Applying Needleman-Wunsch global alignment, we can compute the optimal score of aligning the first i peaks in the former spectrum with the first j peaks in the current spectrum by dynamic programming.
The score for aligning X to itself is the smaller of the expected score of aligning any two standard amino acids and -1, rounded to the nearest integer.
The optimal alignment will maximize the total score of aligning all three fragments: i.e. (4) where TS R (n, m) is a trace−back path for element (n, m) in matrix S R. The last condition states that elements (n, m) and (n′, m′) are on the same alignment path.
The similarity between a i and b j in extension mapping is then defined as (6) By awarding the candidate pairs with a proportion of the score of neighbouring aligned pairs, PINALOG aims at mapping more neighbouring protein pairs.
The latter expected amino acid pair scores are also obtained as weighted sums of scores, in a manner similar to the one described by equations (12) and (13), where the score for aligning two symbols has one of the three established values for match, transition mutation or transversion mutation.
More precisely, we consider the average substitution score of aligned amino acids or the average number of matches for DNA or RNA alignment, respectively, to decide if further fragments starting at i and j are considered.
We carried out this shuffling procedure 200 times and collected the scores of the aligned block.
During this process, the quality of the ungapped alignment is gauged by the score of each pair of aligned amino acids using a scoring matrix, such as the popular BLOSUM62 (Henikoff and Henikoff, 1992).
We obtain the score of a pair of aligned conserved segments from the CHAOS output.
Instead of summing up substitution scores for aligned residues and subtracting gap penalties, the score of an alignment is based on P-values of local sequence similarities.
