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
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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
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4. Orthology Homolog Paralog Ortholog mouse Gene family chicken
Duplication
Ortholog
Speciation
mouse
chicken
frog
(from
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5. Orthology a b Homolog Paralog Ortholog mouse Gene family chicken
Duplication
Ortholog
Speciation
mouse
chicken
frog
(from
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6. Orthology a b Homolog Paralog Ortholog mouse Gene family chicken
Duplication
Ortholog
Speciation
mouse
chicken
frog
(from
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7. Orthology – the more complicated picture
Speciation 1
Gene duplication 1 B C
Speciation 2
Speciation 2
B C1
B2 C C3
True exemplar is the direct descendant of the ancestral gene of a given set of inparalogs. A main ortholog pair is defined as two true exemplar genes of two co-orthologous gene sets.
Gene duplication 2
Outparalogs evolved via a duplication prior to a given speciation event.
B C1 A1
B C1
B2 C C3
Inparalogs evolved via a duplication posterior to a given speciation event.
B2 C C3 G1 G2 G3
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8. 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.
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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
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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
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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.
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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
9/17/2018

13. Molecular Evolution Local mutation
Base substitution
Base insertion
Base deletion
Global rearrangement and duplication
Inversion/Reversal
Translocation
Transposition
Fusion/Fission
Duplication/Loss
A complete ortholog assignment system should make use of information from both levels of molecular evolution.
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14. Genome Rearrangement Operations
Reversal (inversion)
Translocation
Fusion
Fission
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15. Example a1 b c a2 d e f g
The ancestral genome
Speciation a1 c a2 d e f g b
reversal a1 b c a2 d e f g a3
duplication a1 c a2 d e f g b a4
duplication
Genome a1 b c a2 d e f g a3
fission
Genome
Given the evolutionary scenario, main ortholog pairs and inparalogs could be identified in a straightforward way.
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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.
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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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18. 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
A high-throughput system for assigning orthologs on a genome scale.
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19. When there are no (post-speciation) duplications
The most parsimonious rearrangement scenario may suggest the true orthology.
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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
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21. Sorting by reversal
Sorting a permutation into the identity by reversals
Distinct genes only
Signed vs. unsigned version
Sorting signed permutation
Sorting unsigned permutation
A permutation
A high-throughput system for ssigning orthologs on a genome scale.
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22. Sorting signed permutation
Hannenhalli-Pevzner (HP) theory
Polynominal-time solvable
Breakpoint graph
Breakpoint, cycle, hurdle, fortress
HP formula:
Breakpoint graph
d = 3 –
A permutation
Hannenhalli and Pevzner, STOC, , 1995
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23. Sorting unsigned permutation
NP-hard (Caprara, 1997)
Breakpoint graph
Maximum alternating cycle decomposition (NP-hard)
1.375-approximation (Berman, et al. 2002)
Breakpoint graph
Alternating cycle decomposition
d = 3 –
A permutation
Caprara, RECOMB, 75-83, 1997
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24. A brief history signed unsigned Kececioglu and Sankoff (1995)
2-approximation
Bafna and Pevzner (1996)
1.5-approximation
1.75-approximation
Hannenhalli and Pevzner (1995)
Polynomial
Special cases – polynomial
Caprara (1997)
NP-hard
Christie (1998)
Bader, et al (2001)
Linear – distance only
Berman, et al (2002)
1.375-approximation
d = 3 –
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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25. 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
9/17/2018

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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27. 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
An unsigned permutation
A signed sequence with duplicates
No breakpoint
No breakpoint
Case 1:
Case 2:
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28. 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
3h 3t 1t 1h 2t 2h 1h 1t 4h 4t
3h 3t 1h 1t 2h 2t 1h 1t 4h 4t
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29. (Sub)optimal assignment rules
Rule one: a b c f d e
Trivial
Non-trivial a b c f d e
Trivial
Non-trivial /
Rule two: a b c f d -e -d -b -c
Trivial
Non-trivial e a b c f d -e -d -b -c
Trivial
Non-trivial e /
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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
9/17/2018

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 G: H: G: H:
Without loss of generality that the first genes and the last genes of the two related genomes are identical and positive singletons, respectively
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32. Goldstein, Kolman, and Zheng, ISAAC, 473-484, 2004
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 > 1.
Petr Kolman gave a linear time O( )-approximation algorithm for k-MCSP (MFCS’05), and thus k-SRDD. The approximation ratio was recently improved to O(k).
Goldstein, Kolman, and Zheng, ISAAC, , 2004
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33. 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.,
G: 3 1
H: 3 1
G: 2 -1
H: 1 -2 G: H:
G: 1 2
H: -2 -1 G: H: )) , ( ) E V
MIS n H G L Ã - =
Goldstein, Kolman, and Zheng, ISAAC, , 2004
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34. 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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35. 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
9/17/2018

36. 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)
We could approximate the minimum rearrangement distance between two genomes by decomposing the complete-breakpoint graph to maximize , where is the number of cycles and paths and is the number of
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37. 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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38. “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.
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39. An outline of MSOAR Dataset A Dataset B Homology search:
1. Apply all-vs.-all comparison by BLASTp
2. Only select the blast hits with
similarity score above cutoff
3. Keep up to five top bi-directional best hits
List of orthologous
gene pairs output
Assign orthologs by minimizing RD distance:
1. Apply suboptimal rules
2. Apply minimum common partition
3. Maximum graph decomposition
4. Detect inparalogs by identifying “noise”
gene pairs
2. Apply minimum common substring partition
3. Maximum cycle decomposition
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40. 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
9/17/2018

41. 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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42. 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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43. Real data Homo sapiens: Mus musculus:
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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44. MSOAR vs. Inparanoid
Validation: Official gene symbols extracted from the UniProt release 6.0 (September 2005)
For human protein sequences and mouse protein sequences, MSOAR assigned orthologs between Human and Mouse, among which 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)
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45. MSOAR vs. Inparanoid Human chromosome 20 Mouse chromosome 2
SNRPB
STK35
TGM3
TGM6
ZNF343
TMC2
NOL5A
IDH3B
Snrpb
Stk35
Tgm3
Tgm6
Tmc2
Nol5a
Idh3b
Mouse chromosome 2
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.
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46. Number of main ortholog pairs assigned by MSOAR across the chromosome pairs
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47. An alignment between syntenic blocks and MSOAR blocks
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48. 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. (
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49. Other validations
By PANTHER protein sequence classification (ftp://ftp.pantherdb.org/sequence_classifications/)
MSOAR identified ortholog pairs with valid Geneid between human and mouse, among which pairs have both orthologous genes in the same protein subfamily.
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50. 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
9/17/2018

51. 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
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52. 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
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 , 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
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.
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53. 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
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