Genome Rearrangement PhylogenyGenome Rearrangement Phylogeny

Robert K. JansenSchool of Biology

University of Texas at Austin

Bernard M.E. MoretDepartment of Computer Science

University of New Mexico

Li-San Wang Tandy WarnowDepartment of Computer Sciences

University of Texas at Austin

2

Outline

• Introduction• Genome rearrangement phylogeny

reconstruction• Application• Other methods• Future research

3

New Phylogenetic Signals

• Large-throughput sequencing efforts lead to larger datasets− Challenge: inferring deep evolutionary events

• Biologists turning to “rare genomic changes”− Rare− Large state space− High signal-to-noise ratio− Potential for clarifying early evolution− Best studied: gene order evolution

(genome rearrangement)

4

Genomes As Signed Permutations

1 –5 3 4 -2 -6 or5 –1 6 2 -4 -3 etc.

5

Gene Order Data

• Rare changes on the genomic scale• Large state space

− DNA: 4 states/character

− Protein (amino acid sequence): 20 states/character

− Circular gene order with 120 genes:

• High signal-to-noise ratio

232119 107049.3!1192 states/character

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Genomes Evolve by Rearrangements

1 2 3 4 5 6 7 8 9 10

1 2 –6 –5 -4 -3 7 8 9 10

1 2 7 8 3 4 5 6 9 10

1 2 7 8 –6 -5 -4 -3 9 10

Inversion:

Transposition:

Inverted Transposition:

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Edit Distances Between Genomes

• (INV) Inversion distance [Hannenhalli & Pevzner 1995]

− Computable in linear time [Moret et al 2001]• (BP) Breakpoint distance [Watterson et al. 1982]

− Computable in linear time− NJ(BP): [Blanchette, Kunisawa, Sankoff, 1999]

1 2 3 4 5 6 7 8 9 10

1 2 3 -8 -7 -6 4 5 9 10

A =

B =

BP(A,B)=3

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Our Model: the Generalized Nadeau-Taylor Model [STOC’01]

• Three types of events: − Inversions (INV)− Transpositions (TRP)− Inverted Transpositions (ITP)

• Events of the same type are equiprobable• Probabilities of the three types have fixed ratio

• We focus on signed circular genomes in this talk.

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Simulation Study Protocol

Synthetic InputSynthetic Input

PhylogeneticMethod

PhylogeneticMethod

DB

A

CE

FInferred Tree

A B

CD

E F

True TreeEvolutionary Process

Known in simulation

A 1 -4 2 -3 5 6

B 1 3 2 5 4 6

C 1 3 -2 5 6 4

D 1 3 4 5 -2 6

E 1 4 5 -3 -2 6

F 1 2 3 4 5 6

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Quantifying Error

FN: false negative (missing edge)

1/3=33.3% error rate

A B

CD

E F

True Tree

A B

CD

E F

True Tree

A B

CD

E F

True Tree DB

A

CE

F

Inferred Tree

DB

A

CE

F

DB

A

CE

F

Inferred Tree

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Outline

• Genome rearrangement evolution• Genome rearrangement phylogeny

reconstruction• Application• Other methods• Future research

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Gene Order Parsimony

Length (T) = min AX+BX+XY+CY+YZ+DZ+YW+EW+FW

X,Y,Z,W

A

B

C

D

E

F

X

Y

Z W

A

B

C

D

E

F

X

Y

Z W

A

B

C

D

E

F

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Breakpoint Phylogeny[Sankoff & Blanchette 1998]

• “Maximum Parsimony”-style problem:− Find tree(s), leaf-labeled by genomes, with

shortest breakpoint length

• NP-hard problem on two levels:− Find the shortest tree (the space of trees has

exponential size)− Given a tree, find its breakpoint length

(Even for a tree with 3 leaves, but can be reduced to TSP)

• BPAnalysis [Sankoff & Blanchette 1998] − Takes 200 years to compute our 13-taxon

dataset on a Sun workstation

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X

Y

Z W

A

B

C

D

E

F

X

Y

Z W

A

B

C

D

E

F

BPAnalysis

• Tree length evaluation for EVERY tree• Given a fixed tree topology, evaluate the tree

length:− Iteratively evaluate the median problem (tree

length for a 3-leaf tree)

