Information%20Theoretic%20Approach%20to%20Whole%20Genome%20Phylogenies

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Information Theoretic Approach to Whole Genome
Phylogenies

• David Burstein Igor Ulitsky Tamir Tuller
  Benny Chor

School Of Computer Science Tel Aviv University
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Tree of Life

• I believe it has been with the tree of life,
  which fills with its dead and broken branches the
  crust of the earth, and covers the surface with
  its ever branching and beautiful
  ramifications"...
• Charles Darwin, 1859

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Accepted Evolutionary Model Trees

• Initial period Primordial soup, where you are
  what you eat. Recombination events. Horizontal
  transfers.
• Formation of distinct
• taxa. Speciation events
• induce a tree-like
• evolution.

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Phylogenetic Trees Based on What?

1. Morphology
2. Single genes
3. Whole genomes

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Whole Genome Phylogenies Motivation

• Cons for single genes trees
• Require preprocessing
• Gene duplications
• Often too sensitive
• Pros for whole genomes trees
• Fully automatic
• More information
• Seems essential in viruses
• What about proteomes trees?
• Less noise, but do require preprocessing

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Whole Genome Phylogenies Challenges

• Very large inputs Up to 5G bp long
• Extreme length variability (5G to 1M bp)
• No meaningful alignment
• Different segments experienced different
  evolutionary processes

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Previous Approaches

• Genome rearrangements (Hannanelly Pevzner
  1995,)
• Gene/domain contents (Snel et al. 1999,)
• Li et al (2001) Kolmogorov complexity
• Otu et al (2003) Lempel Ziv compression
• Qi et al (2004) Composition vectors
• Common approach (ours too)
• Compute pairwise distances
• Build a tree from distance matrix (e.g. using
  Neighbor Joining, Saitou and Nei 1987)

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Genome Rearrangements

• Emphasis on finding best sequence of
  rearrangements
• Drawbacks
• Requires manual definition of blocks
• Disregards changes within the block

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Gene/Domain Content

• Genome ? equi length Boolean vector
• Various tree construction methods
• The drawback
• Requires gene/domain definition/knowledge
• Disregards most of the genetic information

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Ming Li et al.- Kolomogorov Complexity

• Kolmogorov Complexity is a wonderful measure
• But it is not computable
• Approximate KC by compression
• Drawbacks
• Justification of the approximation
• Compression of one human chromosome
• reportedly took 24 hours (sloooow).

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Otu et al. Lempel-Ziv Distance

• Run LZ compression on genome A.
• Use Genome A dictionary to compress Genome B.
• Log compression ratio (B given A vs. B given B)
• distance (B, A)
• Easy to implement
• Linear running time
• Drawback
• Dictionary size effects

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Qi et al. Composition Vector

• Calculate distributions of the K-tuples.
• For K1 nucleotide/amino acid frequencies.
• For K5 45 (205) possible 5-tuples
• Various methods for scoring distances
• Report K5 as seemingly optimal

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Our Approach Average Common Substring (ACS)

• For every position in Genome A, find the
• longest common substring in Genome B.

Genome A
AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG
Genome B
AAAGCTACCTGGATGAAGGTAGGCTACGCCCTTT
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Our Approach ACS (cont.)

• For every position in Genome A, find the
• longest common substring in Genome B.

Genome A
AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG
Genome B
AAAGCTACCTGGATGAAGGTAGGCTACGCCCTTT
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Our Approach ACS (cont.)

• For every position in Genome A, find the
• longest common substring in Genome B.

Genome A
AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG
Genome B
AAAGCTACCTGGATGAAGGTAGGCTACGCCCTTT
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Our Approach ACS (cont.)

• For every position in Genome A, find the
• longest common substring in Genome B.

Genome A
AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG
Genome B
AAAGCTACCTGGATGAAGGTAGGCTACGCCCTTT
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Our Approach ACS (cont.)

• For every position in Genome A, find the
• longest common substring in Genome B.

Genome A
AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG
Genome B
AAAGCTACCTGGATGAAGGTAGGCTACGCCCTTT
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Our Approach ACS (cont.)

• For every position in Genome A, find the
  length
• of longest common substring in Genome B.
• In this case, l( )5.

Genome A
AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG
Genome B
AAAGCTACCTGGATGAAGGTAGGCTGCGCCCTTT
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Our Approach ACS (cont.)

• For every position in Genome A, find the
  length
• of longest common substring in Genome B.
• In this case, l( )5.
• ACS average l( ) L(Genome A, Genome B)

Genome A
AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG
Genome B
AAAGCTACCTGGATGAAGGTAGGCTGCGCCCTTT
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From ACS to Our Distance Intuition

• High L( A , B ) indicates higher similarity.
• Should normalize to account for length of B.

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From ACS to Our Distance Intuition

• High L( A , B ) indicates higher similarity.
• Should normalize to account for length of B.
• Still, we want distance rather than similarity.

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From ACS to Our Distance Intuition

• High L( A , B ) indicates higher similarity.
• Should normalize to account for length of B.
• Still, we want distance rather than similarity.

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From ACS to Our Distance Intuition

• High L( A , B ) indicates higher similarity.
• Should normalize to account for length of B.
• Still, we want distance rather than similarity.
• And want to have D( A , A ) 0 .

