A Combinatorial Approach to GenomeWide Ortholog Assignment: Beyond Sequence Similarity Search

1
A Combinatorial Approach to Genome-Wide
Ortholog Assignment Beyond Sequence Similarity
Search

• Tao Jiang
• Department of Computer Science
• University of California, Riverside

Joint work with X. Chen, Z. Fu, J. Zheng, V.
Vacic, P. Nan, Y. Zhong, and S. Lonardi
2
Outline

• An introduction to orthology
• Existing ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• Minimum Common Substring Partition
• Maximum Cycle Decomposition
• Experimental results
• Summary and future directions

3
Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• Minimum Common Substring Partition
• Maximum Cycle Decomposition
• Experimental Results
• Summary and future directions

4
Orthology

• Homolog
• Gene family
• Paralog
• Duplication
• Ortholog
• Speciation

5
Orthology
a
b
mouse

• Homolog
• Gene family
• Paralog
• Duplication
• Ortholog
• Speciation

chicken
frog
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Orthology
a
b
mouse

• Homolog
• Gene family
• Paralog
• Duplication
• Ortholog
• Speciation

chicken
frog
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Orthology the more complicated picture
A
Speciation 1
Gene duplication 1
B
C
Speciation 2
Speciation 2
Gene duplication 2
A1
B1 C1
B2 C2 C3
G1
G3
G2
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Significance

• Orthologous genes in different species are
  evolutionary and functional counterparts.
• Many methods use orthologs in a critical way
• Function inference
• Protein structure prediction
• Motif finding
• Phylogenetic analysis
• Pathway reconstruction
• and more ...
• Identification of orthologs, especially exemplar
  genes, is a fundamental and challenging problem.

9
Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• Minimum Common Substring Partition
• Maximum Cycle Decomposition
• Experimental Results
• Summary and future directions

10
Existing Methods

• Methods based on sequence similarity
• BBH
• Inparanoid/Multiparanoid
• PhiGs

• COG/KOG
• OrthoMCL
• MGD

• TOGA/EGO
• KEGG
• HomoloGene

• Methods based on phylogenetic trees
• Reconciled tree
• Orthostrapper
• OrthologID

• RAP
• RIO

• PhyOP
• TreeFam

• Methods based that take into account gene
  locations
• Shared genomic synteny

11
Observations

• Sequence similarity-based methods assume that the
  evolutionary rates of all genes in a homologous
  family are equal and thus the divergence time
  could be estimated by comparing the sequence of
  genes.
• Tree-based methods critically rely on the
  correctness of reconstructed gene and species
  trees.
• Global genome rearrangements are not considered
  in gene location-based methods.

12
Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• NP-hard
• A low bound
• Minimum Common Substring Partition
• Maximum Cycle Decomposition
• Experimental Results
• Summary and future directions

13
Molecular Evolution

• Global rearrangement and duplication
• Inversion/Reversal
• Translocation
• Transposition
• Fusion/Fission
• Duplication/Loss

• Local mutation
• Base substitution
• Base insertion
• Base deletion

A complete ortholog assignment system should make
use of information from both levels of molecular
evolution.
14
Genome Rearrangement Operations
15
Example
Given the evolutionary scenario, main ortholog
pairs and inparalogs could be identified in a
straightforward way.
16
The Parsimony Approach

• Identify homologs using sequence similarity
  search (e.g.) BLASTp.
• Reconstruct the evolutionary scenario on the
  basis of the parsimony principle postulate the
  minimum possible number of rearrangement events
  and duplication events in the evolution of two
  closely related genomes since their splitting so
  as to assign orthologs.
• Ortholog assignment problem could be formulated
  as a problem of finding a most parsimonious
  transformation from one genome into the other,
  without explicitly inferring their ancestral
  genome.

