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

Algorithms for Genotype and Haplotype Inference from Low-

Coverage Short Sequencing Reads

Ion MandoiuComputer Science and Engineering Department

University of Connecticut

Joint work with S. Dinakar, J. Duitama, Y. Hernández, J. Kennedy, and Y. Wu

Outline

Introduction Single SNP Genotype Calling Multilocus Genotyping Problem Experimental Results Conclusion

Illumina Genome Analyzer II35-50bp reads1.5Gb/2.5 day run

Roche/454 FLX Titanium400bp reads400Mb/10h run

ABI SOLiD 2.025-35bp reads3-4Gb/6 day run

Recent massively parallel sequencing technologies deliver orders of magnitude higher throughput compared to classic Sanger sequencing

Ultra-high throughput DNA sequencing

Helicos HeliScope25-55bp reads>1Gb/day

UHTS enable personal genomics

$100

$1,000

$10,000

$100,000

$1,000,000

$10,000,000

$100,000,000

days weeks months years

Sequencing Time

Cost

[email protected]

J. [email protected]

Illumina@36xSOLiD@12x

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

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

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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”

Prior work

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?

Outline


Biallelic SNPs: 0 = major allele, 1 = minor allele SNP genotypes: 0/2 = homozygous major/minor,

1=heterozygous

Inferred genotypesMapped reads with allele 0

Mapped reads with allele 1012100120

Sequencing errors

Basic notations

Let ri denote 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 10/

)()(10 irq

ir

Incorporating base call uncertainty

1)(r

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0)(r

)( )1()0|r(irr

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iriiii

GP

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ir

irr

iriiii

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ic

ii GP

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Probability of observing read set ri conditional on Gi:

Applying Bayes’ formula:

Where are genotype frequencies inferred from a representative panel

}2,1,0{)|r()(

)|r()()r|(g iiii

iiiiiii gGPgGP

gGPgPgGP

)( ii gGP

Single SNP genotype calling

Outline


Haplotype structure in human populations

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]

HMM model of haplotype frequencies

F1 F2 Fn…

H1 H2 Hn

F1 F2 Fn…

H1 H2 Hn

G1 G2 Gn

…R1,1 R2,1

F'1 F'2 F'n…

H'1 H'2 H'n

R1,c … R2,c …Rn,1 Rn,c1 2 n

HF-HMM for multilocus genotype inference

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

F1 F2 Fn…

H1 H2 Hn

G1 G2 Gn

…R1,1 R2,1

F'1 F'2 F'n…

H'1 H'2 H'n

R1,c … R2,c …Rn,1 Rn,c1 2 n


P(gi|hi,h’i) set to 1 if h+h’i=gi and to 0 otherwise

F1 F2 Fn…

H1 H2 Hn

G1 G2 Gn

…R1,1 R2,1

F'1 F'2 F'n…

H'1 H'2 H'n

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)(1)(

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GIVEN: • Shotgun read sets r=(r1, r2, … , rn)• Quality scores• Trained HMM models representing LD in populations of

origin for mother/fatherFIND:

• Multilocus genotype g*=(g*1,g*2,…,g*n) with maximum posterior probability, i.e., g*=argmaxg P(g | r)

Multilocus genotyping problem

Bad news: maxgP(g | r) cannot be approximated within unless ZPP=NP

)( 1 nO

Posterior decoding algorithm1. For each i = 1..n, compute

2. Return *)*,...,(* 1 nggg

)r,(maxarg)r|(maxarg* igigi gPgPgii

)()|r()r,( '' ''1 ,1 ,, i

iff

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…r1,1ri,1

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1i n

…

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Forward-backward computation of posterior probabilities

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Outline


>gi|88943037|ref|NT_113796.1|Hs1_111515 Homo sapiens chromosome 1 genomic contig, reference assemblyGAATTCTGTGAAAGCCTGTAGCTATAAAAAAATGTTGAGCCATAAATACCATCAGAAATAACAAAGGGAGCTTTGAAGTATTCTGAGACTTGTAGGAAGGTGAAGTAAATATCTAATATAATTGTAACAAGTAGTGCTTGGATTGTATGTTTTTGATTATTTTTTGTTAGGCTGTGATGGGCTCAAGTAATTGAAATTCCTGATGCAAGTAATACAGATGGATTCAGGAGAGGTACTTCCAGGGGGTCAAGGGGAGAAATACCTGTTGGGGGTCAATGCCCTCCTAATTCTGGAGTAGGGGCTAGGCTAGAATGGTAGAATGCTCAAAAGAATCCAGCGAAGAGGAATATTTCTGAGATAATAAATAGGACTGTCCCATATTGGAGGCCTTTTTGAACAGTTGTTGTATGGTGACCCTGAAATGTACTTTCTCAGATACAGAACACCCTTGGTCAATTGAATACAGATCAATCACTTTAAGTAAGCTAAGTCCTTACTAAATTGATGAGACTTAAACCCATGAAAACTTAACAGCTAAACTCCCTAGTCAACTGGTTTGAATCTACTTCTCCAGCAGCTGGGGGAAAAAAGGTGAGAGAAGCAGGATTGAAGCTGCTTCTTTGAATTTAC


