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A Guided Tour to Computational Haplotyping

Tobias Marschall

June 15, 2017

Computability in Europe (CiE) @ Turku

Introduction to Haplotyping/Phasing

chr1

chr2

chr3

chr22

GT

TA

AC

TC

TC

CA

TG

CT

CG

TC

GC

AC

Terminology: Phasing = Haplotyping


C/T G/TA/C A/T chr1

G/T C/TA/C chr2

C/T C/G C/T

A/C C/G

chr3

chr22



chr1

chr2

chr3

chr22

GT

TA

AC

TC

TC

CA

TG

CT

CG

TC

GC

AC


Relevance of Haplotyping

[Tewhey et al., Nature Reviews Genetics, 2011]

Haplotype-specific Clinical Conditions

[Tewhey et al., Nature Reviews Genetics, 2011]

Approaches to Phasing

Genetic Haplotyping

Use genotypes across a pedigree

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

Molecular Haplotyping

loca

lg

lob

al

hap

loty

pes

StrandSeq(low cost)

Chromosomesorting

2nd-gen. sequencing(Illumina, ...)

3rd-gen. sequencing(PacBio, ONT, ...)

Read

-based

ph

asin

g

10X Genomics

Hi-C


Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

How to encode alleles/genotypes

TTTCATATCCATGGACACCTTCTGCT reference

T/T G/TA/C A/T genotypes

GT

TA

AC

TT haplotypes

Note

It can be convenient to write genotypes as sums: g ∈ {0, 1, 2}

How to encode alleles/genotypes

TTTCATATCCATGGACACCTTCTGCT reference

1/1 0/10/1 0/1 genotypes

01

10

10

11 haplotypes

Note

It can be convenient to write genotypes as sums: g ∈ {0, 1, 2}

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

??

??

??

??

??

??

??

??

??

??

??

??

??

??

??

??

??

??

??

??

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

??

??

?1

?0

10

??

??

??

??

??

??

??

??

??

??

??

??

??

??

??

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

??

??

?1

?0

10

??

??

?0

?1

01

??

??

??

??

??

??

??

??

??

??

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

??

??

?1

?0

10

??

??

?0

?1

01

??

??

?0

?1

01

??

??

??

??

??

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

??

??

?1

?0

10

??

??

?0

?1

01

??

??

?0

?1

01

??

??

?0

?0

00

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

??

??

?1

10

10

??

??

?0

11

01

??

??

?0

11

01

??

??

?0

10

00

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

??

??

11

10

10

??

??

10

11

01

??

??

10

11

01

??

??

00

10

00

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

??

?1

11

10

10

??

?0

10

11

01

??

?0

10

11

01

??

?0

00

10

00

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

?1

?1

11

10

10

?1

?0

10

11

01

?1

?0

10

11

01

?0

?0

00

10

00

Genetic Haplotyping

A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0

01

01

11

10

10

11

00

10

11

01

01

10

10

11

01

00

10

00

10

00

Overview

Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

Statistical Phasing (n+1 case)

Task: determine haplotype of additional individual

0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 00 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 10 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 00 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 00 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 01 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0

1 2 0 0 1 0 1 0 0 0 0 0 1 1 1 2 1 0 0 1Genotypes of additional individual

Reference Haplotypes

(each genotype is written as the sum of alleles)

Rastas and Ukkonen (WABI, 2007)

This genotype parsing problem can be solved in O(r2 · n) for apanel with r rows and n columns.

Statistical Phasing (whole panel)

0 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 00 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 00 0 1 0 0 0 0 0 0 1 1 0 1 0 0 1 1 0 0 10 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 0 0 0 00 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 00 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 00 0 0 1 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 01 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0

2n (or fewer) haplotypes

1 2 0 0 1 0 1 0 0 0 0 0 1 1 1 2 1 0 0 1Genotypes of n individuals

0 0 2 1 0 1 1 0 0 2 1 0 1 0 1 1 1 0 0 1

“We show here that the Pure-Parsimony approach is practical forgenotype data of up to 30 sites and 50 individuals (which is largeenough for practical use in many current haplotyping projects).”Dan Gusfield, CPM 2003.