17
RD (Rearrangement-Duplication) Distance

• RD distance
• denotes the number of rearrangement
  events in a most parsimonious transformation
• denotes the number of gene duplications
  in a most parsimonious transformation

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The key algorithmic problem -SRDD

• Two related (unichromosomal) genomes
• No inparalogs, i.e. no post-speciation
  duplications
• No gene losses, and thus equal gene content
• Only reversals have occurred
• Signed Reversal Distance with Duplicates
• How to find a shortest sequence of reversals
• Almost untouched in the literature
• Duplicated genes are present
• Generalizes the problem of sorting by reversal

19
When there are no (post-speciation) duplications
The most parsimonious rearrangement scenario may
suggest the true orthology.
20
Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• NP-hard
• A low bound
• Minimum Common Substring Partition
• Maximum Cycle Decomposition
• Experimental Results
• Summary and future directions

21
Sorting by reversal

• Sorting a permutation into the identity by
  reversals
• Distinct genes only
• Signed vs. unsigned version

22
Sorting signed permutation

• Hannenhalli-Pevzner (HP) theory
• Polynominal-time solvable
• Breakpoint graph
• Breakpoint, cycle, hurdle, fortress
• HP formula

Hannenhalli and Pevzner, STOC, 178-187, 1995
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Sorting unsigned permutation

• NP-hard (Caprara, 1997)
• Breakpoint graph
• Maximum alternating cycle decomposition (NP-hard)
• 1.375-approximation (Berman, et al. 2002)

Caprara, RECOMB, 75-83, 1997
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A brief history
The work has also been extended to genomes with
multiple chromosomes (Hannenhalli and Pevaner,
1995 Tesler, 2002 Ozery-Flato and Shamir, 2003)
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Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• Computing Minimum Common Substring Partition
• Computing Maximum Cycle Decomposition
• Experimental results
• Summary and future directions

26
SRDD The exhaustive method

• Given genomes and ,
  .
• the set of all the possible ortholog
  assignments
• the genome after orthologs have been
  assigned
• Assume one family with ten duplicated genes in
  each genome

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SRDD Hardness

• SRDD is NP-hard, even when the maximum size of a
  gene family is limited to two.
• Reduction from the problem of sorting an unsigned
  permutation by reversals

No breakpoint
No breakpoint
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SRDD A lower bound

• Partial graph
• the number of edges linking two
  nodes labeled by and , respectively
• The number of breakpoints
• Let and be a pair of related genomes.
  Their reversal distance is lower bounded by

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(Sub)optimal assignment rules

• Rule one

• Rule two

30
Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• Computing Minimum Common Substring Partition
• Computing Maximum Cycle Decomposition
• Experimental results
• Summary and future directions

31
The MCSP problem

• Minimum Common Substring Partition
• This may help eliminate many duplicates, but is
  different from syntenic blocks.
• Give two related genomes and , we have

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MCSP - Hardness

• Let k-MCSP denote the version of MCSP where each
  gene family is of size at most k. The problem
  k-MCSP is NP-hard, for any k gt 1.

Petr Kolman gave a linear time O(
)-approximation algorithm for k-MCSP (MFCS05),
and thus k-SRDD. The approximation ratio was
recently improved to O(k).
Goldstein, Kolman, and Zheng, ISAAC, 473-484, 2004
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A special case of MCP - MCIP

• Minimum common integer partition (MCIP) Given
  two multisets with equal sum, partition the
  numbers to result in a smallest common multiset.

• For example, given A 3, 5, 7 and B
  2,4,4,5, the answer is C 1,2,3,4,5.
• The problem is NP-hard. A 1.25-approximation
  algorithm based on set packing has been given in
  Chen et al. 2006.
• It can be extended to k input multisets
  (Woodruff06, Zhao et al.06).

Chen, Liu, Liu, and Jiang, CIAC2006.
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MCSP Pair-match graph

• A pair-match graph
• Single match v.s. pair match
• Incompatible pair-matches
• The maximum independent set problem on
  is equivalent to the minimum common substring
  partition problem, i.e.,
  .

