The Better Alignment Among Output Alignments

Abstract— The sequence alignment is the one of the most fundamental technique of nowaday molecular biology. Computer scientists mapped it into the longest common sequence (LCS) problem which is a well-studied problem in algorithms. The optimal alignment score of LCS can be found in O(n1n2) time with the dynamic programming technique, where n1 and n2 is the lengths of the two sequences. Scientists presented many scoring functions to measure the goodness of the alignments in different criteria, such as affine gap penalty, and score matrices like PAMs, Blosums, Gonnets. All of these scoring functions are based on the same core, the dynamic programming. Once the optimal alignment score is found, tracing back the alignment lattice, which is produced during the dynamic programming, will obtain the alignment of the optimal score. Unfortunately, this optimal alignment is not unique in most time and the biologically meaningful alignment may not be optimal alignment. In this paper, we present some new definitions to measure the best alignment of the optimal alignments and illustrate the algorithms to solve them. The proposed algorithms give not only alignment of the optimal score but also more biologically meaningful without increasing the computing complexity of the original algorithm. Additionally new definitions can be used to find the better template when predicting the 3D protein structures. They are also interesting problems even if we do not consider the practical use of them.