Evolution of genes neighborhood within reconciled phylogenies: an ensemble approach

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Evolution of genes neighborhood within reconciled phylogenies: an ensemble approach

Cedric Chauve, Yann Ponty, João Paulo Pereira Zanetti

To cite this version:

Cedric Chauve, Yann Ponty, João Paulo Pereira Zanetti. Evolution of genes neighborhood within reconciled phylogenies: an ensemble approach. RECOMB-CG’14, Oct 2014, Cold Spring HArbour, United States. �hal-01216782�

Evolution of genes neighborhood within reconciled phylogenies:

an ensemble approach

Cedric Chauve (SFU), Yann Ponty (CNRS/LIX/PIMS), Jo˜ ao Paulo Pereira Zanetti (SFU/U. Campinas)

Background: DeCo

Reconstructing ancestral genome features is a classical comparative genomics problem, often addressed with dynamic programming (DP) algorithms. A DP algorithm, called DeCo , was recently introduced for computing parsimonious evolutionary scenarios for gene adjacencies in a duplication-aware framework, motivated by the reconstruction of ancestral gene orders [B´erard et al., 2012 ].

Results: DeClone

We describe DeClone , an extension of DeCo, using Advanced Dynamic Program- ming techniques, that allows the sampling of adjacency forests under the Boltzmann distribution , as well as the computation of probabilities of presence/absence of an- cestral gene adjacencies, again under the Boltzmann distribution.

DeCo

Input:

• Reconciled gene trees G ₁ and G ₂ ;

• Set of extant adjacencies.

Output:

• Max-parsimony adjacency forest

Parsimony: #adjacencies gains/breaks

A B C

A

₁

L

_B

L

_A

B

₁

A

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B

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S

C

₁

C

₂

C

₃

C

₄

C

₅

A

₃

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₃

A

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B

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G 1

C

₆

C

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C

₈

A

₁

A

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A

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A

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B

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B

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G 2

C

₁

C

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C

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C

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C

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C

₅

C

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B

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F

(Score=1)

Min. Parsimony

Dynamic programming algorithm (excerpt):

. . .

c ₁ (v ¹ , v ² ) = min



 

 

 

 

 

 



 

 

 

 

 

 



c ₁ (ca (v ¹ ), cb (v ² )) + c ₁ (cb (v ¹ ), ca (v ² ))

c ₁ (ca (v ¹ ), cb (v ² )) + c ₀ (cb (v ¹ ), ca (v ² )) + Break c ₀ (ca (v ¹ ), cb (v ² )) + c ₁ (cb (v ¹ ), ca (v ² )) + Break c ₀ (ca (v ¹ ), cb (v ² )) + c ₀ (cb (v ¹ ), ca (v ² )) + 2Break c ₁ (ca (v ¹ ), ca (v ² )) + c ₁ (cb (v ¹ ), cb (v ² ))

c ₁ (ca (v ¹ ), ca (v ² )) + c ₀ (cb (v ¹ ), cb (v ² )) + Break c ₀ (ca (v ¹ ), ca (v ² )) + c ₁ (cb (v ¹ ), cb (v ² )) + Break c ₀ (ca (v ¹ ), ca (v ² )) + c ₀ (cb (v ¹ ), cb (v ² )) + 2Break

. . .

DeCo+Advanced Dynamic Programming=DeClone

The whole (sub)optimal space is modelled as a Boltzmann Ensemble

A

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L

_B

L

_A

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G ₁

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Score: 1

Score: 2

Score: 2

Score: 3

···

Boltzmann Distribution P (F ) ∼ e

^{−Score(F)kT}

Analysis

Average properties

Ancestral adjacencies Synthenic inconsistencies

Recurrent patterns . . .

Max. expected accuracy predictions

Robustness assessment . . .

