4 Multiple Sequence Alignment 4.1 Multiple sequence alignment

38 Grundlagen der Bioinformatik, SS’09, D. Huson, May 10, 20094.3.4 Scoring along a treeAssume T is a phylogenetic tree whose leaves are labeled by the sequences to be aligned. Instead ofcomparing all pairs of residues in a column of a MSA, one may instead determine an optimal labelingof the internal nodes of the tree by symbols in a given column (in this case 3) and then sum over alledges in the tree (in this case 7):NNCNNCNSuch an optimal most parsimonious labeling of internal nodes can be computed in polynomial timeusing the Fitch algorithm (discussed later).Based on this tree, the scores for columns (3) is: 4 × 6 + 1 × (−3) + 2 × 9 = 39.C4.3.5 Scoring along a starIn a third alternative, one sequence is treated as the ancestor of all others others in a so-called starphylogeny:N(1) N N (2) N N (3)CNNNNNNCNCBased on this star phylogeny, assuming that sequence 1 is at the center of the star, the scores forcolumns (1), (2) and (3) respectively are: 4 × 6 = 24, 3 × 6 − 3 = 15 and 2 × 6 − 2 × 3 = 6.At present, there is no conclusive argument that gives any one scoring scheme more justification thanthe others. The sum-of-pairs score is most widely used, but it is problematic as we have seen earlier.4.4 Dynamic program for an MSAAlthough local alignments are biologically often more relevant, it is easier to discuss global MSA.Dynamic programs developed for pairwise alignment can be modified to multiple alignments. Wediscuss how to compute a global MSA for three sequences, in the case of a linear gap penalty. Assumewe are given:⎧⎨ A 1 = (a 11 , a 12 , . . . , a 1n1 )A = A 2 =⎩A 3 =(a 21 , a 22 , . . . , a 2n2 )(a 31 , a 32 , . . . , a 3n3 ).We proceed by computing the entries of an (n 1 + 1) × (n 2 + 1) × (n 3 + 1)-matrix F (i, j, k) recursively.After filling the matrix, the cell F (n 1 , n 2 , n 3 ) contains the best score α for a global alignment A ∗ .Traceback recovers an optimal alignment.