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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
Whole-Genome Phylogenetics
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Genomes As Signed Permutations
1 –5 3 4 -2 -6
or
6 2 -4 –3 5 –1
etc.
Genomes Evolve by Rearrangements
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• 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:
2
n 1
(n  1)!
states, 1 site
• Circular genomes (1 site)
– with 37 genes:
– with 120 genes:
2.56 10
3.70 10
52
states
232
states
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!
Phylogeny reconstruction from
gene orders
• Distance-based reconstruction: estimate pairwise
distances, and apply methods like NeighborJoining 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
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
Distance-based methods
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, ISMB’01]
– Approx-IEBP [Wang and Warnow, STOC’01]
– Exact-IEBP [Wang, WABI’01]
Breakpoint Distance
• Breakpoint distance=5
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1 –3 –2
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Minimum Inversion Distance
• Inversion distance=3
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2 –6 –5 –4
Measured Distance vs.
Actual Number of Events
Breakpoint Distance
Inversion Distance
120 genes, inversion-only evolution
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):a:b
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)
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.
Absolute Difference
•120 genes
•Inversion only
evolution
(Similar relative
performance under
other models)
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
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.
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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Total length
= 18
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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)
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
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)
([email protected])
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.)
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)
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)
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
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
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
Phylolab, U. Texas
Please visit us at
http://www.cs.utexas.edu/users/phylo/