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Belle marquise, vosbeauxyeuxme fontmourird'amour.

Vosyeuxbeauxd'amour me font, belle marquise,mourir.

Me font vosbeauxyeux mourir, belle marquise,d'amour.

Genome RearrangementsAnne Bergeron,

Comparative Genomics Laboratory

Université du Québec à Montréal

1. General introduction to genome rearrangements

Examples of rearranged genomes

2. Measures of distance

Rearrangement operations

The Hannenhalli-Pevzner distance equation

3. A unifying view of genome rearrangements

The Double-Cut-and-Join operation

The adjacency graph and the distance equation

1. General introduction to genome rearrangements

Examples of rearranged genomes

2. Measures of distance

Rearrangement operations

The Hannenhalli-Pevzner distance equation

3. A unifying view of genome rearrangements

The Double-Cut-and-Join operation

The adjacency graph and the distance equation

Example of rearranged genomes : Mitochondrial Genomes

Homo sapiens

Bombyx mori

Mitochondria are small, oval

shaped organelles surrounded

by two highly specialized

membranes.

Animal mitochondrial genomes

are normally circular, ~16 kB

in length, and encode:

13 proteins

22 tRNAs and

2 rRNAs.

Example of rearranged genomes : Mitochondrial Genomes

Here is an alignment of the cytochrome c oxidase I

of, respectively, Homo sapiens and Bombyx mori.

RWLFSTNHKDIGTLYLLFGAWAGVLGTALSLLIRAELGQPGNLLGNDHIYNVIVTAHAFVMIFFMVMPIMIGGFGNWLVPLMIGAPDMAFPRMNNM

KWIYSTNHKDIGTLYFIFGIWSGMIGTSLSLLIRAELGNPGSLIGDDQIYNTIVTAHAFIMIFFMVMPIMIGGFGNWLVPLMLGAPDMAFPRMNNM

:*::***********::** *:*::**:**********:**.*:*:*:***.*******:**********************:*************

SFWLLPPSLLLLLASAMVEAGAGTGWTVYPPLAGNYSHPGASVDLTIFSLHLAGVSSILGAINFITTIINMKPPAMTQYQTPLFVWSVLITAVLLLLSLP

SFWLLPPSLMLLISSSIVENGAGTGWTVYPPLSSNIAHSGSSVDLAIFSLHLAGISSIMGAINFITTMINMRLNNMSFDQLPLFVWAVGITAFLLLLSLP

*********:**::*::** ************:.* :*.*:****:********:***:********:***: *: * *****:* ***.*******

VLAAGITMLLTDRNLNTTFFDPAGGGDPILYQHLFWFFGHPEVYILILPGFGMISHIVTYYSGKKEPFGYMGMVWAMMSIGFLGFIVWAHHMFTVGMDVD

VLAGAITMLLTDRNLNTSFFDPAGGGDPILYQHLFWFFGHPEVYILILPGFGMISHIISQESGKKETFGCLGMIYAMLAIGLLGFIVWAHHMFTVGMDID

***..************:***************************************:: *****.** :**::**::**:****************:*

TRAYFTSATMIIAIPTGVKVFSWLATLHGSNMKWSAAVLWALGFIFLFTVGGLTGIVLANSSLDIVLHDTYYVVAHFHYVLSMGAVFAIMGGFIHWFPLF

TRAYFTSATMIIAVPTGIKIFSWLATMHGTQINYNPNILWSLGFVFLFTVGGLTGVILANSSIDITLHDTYYVVAHFHYVLSMGAVFAIIGGFINWYPLF

*************:***:*:******:**:::::.. :**:***:**********::*****:**.***********************:****:*:***

SGYTLDQTYAKIHFTIMFIGVNLTFFPQHFLGLSGMPRRYSDYPDAYTTWNILSSVGSFISLTAVMLMIFMIWEAFASKRKVLMVEEPSMNLE

TGLSLNSYMLKIQFFTMFIGVNMTFFPQHFLGLAGMPRRYSDYPDSYISWNMISSLGSYISLLSVMMMLIIIWESMINQRINLFSLNLPSSIE

:* :*:. **:* ******:**********:***********:* :**::**:**:*** :**:*:::***:: .:* *: : . .:*

