Sequence comparison: Local alignment

Transcription

1 Sequence comparison: Local alignment Genome 559: Introuction to Statistical an Computational Genomics Prof. James H. Thomas

2 Review global alignment en traceback G A A T C C A T A C Fill DP matrix from upper left to lower right, trace back alignment from lower right corner. start traceback

3 FYI - informal inuctive proof of best alignment path Consier the last step in the best alignment path to noe a below from its ajacent noes, where X, Y, an Z are scores of the best alignments up to those noes. We can reach noe a by three possible paths: an A-B match, a gap in sequence A or a gap in sequence B: X seq A Y The best-scoring path to a is the maximum of: seq B Z match gap gap a X + match Y + gap Z + gap BUT the best paths to X, Y, an Z are analogously the max of their three upstream possibilities, etc. Inuctively QED.

4 Local alignment A single-omain protein may be similar to only one region within a multi-omain protein. A DNA query may align to a small part of a genome. An alignment that spans the complete length of both sequences may be unesirable.

5 BLAST oes local alignments Typical search has a short query against long targets. The alignments returne show only the well-aligne match region of both query an target. query targets (e.g. genome contigs) matche regions returne in alignment

6 Review - global alignment DP Align sequence x an y. F is the DP matrix; s is the substitution matrix; is the linear gap penalty. j i F j i F y x s j i F j i F F j i 1, 1,, 1 1, max,,

7 Local alignment DP Align sequence x an y. F is the DP matrix; s is the substitution matrix; is the linear gap penalty. 1, 1,, 1 1, max,, j i F j i F y x s j i F j i F F j i for local

8 A (very) simple example initialize the same way as for global alignment = -5 A F i 1, j 1 j 1 G C F i 1, j j

9 A simple example = -5 A? F i 1, j 1 j 1 G? C? F i 1, j j

10 A simple example = -5 A? F i 1, j 1 j 1 G C F i 1, j j

11 A simple example = -5 A F i 1, j 1 j 1 G C F i 1, j j

12 A A A simple example = -5 A 2 F i 1, j 1 j 1 G C F i 1, j j

13 A simple example = -5 A 2 F i 1, j 1 j 1 G? C? F i 1, j j

14 A simple example = -5 A 2 F i 1, j 1 j 1 G C F i 1, j j

15 A simple example = -5 A 2 F i 1, j 1 j 1 G C F i 1, j j (signify no preceing alignment with no arrow)

16 A simple example = -5 A 2? F i 1, j 1 j 1 G? C? F i 1, j j (signify no preceing alignment with no arrow)

17 A simple example = -5 A 2 2 F i 1, j 1 j 1 G C F i 1, j j

18 A simple example = -5 A 2 2? F i 1, j 1 j 1 G? C? F i 1, j j

19 A simple example = -5 A 2 2 F i 1, j 1 j 1 G 4 C F i 1, j j

20 Traceback AG AG = -5 A 2 2 G 4 F i 1, j 1 j 1 C F i 1, j j Start traceback at highest score anywhere in matrix, follow arrows back until you reach

21 Multiple local alignments Traceback from highest score, setting each DP matrix score along traceback to zero. Now traceback from the remaining highest score, etc. The alignments may or may not inclue the same parts of the two sequences. 2 1

22 Local alignment Two ifferences from global alignment: If a DP score is negative, replace with. Traceback from the highest score in the matrix an continue until you reach. Global alignment algorithm: Neeleman- Wunsch. Local alignment algorithm: Smith- Waterman.

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24 (some) specific uses for alignments make a pairwise or multiple alignment (uh) test whether two sequences share a common ancestor (i.e. are significantly relate) fin matches to a sequence in a large atabase buil a sequence tree (phylogenetic tree) make a genome assembly (fin overlaps of sequence reas) repeat-mask a genome sequence (fin matches to a atabase of known repeats) map sequence reas to a reference genome

25 F i 1, j 1 F i 1, j Another example j Fin the optimal local alignment of AAG an GAAGGC. Use a gap penalty of = -5. j 1 G 2 A 2 2 A 2 4 G 6 G 2 C

26 Traceback G 2 A 2 2 A 2 4 G 6 G 2 C AAG AAG

27 G A A G G C DP matrix Traceback matrix You on t actually nee first row an column (-1) (-1) (-1) (-1) (-1) -1-1 (-1) -1 (-1) -1 (-1) -1-1 (-1) -1-1 (-1) = iagonal, -1 = gap left, +1 = gap top, -1 = no alignment

28 Problem fin the best GLOBAL alignment F i 1, j 1 F i 1, j j Fin the optimal global alignment of AAG an GAAGGC. Use a gap penalty of = -5. j 1 G -5 A -1 A -15 G -2 G -25 C (contrast with the best local alignment)