Theoretical and Computational Aspects of Protein Structural Alignment
Computing alignments of proteins based on their structure is one of the fundamental tasks of bioinformatics. It is crucial in all kinds of comparative analysis as well as in performing evolutionary and functional classification. Whereas determination of sequence relationships is well founded in statistical models, there is still considerable uncertainty over how to describe geometric relationships between proteins. Continuous growth of structural databases calls for fast and reliable algorithmic methods, enabling one to effectively compute alignments of pairs and larger sets of protein molecules. Although such methodologies have been developed over the past two decades, there exist so-called “difficult similarities” which may include repeats, insertions or deletions, permutations and conformational changes. A brief overview of existing methodologies with emphasis on the different approaches to decomposition of structures into smaller fragments is followed by a presentation of a formalism of local descriptors of protein structures. A formal definition of the problem of computing optimal alignments accommodating aforementioned difficulties is presented along with an analysis of the computational complexity of its important variants. Examples of “difficult similarities” and practical aspects of protein structure comparison are discussed.
This study was supported by the Biocentrum-Ochota Project (POIG.02.03.00-00-003/09), the research grant (DEC-2011/03/D/NZ2/02004) of the National Science Centre, and partially by BST/BF funds of the University of Warsaw. Figures 1, 11 and 10 are reproduced from an earlier study by the same authors .
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