RWLFSTNHKDIGTLYLLFGAWAGVLGTALSLLIRAELGQPGNLLGNDHIYNVIVTAHAFVMIFFMVMPIMIGGFGNWLVPLMIGAPDMAFPRMNNM

KWIYSTNHKDIGTLYFIFGIWSGMIGTSLSLLIRAELGNPGSLIGDDQIYNTIVTAHAFIMIFFMVMPIMIGGFGNWLVPLMLGAPDMAFPRMNNM

:X::XXXXXXXXXXX::XXX:X::XX:XXXXXXXXXX:XX.X:X:X:XXX.XXXXXXX:XXXXXXXXXXXXXXXXXXXXXX:XXXXXXXXXXXXX

SFWLLPPSLLLLLASAMVEAGAGTGWTVYPPLAGNYSHPGASVDLTIFSLHLAGVSSILGAINFITTIINMKPPAMTQYQTPLFVWSVLITAVLLLLSLP

SFWLLPPSLMLLISSSIVENGAGTGWTVYPPLSSNIAHSGSSVDLAIFSLHLAGISSIMGAINFITTMINMRLNNMSFDQLPLFVWAVGITAFLLLLSLP

XXXXXXXXX:XX::X::XXXXXXXXXXXXXX:.X :X.X:XXXX:XXXXXXXX:XXX:XXXXXXXX:XXX: X: XXXXXX:XXXX.XXXXXXX

VLAAGITMLLTDRNLNTTFFDPAGGGDPILYQHLFWFFGHPEVYILILPGFGMISHIVTYYSGKKEPFGYMGMVWAMMSIGFLGFIVWAHHMFTVGMDVD

VLAGAITMLLTDRNLNTSFFDPAGGGDPILYQHLFWFFGHPEVYILILPGFGMISHIISQESGKKETFGCLGMIYAMLAIGLLGFIVWAHHMFTVGMDID

XXX..XXXXXXXXXXXX:XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX:: XXXXX.XX :XX::XX::XX:XXXXXXXXXXXXXXXX:X

TRAYFTSATMIIAIPTGVKVFSWLATLHGSNMKWSAAVLWALGFIFLFTVGGLTGIVLANSSLDIVLHDTYYVVAHFHYVLSMGAVFAIMGGFIHWFPLF

TRAYFTSATMIIAVPTGIKIFSWLATMHGTQINYNPNILWSLGFVFLFTVGGLTGVILANSSIDITLHDTYYVVAHFHYVLSMGAVFAIIGGFINWYPLF

XXXXXXXXXXXXX:XXX:X:XXXXXX:XX:::::.. :XX:XXX:XXXXXXXXXX::XXXXX:XX.XXXXXXXXXXXXXXXXXXXXXXX:XXXX:X:XXX

SGYTLDQTYAKIHFTIMFIGVNLTFFPQHFLGLSGMPRRYSDYPDAYTTWNILSSVGSFISLTAVMLMIFMIWEAFASKRKVLMVEEPSMNLE

TGLSLNSYMLKIQFFTMFIGVNMTFFPQHFLGLAGMPRRYSDYPDSYISWNMISSLGSYISLLSVMMMLIIIWESMINQRINLFSLNLPSSIE

:X :X:. XX:XXXXXXX:XXXXXXXXXX:XXXXXXXXXXX:X :XX::XX:XX:XXX :XX:X:::XXX:: .:XX: : . .:X

73% identity over more than 500 amino acids.

Example of rearranged genomes : Mitochondrial Genomes

The 37 genes of animal

mitochondria are highly

conserved.

But the order of the genes

differs from species to

species.

Charles Darwin, 1809 - 1882

A lowly worm

Example of rearranged genomes : Mitochondrial Genomes

The invariant parts

Homo sapiens mitochondrial genome (proteins and rRNAs)

ND4L

ND4

ND5

RNS

RNL

ND1

COX1

COX2

ATP6

ATP8

COX3

ND3

ND4L

ND4

ND5

CYTB

RNS

RNL

ND1

ND2

ND6

COX1 stands for the gene

cytochrome c oxidase I.

ND6

COX1

COX2

ATP6

ATP8

COX3

ND3

ND6

ND6

CYTB

ND2

ND5

ND5

ND4

ND4

ND4L

ND4L

ND1

ND1

RNL

RNL

RNS

RNS

COX1 stands for the gene

cytochrome c oxidase I.

Bombyx mori mitochondrial genome (proteins and rRNAs)

Example of rearranged genomes : Mitochondrial Genomes

Homo sapiens mitochondrial genome (proteins and rRNAs)

COX1

COX2

ATP6

ATP8

COX3

ND3

ND4L

ND4

ND4

ND5

ND5

CYTB

RNS

RNS

RNL

RNL

ND1

ND1

ND2

ND6

ND6

Bombyx mori mitochondrial genome (proteins and rRNAs)

COX1

COX2

ATP6

ATP8

COX3

ND3

ND6

ND6

CYTB

ND2

ND5

ND5

ND4

ND4

ND4L

ND1

ND1

RNL

RNL

RNS

RNS

The modified parts

Mosquito

Silkworm

Locust

Tick

Centipede

Example of rearranged genomes : Mitochondrial Genomes of 6 Arthropoda

Identical ‘runs’ of genes have been grouped.

Example of rearranged genomes : mammal X chromosomes

(Art work by Guillaume Bourque,

scientific work by Guillaume Bourque,

Pavel Pevzner and Glenn Tesler, 2004)

Sixteen large synteny blocks are ordered differently in the X chromosomes of the human, mouse and rat. Blocks have similar gene content and order.

Note that the estimated number of genes in the X chromosome is 2000.

