Using molecular principal axes for structural comparison: determining the tertiary changes of a FAB antibody domain induced by antigenic binding

BACKGROUND: Comparison of different protein x-ray structures has previously been made in a number of different ways; for example, by visual examination, by differences in the locations of secondary structures, by explicit superposition of structural elements, e.g. α-carbon atom locations, or by procedures that utilize a common symmetry element or geometrical feature of the structures to be compared. RESULTS: A new approach is applied to determine the structural changes that an antibody protein domain experiences upon its interaction with an antigenic target. These changes are determined with the use of two different, however comparable, sets of principal axes that are obtained by diagonalizing the second-order tensors that yield the moments-of-geometry as well as an ellipsoidal characterization of domain shape, prior to and after interaction. Determination of these sets of axes for structural comparison requires no internal symmetry features of the domains, depending solely upon their representation in three-dimensional space. This representation may involve atomic, Cα, or residue centroid coordinates. The present analysis utilizes residue centroids. When the structural changes are minimal, the principal axes of the domains, prior to and after interaction, are essentially comparable and consequently may be used for structural comparison. When the differences of the axes cannot be neglected, but are nevertheless slight, a smaller relatively invariant substructure of the domains may be utilized for comparison. The procedure yields two distance metrics for structural comparison. First, the displacements of the residue centroids due to antigenic binding, referenced to the ellipsoidal principal axes, are noted. Second, changes in the ellipsoidal distances with respect to the non-interacting structure provide a direct measure of the spatial displacements of the residue centroids, towards either the interior or exterior of the domain. CONCLUSION: With use of x-ray data from the protein data bank (PDB), these two metrics are shown to highlight, in a manner different from before, the structural changes that are induced in the overall domains as well as in the H3 loops of the complementarity-determining regions (CDR) upon FAB antibody binding to a truncated and to a synthetic hemagglutinin viral antigenic target.