Genome Rearrangement Phylogeny

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Genome Rearrangement Phylogeny
Robert K. Jansen School of Biology University of
Texas at Austin Bernard M.E. MoretDepartment of
Computer ScienceUniversity of New MexicoLi-San
Wang Tandy Warnow Department of Computer
Sciences University of Texas at Austin
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Outline

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

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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)

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Genomes As Signed Permutations
1 5 3 4 -2 -6 or 5 1 6 2 -4
-3 etc.
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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

states/character
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Genomes Evolve by Rearrangements
1 2 3 4 5 6 7 8 9 10
Inversion
1 2 6 5 -4 -3 7 8 9 10
Transposition
1 2 7 8 3 4 5 6 9 10
Inverted Transposition
1 2 7 8 6 -5 -4 -3 9 10
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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

A
1 2 3 4 5 6 7 8 9 10
B
1 2 3 -8 -7 -6 4 5 9 10
BP(A,B)3
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Our Model the Generalized Nadeau-Taylor Model
STOC01

• 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 Input
Evolutionary Process
Known in simulation
PhylogeneticMethod
Inferred Tree
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Quantifying Error
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Outline

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

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Gene Order Parsimony
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Breakpoint PhylogenySankoff 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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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)

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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 ISMB01
• 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

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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
S3
S1 0 9 15 14 17
S1
S2 0 14 13 16
S4
7
5
5
S3 0 13 16
1
3
S4 0 13
4
S5 0
8
S2
S5
Theorem Waterman et al. 1977 Given an mm
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 1999Let 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 havethen neighbor joining returns T.

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BP and INV
INV vs K
(120 genes)
BP/2 vs K
(K Actual number of inversions)
(Inversion-only evolution)
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NJ(BP) Blanchette, Kunisawa, Sankoff 1999 and
NJ(INV)
Transpositions/inverted transpositions only
Inversion only
120 genes, 160 leaves Uniformly Random Tree
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Estimate True Evolutionary DistancesUsing BP

• To use the scatter plot to
• estimate the actual number
• of events (K)
• Compute BP/2
• From the curve, look up the corresponding
  valueof K

(2)
(1)
BP/2 vs K
(120 genes)
(K Actual number of inversions)
(Inversion-only evolution)
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True Evolutionary Distance (t.e.d.) Estimators
for Gene Order Data
IEBP Inverting the Expected BreakPoint
distance EDE Empirically Derived Estimator
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True Evolutionary Distance Estimators
Exact-IEBP vs K
(120 genes)
BP vs K
(K Actual number of inversions)
(Inversion-only evolution)
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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. 2000These 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 WABI02
• Weighbor(IEBP), Weighbor(EDE)

K vs Exact-IEBP (120 genes)
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Using T.E.D. Helps
120 genes160 leaves Uniformly 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
ISMB01
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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
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 ISMB00Maximum Parsimony using Binary
  Encodings
• MPME Boore et al. Nature 95, PSB02Maximum
  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)
Input genome (circular)
A 1 2 3 4 -4 3 2 1 B 1 -4 -3 2
2 3 4 -1 C 1 2 -3 4 4 3 2 -1
MPBE Strings
A 1 1 1 1 0 0 0 0 0 B 0 1 1 0 1 1
0 0 0 C 1 0 0 0 0 0 1 1 1
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Maximum Parsimony using Multistate Encoding (MPME)
Input genome (circular)
A 1 2 3 4 -4 3 2 1 B 1 -4 -3 2
2 3 4 -1 C 1 2 -3 4 4 3 2 -1
MPME Strings
We use PAUP to solve Maximum Parsimony gt
Constraint number of states per site cannot
exceed 32
1 2 3 4 -1 2 3 -4
A 2 3 4 1 4 1 2 -3 B -4 3 4 1 2 1
2 -3 C 2 3 -2 3 4 1 -4 1
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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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DCM-GRAPPA Moret Tang 2003

• 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

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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
SciencesUniversity of Texas at Austin
Please visit us at http//www.cs.utexas.edu/users/
phylo/