1. (Combinatorics of) Alignment and Gene Finding Lior Pachter Basic definitions (alignment) Combinatorics of alignment Pair hidden Markov models Alignment of large sequences Gene structure Generalized HMMs Intro. to comparative genomics GPHMMs Example: the human and mouse genomes Motivation

2. February 2001December 2002

3. DNA - - - - agacgagataaatcgattacagtca - - - - Transcription RNA - - - - agacgagauaaaucgauuacaguca - - - - Translation Protein - - - - - DEI - - - - Protein Folding Problem Exon Intron Exon Intron Exon Protein Splicing Central Dogma Gene finding problem

4. Close this window to return to the previous window Note: Figures may be difficult to render in a web browser. In such cases, we recommend downloading the PDF version of this document. Nat ure © Ma cmil lan Pub lish ers Ltd 200 1 Re gist ere d No. 785 998 Eng lan d. Mouse Human

5. (Pavel Pevzner and Glenn Tesler, GR 2003)

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7. ATCG--GACATTACC-AC AC-GTCA-GAGTA-CAAG 4 … …

9. Part 1: Alignment

10. M X Y M = (mis)match X = insert seq1 Y = insert seq2 Pair HMMs Simple sequence-alignment PHMM

11. MX Y M M Y M Hidden sequence: A A T C C - G G - T - C G A Observed sequence: ATCGG ACGTCA Hidden alignment: ATCG--G AC-GTCA Pair HMMs transition probabilities output probabilities

12. Number of alignments for two sequences is D(m,n), these are known as the Delannoy #s

13. Probability of a state path is the weight of the graph path M X Y 1 - 3 1 - 3 1 - 3 1 - 3 1 - 3 1 - 3 Match prob: p m Mismatch prob: p r Match score: log(p m ) Mismatch score: log(p r ) Gap score: log(p g ) Gap prob: p g

14. Using a Pair HMM for alignment In practice, we have observed sequence ATCGG ACGTCA for which we wish to infer the underlying hidden states One solution: among all possible sequences of hidden states, determine the most likely (Viterbi algorithm). ATCG--G AC-GTCA MMXMYYM

15. In the graph theoretic setting, the optimal alignment is just the maximum weight path in the graph from to An efficient DP algorithm exists for solving this problem: Simply compute the weight of the maximum path from to every vertex in the graph

16. Viterbi in PHMM Needleman Wunsch M X Y 1 - 3 1 - 3 1 - 3 1 - 3 1 - 3 1 - 3 Match prob: p m Mismatch prob: p r Match score: log(p m ) Mismatch score: log(p r ) Gap score: log(p g ) Gap prob: p g

17. The DP algorithm for alignment has running time O(nm) where n and m are the lengths of the sequences. The memory requirements are also O(nm), however it is possible to reduce this to O(n+m) using divide and conquer. This approach is not practical for sequence lengths of much more than 10kb.

18. Alignment Pair Hidden Markov Models Steiner Networks ATCG--G A-CGTCA M X Y biologically meaningful fast alignments based on HMM structure

19. Some basic definitions: Let G be a graph and S  V(G). A k-spanner for S is a subgraph G’  G such that for any u,v  S the length of the shortest path between u,v in G’ is at most k times the distance between u and v in G. Let V(G)=R 2 and E(G)=horizontal and vertical line segments. A Manhattan network is a 1-spanner for a set S of points in R 2. Vertices in the Manhattan network that are not in S are called Steiner points

20. Example: S: red points Manhattan network Steiner point

21. [Gudmundsson-Levcopoulos-Narasimhan 2001] Find the shortest Manhattan network connecting the points 4-approximation in O(n 3 ) and 8-approximation in O(nlogn)

22. [Gudmundsson-Levcopoulos-Narasimhan 2001] proof outline: 1. it suffices to work on the Hanan grid

23. A(v) = {u:v is the topmost node below and to the left of u} [Gudmundsson-Levcopoulos-Narasimhan 2001] proof outline: 2. Construct local slides (for all four orientations) v slide

24. [Gudmundsson-Levcopoulos-Narasimhan 2001] proof outline: 3. Solve each slide The minimum slide arborescense problem: Lingas-Pinter-Rivest-Shamir 1982 O(n 3 ) optimal solution using dynamic programming

25. [Gudmundsson-Levcopoulos-Narasimhan 2001] proof outline: 4. Proof of correctness u v b a

