respe
ctive domain structures, can be examined for structural differences in
regions complementing a rigid domain. (C) 1995 Wiley-Liss, Inc.