Detecting local structural similarity in proteins by maximizing number of equivalent residues

A new algorithm for superimposing protein structures based on maximizing the number of spatially equivalent residues is introduced. The algorithm works in three distinct steps. First, the optimal residue map is calculated by structural alignment. By default, the double dynamic programming algorithm, as implemented in the program ASH, was used for the structure alignment step, but we also present results based on alignments imported from three other programs (Dali, CE, and VAST).Second, the structures are spatially superimposed such that the effective number of equivalent residues (NER)--aligned residue pairs that can be spatially overlapped--is maximized. The NER score is an analytic, differentiable similarity function that rewards spatially equivalent residues but ignores non-equivalent ones. Maximization of the NER score results in accurate superpositions in cases where root mean square deviation (RMSD) minimization fails. Third, the NER function is used in conjunction with traditional dynamic programming to realign the structures based on the proximity of residues in the superposition. Results are presented for a wide range of superposition problems and compared to results from Dali, CE, and VAST. In addition, several structure-structure pairs that show only partial similarity are discussed, and results are compared to those from the LGA, SARF2, and ThreeCa programs.