Aligning multiple protein structures by deterministic annealing.

Protein structure alignment plays a key role in protein structure prediction and fold family classification. An efficient method for multiple protein structure alignment in a mathematical manner is presented, based on deterministic annealing technique. The alignment problem is mapped onto a nonlinear continuous optimization problem (NCOP) with common consensus chain, matching assignment matrices and atomic coordinates as variables. At each step in the annealing procedure, the NCOP is decomposed into as many sub-problems as the number of protein chains, each of which is actually an independent pairwise structure alignment between a protein chain and the consensus chain and hence can be efficiently solved by the parallel computation technique. The proposed method is robust with respect to choice of iteration parameters for a wide range of proteins, and performs well in both multiple and pairwise structure alignment cases, compared with existing alignment methods.