A

BY

X’C

Z

Y’X’

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GRAPPA (Genome Rearrangement Analysis under

Parsimony and other Phylogenetic Algorithms)

http://www.cs.unm.edu/~moret/GRAPPA/• Uses lowerbound techniques to speed up• Used on real datasets, producing thousand-fold

speedups over BPAnalysis [ISMB’01]• Contributors: (led by Bernard Moret at UNM)

U. New MexicoU. Texas at AustinUniversitá di Bologna, Italy

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The Circular Lowerbound of the Length of a Tree

• Given a tree, we can lowerbound its length very quickly:

1 2 3 4

1,44,33,22,1)()(2 ddddTlbTw

)(2 Tw

)(Tlb

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The Lowerbound Technique

• Avoid any tree X without potential:− tree X whose lowerbound lb(X) is higher than

twice the length c(T) of the best tree T

• Finding a good starting tree quickly is of utmost importance

• We turn to distance-based methods− Neighbor joining (NJ) [Saitou and Nei 1987]− Weighbor [Bruno et al. 2000]

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Additive Distance Matrix and True Evolutionary Distance (T.E.D.)

S2 S3 S4 S5

S1 0 9 15 14 17S2 0 14 13 16S3 0 13 16S4 0 13 13

75

4

5

8

S1

S2

S3

S4

S5

S1

S5 0

Theorem [Waterman et al. 1977] Given an m×m additive distance matrix, we can reconstruct a tree realizing the distance in O(m2) time.

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Error Tolerance of Neighbor Joining

Theorem [Atteson 1999]Let {Dij} be the true evolutionary distances, and {dij} be the estimated distances for T. Let be the length of the shortest edge in T. If for all taxa i,j, we have

then neighbor joining returns T.

2

1|| ijij dD

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BP and INV

INV vs K(120 genes)

(K: Actual number of inversions) (Inversion-only evolution)

BP/2 vs K

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NJ(BP) [Blanchette, Kunisawa, Sankoff 1999] and NJ(INV)

120 genes, 160 leavesUniformly Random Tree

Transpositions/inverted transpositions only

Inversion only

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Estimate True Evolutionary DistancesUsing BP

BP/2 vs K (120 genes)

(K: Actual number of inversions) (Inversion-only evolution)

To use the scatter plot to estimate the actual number of events (K):

1. Compute BP/2

2. From the curve, look up the corresponding valueof K

(1)

(2)

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True Evolutionary Distance (t.e.d.) Estimators for Gene Order Data

T.E.D. Estimator

Exact-IEBP [WABI’01]

Approx-IEBP [STOC’01]

EDE [ISMB’01]

Based on the Expectation of

Breakpoint distance (Exact)

Breakpoint distance (Approx.)

Inversion distance (Approx.)

Derivation Analytical Analytical Empirical

Model knowledge

Required Required Inversion-only

IEBP: Inverting the Expected BreakPoint distanceEDE: Empirically Derived Estimator

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True Evolutionary Distance Estimators

Exact-IEBP vs K(120 genes)

(K: Actual number of inversions) (Inversion-only evolution)

BP vs K

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Variance of True Evolutionary Distance Estimators

• There are new distance-based phylogeny reconstruction methods (though designed for DNA sequences) − Weighbor [Bruno et al. 2000]

These methods use the variance of good t.e.d.’s, and yield more accurate trees than NJ.

• Variance estimates for the t.e.d.s [Wang WABI’02]− Weighbor(IEBP),

Weighbor(EDE) K vs Exact-IEBP (120 genes)

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Using T.E.D. Helps

120 genes160 leavesUniformly random treeTranspositions/invertedtranspositions only(180 runs per figure)

5%

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Observations

• EDE is the best distance estimator when used with NJ and Weighbor.

• True evolutionary distance estimators are reliable even when we do not know the GNT model parameters (the probability ratios of the three types of events).