Challenge 1

Scale statistical phasing approaches to panels with millions ofrows and tens of millions of columns. Study the trade-off betweenspeed and accuracy of results.

Overview

Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lg

lob

al

hap

loty

pes

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

Read-Based Phasing

G,A C,A G,T T,C C,A C,T G,A

G T A

A C G

A GC

C G C

T T A

T A C

C C T

A C A

Goal: Partition rows into two conflict-free sets

Read-Based Phasing


G T A

A C G

A GC

C G C

T T A

T A C

C C T

A C A

A C G C C T GG A T T A C A


Read-Based Phasing


G T A

A C G

A GC

C G C

T T A

T A C

C C T

A C A


Read-Based Phasing

0,1 0,1 0,1 0,1 0,1 0,1 0,1

0 0 1

1 0 0

1 00

0 0 1

1 0 1

0 1 0

1 0 1

1 0 1


Read-Based Phasing

0 0 1

1 0 0

1 00

0 0 1

1 0 1

0 1 0

1 0 1

1 0 1

- - - -

- - - -

- - - -

- - -

- -

-

-

-

- -

- - -

- - -

- - - -

SNP Matrix:


Read-Based Phasing

0 0 1

1 0 0

1 01

0 0 1

1 0 1

0 0 0

1 0 1

1 0 1

- - - -

- - - -

- - - -

- - -

- -

-

-

-

- -

- - -

- - -

- - - -

SNP Matrix:


Read-Based Phasing

0 0 1

1 0 0

1 01

0 0 1

1 0 1

0 0 0

1 0 1

1 0 1

- - - -

- - - -

- - - -

- - -

- -

-

-

-

- -

- - -

- - -

- - - -

SNP Matrix: Conflicts


Possible Problem Formalizations

Issue

Sequencing and mapping errors → no conflict-free bipartition

Four problem variants

Given a SNP matrix, perform a minimum number of operationsuntil such a bipartition exists. Allowed operations can be:

1 Delete row

2 Delete column

3 Flip one entry (0↔ 1)

4 Turn entry into dash (0, 1→ −)

Bad news

All these four problem variants are NP-hard.

Bipartite Graphs

But: Computing the minimum number of vertices to be removedis NP-hard.

Bipartite Graphs

This graph is bipartite!


Bipartite Graphs


Bipartite Graphs

This graph is NOT bipartite!


Bipartite Graphs

After removing vertices, it is bipartite.


Deleting Rows and Bipartite Graphs

Given a SNP matrix, perform a minimum number ofoperations until the matrix permits a conflict-free bipartition.Allowed operations can be:

1 Delete row

2 Delete column




0 0 1

1 0 0

1 01

0 0 1

1 0 1

0 0 0

1 0 1

1 0 1

- - - -

- - - -

- - - -

- - -

- -

-

-

-

- -

- - -

- - -

- - - -



0 0 1

1 0 0

0 0 1

1 0 1

1 0 1

1 0 1

- - - -

- - - -

- - -

- -

-

-

- -

- - -

- - - -


Which of the Formulations is Most Relevant?

Given a SNP matrix, perform a minimum number ofoperations until the matrix permits. Allowed operations can be:

1 Delete row

2 Delete column



Problem 3 = Minimum Error Correction (MEC) problem

Problem 3 and 4 are equivalent

Problem 4 can also be expressed as graph bipartization

WhatsHap Algorithm (Sketch)

0

1

1

-

-

-

0

1

0

-

-

-

0

0

0

1

-

-

0

1

0

0

-

-

1

1

1

-

-

-

3 4 5 4 3

Fragment matrix:

Coverage:

Approach: FPT algorithm with “coverage” as parameter.

coverage: number of active rows in a column

can be bounded without loosing relevant information

Dynamic Programming

Proceed column-wise. For each column:

1 Enumerate all bipartitions of rows that cover that column

2 Compute number of bit-flips incurred by each bipartition

3 Project costs to “intersection column”

Adding Weights (wMEC)

0

1

1

-

-

-

0

1

0

-

-

-

0

0

0

1

-

-

0

1

0

0

-

-

1

1

1

-

-

-

MEC Problem

Flip a minimum number ofbits such that a conflict-freebipartition of rows exists.

