Pairwise Sequence Alignment Todays Goal > DNA Sequence 1 - PDF document

Pairwise Sequence Alignment Today’s Goal > DNA Sequence 1 ACTGCGATTGACGTACGATCATCGTACGATCATCATGCTGAGCTATCATCATCGTACTGA TCGTAGACTACGTAGCTAGCATGCAGTCTGATGACGTCATGCTGACGTAGCATGC > DNA Sequence 2 GACTAGCAGCGAGAGATCTCTCGAGTATGCGAGAGCTGATGCATCTACGTATGCAGTCGT GCTAATGCGAGCGTATACGCGGGCATGTAGAGACTTCCTAGTAC How related are two sequences? > Protein Sequence 1 KGLAHDGHNADFLKAMGGPIAFPIDADPFIDFKLHMNI > Protein Sequence 2 LHASDGFKHSADFHNAIFDPAFLKADFPIMADSFN 1

Alignment CGTAGCAGC TGTAGTTCAGC CGTAG--CAGC |||| |||| TGTAGTTCAGC There’s more than one way to align a pair of sequences CGTTACA--TG CGTT-ACATG | || | | || | C-GTT-ACATG T-GT-CACGT- -TGTCACGT- C-G-T-TACATG | | || | CG-TTACATG || -TG-TCACGT- | | TG-T-C-AC-GT TGTC-A-CGT CGTTACATG CGTTACATG- -CGTTACA-TG || || | TGTCACGT | | || TGT--CACGT T-G-T-CACGT CGTTACATG C-----GTTACATG -CGTTAC-ATG || || | || CGTT-ACATG- || | TGTCACGT- TGTCACGT------ | | || | T-GTCA-C-GT TG-TCAC--GT CGTTACATG- CGT-TACATG- | || | CGTTACATG | || | --TGTCACGT | T-G-T-CACGT T-GTCACGT 2

Scoring Alignments Match: +5 Mismatch: -4 Gap: -6 CGCGTTA ACTCGATCG CGTAGCAGCT CGGGTCA ACTTCG CATACAGGACT CGCGTTA ACTCGATCG CGTAGCAG--CT || || | ||| ||| | || ||| || CGGGTCA ACT---TCG CATA-CAGGACT Use the optimal (best scoring) alignment CGTTACA--TG CGTT-ACATG | || | | || | C-GTT-ACATG T-GT-CACGT- -TGTCACGT- C-G-T-TACATG | | || | CG-TTACATG || -TG-TCACGT- | | TG-T-C-AC-GT TGTC-A-CGT CGTTACATG CGTTACATG- -CGTTACA-TG || || | TGTCACGT | | || TGT--CACGT T-G-T-CACGT CGTTACATG C-----GTTACATG -CGTTAC-ATG || || | || CGTT-ACATG- || | TGTCACGT- TGTCACGT------ | | || | T-GTCA-C-GT TG-TCAC--GT CGTTACATG- CGT-TACATG- | || | CGTTACATG | || | --TGTCACGT | T-G-T-CACGT T-GTCACGT 3

Pairwise Sequence Alignment Pairwise Alignment Problem: Given two sequences, determine their optimal (i.e., best scoring) alignment. How many different alignments? CGTTACA--TG CGTT-ACATG | || | | || | C-GTT-ACATG T-GT-CACGT- -TGTCACGT- C-G-T-TACATG | | || | CG-TTACATG || -TG-TCACGT- | | TG-T-C-AC-GT TGTC-A-CGT CGTTACATG CGTTACATG- -CGTTACA-TG || || | TGTCACGT | | || TGT--CACGT T-G-T-CACGT CGTTACATG C-----GTTACATG -CGTTAC-ATG || || | || CGTT-ACATG- || | TGTCACGT- TGTCACGT------ | | || | T-GTCA-C-GT TG-TCAC--GT CGTTACATG- CGT-TACATG- | || | CGTTACATG | || | --TGTCACGT | T-G-T-CACGT T-GTCACGT 4

The Elegance of Alignment The problem of finding the best alignment of two sequences has two important properties: (1) The solution can be found by looking at the solutions to subproblems (2) Subproblems often overlap Indeed, to find the best alignment of two sequences, we need only look at 3 slightly smaller alignments (i.e., remove one or two characters from the sequences). The Elegance of Alignment AGCGTTA ACGTGA AGCGTT A + ACGTGA - 5

