Convergent algorithms for protein structural alignment

Background: Many algorithms exist for protein structural alignment, based on internal protein coordinates or on explicit superposition of the structures. These methods are usually successful for detecting structural similarities. However, current practical methods are seldom supported by convergence theories. In particular, although the goal of each algorithm is to maximize some scoring function, there is no practical method that theoretically guarantees score maximization. A practical algorithm with solid convergence properties would be useful for the refinement of protein folding maps, and for the development of new scores designed to be correlated with functional similarity. Results: In this work, the maximization of scoring functions in protein alignment is interpreted as a Low Order Value Optimization ( LOVO) problem. The new interpretation provides a framework for the development of algorithms based on well established methods of continuous optimization. The resulting algorithms are convergent and increase the scoring functions at every iteration. The solutions obtained are critical points of the scoring functions. Two algorithms are introduced: One is based on the maximization of the scoring function with Dynamic Programming followed by the continuous maximization of the same score, with respect to the protein position, using a smooth Newtonian method. The second algorithm replaces the Dynamic Programming step by a fast procedure for computing the correspondence between C a atoms. The algorithms are shown to be very effective for the maximization of the STRUCTAL score. Conclusion: The interpretation of protein alignment as a LOVO problem provides a new theoretical framework for the development of convergent protein alignment algorithms. These algorithms are shown to be very reliable for the maximization of the STRUCTAL score, and other distance-dependent scores may be optimized with same strategy. The improved score optimization provided by these algorithms provide means for the refinement of protein fold maps and also for the development of scores designed to match biological function. The LOVO strategy may be also used for more general structural superposition problems such as flexible or non-sequential alignments. The package is available on-line at http:// www. ime. unicamp. br/similar to martinez/lovoalign.