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Algorithms for Genotype and Haplotype Inference from Low-Coverage Short Sequencing Reads

This research paper discusses algorithms and methods for inferring genotypes and haplotypes from low-coverage short sequencing reads, improving accuracy and incorporating additional sources of information.

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Algorithms for Genotype and Haplotype Inference from Low-Coverage Short Sequencing Reads

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  1. Algorithms for Genotype and Haplotype Inference from Low-Coverage Short Sequencing Reads Ion Mandoiu Computer Science and Engineering Department University of Connecticut Joint work with S. Dinakar, J. Duitama, Y. Hernández, J. Kennedy, and Y. Wu

  2. Outline Introduction Single SNP Genotype Calling Multilocus Genotyping Problem Experimental Results Conclusion

  3. Ultra-high throughput DNA sequencing • Recent massively parallel sequencing technologies deliver orders of magnitude higher throughput compared to classic Sanger sequencing Roche/454 FLX Titanium 400bp reads 400Mb/10h run ABI SOLiD 2.0 25-35bp reads 3-4Gb/6 day run Helicos HeliScope 25-55bp reads >1Gb/day Illumina Genome Analyzer II 35-50bp reads 1.5Gb/2.5 day run

  4. C.Venter Sanger@7.5x J. Watson 454@7.4x NA18507 Illumina@36x SOLiD@12x UHTS enable personal genomics

  5. Sequencing provides single-base resolution of genetic variation (SNPs, CNVs, genome rearrangements) However, interpretation requires determination of both alleles at variable loci This is limited by coverage depth due to random nature of shotgun sequencing For the Venter and Watson genomes (both sequenced at ~7.5x average coverage), comparison with SNP genotyping chips has shown only ~75% accuracy for sequencing based calls of heterozygous SNPs [Levy et al 07, Wheeler et al 08] Challenges for medical applications of sequencing

  6. Allele coverage for heterozygous SNPs (Watson 454 @ 5.85x avg. coverage)

  7. Allele coverage for heterozygous SNPs (Watson 454 @ 2.93x avg. coverage)

  8. Allele coverage for heterozygous SNPs (Watson 454 @ 1.46x avg. coverage)

  9. Allele coverage for heterozygous SNPs (Watson 454 @ 0.73x avg. coverage)

  10. Prior work • All prior genotype calling methods are based on allele coverage • [Levy et al 07] and [Wheeler et al 08] require that each allele be covered by at least 2 reads in order to be called • Combined with hypothesis testing based on the binomial distribution when calling hets • Binomial probability for the observed number of 0 and 1 alleles must be at least 0.01 • [Wendl&Wilson 08] generalize coverage methods to allow an arbitrary minimum allele coverage k • Estimate that as much as 21x coverage will be required for sequencing of normal tissue samples based on idealized theory that “neglects any heuristic inputs”

  11. We propose methods incorporating additional sources of information: Quality scores reflecting uncertainty in sequencing data Allele/genotype frequency and linkage disequilibrium (LD) info extracted from a reference panel such as Hapmap Experimental results show significantly improved genotyping accuracy Do heuristic inputs help?

  12. Outline Introduction Single SNP Genotype Calling Multilocus Genotyping Problem Experimental Results Conclusion

  13. Biallelic SNPs: 0 = major allele, 1 = minor allele SNP genotypes: 0/2 = homozygous major/minor, 1=heterozygous Mapped reads with allele 0 012100120 Inferred genotypes Mapped reads with allele 1 Sequencing errors Basic notations

  14. Let ridenote the set of mapped reads covering SNP locus i and ci =| ri| For a read r in ri, r(i) denotes the allele observed at locus i If qr(i) is the phred quality score of r(i), the probability that r(i) is incorrect is given by • Probability of observing read set riconditional on Gi: Incorporating base call uncertainty

  15. Applying Bayes’ formula: Where are genotype frequencies inferred from a representative panel Single SNP genotype calling