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Outline

• Genome rearrangement evolution• Genome rearrangement phylogeny reconstruction• Application• Other methods• Future research

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Percentage of Trees Eliminated Through Bounding [ISMB’01]

edge length=2

# taxa 10 20 40 80 160

10 0 0 0 1% 1%

20 0 80% 91% 1% 1%

40 91% 100% 100% 100% 100%

80 99% 100% 100% 100% 100%

160 100% 100% 100% 100% 100%

320 100% 100% 100% 100% 100%

#genes Uses NJ(EDE) as starting tree

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Campanulaceae cpDNA

• 13 taxa (tobacco as outlier)• 105 gene segments• GRAPPA finds 216 trees with shortest breakpoint

length (out of 654,729,075 trees)

• Running Time:− BPAnalysis takes 2 centuries on a Sun

workstation− GRAPPA takes 1.5 hours on a 512-node

supercluster− About 2300-fold speedup on a single node

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Campanulaceae [Moret et al. ISMB 2001]

Strict consensus of 216 optimal trees found by GRAPPA

Tob

acco

Pla

tyco

don

Cya

nant

hus

Cod

onop

sis M

erci

era

Wah

lenb

ergi

a

Tri

odan

is

Asy

neum

a Leg

ousi

a

Sym

phan

dra

Ade

noph

ora

Cam

panu

la Tra

chel

ium

6 out of 10 max. edges found

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Outline

• Genome rearrangement evolution• Genome rearrangement phylogeny reconstruction• Application• Other methods• Future research

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“Fast” Approaches for Genome Rearrangement Phylogeny

• Basic technique: encode data as strings and apply maximum parsimony

• Running time exponential in the number of genomes, but polynomial in the number of genes (faster than GRAPPA)

• MPBE [ISMB’00]Maximum Parsimony using Binary Encodings

• MPME [Boore et al. Nature ’95, PSB’02]Maximum Parsimony using Multi-state Encodings

• The length of a tree using these two methods is a lowerbound of the true breakpoint length [Bryant ’01]

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Maximum Parsimony using Binary Encoding (MPBE)

A: 1 2 3 4 = -4 –3 –2 –1B: 1 -4 -3 –2 = 2 3 4 -1C: 1 2 -3 –4 = 4 3 –2 -1

MPBE Strings

Input genome (circular)(1,2)

(2,3)

(3,4)

(4,1)

(1,-4)

(-2,1)

(2,-3)

(-3,-4)

(-4,1)

A: 1 1 1 1 0 0 0 0 0B: 0 1 1 0 1 1 0 0 0C: 1 0 0 0 0 0 1 1 1

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Maximum Parsimony using Multistate Encoding (MPME)

MPME Strings

Input genome (circular)

A: 2 3 4 1 –4 –1 –2 -3B: -4 3 4 –1 2 1 –2 -3C: 2 –3 -2 3 4 –1 -4 1

1 2 3 4 -1 –2 –3 -4

A: 1 2 3 4 = -4 –3 –2 –1B: 1 -4 -3 –2 = 2 3 4 -1C: 1 2 -3 –4 = 4 3 –2 -1

We use PAUP to solve Maximum Parsimony

=> Constraint: number of states per site cannot exceed 32

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NJ vs MP (120 genes, 160 genomes)

All three event types equiprobable(datasets that exceed 32-state limit for MPME are dropped)

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Inversion Phylogeny

• Inversion median has higher running time than breakpoint median

• Inversion phylogeny overall has shorter running time than breakpoint phylogeny, and returns more accurate trees [Moret et al. WABI ’02]

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• Disk-Covering Method: divide the original problem into subproblems [Huson, Nettles, Parida, Warnow and Yooseph, 1998]

• Uses inversion distance• DCM-GRAPPA: can now process thousands of

genomes, each having hundreds of genes

DCM-GRAPPA [Moret & Tang 2003]

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Ongoing and Future Research

• Genome rearrangement phylogeny with unequal gene content (duplications, deletions, etc.)

• Non-uniform genome rearrangement models(Segment-length dependent model, hotspots)

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Acknowledgements

• University of Texas Tandy Warnow (Advisor) Robert K. Jansen Stacia Wyman Luay Nakhleh Usman Roshan Cara Stockham Jerry Sun

• University of New Mexico Bernard M.E. Moret David Bader Jijun Tang Mi Yan

• Central Washington University Linda Raubeson

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PhylolabDepartment of Computer Sciences

University of Texas at Austin

Please visit us athttp://www.cs.utexas.edu/users/phylo/