Abstract
BackgroundMany 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.ResultsIn 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 Cα atoms. The algorithms are shown to be very effective for the maximization of the STRUCTAL score.ConclusionThe 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/~martinez/lovoalign.
Highlights
Many algorithms exist for protein structural alignment, based on internal protein coordinates or on explicit superposition of the structures
General methodological principles we describe the Low Order Value Optimization problem
We explain the way in which structural alignment can be interpreted as a Low Order Value Optimization (LOVO) problem, and we show how this interpretation naturally suggests robust convergent algorithms for protein alignment
Summary
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. 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. The number of protein structures obtained experimentally becomes larger every year. This large database is the source of data for the study of important problems in structural biology: The classification of protein structures according to their function, and the correlation of sequence and structure. With the increase in computer power and the expansion of the database, using this information for protein design and for the characterization of the protein folding landscape (or fold space) is becoming possible [5,6]
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have