Goldstein, Kolman, and Zheng, ISAAC, 473-484, 2004
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MCSP Approximation

• Algorithm APPROX-MCSP( , )
• / and are a pair of related genomes /
• Construct the pair-match graph for
  and
• Find an approximation of the vertex cover of
  
• Identify segments based on the pair-matches in
• Output all the segments as a common substring
  partition

• If the common substring parititon found by the
  above algorithm APPROX-MCSP is , then
  where is the ratio of
  the approximation algorithm for vertex cover and
  is the genome size. In particular for 2-MCSP,
  the algorithm achieves an approximation ratio of
  1.5.

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MCSP for multi-chromosomal genomes

• For any two genomes and
• is the number of unmatched genes in a
  maximum gene matching between two genomes
  is the number of chromosomes in each genome
  is the minimum common partition between the
  two genomes.

37
Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• Computing Minimum Common Substring Partition
• Computing Maximum Cycle Decomposition
• Experimental results
• Summary and future directions

38
Maximum cycle decomposition
What if there still are some duplicates?

• Given any two genomes without duplicated genes,
  the (revised) HP formula for computing the
  rearrangement distance between the two genomes is
  as follows

Genome rearrangement distance
(Hannenhalli and Pevaner, 1995 Tesler, 2002
Ozery-Flato and Shamir, 2003)
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Generalizing breakpoint graphs to
multi-chromosomal genomes with duplicates

• Maximum Cycle Decomposition
• Complete-breakpoint graph
• Greedy cycle/path decomposition (to maximize
  )
• Vertex disjoint
• Pairing condition
• Edge alternating
• Example
  and

40
MSOAR

• MSOAR is a high-throughput system for ortholog
  assignment between closely related genomes.
• MSOAR employs a heuristic algorithm to calculate
  the rearrangement/duplication (RD) distance
  between two genomes using the sub-optimal
  assignment rules, MCSP and MCD, which can be used
  to reconstruct a most parsimonious evolutionary
  scenario.
• MSOAR extends SOAR by allowing for
  multi-chromosomal genomes and the detection of
  inparalogs.

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Noise gene pair detection

• The previous steps determine a one-to-one gene
  matching between two genomes.
• Unmatched genes are removed and marked as
  inparalogs.
• Remove gene pairs whose deletion decreases the
  rearrangement distance by at least
  two. Since each pair incurs two duplications, the
  RD distance will not increase
• These deleted genes form inparalogs.

42
An outline of MSOAR
43
Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• Computing Minimum Common Substring Partition
• Computing Maximum Cycle Decomposition
• Experimental results
• Summary and future directions

44
Simulated data test

• Simulated genome 100 distinct genes
• Simulated genome Randomly perform
  reversals on to obtain another genome
• Experiments
• One Randomly copy some genes and insert them
  back into
• Two Randomly copy some genes and insert them
  back into and
• (Inserted genes are inparalogs by
  definition.)

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Simulated data test

• Randomly generate two genomes ( , , , )
• Average on 20 random instances for each parameter
  set
• Our heuristic algorithm v.s. the iterated
  exemplar algorithm (Sankoff,
  Bioinformatics, 1999)

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Exemplar algorithm

• Look for the true exemplar gene of a family
• Direct descendants of a gene in the most recent
  common ancestral genome
• Delete all but one member of every gene family on
  each genome
• Return one with the smallest rearrangement
  distance
• By iterating the exemplar algorithm, we can
  assign orthology for all duplicated genes.

Sankoff, Bioinformatics, 1999
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Real data

• Homo sapiens
• Build 36.1 human genome assembly (UCSC hg18,
  March 2006)
• 20161 protein sequences in total
• Mus musculus
• Build 36 mouse genome assembly (UCSC mm8,
  February 2006)
• 19199 protein sequences in total

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MSOAR vs. Inparanoid

• Validation Official gene symbols extracted from
  the UniProt release 6.0 (September 2005)
• For 20161 human protein sequences and 19199 mouse
  protein sequences, MSOAR assigned 14362 orthologs
  between Human and Mouse, among which 11050 are
  true positives, 1748 are unknown pairs and 1508
  are false positives, resulting in a sensitivity
  of 92.26 and a specificity of 87.99.
• The comparison between MSOAR and Inparanoid (Remm
  et al., J. Mol. Biol., 2001)