The Elegance of Alignment AGCGTTA ACGTGA AGCGTT A AGCGTTA - + + ACGTGA - ACGTG A The Elegance of Alignment AGCGTTA ACGTGA AGCGTT A AGCGTTA - AGCGTT A + + + ACGTGA - ACGTG A ACGTG A 6

The Elegance of Alignment AGCGTTA ACGTGA AGCGTT A AGCGTTA - AGCGTT A + + + ACGTGA - ACGTG A ACGTG A AGCGTT- A AGCGTTA - AGCGTT A | ||| + | ||| + | ||| | + A-CGTGA - A-CGTG- A A-CGTG A 4 - 6 4 - 6 10 +5 The Elegance of Alignment AGCGTTA ACGTGA AGCGTT A AGCGTTA - AGCGTT A + + + ACGTGA - ACGTG A ACGTG A AGCGT AGCGTT AGCGT AGCGTT AGCGTTA AGCGTT AGCGT AGCGTT AGCGT ACGTGA ACGTG ACGTG ACGTG ACGT ACGT ACGTG ACGT ACGT 7

The Elegance of Alignment The problem of finding the best alignment of two sequences has two important properties: (1) The solution can be found by looking at the solutions to subproblems (2) Subproblems often overlap The method for determining the best alignment is known as a dynamic programming algorithm . Score Table AGCGTTA A G C G T T A ACGTGA A C G T G A 8

Score Table AGCGTTA A G C G T T A ACGTGA A C AGCGT ACG G T G A Score Table AGCGTTA A G C G T T A ACGTGA A C A ACGTG G T G A 9

How is each block in the table determined? • Each entry depends on 3 previous entries (because of problem’s “elegance”) • Each entry also depends on scores used (match, mismatch, gap) - Score in block to the left minus gap A G C G T T A penalty max A of 3 - Score in block above minus gap penalty C G - Score in block diagonally left/above T G plus match/mismatch score A The Elegance of Alignment AGCGTTA ACGTGA AGCGTT A AGCGTTA - AGCGTT A + + + ACGTGA - ACGTG A ACGTG A AGCGTT- A AGCGTTA - AGCGTT A | ||| | ||| | ||| | + + + A-CGTGA - A-CGTG- A A-CGTG A 10

Alignment Score Table AGCGTTA A G C G T T A ACGTGA 0 -6 -12 -18 -24 -30 -36 -42 A -6 C -12 G -18 T -24 G -30 A -36 Alignment Score Table AGCGTTA A G C G T T A ACGTGA 0 -6 -12 -18 -24 -30 -36 -42 A -6 5 C -12 G -18 T -24 G -30 A -36 11

Alignment Score Table AGCGTTA A G C G T T A ACGTGA 0 -6 -12 -18 -24 -30 -36 -42 A -6 5 -1 C -12 G -18 T -24 G -30 A -36 How do we re-create the alignment? AGCGTTA A G C G T T A ACGTGA 0 -6 -12 -18 -24 -30 -36 -42 A -6 5 -1 -7 -13 -19 -25 -31 C -12 -1 1 4 -2 -8 -14 -20 G -18 -7 4 -2 9 3 -3 -9 T -24 -13 -2 0 3 14 8 2 G -30 -19 -8 -6 5 8 10 4 A -36 -25 -14 -12 -1 2 4 15 12

How do we re-create the alignment? AGCGTTA A G C G T T A ACGTGA 0 -6 -12 -18 -24 -30 -36 -42 A -6 5 -1 -7 -13 -19 -25 -31 C -12 -1 1 4 -2 -8 -14 -20 G -18 -7 4 -2 9 3 -3 -9 T -24 -13 -2 0 3 14 8 2 G A -30 -19 -8 -6 5 8 10 4 | A -36 -25 -14 -12 -1 2 4 15 A How do we re-create the alignment? AGCGTTA A G C G T T A ACGTGA 0 -6 -12 -18 -24 -30 -36 -42 A -6 5 -1 -7 -13 -19 -25 -31 C -12 -1 1 4 -2 -8 -14 -20 G -18 -7 4 -2 9 3 -3 -9 T -24 -13 -2 0 3 14 8 2 G TA -30 -19 -8 -6 5 8 10 4 | A -36 -25 -14 -12 -1 2 4 15 GA 13

