Pairwise alignment II

Transcription

1 Pairwise alignment II

2 Agenda - Previous Lesson: Minhala + Introduction - Review Dynamic Programming - Pariwise Alignment Biological Motivation Today: - Quick Review: Sequence Alignment (Global, Local, Variants). - Heuristic Search

3 Ilan Smoly and Dan Gusfield, WABI 2015 in Atlanta, Georgia 3

4 Sequence Comparison (cont) We seek the following similarities between sequences : Find similar proteins Allows to predict function & structure Locate similar subsequences in DNA Allows to identify (e.g) regulatory elements Locate DNA sequences that might overlap Helps in sequence assembly g 1 g 2 4/64

5

6 Comparison methods Global alignment Finds the best alignment across the whole two sequences. Local alignment Finds regions of similarity in parts of the sequences. Global Local

7 Global Alignment Algorithm of Needleman and Wunsch (1970) Finds the alignment of two complete sequences: ADLGAVFALCDRYFQ ADLGRTQN-CDRYYQ Some global alignment programs trim ends

8 Local Alignment Algorithm of Smith and Waterman (1981). Makes an optimal alignment of the best segment of similarity between two sequences. ADLG CDRYFQ ADLG CDRYYQ Can return a number of highly aligned segments.

9 Global Alignment: Algorithm S T 1.. i 1.. j Prefix oflength i of S Prefix oflength j of T C ( i, j ) Cost of optimum alignment of S and T 1..i 1..j w ( a, b) if if a a b b 47

10 Theorem. C(i,j) satisfies the following relationships: Initial conditions: C(i,0) i C(0, j) j Recurrence relation: For 1 i n, 1 j m: C(i, j) C(i 1, j 1) maxc(i 1, j) C(i, j 1) w(s,t ) i j 48

11 Computation Procedure C(0,0) C(i-1,j-1) C(i-1,j) C(i,j-1) C(i,j) C(n,m) C(i, j) max C(i 1, j 1) w(s,t ), i j C(i 1, j), C(i, j 1) 51

12 λ C T C G C A G C λ C A T T C A C for match, -2 for mismatch, -5 for space 52

13 λ C T C G C A G C λ C A T T C A C * * Traceback can yield both optimum alignments 53

14 Local Alignment Smith-Waterman Best score for aligning part of sequences Often beats global alignment score Global Alignment ATTGCAGTG-TCGAGCGTCAGGCT ATTGCGTCGATCGCAC-GCACGCT Local Alignment CATATTGCAGTGGTCCCGCGTCAGGCT TAAATTGCGT-GGTCGCACTGCACGCT 54

15 Local Alignment: Motivation Ignoring stretches of non-coding DNA: Non-coding regions are more likely to be subjected to mutations than coding regions. Local alignment between two sequences is likely to be between two exons. Locating protein domains: Proteins of different kind and of different species often exhibit local similarities Local similarities may indicate functional subunits. 55

16 Global vs. Local alignment Alignment of two Genomic sequences >Human DNA CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA >Mouse DNA CATGCGTCTGACgctttttgctagcgatatcggactATCGATATA 56

17 Global vs. Local alignment Alignment of two Genomic sequences Global Alignment Human:CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA Mouse:CATGCGTCTGACgct---ttttgctagcgatatcggactATCGAT-ATA ****** ***** * *** * ****** *** Local Alignment Human:CATGCGACTGAC Mouse:CATGCGTCTGAC Human:ATCGATCATA Mouse:ATCGAT-ATA 57

18 Global vs. Local alignment Alignment of DNA and mrna >Human DNA CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA >Human mrna CATGCGACTGACATCGATCATA 58

19 Global vs. Local alignment Alignment of DNA and mrna Global Alignment DNA: CATGCGACTGACcgacgtcgatcgatacgactagctagcATCGATCATA mrna:catgcgactgac atcgatcata ************ ********** Local Alignment DNA: CATGCGACTGAC mrna:catgcgactgac DNA: ATCGATCATA mrna:atcgatcata 59

20 DorothyHodkin DorothyCrowfootHodkin Global vs. Local alignment Global alignment: DOROTHY HODGKIN DOROTHYCROWFOOTHODGKIN Local alignment: DOROTHY DOROTHY HODGKIN HODGKIN 60