Weights set to −10 · log10(pwrong), where pwrong is theprobability that that position has been wrongly sequenced

Minimizing weights = finding maximum likelihood solution

Adding Weights (wMEC)

0

1

1

-

-

-

32

15

7

0

1

0

-

-

-

25

3

12

0

0

0

1

-

-

13

15

23

0

1

0

0

-

-

34

29

17

20

1

1

1

-

-

-

17

31

19

10

wMEC Problem

Flip a minimum-cost set ofbits such that a conflict-freebipartition of rows exists.

Weights set to −10 · log10(pwrong), where pwrong is theprobability that that position has been wrongly sequenced

Minimizing weights = finding maximum likelihood solution

Fixed-parameter tractable (FPT) algorithms

Notation

n: number of columns, i.e. number of variants to be phased

m: number of rows, i.e. number of reads

L: maximum read length, i.e. maximum number of variantscovered by any read

c: maximum coverage, i.e. maximum number of activereads per column

k: maximum number of errors per column

He et al. (2010): O(2Lmn)

Patterson et al. (2014): O(2c · n)

HapCol (Pirola et al., 2015): O(ckLn)

Haplotype distance measures

true haplotype: 0 0 1 1 1 1 1 0 0

predicted: 0 0 1 1 1 0 0 1 1

Hamming distance: 4 (rate: 4/9)

Other measures

Switch/flip decomposition

Decompose into short/long switches

N50/N95/N99 of error-free blocks

etc.

Haplotype distance measures

true haplotype: 0 0 1 1 1 1 1 0 0switch space: 0 1 0 0 0 0 1 0

predicted: 0 0 1 1 1 0 0 1 1switch space: 0 1 0 0 1 0 1 0

Hamming distance: 4 (rate: 4/9)Switch distance: 1 (rate: 1/8)

Other measures

Switch/flip decomposition

Decompose into short/long switches

N50/N95/N99 of error-free blocks

etc.

Phasing Error RateS

witc

h er

ror

rate

2 3 4 5 10 15 60Coverage

Real data

hapCUTGATK/ReadBackedPhasingphASERWhatsHap

0.01%

0.1%

1%

10%

Genome in a Bottle (GIAB) data from PacBio for chromosome 1compared to statistical phasing using 1000 Genomes phase 3reference panel

Phasing Error RateS

witc

h er

ror

rate

2 3 4 5 10 15 60Coverage

0.01%

0.1%

1%

10%

Simulated data

2 3 4 5 10 15 60Coverage

Real data

hapCUTGATK/ReadBackedPhasingphASERWhatsHap

0.01%

0.1%

1%

10%

Genome in a Bottle (GIAB) data from PacBio for chromosome 1compared to statistical phasing using 1000 Genomes phase 3reference panel

Overview

Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lg

lob

al

hap

loty

pes

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

Technology overview

Cloud 1

2*100bp/pair~40%

1 0 0 1 - - - - - - - - - - - - - - - -- - 1 0 0 0 0 - - - - - - - - - - - - -

Read 1Read 2

PacB

io 23 15 7 25

25 17 12 32 17

1 0 - - - - - - - - - - - - - - - - - -- - 1 - - - - - - - - - - - - - - - - -

Read 1Read 2

Illum

ina

23 15

25

Str

Seq 1 - - - - - - 0 - 0 - - 0 - - - - 0 - 00 - - - - 0 - - - 1 - - - - - - - 1 - -

