1. Alignments and Comparative Genomics

2. Welcome to CS374! Today: Serafim: Alignments and Comparative Genomics Omkar: Administrivia

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

4. Complete DNA Sequences nearly 200 complete genomes have been sequenced

5. Evolution

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

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

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

9. Sequence Alignment -AGGCTATCACCTGACCTCCAGGCCGA--TGCCC--- TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC Definition Given two strings x = x 1 x 2...x M, y = y 1 y 2 …y N, 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 AGGCTATCACCTGACCTCCAGGCCGATGCCC TAGCTATCACGACCGCGGTCGATTTGCCCGAC

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 AGTGACCTGGGAAGACCCTGACCCTGGGTCACAAAACTC Too many possible alignments: O( 2 M+N )

13. Dynamic Programming Given two sequences x = x 1 ……x M and y = y 1 ……y N Let F(i, j) = Score of best alignment of x 1 ……x i to y 1 ……y j 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: 1.x i aligns to y j x 1 ……x i-1 x i y 1 ……y j-1 y j 2.x i aligns to a gap x 1 ……x i-1 x i y 1 ……y j - 3.y j aligns to a gap x 1 ……x i - y 1 ……y j-1 y j m, if x i = y j 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(x i, y j ) F(i, j) = maxF(i-1, j) – d F( i, j-1) – d Where s(x i, y j ) = m, if x i = y j ;-s, if not i-1, j-1i-1, j i, j-1i, j

16. Example x = AGTAm = 1 y = ATAs = -1 d = -1 AGTA 0-2-3-4 A10 -2 T 0010 A-3 02 F(i,j) i = 0 1 2 3 4 j = 0 1 2 3 Optimal Alignment: F(4,3) = 2 AGTA A - TA

17. The Needleman-Wunsch Matrix x 1 ……………………………… x M y 1 ……………………………… y N Every nondecreasing path from (0,0) to (M, N) corresponds to an alignment of the two sequences

18. The Needleman-Wunsch Algorithm 1.Initialization. a.F(0, 0) = 0 b.F(0, j) = - j  d c.F(i, 0)= - i  d 2.Main Iteration. Filling-in partial alignments a.For each i = 1……M For eachj = 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(x i, y j ) [case 3] UP, if [case 1] Ptr(i,j)= LEFTif [case 2] DIAGif [case 3] 3.Termination. F(M, N) is the optimal score, and from Ptr(M, N) can trace back optimal alignment

19. Performance Time: O(NM) Space: O(NM)

20. Alignment on a Large Scale Given a newly sequenced organism, Which subregions align with other organisms?  Potential genes  Other biological characteristics Assume we use Dynamic Programming: The entire genomic database Our newly sequenced mammal 3  10 9 10 10 - 10 11

21. Index-based Local Alignment Main idea: 1.Construct a dictionary of all the words in the query 2.Initiate a local alignment for each word match between query and DB Running Time: Theoretical worst case: O(MN) Fast in practice query DB

22. Index-based Local Alignment — BLAST 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 …… query DB query scan

23. Index-based Local Alignment — BLAST A C G A A G T A A G G T C C A G T C C C T T C C T G G A T T G C G A 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

24. Gapped BLAST A C G A A G T A A G G T C C A G T C T G A T C C T G G A T T G C G A 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

25. 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 / Plusgi|28570323|gb|AC108906.9| 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 / Plusgi|28173089|gb|AC104321.7| Query: 4 tacaccccgattacaccccga 24 ||||||| ||||||||||||| Sbjct: 3891 tacacccagattacaccccga 3911 http://www.ncbi.nlm.nih.gov

26. Efficient global alignment

27. Global alignment with the chaining approach 1.Find local alignments 2.Chain them into a rough global map 3.Align regions in-between

28. LAGAN: 1. FIND Local Alignments 1.Find Local Alignments 2.Chain Local Alignments 3.Restricted DP Mike Brudno, Chuong B Do, et al.

29. LAGAN: 2. CHAIN Local Alignments 1.Find Local Alignments 2.Chain Local Alignments 3.Restricted DP Mike Brudno, Chuong B Do, et al.

30. LAGAN: 3. Restricted DP 1.Find Local Alignments 2.Chain Local Alignments 3.Restricted DP Mike Brudno, Chuong B Do, et al.

31. Restricted DP (cont’d) What if a box is too large?  Recursive application of LAGAN, more sensitive word search

32. Multiple Alignment

34. 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

35. Sum Of Pairs (cont’d) The sum-of-pairs score of an alignment is the sum of the scores of all induced pairwise alignments S(m) =  k<l s(m k, m l ) s(m k, m l ):score of induced alignment (k,l)

36. Dynamic Programming for Multiple Alignment AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA AGTGACCTGGGAAGACCCTGACCCTGGGTCACAAAACTC x y z

37. Progressive Alignment Multiple Alignment is NP-complete Most used heuristic: Progressive Alignment Algorithm: Until all sequences are aligned: –Align two (multi-)sequences to each other, and treat the result as a new sequence Example: aligning AACTGTA with AATGTC, gives AACTGTA AA-TGTC, with “letters” (AA), (AA), (C-), (TT), (GG), (TT), (AC) Running Time: O(NL 2 ), where N: #seqs, L: length of a seq

38. MLAGAN: Progressive Alignment Given N sequences, phylogenetic tree Align pairwise, in order of the tree (LAGAN )  With needed generalizations for multi-anchoring & scoring edit distance Human Baboon Mouse Rat

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

40. Local & Global Alignment AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA AGTGACCTGGGAAGACCCTGAACCCTGGGTCACAAAACTC AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA AGTGACCTGGGAAGACCCTGAACCCTGGGTCACAAAACTC Local Global

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

42. SLAGAN: 1. Find Local Alignments 1.Find Local Alignments 2.Build Rough Homology Map 3.Globally Align Consistent Parts

43. SLAGAN: 2. Build Homology Map 1.Find Local Alignments 2.Build Rough Homology Map 3.Globally Align Consistent Parts

44. SLAGAN: 2. Build Homology Map d a b c Chain using Sparse Dynamic Programming Penalties: a)regular b)translocation c)inversion d)inverted translocation

45. SLAGAN: 2. Build Homology Map 1.Find Local Alignments 2.Build Rough Homology Map 3.Globally Align Consistent Parts

46. SLAGAN: 3. Global Alignment 1.Find Local Alignments 2.Build Rough Homology Map 3.Globally Align Consistent Parts

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

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

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

50. Whole-genome alignment with SLAGAN Two-step Shuffle 1.Shuffle for large-scale synteny map 2.Shuffle each syntenic region for microrearrangements

51. The ENCODE Project

52. ENCODE regions shuffled Hum/Mus Hum/Rat

53. ENCODE regions shuffled Hum/Mus Hum/Rat

54. ENCODE regions shuffled Hum/Mus Hum/Rat

55. ENCODE regions shuffled Hum/MusHum/Rat

56. ENCODE regions shuffled Hum/Mus Hum/Rat

57. Constrained Elements in Alignments

58. Human-Mouse-Rat Berkeley Genome Pipeline http://pipeline.lbl.gov

59. Human-Mouse-Rat

60. More DNA is coming…