Diploidy and polyploidy

Definitions

• Haploid, diploid, etc

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• Haplome

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• Haplotype

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• Homologous chromosomes

Human heterozygosity

Heterozygosity is a fraction of polymorphic alleles

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Based on pre-selected 220,247 SNPs

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Herraez et al., 2009

Inbreeding

Inbreeding is widely used to reduce heterozygosity for follow up sequencing:

Takifugu

rubripes

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Kuroyanagi et al, BMC Genomics, 2013

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Drosophila melanogaster

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Swindell and Bouzat, Genetics, 2006

Danio

rerio

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Monson and Sadler, Zebrafish, 2010

Mus

musculus

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Beck et al, Nature Genetics, 2010

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Challenge with inbreeding

Significant parts of a genome can remain outbred

Malaria mosquito

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“Outbred in localized islands comprising the 8% of genome” -

Holt et al, Science, 2002

Nematode

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“Up to 30% heterozygosity persists after 20 generations of inbreeding” -

Barriere et al, Genome Research, 2009

Inbreeding depression

White tiger

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“Breeding practices has been linked with abnormal, debilitating, and, at times, lethal conditions”, -

Association of Zoos & Aquariums, 2011

Outbreeding

Panthera leo♂ × Panthera tigris♀

outbreeding depression

Assembly of diploid genomes

Genome assembly of a polymorphic organism: assembly of TWO DIFFERENT (albeit similar) puzzles at once

Humans have low polymorphism rates due to low effective population size. Most species sequenced so far are

• inbred (mouse, rat, worm, fly, etc.) or
• haploid (bacteria, yeast, etc.)

Genome assembly of an inbred organisms: assembly of a SINGLE jigsaw puzzle

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Low and high polymorphism rates

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human Homo sapiens genome size 2 x 3.1 Gb

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sea squirt Ciona savignyi genome size 2 x 0.2 Gb

Low and high polymorphism rates

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human Homo sapiens genome size 2 x 3.1 Gb

polymorphism rate 0.1%

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sea squirt Ciona savignyi genome size 2 x 0.2 Gb

Low and high polymorphism rates

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human Homo sapiens genome assembly is reduced to

assembling a single haplome

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sea squirt Ciona savignyi genome size 2 x 0.2 Gb

Low and high polymorphism rates

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human Homo sapiens genome size 2 x 3.1 Gb

polymorphism rate 0.1%

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sea squirt Ciona savignyi genome size 2 x 0.2 Gb

polymorphism rate 12%

Problem: polymorphisms are too complex to be ignored

Low and high polymorphism rates

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human Homo sapiens genome size 2 x 3.1 Gb

polymorphism rate 0.1%

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sea squirt Ciona savignyi

If two chromosomes are 0.5 - 15% difference assembly becomes problematic since “double genome” is very repetitive (each black region is a repeat)

Results of diploid assembly

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Consensus contigs

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Haplocontigs

Conventional assemblers produce very fragmented assembly of both haplomes

Polymorphic alleles are randomly chosen from haplomes on consensus contigs. Allelic relations can be further reconstructed by haplotype assembly

Haplotype assembly

Approaches to disease study

• Sequencing
• A single gene or gene panel
• Whole Genome Sequencing
• Whole Exome Sequencing: sequencing coding genomic regions (~85% of Mendelian variants)
• Mapping reads to the reference
• Finding genomic variations
• Associating genomic variations with diseases

Detecting genomic variations

Easy to detect using alignment

Detecting complex genomic variations

An integrated map of structural variation in 2,504 human genomes

1000 genomes

Haplotype assembly

Haplotypes:

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A C T G T C T A T C

A C G G T A T A C C

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Genotypes:

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A C T G T C T A T C

G A C

Possible phases:

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ACTGTCTATC

ACGGTATACC

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ACTGTATACC

ACGGTCTATC

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ACTGTCTACC

ACGGTATATC

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ACGGTCTATC

ACTGTATACC

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Applications

Haplotype assembly: challenges

• Distance between some polymorphisms is too large

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• It is impossible to phase chromosomes
• Works only with short polymorphisms

Haplotype assembly models

Haplotype assembly

Input:

reads covering diploid genome

consensus genome

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Output:

resolved phases of SNPs

Definitions:

F - M x N matrix

rows correspond to fragments (reads)

columns correspond to SNP sites

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f_ij in {0, 1, -}

ACTGTATACC

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ACTGTC

ACGGTA

TGTCTA

GGTNTA

ATACC

CTATC

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Definitions

Conflict fragments:

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Distance between fragments:

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ACTGTATACC

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ACTGTC

ACGGTA

TGTCTA

GGTNTA

ATACC

CTATC

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dist = 2

dist = 1

Definitions

Problem statement:

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Haplotype1: {f_1, f_3, f_6}

Haplotype2: {f_2, f_4, f_5}

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ACTGTATACC

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ACTGTC

ACGGTA

TGTCTA

GGTNTA

ATACC

CTATC

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Fragment conflict graph

G_F = (V, E)

|V| = m (number of fragments)

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Edges:

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Edges weights: w(v1, v2) = d(f1, f2)

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Fragment conflict graph

G_F = (V, E)

|V| = m (number of fragments)

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Edges:

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ACTGTATACC

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ACTGTC

ACGGTA

TGTCTA

GGTNTA

ATACC

CTATC

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1

3

6

2

4

5

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1

2

3

4

5

6

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Fragment conflict graph is bipartite

G_F = (V, E)

|V| = m (number of fragments)

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Edges:

ACTGTATACC

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ACTGTC

ACGGTA

TGTCTA

GGTNTA

ATACC

CTATC

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1

3

6

2

4

5

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1

2

3

4

5

6

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Problem formulation: MER & UMER

Conflicts are caused by:

• sequencing errors
• false alignment to paralogs
• erroneous fragments into the data set

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G_F contains bipartite subgraph G_F’

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Equivalent to minimum graph cut

Problem formulation: MFR & MSR

Equivalent to maximum independent set of graph

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independent set is a set of vertices in a graph,

no two of which are adjacent

Problem formulation: MEC & LHR

MEC tries to break odd-length cycle by flipping minimal number of alleles

LHP is pretty strange and almost abandoned

Examples

A likelihood based approach

Flip-update MC

A difficult example for the flip-update

• n columns, each spanned by d fragments.
• Two haplotypes (H1,H2) are equally likely
• Hard to move from one good haplotype to another

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A new markov chain

Read-haplotype consistency graph

Weighting R-H graph edges

Cuts

Negative cuts are good cuts

-6

HapCUT algorithm

Biological approaches to

haplotype assembly

Sequencing trio

https://experiment.com/u/oSMmA

Strand-Seq

Strand-seq: a unifying tool for studies of chromosome segregation

Assembly of trio

Koren et al., 2018