23 15

25

2317

1315

25 17

15 25

Cell 1Cell 2

10

X 25 12 32 17

37 13 18Cloud 2

1 - - 1 - - - - - - - - - - - - - - - -- - 1 - - - - - - 1 1 - - - - - - - - -

Pair 1Pair 2Hi-

C 23 25

25 12 11

1 - - 1 - - - - - - - - - - - - - - - -- - - 0 - - 0 - - - - - - - - - - - - -

Pair 1Pair 2

mate

pair

s

33 25

2122

Span[bp]

Density

~500bp

~3kbp

~100kbp 10%

~10kbp 100%

fullchromosome

2%

largevariance

2*100bp/pair

2*100bp/pair~6.6%

1 - 0 - - 1 1 - - - - - - - - - - - - -- - - - - - - 1 1 - - - 1 - - - - - - -

In human: ~1 heterzygous variant / 1000bp

Haplotype blocks from individual technologies

0.06% 30204

1927

199

1

1.25%

4.66%

57.6%

Illumina

PacBio

10X Genomics

Strand-seq(134 cells)

SNVs

in la

rges

t

segm

ent

No. o

f seg

men

ts

0 20 40 60 100 102 104

NA12878 Chromosome 1

swit

ch e

rror

rate

[%

]

0.3%

0.2%

0.1%

0%

PacB

io

10X G

enom

ics

Illum

ina

Stra

nd-seq

0.13% 0.025% 0.3% 0.32%

Ground truth: phasing basedon platinum genomespedigree (17 family members)

Combining Data Sources

Cloud 1

2*100bp/pair~40%

1 0 0 1 - - - - - - - - - - - - - - - -- - 1 0 0 0 0 - - - - - - - - - - - - -

Read 1Read 2

PacB

io 23 15 7 25

25 17 12 32 17

1 0 - - - - - - - - - - - - - - - - - -- - 1 - - - - - - - - - - - - - - - - -

Read 1Read 2

Illum

ina

23 15

25

Str

Seq 1 - - - - - - 0 - 0 - - 0 - - - - 0 - 00 - - - - 0 - - - 1 - - - - - - - 1 - -

23 15

25

2317

1315

25 17

15 25

Cell 1Cell 2

10

X 25 12 32 17

37 13 18Cloud 2

1 - - 1 - - - - - - - - - - - - - - - -- - 1 - - - - - - 1 1 - - - - - - - - -

Pair 1Pair 2Hi-

C 23 25

25 12 11

1 - - 1 - - - - - - - - - - - - - - - -- - - 0 - - 0 - - - - - - - - - - - - -

Pair 1Pair 2

mate

pair

s

33 25

2122

Span[bp]

Density

~500bp

~3kbp

~100kbp 10%

~10kbp 100%

fullchromosome

2%

largevariance

2*100bp/pair

2*100bp/pair~6.6%

1 - 0 - - 1 1 - - - - - - - - - - - - -- - - - - - - 1 1 - - - 1 - - - - - - -

In human: ~1 heterzygous variant / 1000bp

Integrating Strand-seq and PacBio data

Varia

nt 1

Varia

nt 2

Varia

nt n

1 - - - - - - 0 - 0 - - 0 - - - - 0 - 00 - - - - 0 - - - 1 - - - - - - - 1 - -- 1 - - - 0 - - - - - 0 1 - - - - - 0 -- - 0 - - - 1 - 0 - 1 - - - - 1 - - - 0- 0 - - - - - 0 - - 1 - - - 1 - - - 1 -0 - - - 0 - - - - - - - - 0 - 1 - - - -

23 15

25

2317

15

25 17

15 25

Cell 1 (W)Cell 1 (C)Cell 2 (W)Cell 2 (C)Cell 3 (W)Cell 3 (C)

21 30 2 25 29

131425233111

43

19 24 19 5

15282631

1 0 0 1 - - - - - - - - - - - - - - - -- 0 0 1 1 - - - - - - - - - - - - - - -- 1 1 1 0 - - - - - - - - - - - - - - -- - 1 0 0 0 0 - - - - - - - - - - - - -