21 Global vs. Local Alignment Source: Jones and Pevzner 61/64

22 Local Alignment: Algorithm C [i, j] = Score of optimally aligning a suffix of S1 i with a suffix of T1 j. C[ i 1, j 1] score s i, t j C i 1, j C i, j max Ci, j 1 0 Initialize top row and leftmost column to zero. 62

23 λ C T C G C A G C λ C A T T C A C for a match, -1 for a mismatch, -5 for a space 63

24 Reducing space requirements O(mn) tables are often the limiting factor in computing large alignments There is a linear space technique that only doubles the time required [Hirschberg, 1977] 64

25 λ C T C G C A G C λ C A T T C A G IDEA: We only need the previous row to calculate the next 65

26 Linear-space Alignments mn + ½ mn + ¼ mn + 1/8 mn + 1/16 mn + = 2 mn 66

27 Some Results Most pairwise sequence alignment problems can be solved in O(mn) time. Space requirement can be reduced to O(m+n), while keeping run-time fixed Hirshberg, 1988]. Highly similar sequences can be aligned in O(dn) time, where d measures the distance between the sequences [Landau, 1986] Time complexity of the fastest known sequence alignment algorithms? O(n 2 /logn) [Crochemore, Landau, Ziv-Ukelson, 2003] For Discrete Scoring Schemes: [Masek and Paterson, 1980] 67

28 Sub Quadratic Sequence Alignment LZ-78 Compression Table Lookup How many points of interest? O(n 2 /t) n/ t rows with n vertices each n/ t columns with n vertices each [Crochemore, Landua and Ziv-Ukelson, 2003] [Masek and Paterson, 1981]

29 Variants of Sequence Alignment We have seen two basic variants of sequence alignment: Global alignment (Needelman-Wunsch) Local alignment (Smith-Waterman) We will pose and solve two problems : Finding the best overlap alignment Using an affine cost for gaps 69/64

30 Overlap Alignment Consider the following question: Can we find the most significant overlap between two sequences s,t? Possible overlap relations: a. b. The difference between this problem and local alignment is that here we require alignment between the endpoints of the two sequences. 70/64

31 End-gap free alignment Gaps at the start or end of alignment are not penalized Match: +2 Mismatch and space: -1 Best global Best end-gap free Score = 1 Score = 9 71

32 Motivation: Shotgun assembly 72

33 Motivation: Shotgun assembly Shotgun assembly produces a large set of partially overlapping subsequences from many copies of one unknown DNA sequence. Problem: Use the overlapping sections to paste the subsequences together. Overlapping pairs will have low global alignment score, but high end-space free score because of overlap. HOW CAN THIS BE SOLVED? 73

34 Algorithm Same as global alignment, except: 1. Initialize with zeros (free gaps at start) Locate max in the last row/column (free gaps at end) 75

35 λ C T C G C A G C λ C A T T C A G for match, -2 for mismatch, -5 for gap 76

36 77/64 Overlap Alignment Initialization: V[i,0]=0, V[0,j]=0 Recurrence: as in global alignment a match starts at the top or left border of the matrix and finishes on the right or bottom border. Score: maximum value at the bottom line and rightmost line in the matrix ]) [, ( ], [ ) ], [ ( ], [ ]) [ ], [ ( ], [ max ], [ 1 j t j 1 i V 1 i s 1 j i V 1 j t 1 i s j i V 1 j 1 i V

37 Overlap Alignment Example H E A G A W G H E E s = PAWHEAE t = HEAGAWGHEE P Scoring system: Match: +4 Mismatch: -1 Indel: -5 A 0 W 0 H 0 E 0 A 0 E 0 78/64

38 Overlap Alignment Example H E A G A W G H E E s = PAWHEAE t = HEAGAWGHEE P A 0-1 W 0-1 Scoring system: Match: +4 Mismatch: -1 Indel: -5 H 0 4 E 0 1 A 0-1 E /64

39 s = PAWHEAE t = HEAGAWGHEE Overlap Alignment Example H E A G A W G H E E P A W Scoring system: Match: +4 Mismatch: -1 Indel: -5 H E A E /64

40 Overlap Alignment Example The best overlap is: PAWHEAE HEAGAWGHEE Remark: A different scoring system could lead us to a different result, such as: ---PAW-HEAE HEAGAWGHEE- 81/64