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Information Theoretic Approach to Whole Genome Phylogenies

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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

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

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.

Accepted Evolutionary Model: Trees

Reconstructing this phylogenetic

treeis the major challenge

in evolutionary biology.

But…

Phylogenetic Trees Based on What?

- Morphology
- Single genes
- Whole genomes

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

Whole Genome Phylogenies: Biological Motivation

- Recently (last 2-4 years) it was

discovered (in laboratories) that ~60%

of the genome transcribes to RNA, but

this RNAdoes not translate to proteins.

- We are in the dark as to what this

non-coding RNA does.

- But we should not ignore it and concentrate just on 3% coding parts!

Whole Genome Phylogenies: Availability

- Due to sequencing techniques that were unthinkable just 15 years ago,

we now have the complete genome

sequences of hundreds of species,

from all ranks and sizes of life.

- These sequences are publicly available.
- They are a true treasure for analysis.

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

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” “IT”
- 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)

Genome Rearrangements

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

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

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”
- Reportedly slow.

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

Genome B

Qi et al.: Composition Vector- Calculate distributions of the K-tuples.
- For K=1 – nucleotide/amino acid frequencies.
- For K=5 – 45 (205) possible 5-tuples
- Various methods for scoring distances
- Report K=5 as seemingly optimal

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

AAAGCTACCTGGATGAAGGTAGGCTGCGCCCTTT

Our Approach: ACS (cont.)

- For every position in Genome A, find the

longest common substring in Genome B.

Genome A

AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG

Genome B

AAAGCTACCTGGATGAAGGTAGGCTGCGCCCTTT

Our Approach: ACS (cont.)

- For every position in Genome A, find the

longest common substring in Genome B.

Genome A

AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG

Genome B

AAAGCTACCTGGATGAAGGTAGGCTGCGCCCTTT

Our Approach: ACS (cont.)

- For every position in Genome A, find the

longest common substring in Genome B.

Genome A

AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG

Genome B

AAAGCTACCTGGATGAAGGTAGGCTGCGCCCTTT

Our Approach: ACS (cont.)

- For every position in Genome A, find the

longest common substring in Genome B.

Genome A

AGGCTTAGATCGAGGCTAGGATCCCCTTAGCG

Genome B

AAAGCTACCTGGATGAAGGTAGGCTACGCCCTTT

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

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

From ACS to OurDistance: Intuition

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

From ACS to OurDistance: Intuition

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

From ACS to OurDistance: Intuition

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

From ACS to OurDistance: 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.

From ACS to OurDistance: 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.

Proteome size

L(H,*)

Ds(H,*)

Mus Musculus (mouse)

12x106

22.97

2.11

Arabidopsis Thaliana

11x106

5.29

5.56

S. Cerevisiae (yeast)

2x106

4.82

8.97

E. coli

0.9x106

4.57

9.13

Comparison to Human (H)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.

An Info Theoretic Measure

Define = number of bits required

to describe distribution p, given q.

is closely related to Kullback Leibler

relative entropy

An Info Theoretic Measure

Both and are common

“distance measures” between two probability

distributions p and q.

In general, the two “distances” are neither

symmetric, nor satisfy triangle inequality.

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

ACS 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).

Results and Comparisons

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

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.)

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)

B

C

D

E

A

0

1.2

2.3

4.6

3.5

B

1.2

0

3.4

2.4

5.3

C

2.3

3.4

0

3.4

5.3

D

4.6

2.4

3.4

0

4.0

E

3.5

5.3

5.3

4.0

0

Tested Methods

Tree Evaluation

A

NJ

E

B

D

C

Results: Quantitative Evaluations- Benchmark dataset
- Genomes/Proteomes of 75 species from archaea, bacteria and eukarya with known genomes, proteomes, and with RDP entries.
- Methods implemented and tested :
- ACS (Ours)
- “Lempel Ziv complexity” (Otu and Sayhood)
- K-mers composition vectors (Qi et al.).

B

C

D

E

A

0

1.2

2.3

4.6

3.5

B

1.2

0

3.4

2.4

5.3

C

2.3

3.4

0

3.4

5.3

D

4.6

2.4

3.4

0

4.0

E

3.5

5.3

5.3

4.0

0

Tested Methods

Tree Evaluation

A

NJ

E

B

D

C

Results: Quantitative Evaluations- Tree evaluation
- Reference tree: “Accepted” tree obtained from ribosomal database project (Cole et al. 2003)
- Tree Distance:Robinson-Foulds (1981)

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

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

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

Genomes

Proteomes

LZ

complexity

118

126

Composition vector

110

92

ACS

(Our method)

108

76

Robinson-Foulds Distance - ResultsBenchmark set has n=75 species, so max distance is 144.

All Proteomes Dataset

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

All Proteomes Dataset

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

All Proteomes Dataset

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

Nanoarchaeum

(parasitic/symbiotic)

Halobacterium

Viral Forest

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

ssRNA Negative Tree

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

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.

Summary

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

Future work

- Statistical significance
- Improved branch lengths estimation
- Handle large eukaryotic genomes via improved suffix array routines (e.g. by Stephan Kurtz enhanced suffix arrays - smaller memory requirements)
- This should enable to have a full comparison of proteome vs. genome trees.
- Not there yet.

Thank you !

Questions ?

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