  16. Outline Introduction Single SNP Genotype Calling Multilocus Genotyping Problem Experimental Results Conclusion

  17. Haplotype structure in human populations

  18. … F1 F2 Fn H1 H2 Hn HMM model of haplotype frequencies • Fi = founder haplotype at locus i, Hi = observed allele at locus i • For given haplotype h, P(H=h|M) can be computed in O(nK2) using forward algorithm • Similar models proposed in [Schwartz 04, Rastas et al. 05, Kennedy et al. 07, Kimmel&Shamir 05, Scheet&Stephens 06]

  19. P(f1), P(f’1), P(fi+1|fi), P(f’i+1|f’i), P(hi|fi), P(h’i|f’i) trained using Baum-Welch algorithm on haplotypes inferred from the populations of origin for mother/father HF-HMM for multilocus genotype inference … F1 F2 Fn H1 H2 Hn … F'1 F'2 F'n H'1 H'2 H'n G1 G2 Gn R1,1 … R1,c R2,1 … R2,c Rn,1 … Rn,c n 1 2

  20. P(gi|hi,h’i) set to 1 if h+h’i=gi and to 0 otherwise HF-HMM for multilocus genotype inference … F1 F2 Fn H1 H2 Hn … F'1 F'2 F'n H'1 H'2 H'n G1 G2 Gn R1,1 … R1,c R2,1 … R2,c Rn,1 … Rn,c n 1 2

  21. HF-HMM for multilocus genotype inference … F1 F2 Fn H1 H2 Hn … F'1 F'2 F'n H'1 H'2 H'n G1 G2 Gn R1,1 … R1,c R2,1 … R2,c Rn,1 … Rn,c n 1 2

  22. Bad news: maxgP(g | r) cannot be approximated within unless ZPP=NP Multilocus genotyping problem • GIVEN: • Shotgun read sets r=(r1, r2, … , rn) • Quality scores • Trained HMM models representing LD in populations of origin for mother/father • FIND: • Multilocus genotype g*=(g*1,g*2,…,g*n) with maximum posterior probability, i.e., g*=argmaxg P(g | r)

  23. Posterior decoding algorithm For each i = 1..n, compute Return

  24. Forward-backward computation of posterior probabilities fi … … hi f’i … … h’i gi r1,c ri,1 ri,c r1,1 … … Rn,1 … Rn,c 1 n i

  25. Forward-backward computation of posterior probabilities fi … … hi f’i … … h’i gi r1,c ri,1 ri,c r1,1 … … Rn,1 … Rn,c 1 n i

  26. Forward-backward computation of posterior probabilities fi … … hi f’i … … h’i gi r1,c ri,1 ri,c r1,1 … … Rn,1 … Rn,c 1 n i

  27. Forward-backward computation of posterior probabilities fi … … hi f’i … … h’i gi r1,c ri,1 ri,c r1,1 … … Rn,1 … Rn,c 1 n i

  28. Forward-backward computation of posterior probabilities fi … … hi f’i … … h’i gi r1,c ri,1 ri,c r1,1 … … Rn,1 … Rn,c 1 n i