How do we re-create the alignment? AGCGTTA A G C G T T A ACGTGA 0 -6 -12 -18 -24 -30 -36 -42 A -6 5 -1 -7 -13 -19 -25 -31 C -12 -1 1 4 -2 -8 -14 -20 G -18 -7 4 -2 9 3 -3 -9 T -24 -13 -2 0 3 14 8 2 G AGCGTTA -30 -19 -8 -6 5 8 10 4 | ||| | A -36 -25 -14 -12 -1 2 4 15 A-CGTGA Let’s recap, shall we? • The problem of finding the best alignment for two sequences has a couple of interesting properties: (1) The best alignment can be determined using the best alignments of subproblems (2) Subproblems often overlap • Because of these properties, we can fill in a table of solutions to subproblems • Each table entry is determined from 3 of the preceding entries • The filled-in table tells us the best alignment! 14

How big is our table? AGCGTTA A G C G T T A ACGTGA 0 -6 -12 -18 -24 -30 -36 -42 A -6 5 -1 -7 -13 -19 -25 -31 C -12 -1 1 4 -2 -8 -14 -20 G -18 -7 4 -2 9 3 -3 -9 T -24 -13 -2 0 3 14 8 2 G -30 -19 -8 -6 5 8 10 4 A -36 -25 -14 -12 -1 2 4 15 Global vs. Local TGGTAGATTCCCACGAGATCTACCGAGTATGAGTAGGGGGACGTTCGCTCGG GCCTCTAACACACTGCACGAGATCAACCGAGATATGAGTAATACAGCGGTACGGG Global Alignment Score: 60 ---TGGTAGATTC-C--CACGAGATCTACCGAG-TATGAGTAGGGGGAC-GTTCGCT-C-GG | || | | | ||||||||| |||||| |||||||| || | || | | || GCCT-CTA-ACACACTGCACGAGATCAACCGAGATATGAGTA---ATACAG--CGGTACGGG Local Alignment Score: 105 CACGAGATCTACCGAG-TATGAGTA ||||||||| |||||| |||||||| CACGAGATCAACCGAGATATGAGTA 15

Local Alignment AGATCAC A G A T C A C CGACAG 0 0 0 0 0 0 0 0 C 0 G 0 A 0 C 0 A 0 G 0 Local Alignment AGATCAC A G A T C A C CGACAG 0 0 0 0 0 0 0 0 C 0 0 G 0 A 0 C 0 A 0 G 0 16

Local Alignment AGATCAC A G A T C A C CGACAG 0 0 0 0 0 0 0 0 C 0 0 0 G 0 A 0 C 0 A 0 G 0 Local Alignment AGATCAC A G A T C A C CGACAG 0 0 0 0 0 0 0 0 C 0 0 0 0 0 5 0 5 G 0 0 5 0 0 0 1 0 A 0 5 0 10 4 0 5 0 C 0 0 1 4 6 9 3 10 A 0 5 0 6 0 3 14 8 G 0 0 10 4 2 0 8 10 17

Local Alignment AGATCAC A G A T C A C CGACAG 0 0 0 0 0 0 0 0 C 0 0 0 0 0 5 0 5 G 0 0 5 0 0 0 1 0 A 0 5 0 10 4 0 5 0 C 0 0 1 4 6 9 3 10 A A 0 5 0 6 0 3 14 8 | G 0 0 10 4 2 0 8 10 A Local Alignment AGATCAC A G A T C A C CGACAG 0 0 0 0 0 0 0 0 C 0 0 0 0 0 5 0 5 G 0 0 5 0 0 0 1 0 A 0 5 0 10 4 0 5 0 C 0 0 1 4 6 9 3 10 A CA 0 5 0 6 0 3 14 8 || G 0 0 10 4 2 0 8 10 CA 18

Local Alignment AGATCAC A G A T C A C CGACAG 0 0 0 0 0 0 0 0 C 0 0 0 0 0 5 0 5 G 0 0 5 0 0 0 1 0 A 0 5 0 10 4 0 5 0 C 0 0 1 4 6 9 3 10 A GATCA 0 5 0 6 0 3 14 8 || || G 0 0 10 4 2 0 8 10 GA-CA Linear Gap Penalty With linear gap scoring, every gap has the same score AGGCTACGATCGATCGG | || | ||| || | A-GCCA---TCG-TC-G c c c c c c 19