LD-Based Genotype and Haplotype Inference from Low-Coverage Short Sequencing Reads

LD-Based 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

Outline

Introduction

Single SNP Genotype Calling

Multilocus Genotyping Problem

HMM-Posterior Algorithm

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 sequencing

Helicos HeliScope25-55bp reads>1Gb/day

UHTS is a transformative technology Numerous applications besides de novo genome

sequencing: RNA-Seq Non-coding RNAs ChIP-Seq Epigenetics Structural variation Metagenomics Paleogenomics …

UHTS applications

Personal genomics

$100

$1,000

$10,000

$100,000

$1,000,000

$10,000,000

$100,000,000

days weeks months years

Sequencing Time

Co

st

[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)

-1

0

1

2

3

4

5

6

-1 0 1 2 3 4 5 6

Reference allele coverage

Var

ian

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co

vera

ge


-1

0

1

2

3

4

5

6

-1 0 1 2 3 4 5 6


Var

ian

t al

lele

co

vera

ge

Most work devoted to de novo variation discovery from sequencing data, e.g., SNPs, CNVs

Unlike genotying known variation, de novo discovery requires very stringent detection criteria

Prior genotyping 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

Prior work

[Wendl&Wilson 08] estimate that 21x coverage will be required for sequencing of normal tissue samples based on idealized theory that “neglects any heuristic inputs”

What coverage is required?

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

Introduction





Conclusion

Biallelic SNPs: 0 = major allele, 1 = minor allele

SNP genotypes: 0/2 = homozygous major/minor,

1=heterozygous

Inferred genotypes

Mapped 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 irqir

Incorporating base call uncertainty

1)(r

)(

0)(r

)( )1()0|r(

irr

ir

irr

irii

ii

GP

0)(r

)(

1)(r

)( )1()2|r(

irr

ir

irr

irii

ii

GP

ic

ii GP

2

1)1|r(

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

Introduction





Conclusion

Haplotype structure in human populations

Fi = founder haplotype at locus i, Hi = observed allele at locus i

P(Fi), P(Fi | Fi-1) and P(Hi | Fi) estimated from reference genotype or haplotype data

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

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

Model training

1)(r

)(

0)(r

)( )1()0|r(

irr

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irr

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ii

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iiji

gggGrRP

This gives

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)

Multilocus genotyping problem

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

Computational complexity of MGP

)( 1 nO

Idea: reduction from the clique problem

Outline

Introduction





Conclusion

Posterior decoding algorithm

1. For each i = 1..n, compute

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

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

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

i

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fi …

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…r1,1

ri,1

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h’i

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1i n

…

…

Forward-backward computation of posterior probabilities

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Runtime Direct recurrences for computing forward

probabilities:

Runtime reduced to O(m+nK3) by reusing common terms:

where

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Outline

Introduction





Conclusion

>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 calls

rs12095710 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 Excluded discordant genotypes and SNPs for which Hapmap and

Affymetrix annotations have more than 5% difference in same-strand CEU allele frequency

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 for NA18507

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

Mapping statistics

DatasetRaw

reads

Raw sequenc

e

Mapped reads

Test SNPs

Avg. mapped SNP cov.

Watson 74.2M 19.7Gb49.8M(67%)

443K 5.85x

NA18507Illumina

525M 18.9Gb397M(78%)

2.85M 6.10x

NA18507SOLiD

764M 21.15Gb324M(42%)

2.85M 3.21x

Concordance vs. avg. coverage(Watson 454 reads)

0

10

20

30

40

50

60

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80

90

100

0 1 2 3 4 5 6

Avg. Coverage

% C

on

cord

an

ce

Binomial (Homo)

HMM-Posterior (Homo)

Binomial (Het)

HMM-Posterior (Het)

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

97

97.5

98

98.5

99

99.5

100

0 10 20 30 40 50

% uncalled

% c

on

cord

ance

1SNP-Posterior Binomial0.01 HMM-Posterior

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

80

82

84

86

88

90

92

94

96

98

100

0 5 10 15 20 25 30 35 40 45 50

% uncalled

% c

on

co

rda

nc

e

1SNP-Posterior Binomial0.01 HMM-Posterior

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

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6

Avg. Coverage

% C

on

cord

an

ce

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

Recombination rate effects (NA18507 Illumina)

91%

92%

93%

94%

95%

96%

97%

98%

99%

100%

-4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5

log(cM/Mb)

% C

on

cord

ance

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

% H

apm

ap S

NP

s

Concordance (homo) Concordance (het)

% of homo % of het

Coverage effects (NA18507 Illumina)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

SNP coverage

% C

on

cord

ance

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

% H

apm

ap S

NP

s

Concordance (homo) Concordance (het)% of homo % of het

Exploiting LD information yields significant improvements in genotyping calling accuracy and/or cost reductions

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

Ongoing work Extension to population sequencing data (removing need for

reference panels) Mapping repetitive reads & haplotype inferrence

Conclusions & ongoing work

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.

LD-Based Genotype and Haplotype Inference from Low-Coverage Short Sequencing Reads

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