1. CIS 4930/6930 – Recent Advances in Bioinformatics Spring 2014
Network alignment
Tamer Kahveci
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2. What is Network Alignment?
Global Alignment is GI-Complete
Local Alignment is NP-Complete
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3. Metabolic Pathways
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4. What and Why? Applications Metabolic Pathway Alignment
Finding a mapping of the entities of the pathways C2 C3 C4 C5 R1 R2 C1 E1 E2
Applications
Drug Target Identification
Metabolic Reconstruction
Phylogeny Prediction C2 C4 R1 R2 C1 C5 E1 E2
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5. Challanges - Where are the compounds? - E1  C1  E2 or E1  C2  E2 ?
Abstraction
Graph Alignment
Even after Abstraction Metabolic Pathway Alignment problem is NP Complete!
Existing Algorithms
Heymans et al. (2003)
Clemente et al. (2005)
Pinter et al. (2005)
Singh et al. (2007) ….
- Where are the compounds?
- E1  C1  E2 or
E1  C2  E2 ? E1 E2 E3 E4 E1 C1 C2 E2 C3 C4 E3 E4 E1 E2 E3 E1 C1 E2 C3 E3
Pathway Alignment is hard !
Abstraction is a problem !
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6. Outline Graph Model of Pathways Consistency of an Alignment
Homological & Topological Similarities
Eigenvalue Problem
Similarity Score
Experimental Results
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7. Non-Redundant Graph Model
Pyruv.
Lip-E
ThPP
R0014
S-Ac
2-ThP
A-CoA
Di-hy
R7618
R3270
R2569
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8. Consistency 1- Align only the entities of the same type (compatible)R1 R2 C1 C2 R1 C1
2- The overall mapping should be 1-1 R1 R2 R3
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9. Consistency
3- Align two entities ui , vi only if there exists an aligned entity pair uj , vj such that uj and vj are on the reachability paths of ui and vi respectively. C3 C2 C5 C4 R1 R2 C1
Aligned Entities
Backward Reachability
Path
Forward Reachability C2 C4 R1 R2 C1 C5
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10. Problem Statement
Given a pair of metabolic pathways, our aim is to find the consistent alignment (mapping) of the entities (enzymes, reactions, compounds) such that the similarity between the pathways (SimP score) is maximized.
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11. Pairwise Similarities
(Homology of Entities)
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12. Pairwise Similarities (Homology)
Enzyme Similarity (SimE)
Hierarchical Enzyme Similarity - Webb EC.(2002)
Information-Content Enzyme Similarity - Pinter et al.(2005)
Compound Similarity (SimC)
Identity Score for compounds
SIMCOMP Compound Similarity – Hattori et al.(2003)
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13. Pairwise Similarities
Reaction Similarity
(SimR)
SimR (R1,R2) =
Enzymes
max ( SimE (E1,E3) , SimC (E2,E3) )
Input Compounds
+ max ( SimC (C1,C4) , SimC (C2,C4) )
Output Compounds
+ max ( SimC (C3,C5) , SimC (C3,C6), SimC (C3,C7) ) C1 C3 R1 C2 E1 E2 C5 C4 R2 C6 C7 E3
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14. Topological Similarity
(Topology of Pathways)
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15. Neighborhood Graphs Reactions Enzymes Compounds C1 R1 C4 C8 C2 C6 E1
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16. Topological Similarities
BN (R3)= {R1,R2}
FN (R3)= {R4}
BN (R3)= {R1}
FN (R3)= {R4,R5} R1 R3 R4
AR [R3 ,R3][R2,R1] = = 1
2*1 + 1* R2 R4
(|R| |R| ) x (|R| |R| ) = 16 x 16
AR matrix R1 R3 R5
R1-R1 …
R2-R1
R4-R4
R4-R5
....
R3 -R3
1 / 4
…..
|R| = 4
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17. Problem Formulation
Iteration 3: Support of aligned third degree neighbors added
Iteration 0: Only pairwise similarity of R3 and R3
Iteration 1: Support of aligned first degree neighbors added
Iteration 2: Support of aligned second degree neighbors added R1 R4 R6 R1 R3 R3 R2 R8 R2 R5 R7 R8 R5 R7
Focus on R3 – R3 matching
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18. Problem Formulation HR0 Vector HRs Vector Initial Reaction
Similarity Matrix
HR0 Vector
HRs Vector
Final Reaction
Similarity Matrix
0.5
1.0
0.4
0.3
0.6
0.9
0.5
0.6
0.9
0.5
0.6
0.9
0.5
Power
Method
Iterations
0.5
1.0
0.4
0.3
0.5
1.0
0.4
0.3
0.3
0.5
0.8
0.3
0.5
0.8
0.1
1.0
0.2
0.9
0.1
1.0
0.2
0.9
0.3
0.5
0.8
0.2
0.3
0.6
0.9
0.2
0.3
0.6
0.9
0.2
0.3
0.6
0.9
0.1
1.0
0.2
0.9
0.2
1.0
0.4
0.6
0.2
1.0
0.4
0.6
0.2
1.0
0.4
0.6
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19. Max Weight Bipartite Matching
Six Possible Orderings
ONLY 3 ARE UNIQUE
Reactions First
Enzymes First
Compounds First
R First Pruning
Weighted Edges
Aligned Entities
Inconsistent Edges
Consistency
Assured ! C1 E1 C1 R1 R1 E1 C2 C2 E2 R2 R2 E2 C3 C3 R3 R3 E3 C4
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20. Alignment Score ( SimP )
SimP =1 for identical pathways
SimP = b Sim(C1) + Sim(C2) +Sim(C4) + (1 – b) Sim(E1) + Sim(E2) C2 C4 R1 R2 C1 C5 C2 C3 C4 C5 R1 R2 C1 E1 E2 E1 E2
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21. Outline Graph Model of Pathways Consistency of an Alignment
Homological & Topological Similarities
Eigenvalue Problem
Similarity Score
Experimental Results
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22. Impact of Alpha
= 0 : Only pairwise similarities of entities - No iterations
= 1 : Only topology of the graphs
a = 0.7 is good !
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23. Alternative Entities & Paths
Kim J. et al. (2007)
Kuzuyama T. et al. (2006)
Eukaryotes (e.g. H.Sapiens)  Mevalonate Path
Bacterias (e.g. E.Coli)  Non-Mevalonate Path
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24. Phylogeny Prediction Archaea Our NCBI Prediction Taxonomy Eukaryota
Thermoprotei
Our
Prediction
NCBI
Taxonomy
Deuterostomia
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25. Effect Of Consistency Restriction
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26. Running Time
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27. How to allow subnetwork mapping
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28. Different Paths, Same Function
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29. How bad can it be?
Lysine Biosynthesis
E.coli
A.thaliana
MetNetAligner: Cheng & Zelikovsky, Bioinformatics 2009.
SubMAP: Ay & Kahveci, RECOMB 2010.
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30. Alternative paths -1
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31. Alternative paths - 2
Work on this
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32. Alternative paths - 3
Work on this
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33. Mappings among major clades
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34. Dynamic programming approach
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