Hidden Markov models in gene finding. Bioinformatics research group David R. Cheriton School of Computer Science University of Waterloo

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1 Hidden Markov models in gene finding Broňa Brejová Bioinformatics research group David R. Cheriton School of Computer Science University of Waterloo 1

2 Topics for today What is gene finding (biological background) HMMs in gene finding tools of the trade: Viterbi algorithm Higher order states State transition diagram 2

3 What is a genome? cggtgaaactgcacgattgttgctggcttaaagatagaccaatcagagtgtgtaacgtca tatttagcgtcttctatcatccaatcactgcactttacacactataaatagagcagctca tgggcgtatttgcgctagtgttgggtgttccgctgtgctgtttttccgtcatggctcgca ctaagcaaactgctcggaagtctactggtggcaaggcgccacgcaaacagttggccacta aggcagcccgcaaaagcgctccggccaccggcggcgtgaaaaagccccaccgctaccggc cgggcaccgtggctctgcgcgagatccgccgttatcagaagtccactgaactgcttattc gtaaactacctttccagcgcctggtgcgcgagattgcgcaggactttaaaacagacctgc gtttccagagctccgctgtgatggctctgcaggaggcgtgcgaggcctacttggtagggc tatttgaggacactaacctgtgcgccatccacgccaagcgcgtcactatcatgcccaagg acatccagctcgcccgccgcatccgcggagagagggcgtgattactgtggtctctctgac ggtccaagcaaaggctcttttcagagccaccaccttttcaagtaaagtagctgtaagaaa ccaatttaagacaaaagggaatgcattgggagcacttttcgttttaatgctactgaaggc Human genome: 3 billion letters (sequenced in 2001) What do they mean? 3

4 What are genes? Genes are portions of genome encoding proteins 4

5 Closer look on genes Process of protein production: gene DN: transcription splicing mrn: translation protein: Intergenic Exon (coding region) Intron Translation: triple of letters in mrn one amino acid in protein mrn: protein: U G G U U U U C } {{ } } {{ } } {{ } W F S 5

6 Task of gene finding cggtgaaactgcacgattgttgctggcttaaagatagaccaatcagagtgtgtaacgtca tatttagcgtcttctatcatccaatcactgcactttacacactataaatagagcagctca tgggcgtatttgcgctagtgttgggtgttccgctgtgctgtttttccgtcatggctcgca ctaagcaaactgctcggaagtctactggtggcaaggcgccacgcaaacagttggccacta aggcagcccgcaaaagcgctccggccaccggcggcgtgaaaaagccccaccgctaccggc cgggcaccgtggctctgcgcgagatccgccgttatcagaagtccactgaactgcttattc gtaaactacctttccagcgcctggtgcgcgagattgcgcaggactttaaaacagacctgc gtttccagagctccgctgtgatggctctgcaggaggcgtgcgaggcctacttggtagggc tatttgaggacactaacctgtgcgccatccacgccaagcgcgtcactatcatgcccaagg acatccagctcgcccgccgcatccgcggagagagggcgtgattactgtggtctctctgac 6

7 Task of gene finding cggtgaaactgcacgattgttgctggcttaaagatagaccaatcagagtgtgtaacgtca tatttagcgtcttctatcatccaatcactgcactttacacactataaatagagcagctca tgggcgtatttgcgctagtgttgggtgttccgctgtgctgtttttccgtcatggctcgca ctaagcaaactgctcggaagtctactggtggcaaggcgccacgcaaacagttggccacta aggcagcccgcaaaagcgctccggccaccggcggcgtgaaaaagccccaccgctaccggc cgggcaccgtggctctgcgcgagatccgccgttatcagaagtccactgaactgcttattc gtaaactacctttccagcgcctggtgcgcgagattgcgcaggactttaaaacagacctgc gtttccagagctccgctgtgatggctctgcaggaggcgtgcgaggcctacttggtagggc tatttgaggacactaacctgtgcgccatccacgccaagcgcgtcactatcatgcccaagg acatccagctcgcccgccgcatccgcggagagagggcgtgattactgtggtctctctgac gene 1 gene 2 Intergenic Intron Exon (coding region) 7

8 Toy Hidden Markov model for gene finding π q 0 q 1 q 2 η η η... q t {,, } y t {a, c, g, t} y 0 y 1 y 2 p(q, y): joint prob. over genomic sequences y and gene structures q gene 1 gene 2 Intergenic Intron Exon (coding region) 8