Read 1Read 2

PacB

io 23 15 7 25

25 17 12 32

Str

an

d-s

eq

37 18 23 31 22

14 25 4 31Read 3Read 4

[Porubsky∗, Garg∗, Sanders∗, ..., Marschall, in revision]

Integrating Strand-seq and PacBio data

Varia

nt 1

Varia

nt 2

Varia

nt n

1 0 0 - - - 1 0 0 0 1 - 0 - 1 1 - 0 1 00 1 - - 0 0 - - - 1 - 0 1 0 - 1 - 1 0 -

23 15

25

1725 17

15 25

Hap 1Hap 2 21 30 2 25 29

25142523311143

24 19 5

1528

1 0 0 1 - - - - - - - - - - - - - - - -- 0 0 1 1 - - - - - - - - - - - - - - -- 1 1 1 0 - - - - - - - - - - - - - - -- - 1 0 0 0 0 - - - - - - - - - - - - -

Read 1Read 2

PacB

io 23 15 7 25

25 17 12 32

Str

an

d-s

eq

conse

nsu

s

37 18 23 31 22

14 25 4 31Read 3Read 4


Haplotype blocks: Strand-seq + PacBio (10-fold)

0

25

50

75

10

0

0

5

10

20

40

60

80

100

120

134

Strand-seqcells

SNVs in largest block

0

25

50

75

10

0

0

5

10

20

40

60

80

100

120

134


Hamming error rates

Depth of coverage

Ham

min

g e

rror

rate

Strand-seqcells

51020406080100120134

2 3 4 5 10 15 25 30 all

2%

3%

4%

Ground truth: Illumina Platinum genomes, genetic phasing from17-member pedigree


Challenge 2

Solve sparse MEC instances optimally. In particular thoseresulting from combinations of technologies.

Overview

Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

Overview

Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

Supported by mostpackages for statistical phasing(SHAPEIT, beagle, etc.)

Overview

Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

SHAPEIT extension

(Delaneau et al., 2013)


Overview

Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

SHAPEIT extension

(Delaneau et al., 2013)


Garg, Martin, Marschall

(ISMB 2016)

Phasing Related Individuals

Genetic haplotyping: cannot phase SNP 3 (all heterozygous)

Read-based haplotyping: cannot connect SNPs 3-5 in child

Solution: combine genetic and read-based haplotyping

Child

SNP 1 SNP 2 SNP 3 SNP 4 SNP 5 SNP 6 SNP 7

1/1 1/1 1/10/1 0/1 0/10/0

Mother

0/0 0/0 0/00/0 0/10/10/1

0/1 0/1 0/1 0/1 0/1 0/11/1

Father

[Garg, Martin, Marschall, Bioinformatics (Proc. of ISMB), 2016]

From wMEC to “MEC on Pedigrees” (PedMEC)