  29. Outline Introduction Single SNP Genotype Calling Multilocus Genotyping Problem Experimental Results Conclusion

  30. Mapped reads … … … … … … … Pipeline for LD-Based Genotype Calling Reference genome sequence Read sequences >gnl|ti|1779718824 name:EI1W3PE02ILQXT TCAGTGAGGGTTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTTGAGACAGAATTTTGCTCTT GTCGCCCAGGCTGGTGTGCAGTGGTGCAACCTCAGCTCACTGCAACCTCTGCCTCCAGGTTCAAGCAATT CTCTGCCTCAGCCTCCCAAGTAGCTGGGATTACAGGCGGGCGCCACCACGCCCAGCTAATTTTGTATTGT TAGTAAAGATGGGGTTTCACTACGTTGGCTGAGCTGTTCTCGAACTCCTGACCTCAAATGAC >gnl|ti|1779718825 name:EI1W3PE02GTXK0 TCAGAATACCTGTTGCCCATTTTTATATGTTCCTTGGAGAAATGTCAATTCAGAGCTTTTGCTCAGCTTT TAATATGTTTATTTGTTTTGCTGCTGTTGAGTTGTACAATGTTGGGGAAAACAGTCGCACAACACCCGGC AGGTACTTTGAGTCTGGGGGAGACAAAGGAGTTAGAAAGAGAGAGAATAAGCACTTAAAAGGCGGGTCCA GGGGGCCCGAGCATCGGAGGGTTGCTCATGGCCCACAGTTGTCAGGCTCCACCTAATTAAATGGTTTACA >gnl|ti|1779718824 name:EI1W3PE02ILQXT TCAGTGAGGGTTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTTGAGACAGAATTTTGCTCTT GTCGCCCAGGCTGGTGTGCAGTGGTGCAACCTCAGCTCACTGCAACCTCTGCCTCCAGGTTCAAGCAATT CTCTGCCTCAGCCTCCCAAGTAGCTGGGATTACAGGCGGGCGCCACCACGCCCAGCTAATTTTGTATTGT TAGTAAAGATGGGGTTTCACTACGTTGGCTGAGCTGTTCTCGAACTCCTGACCTCAAATGAC >gnl|ti|1779718825 name:EI1W3PE02GTXK0 TCAGAATACCTGTTGCCCATTTTTATATGTTCCTTGGAGAAATGTCAATTCAGAGCTTTTGCTCAGCTTT TAATATGTTTATTTGTTTTGCTGCTGTTGAGTTGTACAATGTTGGGGAAAACAGTCGCACAACACCCGGC AGGTACTTTGAGTCTGGGGGAGACAAAGGAGTTAGAAAGAGAGAGAATAAGCACTTAAAAGGCGGGTCCA GGGGGCCCGAGCATCGGAGGGTTGCTCATGGCCCACAGTTGTCAGGCTCCACCTAATTAAATGGTTTACA >gnl|ti|1779718824 name:EI1W3PE02ILQXT TCAGTGAGGGTTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTTGAGACAGAATTTTGCTCTT GTCGCCCAGGCTGGTGTGCAGTGGTGCAACCTCAGCTCACTGCAACCTCTGCCTCCAGGTTCAAGCAATT CTCTGCCTCAGCCTCCCAAGTAGCTGGGATTACAGGCGGGCGCCACCACGCCCAGCTAATTTTGTATTGT TAGTAAAGATGGGGTTTCACTACGTTGGCTGAGCTGTTCTCGAACTCCTGACCTCAAATGAC >gnl|ti|1779718825 name:EI1W3PE02GTXK0 TCAGAATACCTGTTGCCCATTTTTATATGTTCCTTGGAGAAATGTCAATTCAGAGCTTTTGCTCAGCTTT TAATATGTTTATTTGTTTTGCTGCTGTTGAGTTGTACAATGTTGGGGAAAACAGTCGCACAACACCCGGC AGGTACTTTGAGTCTGGGGGAGACAAAGGAGTTAGAAAGAGAGAGAATAAGCACTTAAAAGGCGGGTCCA GGGGGCCCGAGCATCGGAGGGTTGCTCATGGCCCACAGTTGTCAGGCTCCACCTAATTAAATGGTTTACA >gi|88943037|ref|NT_113796.1|Hs1_111515 Homo sapiens chromosome 1 genomic contig, reference assembly GAATTCTGTGAAAGCCTGTAGCTATAAAAAAATGTTGAGCCATAAATACCATCAGAAATAACAAAGGGAG CTTTGAAGTATTCTGAGACTTGTAGGAAGGTGAAGTAAATATCTAATATAATTGTAACAAGTAGTGCTTG GATTGTATGTTTTTGATTATTTTTTGTTAGGCTGTGATGGGCTCAAGTAATTGAAATTCCTGATGCAAGT AATACAGATGGATTCAGGAGAGGTACTTCCAGGGGGTCAAGGGGAGAAATACCTGTTGGGGGTCAATGCC CTCCTAATTCTGGAGTAGGGGCTAGGCTAGAATGGTAGAATGCTCAAAAGAATCCAGCGAAGAGGAATAT TTCTGAGATAATAAATAGGACTGTCCCATATTGGAGGCCTTTTTGAACAGTTGTTGTATGGTGACCCTGA AATGTACTTTCTCAGATACAGAACACCCTTGGTCAATTGAATACAGATCAATCACTTTAAGTAAGCTAAG