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Genomic Sequence Alignment

Genomic Sequence Alignment. Overview. Dynamic programming & the Needleman-Wunsch algorithm Local alignment—BLAST Fast global alignment Multiple sequence alignment Rearrangements in genomic sequences. Biology in One Slide – Twentieth Century. …and today. …ACGTGACTGAGGACCGTG

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Genomic Sequence Alignment

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  1. Genomic Sequence Alignment

  2. Overview • Dynamic programming & the Needleman-Wunsch algorithm • Local alignment—BLAST • Fast global alignment • Multiple sequence alignment • Rearrangements in genomic sequences

  3. Biology in One Slide – Twentieth Century …and today …ACGTGACTGAGGACCGTG CGACTGAGACTGACTGGGT CTAGCTAGACTACGTTTTA TATATATATACGTCGTCGT ACTGATGACTAGATTACAG ACTGATTTAGATACCTGAC TGATTTTAAAAAAATATT…

  4. Complete DNA Sequences About 300 complete genomes have been sequenced

  5. Evolution

  6. Evolution at the DNA level Deletion Mutation …ACGGTGCAGTTACCA… SEQUENCE EDITS …AC----CAGTCCACCA… REARRANGEMENTS Inversion Translocation Duplication

  7. Evolutionary Rates next generation OK OK OK X X Still OK?

  8. Sequence conservation implies function • Alignment is the key to • Finding important regions • Determining function • Uncovering the evolutionary forces

  9. Sequence Alignment AGGCTATCACCTGACCTCCAGGCCGATGCCC TAGCTATCACGACCGCGGTCGATTTGCCCGAC -AGGCTATCACCTGACCTCCAGGCCGA--TGCCC--- TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC Definition Given two strings x = x1x2...xM, y = y1y2…yN, an alignment is an assignment of gaps to positions 0,…, N in x, and 0,…, N in y, so as to line up each letter in one sequence with either a letter, or a gap in the other sequence

  10. What is a good alignment? Alignment: The “best” way to match the letters of one sequence with those of the other How do we define “best”? Alignment: A hypothesis that the two sequences come from a common ancestor through sequence edits Parsimonious explanation: Find the minimum number of edits that transform one sequence into the other

  11. Scoring Function • Sequence edits: AGGCCTC • Mutations AGGACTC • Insertions AGGGCCTC • Deletions AGG.CTC Scoring Function: Match: +m Mismatch: -s Gap: -d Score F = (# matches)  m - (# mismatches)  s – (#gaps)  d

  12. How do we compute the best alignment? AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA Too many possible alignments: O( 2N) AGTGACCTGGGAAGACCCTGACCCTGGGTCACAAAACTC

  13. Dynamic Programming • Given two sequences x = x1……xM and y = y1……yN • Let F(i, j) = Score of best alignment of x1……xi to y1……yj • Then, F(M, N) == Score of best alignment Idea: • Compute F(i, j) for all i and j • Do this by using F(i–1 , j), F(i, j–1), F(i–1, j–1)

  14. Dynamic Programming (cont’d) Notice three possible cases: • xialigns to yj x1……xi-1 xi y1……yj-1 yj 2. xialigns to a gap x1……xi-1 xi y1……yj - • yjaligns to a gap x1……xi - y1……yj-1 yj m, if xi = yj F(i,j) = F(i-1, j-1) + -s, if not F(i,j) = F(i-1, j) - d F(i,j) = F(i, j-1) - d

  15. Dynamic Programming (cont’d) • How do we know which case is correct? Inductive assumption: F(i, j-1), F(i-1, j), F(i-1, j-1) are optimal Then, F(i-1, j-1) + s(xi, yj) F(i, j) = max F(i-1, j) – d F( i, j-1) – d Where s(xi, yj) = m, if xi = yj; -s, if not i-1, j-1 i-1, j i, j-1 i, j

  16. Example x = AGTA m = 1 y = ATA s = -1 d = -1 F(i,j) i = 0 1 2 3 4 Optimal Alignment: F(4,3) = 2 AGTA A - TA j = 0 1 2 3

