A pictorial representation of the matching of *n*-body cliques. The structures of two proteins, PDB codes 1xxa chain A and 1tig chain A, are shown in red and blue respectively. The representation of the 3D structure is a composite of the C^{?} trace, secondary structure, and accessible surface area (shown in mesh representation). The two sets of 6 points encircled in red and blue represent 6-body (*n*=6) cliques in **Clique Matching** step. The line that connects them symbolizes the matching of the Cartesian coordinates (by least square fitting), the secondary structure, and the solvent accessible surface area.

A pair of *n*-body cliques is matched if their RMSD on superimposition is smaller than a preset threshold. RMSD between cliques is calculated by 3D least squares fit. Then all matched pairs of *n*-body cliques are extended to all possible higher order cliques. To begin with, all possible 3-body cliques are compared to one another. Cliques are then extended to a maximum of 7 constituent residues.

Matching cliques helps in identifying structurally equivalent residues in the two structures. Using these equivalences, a final 3D least squares fit is performed to superimpose the two structures (**Global Alignment** step). Given that the matching of cliques is not unique, ie. many cliques comparisons could fit the criteria for a match. Of all the possible least square fits, the comparison that yields the best structure overlap is considered.