Example of rearranged genomes : mammal X chromosomes

(Art work by Guillaume Bourque,

scientific work by Guillaume Bourque,

Pavel Pevzner and Glenn Tesler, 2004)

Problem: Given two or more genomes,

How do we measure their similarity and/or

distance with respect to gene order and

gene content?

Sub-problem: How do we know

that two genes or blocks are the "same" in two different species?

1. General introduction to genome rearrangements

Examples of rearranged genomes

2. Measures of distance

Rearrangement operations

The Hannenhalli-Pevzner distance equation

3. A unifying view of genome rearrangements

The Double-Cut-and-Join operation

The adjacency graph and the distance equation

Rearrangement operations

Rearrangement operations affect gene order

and gene content. There are various types:

• Inversions

• Transpositions

• Reverse transpositions

• Translocations, fusions and fissions

• Duplications and losses

• Others...

Any set of operations yields a distance between genomes, by counting the minimum number of operations needed to transform one genome into the other.

Rearrangement operations

• Inversions

Rearrangement operations

• Inversions

Example: Mitochondrial Genomes of 6 Arthropoda

Fruit Fly

Mosquito

Silkworm

Locust

Tick

Centipede

An inversion.

• Transpositions

• Transpositions

• Transpositions

Example: Mitochondrial Genomes of 6 Arthropoda

Fruit Fly

Mosquito

Silkworm

Locust

Tick

Centipede

A transposition

• Reverse transpositions

• Reverse transpositions

• Reverse transpositions

Example: Mitochondrial Genomes of 6 Arthropoda

Fruit Fly

Mosquito

Silkworm

Locust

Tick

Centipede

A reverse transposition

• Translocations, fusions and fissions

• Translocations, fusions and fissions

• Translocations, fusions and fissions

• Translocations, fusions and fissions

• Translocations, fusions and fissions

• Translocations, fusions and fissions

1. General introduction to genome rearrangements

Examples of rearranged genomes

2. Measures of distance

Rearrangement operations

The Hannenhalli-Pevzner distance equation

3. A unifying view of genome rearrangements

The Double-Cut-and-Join operation

The adjacency graph and the distance equation

The Hannenhalli-Pevzner distance equation

In 1995, Hannenhalli and Pevzner found a formula to compute the minimum number of inversions, translocations, fusions or fissions necessary to transform a multichromosomal genome into another.

Sketch of the approach:

• Cap the chromosomes

• Concatenate all the chromosomes

• Sort the resulting genome by inversions

1. General introduction to genome rearrangements

Examples of rearranged genomes

2. Measures of distance

Rearrangement operations

The Hannenhalli-Pevzner distance equation

3. A unifying view of genome rearrangements

The Double-Cut-and-Join operation

The adjacency graph and the distance equation

The Double-Cut-and-Join operation

Acts on up to 4 gene extremities:

,

,

,

Reminder

Yancopoulos et al. 2005

The Double-Cut-and-Join operation

Linear chromosomes

Translocation

Translocation

Translocation

Translocation

Translocation

Translocation

Reminder

The Double-Cut-and-Join operation

Linear and circular chromosomes

Inversion

Inversion

Fusion

Fusion

Fission

Fission

Reminder

The Double-Cut-and-Join operation

Circular chromosomes

Inversion

Inversion

Fusion

Fusion

Fission

Fission

Reminder

1. General introduction to genome rearrangements

Examples of rearranged genomes

2. Measures of distance

Rearrangement operations

The Hannenhalli-Pevzner distance equation

3. A unifying view of genome rearrangements

The Double-Cut-and-Join operation

The adjacency graph and the distance equation

4. Breakpoint reuse

Breakpoint reuse estimates

Minimizing breakpoint reuse

The adjacency graph and the distance equation

Genome A

Genome B

4

1

6

3

5

2

1

2

3

4

5

6

Joint work with Julia Mixtacki and Jens Stoye

The adjacency graph and the distance equation

4

1

6

3

5

2

Genome A

Genome B

1

2

3

4

5

6

Joint work with Julia Mixtacki and Jens Stoye

The adjacency graph and the distance equation

4

1

6

3

5

2

Genome A

Genome B

1

2

3

4

5

6

Joint work with Julia Mixtacki and Jens Stoye

The adjacency graph and the distance equation

4

1

6

3

5

2

Genome A

Genome B

1

2

3

4

5

6

Joint work with Julia Mixtacki and Jens Stoye

The adjacency graph and the distance equation

4

1

6

3

5

2

Genome A

Genome B

1

2

3

4

5

6

Joint work with Julia Mixtacki and Jens Stoye

The adjacency graph and the distance equation

4

1

6

3

5

2

Genome A

Genome B

1

2

3

4

5

6

Joint work with Julia Mixtacki and Jens Stoye

The adjacency graph and the distance equation

4

1

6

3

5

2

Genome A

Genome B

1

2

3

4

5

6

C = number of cycles

I = number of odd paths

G = number of “genes”

D = G - (C + I/2)

D = 6 - (1 + 2/2) = 4

Joint work with Julia Mixtacki and Jens Stoye

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