26. Want to take into account that the sequences are genomic sequences: Example: a pair of syntenic genomic regions

27. YX PHMM M X Y

28. YX A property of “single sequence” states is that all paths in the Viterbi graph between two vertices have the same weight

29. Strategy for Alignment GATTACATTGATCAGACAGGTGAAGA G A T C T T C A T G T A G

30. Suffix trees A suffix tree is a data structure which encodes much of the structure of a string in a way which is compact but which allows for rapid match finding. GATTAGA$ $ T TTAGA$ GA A GA$ $$ TTAGA$ TAGA$ AGA$

31. Finding maximal repeats in a string A maximal repeat in a string corresponds to an internal node in the suffix tree for that string. GATTAGA$ $ T TTAGA$ GA A GA$ $$ TTAGA$ TAGA$ AGA$

32. Finding matches between two strings Given two sequences, simply glue them together. Instead of finding all maximal repeats, just find those repeats where: One of the substrings is in the first sequence and the other is in the second. Neither substring contains an N. ATCGATGCTACGTACGTCGATGCACGTGCCGTAGCTGATCGTACGTACTAGCTCGTC ATCGATGCTACGTACGTCGATGCACGTGC N CGTAGCTGATCGTACGTACTAGCTCGTC

33. GATCAACTGACGGACGTACCGTGAACCGTCACGTACGCGATCATCGACGTAACGACGTCGCGAATA CGCTACTGACCTAGTGACCGTGAACACTGACTCGTACGCGTACGCATCGACGTCGAGTCGCGACTGCG Anchoring: E pluribus aliquot.

34. The CD4 region (with Lam and Alexandersson) human mouse 50000 0 0

35. 5’ 3’ Exon 1 Exon 2Exon 3Exon 4 Intron 1Intron 2Intron 3

36. Suggests a new Steiner problem Find the shortest 1-spanner connecting reds to blues There exists a 12-approximation algorithm (Fumei Lam)

37. Generalizes the Manhattan network problem (all points red and blue) Generalizes the Rectilinear Steiner Arborescence problem

38. 1985, Trubin - polynomial time algorithm History of the Rectilinear Steiner Arborescence Problem 1992, Rao-Sadayappan-Hwang-Shor - error in Trubin 2000, Shi and Su - NP complete!

39. Enumeration of approximate alignments Recall: AAT is a union of alignment paths HVC

40. Observations (Eric Kuo): 1.The number of HVC approximate alignments in an m x n array is equal to the number of plane partitions that fit in a 2 x (m-1) x (n-1) box 2.The number of HVC approximate alignments of weight k in a 3 x n box, h(3,n,k), is unimodal Conjecture: this is true for all m,n. 3.Conjecture: the unimodality conjecture applies to all approximate alignments, G(m,n,k). 4. lim m,n ∞ [ G(m+1,n+1)G(m,n)]/[G(m+1,n)G(m,n+1)] = 1.6479 +

42. Part 2: Gene Finding (and alignment) joint work with Simon Cawley and Marina Alexandersson

43. DNA - - - - agacgagataaatcgattacagtca - - - - Transcription RNA - - - - agacgagauaaaucgauuacaguca - - - - Translation Protein - - - - - DEI - - - - Protein Folding Problem Exon Intron Exon Intron Exon Protein Splicing Central Dogma Gene finding problem

44. Gene Structure II AUG - X 1 …X n - STOP SPLICING TRANSLATION 3’ pre-mRNA mRNA protein sequenceprotein 3D structure Exon 1 Exon 2Exon 3Exon 4 Intron 1Intron 2Intron 3 DNA TRANSCRIPTION 5’

45. Gene Structure III 5’3’ DNA Exon 1 Exon 2Exon 3Exon 4 Intron 1Intron 2Intron 3 polyA signalPyrimidine tract Branchpoint CTG A C Splice site CAG Splice site GGTGAG Translation Initiation ATG Stop codon TAG/TGA/TAA Promoter TATA

46. How Difficult is the Problem? n = number of acceptor splice sites m = number of donor splice sites n+m+1 (Fibonacci) Number of parses is at most F n+m+1 (Fibonacci)

48. Additional Difficulties Alternative splicing SPLICING TRANSLATION pre-mRNA Pseudo genes ALTERNATIVE SPLICING TRANSLATION Protein II Protein I mRNA DNA

49. Smaller problems Single gene  One strand  Ends well-defined BAC (Bacterial Artificial Chromosome)  ~200 kB  Multiple genes

50. Example: Glimmer Gene Finding in Microbial DNA No introns 90% coding Shorter genomes (less than 10 million bp) Lots of data

