Inexact Alignment: Dynamic Programming for Bioinformatics, Study notes of Computer Science

Download Inexact Alignment: Dynamic Programming for Bioinformatics and more Study notes Computer Science in PDF only on Docsity! CMSC423 Fall 2008 1 CMSC423: Bioinformatic Algorithms, Databases and Tools Lecture 9 inexact alignment dynamic programming, gapped alignment CMSC423 Fall 2008 2 Inexact alignment CMSC423 Fall 2008 5 HBB_HUMAN      FFESFGDLSTPDAVMGNPKVKAHGKKVL-----GAFSDGLAHLDNLKGTF HBB_HORSE      FFDSFGDLSNPGAVMGNPKVKAHGKKVL-----HSFGEGVHHLDNLKGTF HBA_HUMAN      YFPHF-DLS-----HGSAQVKGHGKKVA-----DALTNAVAHVDDMPNAL HBA_HORSE      YFPHF-DLS-----HGSAQVKAHGKKVG-----DALTLAVGHLDDLPGAL MYG_PHYCA      KFDRFKHLKTEAEMKASEDLKKHGVTVL-----TALGAILKKKGHHEAEL GLB5_PETMA     FFPKFKGLTTADQLKKSADVRWHAERII-----NAVNDAVASMDDTEKMS LGB2_LUPLU     LFSFLKGTSEVP--QNNPELQAHAGKVFKLVYEAAIQLQVTGVVVTDATL                *  :   .       . .:: *.  :       :.   : Several hemoglobins From http://bioinfo.cnio.es/docus/courses/SEK2003Filogenias/seq_analysis/multiple.html CMSC423 Fall 2008 6 Warm-up – Longest Common Subsequence • Given two strings of letters, identify longest string of letters that occurs, in the same order, in both strings AG C GTAG G C G A GTCAG A • Find the longest chain of 1s, moving to the right and down 11A G A C T G 111 11 A 1 G 1 1 11 GATGC CMSC423 Fall 2008 7 Dynamic programming • Idea: re-use previously computed information • LCS[i,j] – longest common subsequence of strings S1[1..i], S2[1..j] 11A G A C T G 111 11 A 1 G 1 1 11 GATGC i j LCS[i,j] is the maximum of: 1.if S1[i] = S2[j] LCS[i-1, j-1] + 1 else LCS[i -1, j-1] 2. LCS[i – 1, j] 3. LCS[i, j – 1] Goal: find LCS[m,n] CMSC423 Fall 2008 10 The recurrences AG-C-GTAG -GTCAG-A- Score[i,j] is the maximum of: 1. Score[i-1, j-1] + Value[S1[i],S2[j]] AG-C-G AG-C-G -GTCAG -GTCAT 2. Score[i – 1, j] + Value[S1[i], -] (S1[i] aligned to gap) AG-C-GT -GTCAG- 3. Score[i, j – 1] + Value[-, S2[j]] (S2[j] aligned to gap) AG-C- -GTCA CMSC423 Fall 2008 11 The dynamic programming table Score[i,j] is the maximum of: 1. Score[i-1, j-1] + Value[S1[i-1],S2[j-1]] (S1[i-1], S2[j-1] aligned) 2. Score[i – 1, j] + Value[S1[i], -] (S1[i] aligned to gap) 3. Score[i, j – 1] + Value[-, S2[j]] (S2[j] aligned to gap) -14-12-10-8-6-4-20- -14 -10 -8 -6 -4 -2 - A G A C T G -8 -6 -4 A 4 6 8 G 16 4 6 GATGC Value (A, A) = 10 Value (A, G) = -5 Value (A, -) = -2 Note: we only look at 3 adjacent boxes