Suboptimality vs combinatorics

0 2000 4000 6000 8000 10000 12000 14000 16000 18000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

#Adjacency forests

Score

Score vs #Adjacency Forests

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

1 6 11 16

Probability

Score

Score vs Boltzmann probability (Density of states)

kT=0.1 kT=1 kT=10

Impact of pseudo-temperature kT on predicted adjacencies

G1 (Horiz.)

1: B2 2: C3 3: A2 4: C4 5: B1 6: C2 7: LA 8: C5 9: LB 10: C1 11: A1

G2 (Vert.)

1: B4 2: C7 3: A4 4: C8 5: B3 6: C6 7: A3

kT=1

kT=0.1 kT=10

Adjacency probability010.250.50.75

Temperature

Co-optimals Uniform

(kT → ^{0) (kT} →∞ ⁾

1 2

3 4

5 6

7 8

9 10

11 13 2 4

5 67

1 2

3 4

5 6

7 8

9 10

11 13 2 4

5 67

1 2

3 4

5 6

7 8

9 10

11 13 2 4

5 67

distribution

Algorithmic aspects

Algorithmic framework [Ponty/Saule, 2011]

Dyn. Prog. equations → Weighted Hypergraphs

c ₁ (v ¹ , v ² ) = min

 

 

 

 

 



c ₁ (ca(v ¹ ), cb(v ² )) + c ₁ (cb(v ¹ ), ca(v ² ))

c ₁ (ca(v ¹ ), cb(v ² )) + c ₀ (cb(v ¹ ), ca(v ² )) + Break ...

c ₁ (v ¹ , v ² )

c ₁ (cb(v ¹ ), ca(v ² )) c ₁ (ca(v ¹ ), cb(v ² )) c ₀ (cb(v ¹ ), ca(v ² ))

∅

Break

Deco: MaxPars(q ) = min

e=q→(q ₁ ,q ₂ ...)

w(e) + X

i

MaxPars(q _i )

!

Claim: The DeCo DP scheme is unambiguous and complete

Algorithmic corollaries

• Computing the partition function Z in O (|G ₁ ||G ₂ |) Simple change of algebra (min, +, C ) → ( P

, ×, e ^{− kT C} )

• Boltzmann sampling of adjacency forests

Each hyperedge chosen with probability proportional to its overall contribution to Z .

• Adjacency dot-plot: O(|G ₁ ||G ₂ |) inside/outside algo- rithm computes the probability of ancestral adjacencies.

Experiments

Data: 6, 074 DeCo instances, with genes taken from 36 mammalian genomes from the Ensembl database in 2012. Syntenic inconsistencies with parsimonious scenarios concern 5, 817 , genes over 112, 188 ancestral and extant adjacencies.

Methods: for each instance, we sampled 1, 000 ad- jacency forests under a Boltzmann distribution that favours highly co-optimal scenarios.

Results:

Adj. freq. Anc. genes Anc. adj. Synt. Inc.

≥ 0.3 118,687 110,180 10,351

≥ 0.4 117,639 106,973 8,330

≥ 0.5 116,231 103,479 6,677

≥ 0.6 114,538 99,720 5,113

≥ 0.7 112,564 96,039 4,092

≥ 0.8 110,086 91,821 3,276

≥ 0.9 107,564 87,790 2,710

= 1 100,443 79,078 1,348

Discussion

DeClone allows a controlled exploration of the space of all gene adjacency evolution scenarios: exhaustive enumeration, sampling, probabilities computation.

Experiments show that exploring the whole solution space under a Boltzmann distribution biased toward co-optimals allows to reduce significantly the number of syntenic inconsistencies observed when a single ar- bitrary optimal scenario is considered.

References

S. B´ erard, et al.. 2012. Evolution of gene neighbor- hoods within reconciled phylogenies. Bioinformatics, 28(18):382–388.

Y. Ponty and C. Saule. 2011. A Combinatorial Frame- work for Designing (Pseudoknotted) RNA Algorithms.

WABI 2011, pp. 259–269.

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