TCCTTACTAAATTGATGAGACTTAAACCCATGAAAACTTAACAGCTAAACTCCCTAGTCAACTGGTTTGA ATCTACTTCTCCAGCAGCTGGGGGAAAAAAGGTGAGAGAAGCAGGATTGAAGCTGCTTCTTTGAATTTAC >gi|88943037|ref|NT_113796.1|Hs1_111515 Homo sapiens chromosome 1 genomic contig, reference assembly GAATTCTGTGAAAGCCTGTAGCTATAAAAAAATGTTGAGCCATAAATACCATCAGAAATAACAAAGGGAG CTTTGAAGTATTCTGAGACTTGTAGGAAGGTGAAGTAAATATCTAATATAATTGTAACAAGTAGTGCTTG GATTGTATGTTTTTGATTATTTTTTGTTAGGCTGTGATGGGCTCAAGTAATTGAAATTCCTGATGCAAGT AATACAGATGGATTCAGGAGAGGTACTTCCAGGGGGTCAAGGGGAGAAATACCTGTTGGGGGTCAATGCC CTCCTAATTCTGGAGTAGGGGCTAGGCTAGAATGGTAGAATGCTCAAAAGAATCCAGCGAAGAGGAATAT TTCTGAGATAATAAATAGGACTGTCCCATATTGGAGGCCTTTTTGAACAGTTGTTGTATGGTGACCCTGA AATGTACTTTCTCAGATACAGAACACCCTTGGTCAATTGAATACAGATCAATCACTTTAAGTAAGCTAAG TCCTTACTAAATTGATGAGACTTAAACCCATGAAAACTTAACAGCTAAACTCCCTAGTCAACTGGTTTGA ATCTACTTCTCCAGCAGCTGGGGGAAAAAAGGTGAGAGAAGCAGGATTGAAGCTGCTTCTTTGAATTTAC >gi|88943037|ref|NT_113796.1|Hs1_111515 Homo sapiens chromosome 1 genomic contig, reference assembly GAATTCTGTGAAAGCCTGTAGCTATAAAAAAATGTTGAGCCATAAATACCATCAGAAATAACAAAGGGAG CTTTGAAGTATTCTGAGACTTGTAGGAAGGTGAAGTAAATATCTAATATAATTGTAACAAGTAGTGCTTG GATTGTATGTTTTTGATTATTTTTTGTTAGGCTGTGATGGGCTCAAGTAATTGAAATTCCTGATGCAAGT AATACAGATGGATTCAGGAGAGGTACTTCCAGGGGGTCAAGGGGAGAAATACCTGTTGGGGGTCAATGCC CTCCTAATTCTGGAGTAGGGGCTAGGCTAGAATGGTAGAATGCTCAAAAGAATCCAGCGAAGAGGAATAT TTCTGAGATAATAAATAGGACTGTCCCATATTGGAGGCCTTTTTGAACAGTTGTTGTATGGTGACCCTGA AATGTACTTTCTCAGATACAGAACACCCTTGGTCAATTGAATACAGATCAATCACTTTAAGTAAGCTAAG TCCTTACTAAATTGATGAGACTTAAACCCATGAAAACTTAACAGCTAAACTCCCTAGTCAACTGGTTTGA ATCTACTTCTCCAGCAGCTGGGGGAAAAAAGGTGAGAGAAGCAGGATTGAAGCTGCTTCTTTGAATTTAC Quality scores >gnl|ti|1779718824 name:EI1W3PE02ILQXT 28 28 28 28 26 28 28 40 34 14 44 36 23 13 2 27 42 35 21 7 27 42 35 21 6 28 43 36 22 10 27 42 35 20 6 28 43 36 22 9 28 43 36 22 9 28 44 36 24 14 4 28 28 28 27 28 26 26 35 26 40 34 18 3 28 28 28 27 33 24 26 28 28 28 40 33 14 28 36 27 26 26 37 29 28 28 28 28 27 28 28 28 37 28 27 27 28 36 28 37 28 28 28 27 28 28 28 24 28 28 27 28 28 37 29 36 27 27 28 27 28 33 23 28 33 23 28 36 27 33 23 28 35 25 28 28 36 27 36 27 28 28 28 24 28 37 29 28 19 28 26 37 29 26 39 33 13 37 28 28 28 21 24 28 27 41 34 15 28 36 27 26 28 24 35 27 28 40 34 15 >gnl|ti|1779718824 name:EI1W3PE02ILQXT 28 28 28 28 26 28 28 40 34 14 44 36 23 13 2 27 42 35 21 7 27 42 35 21 6 28 43 36 22 10 27 42 35 20 6 28 43 36 22 9 28 43 36 22 9 28 44 36 24 14 4 28 28 28 27 28 26 26 35 26 40 34 18 3 28 28 28 27 33 24 26 28 28 28 40 33 14 28 36 27 26 26 37 29 28 28 28 28 27 28 28 28 37 28 27 27 28 36 28 37 28 28 28 27 28 28 28 24 28 28 27 28 28 37 29 36 27 27 28 27 28 33 23 28 33 23 28 36 27 33 23 28 35 25 28 28 36 27 36 27 28 28 28 24 28 37 29 28 19 28 26 37 29 26 39 33 13 37 28 28 28 21 24 28 27 41 34 15 28 36 27 26 28 24 35 27 28 40 34 15 >gnl|ti|1779718824 name:EI1W3PE02ILQXT 28 28 28 28 26 