>gnl|ti|1779718824 name:EI1W3PE02ILQXT28 28 28 28 26 28 28 40 34 14 44 36 23 13 2 27 42 35 21 727 42 35 21 6 28 43 36 22 10 27 42 35 20 6 28 43 36 22 928 43 36 22 9 28 44 36 24 14 4 28 28 28 27 28 26 26 35 2640 34 18 3 28 28 28 27 33 24 26 28 28 28 40 33 14 28 36 2726 26 37 29 28 28 28 28 27 28 28 28 37 28 27 27 28 36 28 3728 28 28 27 28 28 28 24 28 28 27 28 28 37 29 36 27 27 28 2728 33 23 28 33 23 28 36 27 33 23 28 35 25 28 28 36 27 36 2728 28 28 24 28 37 29 28 19 28 26 37 29 26 39 33 13 37 28 2828 21 24 28 27 41 34 15 28 36 27 26 28 24 35 27 28 40 34 15


>gnl|ti|1779718824 name:EI1W3PE02ILQXTTCAGTGAGGGTTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTTGAGACAGAATTTTGCTCTTGTCGCCCAGGCTGGTGTGCAGTGGTGCAACCTCAGCTCACTGCAACCTCTGCCTCCAGGTTCAAGCAATTCTCTGCCTCAGCCTCCCAAGTAGCTGGGATTACAGGCGGGCGCCACCACGCCCAGCTAATTTTGTATTGTTAGTAAAGATGGGGTTTCACTACGTTGGCTGAGCTGTTCTCGAACTCCTGACCTCAAATGAC>gnl|ti|1779718825 name:EI1W3PE02GTXK0TCAGAATACCTGTTGCCCATTTTTATATGTTCCTTGGAGAAATGTCAATTCAGAGCTTTTGCTCAGCTTTTAATATGTTTATTTGTTTTGCTGCTGTTGAGTTGTACAATGTTGGGGAAAACAGTCGCACAACACCCGGCAGGTACTTTGAGTCTGGGGGAGACAAAGGAGTTAGAAAGAGAGAGAATAAGCACTTAAAAGGCGGGTCCAGGGGGCCCGAGCATCGGAGGGTTGCTCATGGCCCACAGTTGTCAGGCTCCACCTAATTAAATGGTTTACA

>gnl|ti|1779718824 name:EI1W3PE02ILQXTTCAGTGAGGGTTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTTGAGACAGAATTTTGCTCTTGTCGCCCAGGCTGGTGTGCAGTGGTGCAACCTCAGCTCACTGCAACCTCTGCCTCCAGGTTCAAGCAATTCTCTGCCTCAGCCTCCCAAGTAGCTGGGATTACAGGCGGGCGCCACCACGCCCAGCTAATTTTGTATTGTTAGTAAAGATGGGGTTTCACTACGTTGGCTGAGCTGTTCTCGAACTCCTGACCTCAAATGAC>gnl|ti|1779718825 name:EI1W3PE02GTXK0TCAGAATACCTGTTGCCCATTTTTATATGTTCCTTGGAGAAATGTCAATTCAGAGCTTTTGCTCAGCTTTTAATATGTTTATTTGTTTTGCTGCTGTTGAGTTGTACAATGTTGGGGAAAACAGTCGCACAACACCCGGCAGGTACTTTGAGTCTGGGGGAGACAAAGGAGTTAGAAAGAGAGAGAATAAGCACTTAAAAGGCGGGTCCAGGGGGCCCGAGCATCGGAGGGTTGCTCATGGCCCACAGTTGTCAGGCTCCACCTAATTAAATGGTTTACA Mapped reads

Hapmap genotypesor haplotypes

90 20934216 F 0 02110001?0100210010011002122201210211?122122021200018 F 15 1621100012010021001001100?100201?10111110111?021200015 M 0 0211200100120012010011200101101010111110111102120007 M 0 02110001001000200122110001111011100111?1212102220008 F 0 0011202100120022012211200101101210211122111?012000012 F 9 10211000100100020012211000101101110011121212102200009 M 0 0011?001?012002201221120010?1012102111221111012000011 M 7 821100210010002001221100012110111001112121210222000