51. Translation Initiation ATG Stop codon TAG/TGA/TAA ORF Gene Structure in Prokaryotes

52. Bacteriomaker Machine Intergene ATGTAA Coding A 0.25 C 0.25 G 0.25 T 0.25 A 0.9 C 0.03 G 0.04 T 0.03 1 1 0.9 0.1 0.9

53. Example: Genscan Gene Finding in Human DNA Introns 1.2% coding Large genome (3.2 billion bp) Alternative splicing

54. The Genscan HMM

55. Using GHMMs for ab-initio gene finding In practice, have observed sequence Predict genes by estimating hidden state sequence Usual solution: single most likely sequence of hidden states (Viterbi). TAATATGTCCACGGTTGTACACGGCAG GTATTG AG GTATTG AG ATGTAACTG AA TAATATGTCCACGGTTGTACACGGCAG GTATTG AG GTATTG AG ATGTAACTG AA

56. TAATATGTCCACGGTTGTACACGGCAG GTATTG AG GTATTG AG ATGTAACTG AA

57. Observed lengths Internal exons Single exons

58. HMM state duration times p duration Pr(leaving state) = p Pr(staying in state) = 1 - p Pr(output of exactly r in state) = (1-p) p Geometric distribution r A 1-p p

59. Performance of single organism gene finders Estimated ~45,000 genes in the human genome Sensitive but not specific Bad at accurately identifying exon boundaries

62. Comparison of 1196 orthologous genes (Makalowski et al., 1996) Sequence identity: –exons: 84.6% –protein: 85.4% –introns: 35% –5’ UTRs: 67% –3’ UTRs: 69% 27 proteins were 100% identical.

63. Example: a human/mouse ortholog Human Locus Mouse Locus Alignment:CDS coding exons noncoding exons introns intergenic regions strong alignment weak alignment intergenic regions Proliferating cell nuclear antigen (PCNA)

64. Observation: - Finding the genes will help to find biologically meaningful alignments. -Finding a good alignment will help in finding the genes.

65. Hidden Markov models –Sequence alignment with Pair HMMs –Gene Prediction with Generalized HMMs –Both simultaneously with GPHMMs

66. Using GPHMMs for cross-species gene finding given a pair of syntenic sequences predict genes by estimating hidden state sequence Predict exon-pairs using single most likely sequence of hidden states (Viterbi). TAAT GTATTG AG GTATTG AG TG AA CT G GT T GG T CC T CA G G TG T G TC ATGTCCACGG G A GT T A C A TC TTGTACACGGCAG T GT A C G CT GG ATGTAACC A CC A T G TA

67. TAAT GTATTG AG GTATTG AG TG AA CTGGTTGGTCCTCAGGTGTGTC ATGTCCACGG G A GT T A C A TC TTGTACACGGCAG T GT A C G CT GG ATGTAAC A C A T G TA

68. Computational Complexity # HMM states max duration length seq1 length seq2

69. lattice view Introns Exons

70. Approximate alignment Reduces from O(TU) to O(max(T,U))

71. A GPHMM implementation SLAM SLAM components –Splice sites (Variable length Markov models). –Introns and Intergenic regions (2nd order Markov models, independent geometric lengths, CNS states). –Coding sequences (3-periodic Markov models, generalized length distributions, protein-based pairHMM.) Input –Pair of syntenic genomic sequences. –Approximate alignment. Output –CDS predictions in both sequences.

72. http://bio.math.berkeley.edu/slam/

73. Input:

74. Output:

75. The SLAM hidden Markov model

76. Allowing for inserted exons

77. Example: Rosetta Set. SnSpAC Genscan.908.929 SLAM.975.981.960 Rosetta.935.978.949 Nucl..951

78. Example: HoxA SnSpAC Genscan.687.796 SLAM.932.896.864 Twinscan.949.976.511.829.704.896 Nucl..852

79. Comparing and annotating the entire human and mouse genomes

80. Godzilla - automatic computational system for comparative analysis of genomes http://pipeline.lbl.govhttp://www-gsd.lbl.gov/vista DATA Base Human Genome – Golden Path Assembly Mouse assemblies: Arachne October 2001 Phusion November 2001 MGSC v3 April 2002

81. Main modules of Godzilla Visualization Analysis of conservation Mapping and alignment of mouse contigs against the human genome Annotation

82. Tandem Local/Global Alignment Approach Sequence fragment anchoring (DNA and/or translated BLAT) Multi-step verification of potential regions using global alignment (AVID)

