GRAPPA: Large-scale whole genome phylogenies based upon gene order evolution

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GRAPPA Large-scale whole genome phylogenies
based upon gene order evolution

• Tandy Warnow, UT-Austin
• Department of Computer Sciences
• Institute for Cellular and Molecular Biology
• Program in Evolution, Ecology, and Behavior
• Center for Computational Biology and
  Bioinformatics

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Whole-Genome Phylogenetics
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Genomes As Signed Permutations
1 5 3 4 -2 -6or6 2 -4 3 5 1 etc.
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Genomes Evolve by Rearrangements
1 2 3 4 5 6 7 8 9 10

• Inversion (Reversal)

• Transposition

• Inverted Transposition

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Genome Rearrangement Has A Huge State Space

• DNA sequences 4 states per site
• Signed circular genomes with n genes
  states, 1
  site
• Circular genomes (1 site)
• with 37 genes
  states
• with 120 genes
  states

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Why use gene orders?

• Rare genomic changes huge state space and
  relative infrequency of events (compared to site
  substitutions) could make the inference of deep
  evolution easier, or more accurate.
• Our research shows this is true, but accurate
  analysis of gene order data is computationally
  very intensive!

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Phylogeny reconstruction from gene orders

• Distance-based reconstruction estimate pairwise
  distances, and apply methods like
  Neighbor-Joining or Weighbor
• Maximum Parsimony find tree with the minimum
  length (inversions, transpositions, or other edit
  distances)
• Maximum Likelihood find tree and parameters of
  evolution most likely to generate the observed
  data

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This talk

• Distance-based methods we show how to estimate
  genomic distances appropriately for the
  Generalized Nadeau-Taylor model
• Parsimony-style methods we can find very good
  solutions to NP-hard problems (inversion and
  breakpoint phylogeny) quite quickly
• Validation of these approaches on real and
  simulated data

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Distance-based methods
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Genomic Distance Estimators

• Standard
• Breakpoint distance
• (Minimum) Inversion distance
• Our estimators We attempt to estimate the actual
  number of events (the true evolutionary
  distance)
• EDE Moret et al, ISMB01
• Approx-IEBP Wang and Warnow, STOC01
• Exact-IEBP Wang, WABI01

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Breakpoint Distance

• Breakpoint distance5

1 2 3 4 5 6 7 8 9 10
1 3 2 4 5 9 6 7 8 10
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Minimum Inversion Distance

• Inversion distance3

1 2 3 4 5 6 7 8 9 10
1 2 3 8 7 6 5 4 9 10
1 8 3 2 7 6 5 4 9 10
1 8 3 7 2 6 5 4 9 10
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Measured Distance vs. Actual Number of Events
Breakpoint Distance
Inversion Distance
120 genes, inversion-only evolution
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Generalized Nadeau-Taylor Model

• Three types of events
• Inversions
• Transpositions
• Inverted Transpositions
• Events of the same type are equiprobable
• Probability of the three types have fixed ratio
  
• Inv Trp Inv.Trp (1-a-b)ab

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Estimating True Evolutionary Distances for Genomes

• Given fixed probabilities for each type of
  event, we estimate the expected breakpoint
  distance after k random events, or the expected
  inversion distance after k random events.
  Inverting these functions gives us a better
  estimate of true evolutionary distances.
• Approx-IEBP Wang and Warnow 2001
• Exact-IEBP Wang 2001
• EDE Moret et al, ISMB 2001 (inversion based)

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Estimating True Evolutionary Distances for
Genomes (cont.)

• Estimating the expected Inversion distance
• EDE Moret, Wang, Warnow, Wyman 2001
• Closed-form formula based upon an empirical
  estimation of the expected inversion distance
  after k random events (based upon 120 genes and
  inversion only, but robust to errors in the
  model) .
• Polynomial time, fastest of the three.

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Absolute Difference

• 120 genes
• Inversion only evolution
• (Similar relative
• performance under
• other models)

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Accuracy of Neighbor Joining Using Distance
Estimators

• 120 genes
• All three event types equiprobable
• 10, 20, 40, 80, and 160 genomes
• Similar relative
• performance under
• other models

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Summary of Distance-based Reconstruction Methods

• Statistically-based estimation of genomic
  distances improves NJ analyses.
• Our IEBP estimators assume knowledge of the
  probabilities of each type of event, but are
  robust to model violations.
• EDE is based upon an inversion-only evolutionary
  model, but is robust.
• Best performing method Weighbor(EDE) second
  best is NJ(EDE) both are robust to model
  violations.
• Worst performing is NJ(BP).
• Accuracy is very good, except when very close to
  saturation.