  17. The Needleman-Wunsch Algorithm • Initialization. • F(0, 0) = 0 • F(0, j) = - j  d • F(i, 0) = - i  d • Main Iteration. Filling-in partial alignments • For each i = 1……M For each j = 1……N F(i-1,j) – d [case 1] F(i, j) = max F(i, j-1) – d [case 2] F(i-1, j-1) + s(xi, yj) [case 3] UP if [case 1] Ptr(i,j) = LEFT if [case 2] DIAG if [case 3] • Termination. F(M, N) is the optimal score, and from Ptr(M, N) can trace back optimal alignment

  18. Alignment on a Large Scale • Given a gene that we care about, how can we compare it to all existing DNA? • Assume we use Dynamic Programming: gene of interest ~105 The entire genomic database ~1011

  19. Index-based Local Alignment Main idea: • Construct a dictionary of all the words in the query • Initiate a local alignment for each word match between query and DB Running Time: Theoretical worst case: O(MN) Fast in practice query DB

  20. Index-based Local Alignment — BLAST …… query Dictionary: All words of length k (~11) Alignment initiated between exact-matching words (more generally, between words of alignment score  T) Alignment: Ungapped extensions until score below statistical threshold Output: All local alignments with score > statistical threshold …… scan DB query

  21. Index-based Local Alignment — BLAST A C G A A G T A A G G T C C A G T Example: k = 4, T = 4 The matching word GGTC initiates an alignment Extension to the left and right with no gaps until alignment falls < 50% Output: GTAAGGTCC GTTAGGTCC C C C T T C C T G G A T T G C G A

  22. Gapped BLAST A C G A A G T A A G G T C C A G T Added features: • Pairs of words can initiate alignment • Nearby alignments are merged • Extensions with gaps until score < T below best score so far Output: GTAAGGTCCAGT GTTAGGTC-AGT C T G A T C C T G G A T T G C G A

  23. Example Query:gattacaccccgattacaccccgattaca (29 letters) [2 mins] Database: All GenBank+EMBL+DDBJ+PDB sequences (but no EST, STS, GSS, or phase 0, 1 or 2 HTGS sequences) 1,726,556 sequences; 8,074,398,388 total letters >gi|28570323|gb|AC108906.9|Oryza sativa chromosome 3 BAC OSJNBa0087C10 genomic sequence, complete sequence Length = 144487 Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plus Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: 125138 tacacccagattacaccccga 125158 Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plus Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: 125104 tacacccagattacaccccga 125124 >gi|28173089|gb|AC104321.7| Oryza sativa chromosome 3 BAC OSJNBa0052F07 genomic sequence, complete sequence Length = 139823 Score = 34.2 bits (17), Expect = 4.5 Identities = 20/21 (95%) Strand = Plus / Plus Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: 3891 tacacccagattacaccccga 3911 http://www.ncbi.nlm.nih.gov

  24. Efficient global alignment

  25. Global alignment with the chaining approach Find local alignments Chain them into a rough global map Align regions in-between

  26. LAGAN: 1. FIND Local Alignments • Find Local Alignments • Chain Local Alignments • Restricted DP Mike Brudno, Chuong Do, et al.

  27. LAGAN: 2. CHAIN Local Alignments • Find Local Alignments • Chain Local Alignments • Restricted DP Mike Brudno, Chuong Do, et al.

  28. LAGAN: 3. Restricted DP • Find Local Alignments • Chain Local Alignments • Restricted DP Mike Brudno, Chuong Do, et al.

  29. Multiple Alignment

  30. Definition • Given N sequences x1, x2,…, xN: • Insert gaps (-) in each sequence xi, such that • All sequences have the same length L • Score of the global map is maximum • A faint similarity between two sequences becomes significant if present in many • Multiple alignments can help improve the pairwise alignments

  31. Scoring Function: Sum Of Pairs Definition:Induced pairwise alignment A pairwise alignment induced by the multiple alignment Example: x: AC-GCGG-C y: AC-GC-GAG z: GCCGC-GAG Induces: x: ACGCGG-C; x: AC-GCGG-C; y: AC-GCGAG y: ACGC-GAC; z: GCCGC-GAG; z: GCCGCGAG Given sequences x1, …, xN, aligned in a multiple alignment m, S(m) = k<l wkl s(xk, xl)

  32. A Profile Representation - A G G C T A T C A C C T G T A G – C T A C C A - - - G C A G – C T A C C A - - - G C A G – C T A T C A C – G G C A G – C T A T C G C – G G A 1 1 .8 C .6 1 .4 1 .6 .2 G 1 .2 .2 .4 1 T .2 1 .6 .2 - .2 .8 .4 .8 .4 • Given a multiple alignment M = m1…mn • Replace each column mi with profile entry pi • Frequency of each letter in  • # gaps • Can think of this as a “likelihood” of each letter in each position