49
MSOAR vs. Inparanoid
The ortholog pair SNRPB (Human) and Snrpb (Mouse)
are not bi-directional best hits, which could be
missed by the sequence-similarity based ortholog
assignment methods like Inparanoid.
50
Number of main ortholog pairs assigned by MSOAR
across the chromosome pairs
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An alignment between syntenic blocks and MSOAR
blocks
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Validation by HCOP

• The HGNC Comparison of Orthology Predictions
  (HCOP) is a tool that integrates and displays the
  human-mouse orthology assertions made by Ensembl,
  Homologene, Inparanoid, PhIGS, MGD and HGNC.
  (http//www.gene.ucl.ac.uk/cgi-bin/nomenclature/hc
  op.pl)

53
Other validations

• By PANTHER protein sequence classification
  (ftp//ftp.pantherdb.org/sequence_classifications/
  )
• MSOAR identified 14083 ortholog pairs with
  valid Geneid between human and mouse, among which
  11887 pairs have both orthologous genes in the
  same protein subfamily.

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Orthology mapping human/mouse
55
Orthology mapping human/rat
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Orthology mapping mouse/rat
57
Sequence-based mapping
Pevzner and Tesler, Genome Research, 2003
58
Outline

• An introduction to orthology
• Previous ortholog assignment methods
• Ortholog assignment via genome rearrangement
• An introduction to genome rearrangement
• Computing signed reversal distance with
  duplicates
• Computing Minimum Common Substring Partition
• Computing Maximum Cycle Decomposition
• Experimental results
• Summary and future directions

59
Summary and future work

• Presented a novel approach to assign orthologs
  between two genomes via genome rearrangement and
  gene duplication
• Introduced a rearrangement/duplication (RD)
  distance for genome comparisons
• Proposed a heuristic algorithm for assigning
  orthologs under maximum parsimony
• Developed a high-throughput system for ortholog
  assignment (MSOAR)
• Tested the system on simulated data and real
  genomic data of human and mouse
• MSOAR vs. Iterated exemplar algorithm
• MSOAR vs. Inparanoid
• Various validation methods
• Future directions
• More efficient algorithms for MCSP and MCD
• Refine the evolutionary model for MSOAR
  (transposition, tandem duplication, gene loss,
  etc.)
• Ortholog assignment for multiple genome
  comparison
• More explicit treatment of one-to-many and
  many-to-many orthology relationship

60
References

• X. Chen, J. Zheng, Z. Fu, P. Nan, Y. Zhong, S.
  Lonardi, and T. Jiang. Computing the assignment
  of orthologous genes via genome rearrangement.
  Proc. 3rd Asia-Pacific Bioinformatics Conference
  (APBC), 2005, pp. 363-378.
• X. Chen, J. Zheng, Z. Fu, P. Nan, Y. Zhong, S.
  Lonardi, and T. Jiang. Assignment of orthologous
  genes via genome rearrangement. IEEE/ACM
  Transactions on Computational Biology and
  Bioinformatics (TCBB) 2-4, pp. 302-315, 2005.
• Z. Fu, X. Chen, V. Vacic, P. Nan, Y. Zhong, and
  T. Jiang. A parsimony approach to
  genome-wide ortholog assignment. Proc.
  10th Annual International Conference on Research
  in Computational Molecular Biology (RECOMB),
  2006, pp. 578-594.
• Z. Fu, X. Chen, V. Vacic, P. Nan, Y. Zhong, and
  T. Jiang. MSOAR A High-throughput ortholog
  assignment system based on genome rearrangement.
  Submitted, 2007.
• Z. Fu and T. Jiang. Clustering of main orthologs
  for multiple genomes. To be presented at LSI
  Conference on Computational Systems Biology
  (CSB), 2007.

61
Acknowledgement

• NSF
• DoE Genomes to Life (GtL) program
• National Key Project for Basic Research
• NSFC
• Changjiang Visiting Professorship, Tsinghua Univ.
• Discussion with Marek Chrobak, Petr Kolman, and
  Lan Liu on MCSP and MCIP