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Introduction To Bioinformatics Tutorial 2
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Local Alignment Tutorial 2
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Usage: Spelling,.. Different Types: –Hamming –Levenshtein Algorithm –Naïve solution –Dynamic programming Edit Distance
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Richard Bellman (1940) “Program” –Computer program? –Optimal Schedule Dynamic Programming
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Conditions –Division to sub-problems possible –(Optimal) Sub-problem solution usable (many times?) –“Bottom-up” approach Dynamic Programming
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Examples –Shortest path –Fibonacci Dynamic Programming
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Usage: Spelling, Biology,… Compare sequences Similar sequence Ancestral origin Function … Edit Distance
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Dynamic Programming algorithm for finding local matches between two sequences. What is a local match?: –It is a best-matching, highest-scoring region between two sequences. –It is a well conserved region between two sequences. Local Alignment
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Alignment NnNn N1N1 M1M1 MmMm
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NnNn N1N1 M1M1 MmMm [I,J] Best alignment M 1..I, N 1..J
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Alignment All possible alignments encoded as path in matrix
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The differences: 1.We can start a new match instead of extending a previous alignment. 2.Instead of looking only at the far corner, we look anywhere in the table for the best score Global vs Local Global Local Scoring System Match : +1 Mismatch: -2 Indel : -1
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Local Alignment Scoring System –Match : +1N i =M j –Mismatch: -1N i =M j –Indel : -2 NnNn N1N1 M1M1 MmMm
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Local Alignment Scoring System –Match : +1N i =M j –Mismatch : -1N i =M j –Indel : -2 NnNn N1N1 M1M1 MmMm
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Local Alignment Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 NnNn N1N1 M1M1 MmMm
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Local Alignment Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 NnNn N1N1 M1M1 MmMm N1-N1-
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Local Alignment Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 NnNn N1N1 M1M1 MmMm -M1-M1
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Local Alignment Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 NnNn N2N2 N1N1 M1M1 M2M2 MmMm N1 -.. M1M2..
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Local Alignment Fill: 1.We fill the table like in global alignment, but we don’t allow negative numbers (turn every negative number to 0) 2.No arrows coming out from cells with a 0. Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 +1 if M 2 =N 2 ; -1 if M 2 =N 2 -2 NnNn N2N2 N1N1 M1M1 M2M2 MmMm N 1 N 2.. M 1 M 2.. N 1 -.. M 1 M 2.. N 1 N 2.. M 1 -..
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Local Alignment Trace: We trace back from the highest scoring cells. +1 if M 2 =N 2 ; -1 if M 2 =N 2 -2 NnNn N2N2 N1N1 M1M1 M2M2 MmMm N 1 N 2.. M 1 M 2.. N 1 -.. M 1 M 2.. N 1 N 2.. M 1 -..
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Local Alignment Question: Will there be gaps at the start/end? NnNn N2N2 N1N1 M1M1 M2M2 MmMm
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0 T 1 A 2 A 3 T 4 A 5
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 A 2 A 3 T 4 A 5
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0 A 2 0 A 3 0 T 4 0 A 5 0
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0 A 2 0 A 3 0 T 4 0 A 5 0 -T-T
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0 A 2 0 A 3 0 T 4 0 A 5 0 T-T-
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0? A 2 0 A 3 0 T 4 0 A 5 0
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 0? A 2 0 A 3 0 T 4 0 A 5 0 -T T- -T T- -T +1 -2
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 01 A 2 0 A 3 0 T 4 0 A 5 0
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 0000000 T 1 010 A 2 0 A 3 0 T 4 0 A 5 0
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0 0T 4 0A 3 0A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10
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0A 5 0T 4 0A 3 1200200A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10
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0A 5 0T 4 3101100A 3 1200200A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10
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0A 5 1020010T 4 3101100A 3 1200200A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10
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1300200A 5 1020010T 4 3101100A 3 1200200A 2 0010010T 1 00000000 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 000000 010010 A 2 0020021 A 3 001101 3 T 4 0100201 A 5 00200 3 1
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0 T1T1 A2A2 C3C3 T4T4 A5A5 A6A6 0 000000 T 1 010010 A 2 0020021 A 3 0011013 T 4 0100201 A 5 0020031 Leave only paths from highest score
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TAA TACTA TAATA
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And Now… Global Alignment 1.We keep negative numbers. 2.Arrows coming out from any cell. 3.We trace back from right-bottom to left-top of the table. Scoring System –Match : +1 –Mismatch: -1 –Indel : -2 +1 if M 2 =N 2 ; -1 if M 2 =N 2 -2 NnNn N2N2 N1N1 M1M1 M2M2 MmMm N 1 N 2.. M 1 M 2.. N 1 -.. M 1 M 2.. N 1 N 2.. M 1 -..
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A 5 T 4 A 3 A 2 T 1 0 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10 Match: +1 Mismatch:-1 Indel: -2 -12-10-8-6-4-2 -10 -8 -6 -4 -2 0 -9-7-5-31 130-3-4-7 -202-2-5 -3 10-3 -6-4-202
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A 5 T 4 A 3 A 2 T 1 0 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10 Match: +1 Mismatch:-1 Indel: -2 -12-10-8-6-4-2 -10 -8 -6 -4 -2 0 -9-7-5-31 130-3-4-7 -202-2-5 -3 10-3 -6-4-202
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130-3-4-5A 5 02 -2 -4T 4 1 10-3 A 3 -20 02-2A 2 -6-4-2-31 T 1 -6-5-4-3-200 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10
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TACTAA TAATA- TACTAA TAAT-A
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A 5 T 4 A 3 A 2 T 1 0 A6A6 A5A5 T4T4 C3C3 A2A2 T1T10
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