CMSC423: Bioinformatic Algorithms, Databases and Tools Lecture 8. Note

Transcription

1 MS: Bioinformatic lgorithms, Databases and ools Lecture 8 Sequence alignment: inexact alignment dynamic programming, gapped alignment Note Lecture 7 suffix trees and suffix arrays will be rescheduled

2 Exact alignment recap Exact matching can be done efficiently: O( ext + Pattern ) Key idea: preprocess data to keep track of similar regions, then use information to "jump" over places where no match can occur Z KMP B-M Inexact matching: why? Redundancy in genetic code: nucleotide sequence may differ, but proteins the same S Y P D Different amino-acid sequences still fold the same way: function unchanged (generally changing an amino-acid with a similar one doesn't affect protein function) ligning ESs (RN sequences) to DN need to account for gaps corresponding to exons Need to account for sequencing errors

3 Several hemoglobins HBB_HUMN HBB_HORSE HB_HUMN HB_HORSE MY_PHY LB5_PEM LB_LUPLU FFESFDLSPDVMNPKVKHKKVL-----FSDLHLDNLKF FFDSFDLSNPVMNPKVKHKKVL-----HSFEVHHLDNLKF YFPHF-DLS-----HSQVKHKKV-----DLNVHVDDMPNL YFPHF-DLS-----HSQVKHKKV-----DLLVHLDDLPL KFDRFKHLKEEMKSEDLKKHVVL-----LILKKKHHEEL FFPKFKLDQLKKSDVRWHERII-----NVNDVSMDDEKMS LFSFLKSEVP--QNNPELQHKVFKLVYEIQLQVVVVDL * :...:: *. : :. : From

4 Warm-up Longest ommon Subsequence iven two strings of letters, identify longest string of letters that occurs, in the same order, in both strings Find the longest chain of s, moving to the right and down Dynamic programming Idea: re-use previously computed information LS[i,j] longest common subsequence of strings S[..i], S[..j] i LS[i,j] is the maximum of: j.if S[i] = S[j] LS[i-, j-] + else LS[i -, j-]. LS[i, j]. LS[i, j ] oal: find LS[m,n]

5 5 omputing the LS table Row and column easy to fill Fill the rest column by column Find the actual sequence: trace-back pointers Extending to sequence alignment In LS, mis-alignments were free What happens if we pay for our "mistakes"? (this also allows us to account for "similar" aminoacids) Value[, ] = Value[,] = -5 Value[,-] = - etc. he same dynamic programming algorithm works!

6 he recurrences Score[i,j] is the maximum of: Score[i-, j-] + Value[S[i],S[j]] Score[i, j] + Value[S[i], -] (S[i] aligned to gap) Score[i, j ] + Value[-, S[j]] (S[j] aligned to gap) -- - he dynamic programming table Score[i,j] is the maximum of:. Score[i-, j-] + Value[S[i-],S[j-]] (S[i-], S[j-] aligned). Score[i, j] + Value[S[i], -] (S[i] aligned to gap). Score[i, j ] + Value[-, S[j]] (S[j] aligned to gap) Value (, ) = Value (, ) = -5 Value (, -) = - Note: we only look at adjacent boxes 6

7 Local vs. global alignment an we change the algorithm to allow S to be a substring of S? Key idea: gaps at the end of S are free Simply change the first row in the DP table to s nswer is no longer Score[n, m], rather the largest value in the last row Sub-string alignment

8 Local alignment What if we just want a region of similarity? -- First row and column set to s llow alignment to start anywhere: Score[i,j] = max{, case, case, case } nswer is location in matrix with highest score Local alignment 8

9 Various flavors of alignment lignment problem also called "edit distance" how many changes do you have to make to a string to convert it into another one. Edit distance also called Levenshtein distance Local alignment Smith-Waterman lobal alignment Needleman-Wunsch 9