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From ACS to Our Distance Intuition

• High L( A , B ) indicates higher similarity.
• Should normalize to account for length of B.
• Still, we want distance rather than similarity.
• And want to have D( A , A ) 0 .
• Finally, we want to ensure symmetry.

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Comparison to Human (H)
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What Good is this Weird Measure?
1) Our ACS distance is related to an
information theoretic measure that is close to
Kullback Leibler relative entropy between two
distributions. 2) The proof of the pudding is in
the eating Will show this weird measure is
empirically good.
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An Info Theoretic Measure

• Define number of bits required
  
• to describe distribution p, given q.
• is closely related to Kullback
  Leibler
• relative entropy

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An Info Theoretic Measure

• Both and are
  common
• distance measures between two probability
• distributions p and q.
• Both distances are neither symmetric, nor
• satisfy triangle inequality.

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Relations Between ACS and

• Suppose p and q are Markovian probability
• distributions on strings, and A, B are
• generated by them.
• Abraham Wyner (1993) showed that w.h.p

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Computing Our Distance

• Average number of bits for compression a bit from
  one genome by the other vice versa.
• Practically achieved better results than the sum
  of relative entropies.

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Implementation and Complexity

• Computation distance of two k long genomes
• Naïve implementation requires O(k2)
• (disaster on billion letters long genomes)
• With suffix trees/arrays Total time for
• computing is O(k) (much
  nicer).

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Results and Comparisons

• Many genomes and proteomes
• Small ribosomal subunit ML tree
• Compare to other whole-genome methods
• Quantitative and qualitative evaluation

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Four Datasets Used

• Benchmark dataset 75 species
• 191 species (all non-viral proteomes in NCBI)
• 1,865 viral genomes
• 34 mitochondrial DNA of
• mammals (same as Li et al.)

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Benchmark Dataset 75 Species

• Genomes and proteomes of archaea, bacteria and
  eukarya
• Tree topologies reconstructed from distance
  matrix using Neighbor Joining (Saitou and Nei
  1987)
• Reference tree and distance matrix obtained from
  the RDP (ribosomal database)

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Results Quantitative Evaluations

• Benchmark dataset
• Genomes/Proteomes of 75 species from archaea,
  bacteria and eukarya.
• Methods tested
• ACS (Ours)
• Lempel Ziv complexity (Otu and Sayhood)
• K-mers composition vectors (Qi et al.).

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Results Quantitative Evaluations

• Tree evaluation
• Reference tree Accepted tree obtained from
  ribosomal database project (Cole et al. 2003)
• Tree Distance Robinson-Foulds (1981)

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Robinson-Foulds Distance

• Each tree edge partitions species into 2 sets.
• Search which partitions exist only in one of the
  trees.

A
C
A
E
Common Partition
x
A,B
C,D,E
A,B
C,D,E
y
B
B
D
E
D
C
Tree A
Tree B
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Robinson-Foulds Distance

• Each tree edge partitions species into 2 sets.
• Search which partitions exist only in one of the
  trees.

A
C
A
E
A,B,C
Partition Not in B
x
y
B
B
D,E
D
E
D
C
Tree A
Tree B
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Robinson-Foulds Distance

• Distance number of edges inducing partitions
  existing only in one of the trees.
• For n leaves, distance ranges from 0 through
  2n-6.

A
C
A
E
A,B,C
Partition Not in B
x
y
B
B
D,E
D
E
D
C
Tree A
Tree B
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Robinson-Foulds Distance - Results
Benchmark set has n75 species, so max distance
is 144.
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All Proteomes Dataset

• 191 proteomes from NCBI Genome
• 11 Eukarya, 19 Archaea, 161 Bacteria
• Compared to NCBI Taxonomy

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All Proteomes Dataset

• 191 proteomes from NCBI Genome
• 11 Eukarya, 19 Archaea, 161 Bacteria
• Compared to NCBI Taxonomy

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All Proteomes Dataset

• 191 proteomes from NCBI Genome
• 11 Eukarya, 19 Archaea, 161 Bacteria
• Compared to NCBI Taxonomy

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Viral Forest

• 1865 viral genomes from EBI
• Split into super-families
• dsDNA
• ssDNA
• dsRNA
• ssRNA positive
• ssRNA negative
• Retroids
• Satellite nucleic acid

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Retroid Tree

• 83 Reverse-transcriptases
• Hepatitis B viruses
• Circular dsDNA
• ssRNA

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ssRNA Negative Tree

• Each segment treated separately
• 174 segments of 74 viruses.

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Mammalian mtDNA Tree
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Throwing Branch Lengths In
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General Insights

• Proteomes vs. Genomes
• Overlapping vs. Non-overlapping
• Triangle inequality held in all cases

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Additional Directions attempted

• Naïve introduction of mismatches
• Division into segments
• Weighted combinations of genome and proteome data
  
• Bottom line (subject to change)
• Simple is beautiful.

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Summary

• Whole genome phylogeny based on ACS method
• Effective algorithm
• Information theoretic justification
• Successful reconstruction of known phylogenies.

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Future work

• Additional datasets
• Statistical significance
• Improved branch lengths estimation
• Better time and space complexities

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Questions ?