1

0

1

-

-

32

15

27

0

0

0

-

-

25

33

42

0

1

1

0

-

13

25

23 0

0

-

-

124

29

17

1

1

1

-

-

32

5

17

0

1

0

-

25

31

12

0

1

0

1

13

15

23 0

1

-

-

34

29

17

0

1

1

-

-

32

15

7

0

1

0

-

-

25

3

12

0

0

0

1

-

13

15

23

0

1

0

-

-

34

29

17

A B

C

1 1 12112

18

Input

25


1

0

1

-

-

32

15

27

0

0

0

-

-

25

33

42

0

1

1

0

-

13

25

23 0

0

-

-

124

29

17

1

1

1

-

-

32

5

17

0

1

0

-

25

31

12

0

1

0

1

13

15

23 0

1

-

-

34

29

17

0

1

1

-

-

32

15

7

0

1

0

-

-

25

3

12

0

0

0

1

-

13

15

23

0

1

0

-

-

34

29

17

A B

C

1 1 12112

18

Input0/1 0/1 0/1 0/0

genotypes

0/1 0/1 0/1 0/1

0/1 0/0 0/1 0/0

25


1

0

1

-

-

32

15

27

0

0

0

-

-

25

33

42

0

1

1

0

-

13

25

23 0

0

-

-

124

29

17

1

1

1

-

-

32

5

17

0

1

0

-

25

31

12

0

1

0

1

13

15

23 0

1

-

-

34

29

17

0

1

1

-

-

32

15

7

0

1

0

-

-

25

3

12

0

0

0

1

-

13

15

23

0

1

0

-

-

34

29

17

A B

C

1 1 12112

18

91 22 87recombination costInput

0/1 0/1 0/1 0/0genotypes

0/1 0/1 0/1 0/1

0/1 0/0 0/1 0/0

25


1

0

1

-

-

32

15

27

0

0

0

-

-

25

33

42

0

1

1

0

-

13

25

23 0

0

-

-

124

29

17

1

1

1

-

-

32

5

17

0

1

0

-

25

31

12

0

1

0

1

13

15

23 0

1

-

-

34

29

17

0

1

1

-

-

32

15

7

0

1

0

-

-

25

3

12

0

0

0

1

-

13

15

23

0

1

0

-

-

34

29

17

A B

C

1 1 12112

18

91 22 87recombination costInput

1

0

1

-

-

0

0

0

-

-

0

1

1

0

-

0

0

-

-

1

1

1

-

-

0

1

0

-

0

1

0

1

0

1

-

-

0

1

1

-

-

0

0

0

-

-

0

0

0

1

- 0

0

0

-

-

1 1 1

0

1 0 0 0

0 1 1 0

haplotypes:

1 1 1 1

0 0 0 0

haplotypes:

0 0 0 0

1 0 1 0

haplotypes:

Output

3

5

22

Cost:3+5+ 22

0/1 0/1 0/1 0/0genotypes

0/1 0/1 0/1 0/1

0/1 0/0 0/1 0/0

25

29

29+

Solving PedMEC

Ideas

Use similar approach as for wMEC

Add additional dimension to DP table: transmission statusi.e. which haplotype in each parent was transmitted to child

Runtime

Two extra bits for each mother-father-child relationship:

O(22t+c ·M) (hiding some ugly terms)

where c is the maximum of sum of coverages across individualsand t is the number mother-father-child relationship.

Still feasible for, e.g., t = 1 and c = 3 · 5. Linear in the number ofvariants. Independent of read length.

Phasing Related Individuals (Performance)

single individual2x

3x

5x

10x15x

0 0.5 1.0 1.5 2.0

0

5

10

15

20

unph

ase

d h

ete

rozy

gous

SN

Ps

[%]

phasing error rate [%]

(simulated PacBio data)


Phasing Related Individuals (Performance)

single individualpedigree

2x

3x

5x

10x15x

2x3x

5x

0 0.5 1.0 1.5 2.0

0

5

10

15

20

unph

ase

d h

ete

rozy

gous

SN

Ps

[%]

phasing error rate [%]

(simulated PacBio data)


Challenge 3: Solving PedMEC

High coverage: Solve the PedMEC problem for cases wheretime linear in 2c is infeasible.

Large pedigrees: Solve the PedMEC problem for cases wheretime linear in 22t is infeasible.

Challenge 4: Unify all three paradigms

Statistical Phasing


Genetic Haplotyping


A B

C D

E

A: 0/1 1/1 0/1 0/0

B: 0/1 0/0 0/1 0/1

C: 1/1 0/1 0/1 0/0

D: 0/1 1/1 1/1 0/1

E: 0/1 0/1 0/1 0/0


loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting



Read

-based

ph

asin

g

10X Genomics

Hi-C

CHALLENGE:Unify all

three paradigms

Summary

Intro to genetic, read-based, and population-based haplotyping

Chromosome-length haplotyping feasible for singleindividuals

PedMEC unifies read-based and pedigree-based haplotyping

Four challenges:

1 Scale statistical phasing approaches to panels with millions ofrows and tens of millions of columns

2 Solve sparse MEC instances3 Solve PedMEC for high coverages and large pedigrees4 Integrate genetic, read-based, and population-based

haplotyping

a guided tour to computational haplotyping - · pdf filea guided tour to computational...

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