28 28 40 34 14 44 36 23 13 2 27 42 35 21 7 27 42 35 21 6 28 43 36 22 10 27 42 35 20 6 28 43 36 22 9 28 43 36 22 9 28 44 36 24 14 4 28 28 28 27 28 26 26 35 26 40 34 18 3 28 28 28 27 33 24 26 28 28 28 40 33 14 28 36 27 26 26 37 29 28 28 28 28 27 28 28 28 37 28 27 27 28 36 28 37 28 28 28 27 28 28 28 24 28 28 27 28 28 37 29 36 27 27 28 27 28 33 23 28 33 23 28 36 27 33 23 28 35 25 28 28 36 27 36 27 28 28 28 24 28 37 29 28 19 28 26 37 29 26 39 33 13 37 28 28 28 21 24 28 27 41 34 15 28 36 27 26 28 24 35 27 28 40 34 15 SNP genotype calls Hapmap genotypes or haplotypes rs12095710 T T 9.988139e-01 rs12127179 C T 9.986735e-01 rs11800791 G G 9.977713e-01 rs11578310 G G 9.980062e-01 rs1287622 G G 8.644588e-01 rs11804808 C C 9.977779e-01 rs17471528 A G 5.236099e-01 rs11804835 C C 9.977759e-01 rs11804836 C C 9.977925e-01 rs1287623 G G 9.646510e-01 rs13374307 G G 9.989084e-01 rs12122008 G G 5.121655e-01 rs17431341 A C 5.290652e-01 rs881635 G G 9.978737e-01 rs9700130 A A 9.989940e-01 rs11121600 A A 6.160199e-01 rs12121542 A A 5.555713e-01 rs11121605 T T 8.387705e-01 rs12563779 G G 9.982776e-01 rs11121607 C G 5.639239e-01 rs11121608 G T 5.452936e-01 rs12029742 G G 9.973527e-01 rs562118 C C 9.738776e-01 rs12133533 A C 9.956655e-01 rs11121648 G G 9.077355e-01 rs9662691 C C 9.988648e-01 rs11805141 C C 9.928786e-01 rs1287635 C C 6.113270e-01 90 209342 16 F 0 0 2110001?0100210010011002122201210211?1221220212000 18 F 15 16 21100012010021001001100?100201?10111110111?0212000 15 M 0 0 21120010012001201001120010110101011111011110212000 7 M 0 0 2110001001000200122110001111011100111?121210222000 8 F 0 0 011202100120022012211200101101210211122111?0120000 12 F 9 10 21100010010002001221100010110111001112121210220000 9 M 0 0 011?001?012002201221120010?10121021112211110120000 11 M 7 8 21100210010002001221100012110111001112121210222000 90 209342 16 F 0 0 2110001?0100210010011002122201210211?1221220212000 18 F 15 16 21100012010021001001100?100201?10111110111?0212000 15 M 0 0 21120010012001201001120010110101011111011110212000 7 M 0 0 2110001001000200122110001111011100111?121210222000 8 F 0 0 011202100120022012211200101101210211122111?0120000 12 F 9 10 21100010010002001221100010110111001112121210220000 9 M 0 0 011?001?012002201221120010?10121021112211110120000 11 M 7 8 21100210010002001221100012110111001112121210222000 90 209342 16 F 0 0 2110001?0100210010011002122201210211?1221220212000 18 F 15 16 21100012010021001001100?100201?10111110111?0212000 15 M 0 0 21120010012001201001120010110101011111011110212000 7 M 0 0 2110001001000200122110001111011100111?121210222000 8 F 0 0 011202100120022012211200101101210211122111?0120000 12 F 9 10 21100010010002001221100010110111001112121210220000 9 M 0 0 011?001?012002201221120010?10121021112211110120000 11 M 7 8 21100210010002001221100012110111001112121210222000

