4 Multiple Sequence Alignment 4.1 Multiple sequence alignment

Grundlagen der Bioinformatik, SS’09, D. Huson, May 10, 2009 41For example, consider: A = {CGCTTTA, ACGTT, GCTAG}. Assume 0 for a match score and +1 for amismatch, deletion and insertion. Then D(A 1 , A 2 ) = 4, D(A 1 , A 3 ) = 4 and D(A 2 , A 3 ) = 4. Choosec = A 1 as center. First align A 1 and A 2 :Then align A ′ 1 and A 3:Combine both to obtain the following alignment:-CGCTTTAACG--TT--CGCTTTA---GC--TAG-CGCTTTA-ACG--TT----GC--TAGLet A ∗ c denote the multiple alignment obtained by successively aligning all other sequences to thecenter sequence A c .Theorem 4.6.2 If the pairwise distances satisfy the triangle inequality, then D(A ∗ c) < 2D SP (A ∗ ).(Proof: see Gusfield, pg. 350)4.7 Multiple alignment to a treeDefinition 4.7.1 (Phylogenetic alignment tree) Suppose we are given a set of sequences A ={A 1 , A 2 , . . . , A r } and a tree T A = (V, E) whose leaves are labeled by A. Let each internal node u of Twith children v and w be labeled with an ancestral sequence of the labels of v and w. Then T is calleda phylogenetic alignment tree of A.Example: Let A = {bog,dog,hag,bad}hodboghadbog dog hag badTree T with sequences at leaves→bog dog hag badA phylogenetic alignment tree of AEach edge in a phylogenetic alignment tree T can be assigned a distance:Definition 4.7.2 (edge distance) If e = (U, V ) is an edge that joins sequences U and V , then wedefine the edge distance of e as the edit distance D L (U, V ). The distance D(T ) of a phylogeneticalignment T is the sum of its edge distances.