A Guided Tour to Computational Haplotyping - · PDF fileA Guided Tour to Computational Haplotyping Tobias Marschall June 15, 2017 Computability in Europe (CiE) @ Turku

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

Introduction to Haplotyping/Phasing

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

Terminology: Phasing = Haplotyping

Introduction to Haplotyping/Phasing

chr1

chr2

chr3

chr22

GT

TA

AC

TC

TC

CA

TG

CT

CG

TC

GC

AC

Terminology: Phasing = Haplotyping

Relevance of Haplotyping

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

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

Approaches to Phasing

Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

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

Approaches to Phasing

Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

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

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

Approaches to Phasing

Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

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

Molecular Haplotyping

loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting

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

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

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}

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

Use haplotypes from reference panelto phase sample based on genotypes

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

Molecular Haplotyping

loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting

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

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

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 (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 (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.

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

Use haplotypes from reference panelto phase sample based on genotypes

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

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

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,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

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

Goal: Partition rows into two conflict-free sets

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

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

Goal: Partition rows into two conflict-free sets

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

Goal: Partition rows into two conflict-free sets

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:

Goal: Partition rows into two conflict-free sets

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:

Goal: Partition rows into two conflict-free sets

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

Goal: Partition rows into two conflict-free sets

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.

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.

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!

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

Bipartite Graphs

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

Bipartite Graphs

This graph is NOT bipartite!

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

Bipartite Graphs

After removing vertices, it is bipartite.

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

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

3 Flip one entry (0↔ 1)

4 Turn entry into dash (0, 1→ −)

Deleting Rows and Bipartite Graphs

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

Deleting Rows and Bipartite Graphs

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

Deleting Rows and Bipartite Graphs

0 0 1

1 0 0

0 0 1

1 0 1

1 0 1

1 0 1

- - - -

- - - -

- - -

- -

-

-

- -

- - -

- - - -

SNP Matrix: Conflicts

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

3 Flip one entry (0↔ 1)

4 Turn entry into dash (0, 1→ −)

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”

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

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.

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

Use haplotypes from reference panelto phase sample based on genotypes

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

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

Overview

Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

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

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

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)

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

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

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

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

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

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

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

Challenge 2

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

Overview

Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

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

Molecular Haplotyping

loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting

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

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

Read

-based

ph

asin

g

10X Genomics

Hi-C

Overview

Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

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

Molecular Haplotyping

loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting

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

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

Read

-based

ph

asin

g

10X Genomics

Hi-C

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

Overview

Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

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

Molecular Haplotyping

loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting

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

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

Read

-based

ph

asin

g

10X Genomics

Hi-C

SHAPEIT extension

(Delaneau et al., 2013)

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

Overview

Statistical Phasing

Use haplotypes from reference panelto phase sample based on genotypes

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

Molecular Haplotyping

loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting

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

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

Read

-based

ph

asin

g

10X Genomics

Hi-C

SHAPEIT extension

(Delaneau et al., 2013)

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

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]

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]

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

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

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

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

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

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

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.

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.

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)

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

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)

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

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

Use haplotypes from reference panelto phase sample based on genotypes

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

Molecular Haplotyping

loca

lglo

bal

haplo

types

StrandSeq(low cost)

Chromosomesorting

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

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

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