9 Toy Hidden Markov model for gene finding π q 0 q 1 q 2 η η η... q t {,, } y t {a, c, g, t} y 0 y 1 y 2 η a c g t p(q t q t 1 ) p(y t q t ) 9

10 HMMs for gene finding: training π q 0 q 1 q 2 η η η... q t {,, } y t {a, c, g, t} y 0 y 1 y 2 Training: Training set of sequences with known gene structures Fully observed model (both q and y known) Maximum likelihood estimation by relative frequencies 10

11 HMMs for gene finding: inference π q 0 q 1 q 2 η η η... q t {,, } y t {a, c, g, t} y 0 y 1 y 2 Inference: Viterbi algorithm Genomic sequence y observed, state sequence q unknown Viterbi algorithm computes state sequence q with highest probability given y: q = arg max q p(q y) = arg max q p(q, y) 11

12 HMMs for gene finding: higher order states Order 0: π q 0 q 1 q 2 η η η y 0 y 1 y 2... η specifies p(y t q t ) Order 1: q 0 q 1 q π 2 η η η y 0 y 1 y η specifies p(y t q t, y t 1 ) 12

13 HMMs for gene finding: higher order states η specifies p(y t q t, y t 1 ): q t y t 1 a c g t a c g t a c g t

14 HMMs for gene finding: state transition diagrams π q 0 q 1 q 2 η η η... q t {,, } y t {a, c, g, t} y 0 y 1 y 2 Graph representation of : p(q t q t 1 )

15 More complex HMMs: change state transition diagrams Recall: triple of letters in exon one amino acid DN: protein: T G G T T T T C } {{ } } {{ } } {{ } W F S p(q t q t 1 )

16 New states have separate emission probability η a c g t η a c g t

17 More complex HMMs: change state transition diagrams Keep consistent triples across introns: DN: protein: T G G T G T T G T T T C } {{ } } {{ } } {{ } W F S

18 More complex HMMs: remember those signals? Exon Intron ccatcccctatatttatggcaggtgaggaaagggtgggggctgggg attcatcatcatgggtgcatcggtgagtatctcccaggccccaatc agaagatctaccccaccatctggtaagtgtgtcccaccactgcccc acagagtgagcccttcttcaaggtgggtggtgtcagggcctccccc acgagtcctgcatgagccagatgtaaggcttgccgttgccctccct tgcagaacctcatggtgctgaggtggggccaagcctgggccggggg tcgatgaatttgggatcatccggtgagagctcttcctctctcctgg agatgacgtccgtgatgagaaggtagggggtgcaccccagtcccca gtggagaatgagaggtgggatggtaggtgatgccttcgaggcccag tttcttgtggctattttaaaaggtaattcatggagaaatagaaaaa tttcttgtggctattttaaaaggtaattcatggagaaatagaaaaa tttgaagaaactccacgaagaggttgatggcagtgactttcggaaa agtggatgcccttaaaggaaccgtggagtaccaacccccctgcagt cgacccgtgaccctcgtgagaggtacgaagccccagcccggggctc aaatgcagtggaagagggactagtacgtgagccatgctgggagtgt catggcgggtgtgctgaagaaggtgagacgaatggaggtcactgtt tgtgtgcaatactcctcacgaggtatgtacctttgttctttcttcg gaagctggctatggttaaagcggtaagtagctaagtcagttttgtt attagaagaggtgattcttcaggtaaagaaaaagttgactatttag 18

19 More complex HMMs: remember those signals? Exon Intron ccatcccctatatttatggcaggtgaggaaagggtgggggctgggg attcatcatcatgggtgcatcggtgagtatctcccaggccccaatc agaagatctaccccaccatctggtaagtgtgtcccaccactgcccc acagagtgagcccttcttcaaggtgggtggtgtcagggcctccccc Insert a series of states between exon and intron: d1 d2 d3 d4 d5 d6 d7 d8 d9 19

20 donor0 intron0 acceptor0 donor4 intron4 acceptor4 donor5 intron5 acceptor5 donor3 intron3 acceptor3 Example of an HMM for gene finding translation start translation start exon intergenic exon translation stop translation stop Reverse strand Forward strand 20 donor2 intron2 acceptor2 donor1 intron1 acceptor1

21 Summary HMMs are useful tool for gene finding Viterbi algorithm used for inference Higher order states model dependencies among adjacent letters Complex state transition diagrams incorporate biological knowledge This is just a beginning More complex models used in practice: lengths of exons/introns, complex signal models, experimental information, multiple species,... HMMs for other bioinformatics tasks: protein secondary structure, protein families, segmenting genome,... 21