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Maximum Parsimony on Rearranged Genomes (MPRG)

• The leaves are rearranged genomes.
• Find the tree that minimizes the total number of
  rearrangement events

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Optimization problems for gene order phylogeny

• Breakpoint phylogeny find the phylogeny which
  minimizes the total number of breakpoints
  (NP-hard, even to find the median of three
  genomes)
• Inversion phylogeny find the phylogeny which
  minimizes the sum of inversion distances on the
  edges (NP-hard, even to find the median of three
  genomes)

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Inversion and Breakpoint phylogenies

• When the data are close to saturated, even
  Weighbor(EDE) analyses are insufficiently
  accurate. In these cases, our initial
  investigations suggest that the inversion and
  breakpoint phylogeny approaches may be superior.
• Problem finding the best trees is enormously
  hard, since even the point estimation problem
  is hard (worse than estimating branch lengths in
  ML).

Local optimum
MP score
Global optimum
Phylogenetic trees
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GRAPPA (Genome Rearrangement Analysis under
Parsimony and other Phylogenetic Algorithms)

• http//www.cs.unm.edu/moret/GRAPPA/
• Heuristics for NP-hard optimization problems
• Fast polynomial time distance-based methods
• Contributors U. New Mexico,U. Texas at Austin,
  Universitá di Bologna, Italy
• Freely available in source code at this site.
• Project leader Bernard Moret (UNM)
  (moret_at_cs.unm.edu)

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Benchmark gene order dataset Campanulaceae

• 12 genomes 1 outgroup (Tobacco), 105 gene
  segments
• NP-hard optimization problems breakpoint and
  inversion phylogenies (techniques score every
  tree)
• 1997 BPAnalysis (Blanchette and Sankoff) 200
  years (est.)

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Benchmark gene order dataset Campanulaceae

• 12 genomes 1 outgroup (Tobacco), 105 gene
  segments
• NP-hard optimization problems breakpoint and
  inversion phylogenies (techniques score every
  tree)
• 1997 BPAnalysis (Blanchette and Sankoff) 200
  years (est.)
• 2000 Using GRAPPA v1.1 on the 512-processor Los
  Lobos Supercluster machine 2 minutes
  (200,000-fold speedup per processor)

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Benchmark gene order dataset Campanulaceae

• 12 genomes 1 outgroup (Tobacco), 105 gene
  segments
• NP-hard optimization problems breakpoint and
  inversion phylogenies (techniques score every
  tree)
• 1997 BPAnalysis (Blanchette and Sankoff) 200
  years (est.)
• 2000 Using GRAPPA v1.1 on the 512-processor Los
  Lobos Supercluster machine 2 minutes
  (200,000-fold speedup per processor)
• 2003 Using latest version of GRAPPA 2 minutes
  on a single processor (1-billion-fold speedup per
  processor)

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Summary

• Weighbor(EDE) and NJ(EDE) are highly accurate
  polynomial time distance-based reconstructions,
  except when datasets are close to saturated
• GRAPPA (inversion phylogeny or breakpoint
  phylogeny) produces highly accurate estimates of
  trees, and even of ancestral gene orders,
  acceptably fast

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DCM-boosting MP and ML

• Idea it may be faster to run a computationally
  expensive method on a few overlapping subproblems
  of somewhat smaller size
• Challenge how to pick the best decomposition?

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Addressing the accuracy/time issues
Disk-Covering Methods
DCM1 decomposition lots of small diameter
subproblems. (Used for NJ.)
DCM2 decomposition Very few subproblems, each
somewhat smaller. (Used for MP or ML.)
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DCM-boosting Speeding up MP/ML heuristics
Fake study
Performance of hill-climbing heuristic
MP score of best trees
Desired Performance
Time
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The DCM2 technique for speeding up MP/ML searches
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GRAPPA (Genome Rearrangement Analysis under
Parsimony and other Phylogenetic Algorithms)

• http//www.cs.unm.edu/moret/GRAPPA/
• Heuristics for NP-hard optimization problems
• Fast polynomial time distance-based methods
• Contributors U. New Mexico,U. Texas at Austin,
  Universitá di Bologna, Italy
• Freely available in source code
• Project leader Bernard Moret (UNM)
  (moret_at_cs.unm.edu)

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Limitations and ongoing research

• Current methods limited to single chromosomes
  with equal gene content (or very small amounts of
  deletions and duplications) -- we are working on
  developing reliable techniques for genomes with
  unequal gene content

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Acknowledgements

• Funding
• The David and Lucile Packard Foundation, and
• The National Science Foundation.
• Collaborators
• Bernard Moret (UNM), David Bader (UNM), Bob
  Jansen (UT), Linda Raubeson (CWU)
• Students Li-San Wang (now postdoc of Junhyong
  Kim at Penn), Jijun Tang (UNM), and others at UNM
  

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Phylolab, U. Texas
Please visit us at http//www.cs.utexas.edu/users/
phylo/