Automated calculation of coordinate transformations for the superposition of protein structures

A computer program is described that performs a superposition of two protein structures. The program calculates a coordinate transformation that minimizes the root-mean-square deviation between atoms representing homologous structure in the two proteins. All atoms of the main chain and those atoms of side chains that bear common labels contribute to the calculation of the transformation. Required input by the user is either a small set of integers representing the sequence numbers of spatially equivalent residues in the two proteins and/or the initial and terminal residues of homologous elements of secondary structure. After using the starting set of homologies to calculate an initial transformation, the program discards the user input and then determines the full set of homologous residues by application of simple criteria. The superposition that results is the point of departure of a search for alternative transformations that represent superpositions of merit. The computation time for the superposition of two structures of 150 residues is approximately 20 s on a VAX 11/780 and rises linearly with the size of the problem. Thus, the program is inexpensive in computer time and applicable to even the largest of macromolecules whose three-dimensional structures are known.