90 20934216 F 0 02110001?0100210010011002122201210211?122122021200018 F 15 1621100012010021001001100?100201?10111110111?021200015 M 0 0211200100120012010011200101101010111110111102120007 M 0 02110001001000200122110001111011100111?1212102220008 F 0 0011202100120022012211200101101210211122111?012000012 F 9 10211000100100020012211000101101110011121212102200009 M 0 0011?001?012002201221120010?1012102111221111012000011 M 7 821100210010002001221100012110111001112121210222000

90 20934216 F 0 02110001?0100210010011002122201210211?122122021200018 F 15 1621100012010021001001100?100201?10111110111?021200015 M 0 0211200100120012010011200101101010111110111102120007 M 0 02110001001000200122110001111011100111?1212102220008 F 0 0011202100120022012211200101101210211122111?012000012 F 9 10211000100100020012211000101101110011121212102200009 M 0 0011?001?012002201221120010?1012102111221111012000011 M 7 821100210010002001221100012110111001112121210222000

Reference genome sequence


…

…

…

… …

…

…

>gnl|ti|1779718824 name:EI1W3PE02ILQXTTCAGTGAGGGTTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTGTTTTTGAGACAGAATTTTGCTCTTGTCGCCCAGGCTGGTGTGCAGTGGTGCAACCTCAGCTCACTGCAACCTCTGCCTCCAGGTTCAAGCAATTCTCTGCCTCAGCCTCCCAAGTAGCTGGGATTACAGGCGGGCGCCACCACGCCCAGCTAATTTTGTATTGTTAGTAAAGATGGGGTTTCACTACGTTGGCTGAGCTGTTCTCGAACTCCTGACCTCAAATGAC>gnl|ti|1779718825 name:EI1W3PE02GTXK0TCAGAATACCTGTTGCCCATTTTTATATGTTCCTTGGAGAAATGTCAATTCAGAGCTTTTGCTCAGCTTTTAATATGTTTATTTGTTTTGCTGCTGTTGAGTTGTACAATGTTGGGGAAAACAGTCGCACAACACCCGGCAGGTACTTTGAGTCTGGGGGAGACAAAGGAGTTAGAAAGAGAGAGAATAAGCACTTAAAAGGCGGGTCCAGGGGGCCCGAGCATCGGAGGGTTGCTCATGGCCCACAGTTGTCAGGCTCCACCTAATTAAATGGTTTACA


Read sequences

Quality scores

SNP genotype callsrs12095710 T T 9.988139e-01rs12127179 C T 9.986735e-01rs11800791 G G 9.977713e-01rs11578310 G G 9.980062e-01rs1287622 G G 8.644588e-01 rs11804808 C C 9.977779e-01rs17471528 A G 5.236099e-01rs11804835 C C 9.977759e-01rs11804836 C C 9.977925e-01rs1287623 G G 9.646510e-01 rs13374307 G G 9.989084e-01rs12122008 G G 5.121655e-01rs17431341 A C 5.290652e-01rs881635 G G 9.978737e-01 rs9700130 A A 9.989940e-01 rs11121600 A A 6.160199e-01rs12121542 A A 5.555713e-01rs11121605 T T 8.387705e-01rs12563779 G G 9.982776e-01rs11121607 C G 5.639239e-01rs11121608 G T 5.452936e-01rs12029742 G G 9.973527e-01rs562118 C C 9.738776e-01 rs12133533 A C 9.956655e-01rs11121648 G G 9.077355e-01rs9662691 C C 9.988648e-01 rs11805141 C C 9.928786e-01rs1287635 C C 6.113270e-01

Pipeline for LD-Based Genotype Calling

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

Mapping statistics

Dataset Raw reads

Raw sequenc

eMapped reads

Test SNPs

Avg. mapped SNP cov.

Watson 74.2M 19.7Gb 49.8M(67%) 443K 5.85x

NA18507Illumina 525M 18.9Gb 397M

(78%) 2.85M 6.10x

NA18507SOLiD 764M 21.15Gb 324M

(42%) 2.85M 3.21x

Concordance vs. avg. coverage(Watson 454 reads)

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Binomial (Homo)HMM-Posterior (Homo)Binomial (Het)HMM-Posterior (Het)

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

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1SNP-Posterior Binomial0.01 HMM-Posterior

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

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

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Binomial (Homo) Illumina

HMM-Posterior (Homo) Illumina

Binomial (Het) Illumina

HMM-Posterior (Het) Illumina

Binomial (Homo) SOLiD

HMM-Posterior (Homo) SOLiD

Binomial (Het) SOLiD

HMM-Posterior (Het) SOLiD

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

http://dna.engr.uconn.edu/software/GeneSeq/

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.

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

Recombination rate effects (NA18507 Illumina)

91%

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100%

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% of homo % of het

Coverage effects (NA18507 Illumina)

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SNP coverage

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Documents

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