83. Advantage of the tandem approach: better sensitivity/specificity trade-off fill-in effect scoring longer alignments AVID Global alignment NT_002606 at Chr.17:2909457-29116113 BLAT Local alignment

84. Our vegetable garden

85. MyGodzilla Tool Submit a DNA sequence of ANY organism... … or submit a whole chromosome and analyze another Genome

86. “Gene Deserts” in the human genome – Long stretches of DNA lacking genes Calculate Intergenic Lengths ENSEMBL- 24,179 genes REFSEQ Annotation- 14,569 genes Exclude Heterochromatic DNA & Clone Gaps. # of Intervals 50 100 Intergenic interval length (Kb) 0 1002003004005006007008009001000 4200 “Gene Deserts” Longest 1% 620Kb – 4,120Kb (work of Marcelo Nobrega, Ivan Ovcharenko, And Eddy Rubin)

87. Distribution of Human “Gene Deserts” Total # 234 deserts Size Range 680 – 4,120 Kbp % of Genome 9% (287 Mbp)

88. Comparing Human “Gene Deserts” to Mouse Genome Assembly Search for predicted genes in orthologous mouse DNA. Are Human “Gene Deserts” Also Deserts in Mouse? Deserts: do not contain - Public Mouse Assembly RefSeq Annotation(8,438 genes) - Celera Mouse Assembly Gene prediction with more than one line of evidence

89. HUMAN 234 Gene Deserts Ortholgous MOUSE 178 (74%) are also Deserts Orthologous Mouse “Gene Deserts”

90. Human-Mouse Conservation in “Gene Deserts” Low ConservationHigh Conservation Both intervals are ~ 1Mb long, on Chr.13

91. Do “gene deserts” have any function? Cre-mediated deletion loxP ES cells Generating mouse “gene desert” deletions: Phenotypic Analysis: Lethal No effect (Spectrum)

92. SLAM whole genome run Align the genomes Construct a synteny map Chop up into SLAMable pieces Run SLAM Collate results

93. Summary of human/mouse whole genome predictions: Sensitivity: ~ 88% Specificity: ~ 60-70%

94. http://bio.math.berkeley.edu/slam/mouse/

95. Number of coding exons in each colored set (exon analysis) SLAMRefSeqEnsemblGenscan Violet1434 (2.0/1.1%) Brown3338 (3.4/1.9%) Blue50518 (37.5/37.5%) Red64746 (43.7/19.1%) Purple2651 (3.7/2.1%)3065 (3.2/1.7%) Green1236 (0.9/0.9%)1308 (1.8/1.0%) Grey1633 (2.3/1.3%)1400 (0.9/0.4%) Light Blue2670 (2.0/2.0%)2939 (3.0/1.7%) Peach4210 (4.3/2.4%)3711 (2.5/1.1%) Yellow12358 (9.2/9.2%)11781 (8.0/3.5%) Dark Green7708 (5.7/5.7%)8008 (11.1/6.4%)8752 (9.0/5.0%) Gold4018 (3.0/3.0%)4385 (6.1/3.5%)3926 (2.6/1.2%) Dark Grey8621 (11.9/6.9%)9530 (9.8/5.4%)7988 (5.4/2.4%) Light Yellow14478 (10.7/10.7%)16169 (16.7/9.2%)13970 (9.4/4.1%) Orange41872 (31.0/31.0%)44355 (61.3/35.4%)48831 (50.4/27.8%)40658 (27.4/12.0%) Total in Mouse134858 (100.0/100.0%)72395 (100.0/57.8%)96834 (100.0/55.1%)148180 (100.0/43.6%) Percentages given are (% out of mouse exons / % out of all exons)

99. Experimental gene verification with RT-PCR predicted intron primer

100. SLAM CNS data

101. Transfac Hits in CNS/Random

103. Summary Thanks: Marina Alexandersson, Nick Bray, Simon Cawley, Colin Dewey and Eric Kuo, Ivan Ovcharenko, Marcelo Nobrega and Eddy Rubin mAVID (alignment): http://bio.math.berkeley.edu/mavid/http://bio.math.berkeley.edu/mavid/ SLIM (network build): http://bio.math.berkeley.edu/slim/http://bio.math.berkeley.edu/slim/ SLAM (gene finding): http://bio.math.berkeley.ed/slam/http://bio.math.berkeley.ed/slam/ Whole genome alignments: http://pipeline.lbl.gov/http://pipeline.lbl.gov/ Websites: