Matching protein structures with fuzzy alignments.

Unraveling functional and ancestral relationships between proteins as well as structure-prediction procedures require powerful protein-alignment methods. A structure-alignment method is presented where the problem is mapped onto a cost function containing both fuzzy (Potts) assignment variables and atomic coordinates. The cost function is minimized by using an iterative scheme, where at each step mean field theory methods at finite "temperatures" are used for determining fuzzy assignment variables followed by exact translation and rotation of atomic coordinates weighted by their corresponding fuzzy assignment variables. The approach performs very well when compared with other methods, requires modest central processing unit consumption, and is robust with respect to choice of iteration parameters for a wide range of proteins.