  31. Datasets Watson Sequencing data: 74.4 million 454 reads (average length 265bp) Reference panel: CEU genotypes from Hapmap r23a phased using the ENT algorithm [Gusev et al. 08] Ground truth: duplicate Affymetrix 500k SNP genotypes NA18507 (Illumina & SOLiD) Sequencing data: 525 million Illumina reads (36bp, paired) and 764 million SOLiD reads (24 - 44bp, unpaired) Reference panel: YRI haplotypes from Hapmap r22 excluding NA18507 haplotypes Ground truth: Hapmap r22 genotypes

  32. Mapping statistics

  33. Concordance vs. avg. coverage(Watson 454 reads)

  34. Tradeoff with call rate (5.85x Watson 454 reads, homo SNPs)

  35. Tradeoff with call rate (5.85x Watson 454 reads, het SNPs)

  36. Concordance vs. avg. coverage for NA18507 (Illumina & SOLiD reads)

  37. Posterior decoding algorithm has scalable running time and yields significant improvements in genotyping calling accuracy Improvement depends on the coverage depth (higher at lower coverage), e.g., accuracy achieved by previously proposed binomial test at 5-6x average coverage is achieved by HMM-based posterior decoding algorithm using less than 1/4 of the reads Open source code available at http://dna.engr.uconn.edu/software/GeneSeq/ Ongoing work Extension to population sequencing data (removing need for reference panels) Haplotype reconstruction Conclusions & ongoing work

  38. Acknowledgments • Work supported in part by NSF awards IIS-0546457 and DBI-0543365 to IM and IIS-0803440 to YW. SD and YH performed this research as part of the Summer REU program “Bio-Grid Initiatives for Interdisciplinary Research and Education" funded by NSF award CCF-0755373.

  39. Mapping Procedure 454 reads mapped on human genome build 36.3 using the NUCMER tool of the MUMmer package [Kurtz et al 04] with default parameters Additional filtering: at least 90% of the read length matched to the genome, no more than 10 errors (mismatches or indels) Reads meeting above conditions at multiple genome positions (likely coming from genomic repeats) were discarded Illumina and SOLiD reads mapped using MAQ [Li et al 08] with default parameters For reads mapped at multiple positions MAQ returns best position (breaking ties arbitrarily) together with mapping confidence We filtered bad alignments and discarded paired end reads that are not mapped in pairs using the “submap -p” command

  40. Recombination rate effects (NA18507 Illumina)

  41. Coverage effects (NA18507 Illumina)

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