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Ferhat Ay , Tamer Kahveci & Valerie de-Crecy Lagard. Consistent alignment of metabolic pathways without abstraction. www.cise.ufl.edu/~fay. Metabolic Pathways. What and Why?. C2. C4. C1. R1. R2. C3. C5. E1. E2. Metabolic Pathway Alignment

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ferhat ay tamer kahveci valerie de crecy lagard
Ferhat Ay, Tamer Kahveci

& Valerie de-Crecy Lagard

Consistent alignment of metabolic pathways without abstraction

www.cise.ufl.edu/~fay

Ferhat Ay

what and why
What and Why?

C2

C4

C1

R1

R2

C3

C5

E1

E2

Metabolic Pathway Alignment

Finding a mapping of the entities of the pathways

Applications

  • Drug Target Identification
  • Metabolic Reconstruction
  • Phylogeny Prediction

C2

C4

C1

R1

R2

E1

E2

C5

Ferhat Ay

challanges
Challanges

Abstraction

Graph Alignment

  • Even after Abstraction Metabolic Pathway Alignment problemis NP Complete!
  • Existing Algorithms
    • Heymans et al. (2003)
    • Clemente et al. (2005)
    • Pinter et al. (2005)
    • Singh et al. (2007)
    • ….

E1

E2

E3

E1

E2

E3

C1

C3

C2

C4

E4

E4

E1

E2

E3

E1

E2

E3

C1

C3

- Where are the compounds?

  • Pathway Alignment is hard !

- E1  C1  E2

or

E1  C2  E2 ?

  • Abstraction is a problem !

Ferhat Ay

outline
Outline
  • Graph Model of Pathways
  • Consistency of an Alignment
  • Homological & Topological Similarities
  • Eigenvalue Problem
  • Similarity Score
  • Experimental Results

Ferhat Ay

non redundant graph model
Non-Redundant Graph Model

ThPP

Lip-E

Pyruv.

1.8.1.4

R3270

R7618

R0014

1.2.4.1

A-CoA

2-ThP

S-Ac

Di-hy

R2569

2.3.1.12

Ferhat Ay

consistency
Consistency

1- Align only the entities of the same type (compatible)

R1

R2

C1

C2

C1

R1

  • 2- The overall mapping should be 1-1

R2

R1

R3

Ferhat Ay

consistency1
Consistency

3- Align two entities ui, vionly if there exists an aligned entity pair uj, vjsuch that ujand vj are on the reachability paths of uiand virespectively.

C3

C5

C1

R1

R2

C2

C4

Aligned Entities

Backward Reachability

Path

C2

C4

C1

R1

R2

Forward Reachability

Path

C5

Ferhat Ay

problem statement
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.

Ferhat Ay

slide10

Pairwise Similarities

(Homology of Entities)

Ferhat Ay

pairwise similarities homology
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)

Ferhat Ay

pairwise similarities
Pairwise Similarities

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) )

  • Reaction Similarity

(SimR)

C1

C3

R1

C2

E1

E2

C5

C4

R2

C6

C7

E3

Ferhat Ay

slide13

Topological Similarity

(Topology of Pathways)

Ferhat Ay

neighborhood graphs
Neighborhood Graphs

C1

R1

C4

C8

C2

C6

E1

R3

R4

C9

C3

C5

C7

E3

R2

E2

Reactions

Enzymes

Compounds

C1

R1

C4

C6

C8

R3

R4

E1

E2

E3

C2

R2

C5

C7

C9

C3

Ferhat Ay

topological similarities
Topological Similarities

|R| = 4

BN (R3)= {R1,R2}

FN (R3)= {R4}

BN (R3)= {R1}

FN (R3)= {R4,R5}

R1

R3

R4

AR [R3 ,R3][R2,R1] = 1 = 1

2*1 + 1*2 4

R2

R4

(|R| |R| ) x (|R| |R| ) = 16 x 16

AR matrix

R1

R3

R5

|R| = 4

Ferhat Ay

problem formulation
Problem Formulation

Iteration 1: Support of aligned first degree neighbors added

Iteration 2: Support of aligned second degree neighbors added

Iteration 3: Support of aligned third degree neighbors added

Iteration 0: Only pairwise similarity of R3 and R3

R1

R4

R6

R1

R3

R3

R2

R8

R2

R5

R7

R8

R5

R7

Focus on R3 – R3 matching

Ferhat Ay

slide17

Problem Formulation

Initial Reaction

Similarity Matrix

HR0Vector

HRsVector

Final Reaction

Similarity Matrix

0.5

1.0

0.4

0.3

0.6

0.9

0.5

0.5

0.6

0.9

0.5

0.5

0.6

0.9

0.5

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

0.8

0.3

0.5

0.8

0.8

0.1

1.0

0.2

0.9

0.1

1.0

0.2

0.9

0.3

0.5

0.8

0.8

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

Ferhat Ay

max weight bipartite matching
Max Weight Bipartite Matching
  • Six Possible Orderings
    • ONLY 3 ARE UNIQUE
      • Reactions First
      • Enzymes First
      • Compounds First
  • R First Pruning

Consistency

Assured !

Weighted Edges

Aligned Entities

C1

E1

C1

Inconsistent Edges

R1

R1

E1

C2

C2

E2

R2

R2

E2

C3

C3

R3

R3

E3

C4

Ferhat Ay

alignment score simp
Alignment Score ( SimP )

0 =< SimP <= 1

SimP =1 for identical pathways

SimP= bSim(C1) + Sim(C2) +Sim(C4) + (1 – b)Sim(E1) + Sim(E2)

3 2

C2

C4

C1

R1

R2

C3

C5

C2

C4

C1

R1

R2

E1

E2

C5

E1

E2

Ferhat Ay

outline1
Outline
  • Graph Model of Pathways
  • Consistency of an Alignment
  • Homological & Topological Similarities
  • Eigenvalue Problem
  • Similarity Score
  • Experimental Results

Ferhat Ay

impact of alpha
Impact of Alpha
  • = 0 : Only pairwise similarities of entities - No iterations
  • = 1 : Only topology of the graphs

a = 0.7 is good !

Ferhat Ay

alternative entities paths
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

Ferhat Ay

phylogeny prediction
Phylogeny Prediction

Deuterostomia

Thermoprotei

Archaea

Our

Prediction

NCBI

Taxonomy

Eukaryota

Ferhat Ay

running time
Running Time

Ferhat Ay

thank you

Thank YOu

For source code and more information:

www.cise.ufl.edu/~fay

Ferhat Ay

appendix

Appendix

Ferhat Ay

challanges1
Challanges

NO Abstraction

Abstraction

Pathway 1

Pathway 1 Abstracted

E1

E2

E3

E1

E2

E3

C1

C3

C2

C4

E4

E4

  • Alignment Problem is NP Complete !

Pathway 2

Pathway 2 Abstracted

E1

E2

E3

E1

E2

E3

C1

C3

- Where are the compounds?

- E1  C1  E2

or

E1  C2  E2 ?

Abstraction is a Problem!

Ferhat Ay