  33. Multiple Sequence Alignments Algorithms

  34. Multidimensional DP Generalization of Needleman-Wunsh: S(m) = i S(mi) (sum of column scores) F(i1,i2,…,iN): Optimal alignment up to (i1, …, iN) F(i1,i2,…,iN) = max(all neighbors of cube)(F(nbr)+S(nbr))

  35. Multidimensional DP • Example: in 3D (three sequences): • 7 neighbors/cell F(i,j,k) = max{ F(i-1,j-1,k-1)+S(xi, xj, xk), F(i-1,j-1,k )+S(xi, xj, - ), F(i-1,j ,k-1)+S(xi, -, xk), F(i-1,j ,k )+S(xi, -, - ), F(i ,j-1,k-1)+S( -, xj, xk), F(i ,j-1,k )+S( -, xj, xk), F(i ,j ,k-1)+S( -, -, xk) }

  36. Multidimensional DP Running Time: • Size of matrix: LN; Where L = length of each sequence N = number of sequences • Neighbors/cell: 2N – 1 Therefore………………………… O(2N LN)

  37. Multidimensional DP Running Time: • Size of matrix: LN; Where L = length of each sequence N = number of sequences • Neighbors/cell: 2N – 1 Therefore………………………… O(2N LN)

  38. Progressive Alignment x pxy y • When evolutionary tree is known: • Align closest first, in the order of the tree • In each step, align two sequences x, y, or profiles px, py, to generate a new alignment with associated profile presult Weighted version: • Tree edges have weights, proportional to the divergence in that edge • New profile is a weighted average of two old profiles z pxyzw pzw w

  39. Progressive Alignment x y • When evolutionary tree is known: • Align closest first, in the order of the tree • In each step, align two sequences x, y, or profiles px, py, to generate a new alignment with associated profile presult Weighted version: • Tree edges have weights, proportional to the divergence in that edge • New profile is a weighted average of two old profiles z w

  40. Progressive Alignment x y • When evolutionary tree is unknown: • Perform all pairwise alignments • Define distance matrix D, where D(x, y) is a measure of evolutionary distance, based on pairwise alignment • Construct a tree • Align on the tree ? z w

  41. Some useful sites • Genome browsers • Ensembl: www.ensembl.org • UCSC: genome.ucsc.edu/cgi-bin/hgGateway • Genomic alignment • LAGAN: lagan.stanford.edu • MAVID: baboon.math.berkeley.edu/mavid • Protein multiple alignment • MUSCLE: www.drive5.com • ProbCons: probcons.stanford.edu

  42. Evolution at the DNA level Deletion Mutation …ACGGTGCAGTTACCA… SEQUENCE EDITS …AC----CAGTCACCA… REARRANGEMENTS Inversion Translocation Duplication

  43. Local & Global Alignment AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA AGTGACCTGGGAAGACCCTGAACCCTGGGTCACAAAACTC Global Local AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA AGTGACCTGGGAAGACCCTGAACCCTGGGTCACAAAACTC

  44. Glocal Alignment Problem Find least cost transformation of one sequence into another using shuffle operations AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA • Sequence edits • Inversions • Translocations • Duplications • Combinations of above AGTGACCTGGGAAGACCCTGAACCCTGGGTCACAAAACTC

  45. SLAGAN: 1. Find Local Alignments • Find Local Alignments • Build Rough Homology Map • Globally Align Consistent Parts Mike Brudno, Sanket Malde, et al.

  46. SLAGAN: 2. Build Homology Map • Find Local Alignments • Build Rough Homology Map • Globally Align Consistent Parts Mike Brudno, Sanket Malde, et al.

  47. SLAGAN: 3. Global Alignment • Find Local Alignments • Build Rough Homology Map • Globally Align Consistent Parts Mike Brudno, Sanket Malde, et al.

  48. SLAGAN Example: Chromosome 20 • Human Chromosome 20 versus Mouse Chromosome 2 • 270 Segments of conserved synteny • 70 Inversions

  49. SLAGAN example: HOX cluster • 10 paralogous genes • Conserved order in Human/Mouse/Rat

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