Ferhat Ay, Tamer Kahveci

& Valerie de-Crecy Lagard

04/21/23 1Ferhat Ay

www.cise.ufl.edu/~fay

Metabolic Pathways

04/21/23 2Ferhat Ay

What and Why?

04/21/23 3Ferhat Ay

Metabolic Pathway AlignmentFinding a mapping of the entities of the pathways

C2

C3

C4

C5

R1 R2C1

E1 E2

C2 C4R1 R2C1

C5

E1 E2

Applications○ Drug Target Identification○ Metabolic Reconstruction○ Phylogeny Prediction

Challanges

04/21/23 4Ferhat Ay

E1 E2 E3

E4

E1 E2 E3

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) ….

Abstraction is a problem !

E1 C1

C2

E2 C3

C4

E3

E4

E1 C1 E2 C3 E3- Where are the compounds?

- E1 C1 E2 or E1 C2 E2 ?

Pathway Alignment is hard !

Abstraction

Outline

04/21/23 5Ferhat Ay

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

Non-Redundant Graph Model

04/21/23 6Ferhat Ay

Pyruv.

1.2.4.1

Lip-EThPP

R0014

S-Ac 2-ThP A-CoADi-hy

R7618R3270

R2569

2.3.1.12

1.8.1.4

Consistency

04/21/23 7Ferhat Ay

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

R1 R2 C1 C2

R1C1

2- The overall mapping should be 1-1

R1R2

R3

Consistency

04/21/23 8Ferhat Ay

C3

C2

C5

C4

R1 R2C1

C2 C4R1 R2C1

C5

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.

Aligned Entities

Backward Reachability Path

Forward Reachability Path

Problem Statement

04/21/23 9Ferhat Ay

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.

04/21/23 10Ferhat Ay

Pairwise Similarities (Homology of Entities)

Pairwise Similarities (Homology)

04/21/23 11Ferhat Ay

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)

Pairwise Similarities

04/21/23 12Ferhat Ay

Reaction Similarity

(SimR)

E1

R1 C3

C1

C2

R2 C6C4

C7

C5

E2

E3

SimR (R1,R2) =

Enzymesmax ( 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) )

SimR (R1,R2) =

Enzymesmax ( 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) )

04/21/23 13Ferhat Ay

Topological Similarity (Topology of Pathways)

Neighborhood Graphs

04/21/23 14Ferhat Ay

C4

C5

C6

C7

R1

R2

C1

E2

R3 R4E1

E3C3

C2

C9

C8

E1 E2 E3

Enzymes

R2

R3R1

R4

ReactionsC1

C3

C2

C4

C5

C6

C7

C8

C9

Compounds

Topological Similarities

04/21/23 15Ferhat Ay

R2

R3

R1

R4

R1 R3

R4

R5

|R| = 4

|R| = 4

BN (R3)= {R1,R2}FN (R3)= {R4}

BN (R3)= {R1}FN (R3)= {R4,R5}

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

AR matrix

R1-R1 … R2-R1 … R4-R4 … R4-R5

....

R3 -R3 1 / 4 0 1 / 4 0 1 / 4 0 1 / 4

…..

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

2*1 + 1*2 4

Problem Formulation

04/21/23 16Ferhat Ay

R2

R3

R1 R4

R5

R6

R7R8

R3

R1

R2

R5 R7R8

Focus on R3 – R3 matching

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

1 0(1 )k kR R R RH A H H

******************************************

04/21/23 17Ferhat Ay

Initial ReactionSimilarity Matrix

HR0 Vector

0.11.00.20.9

0.30.50.80.8

0.51.00.40.3

HRs Vector Final Reaction

Similarity Matrix

0.21.00.40.6

0.20.30.60.9

0.60.90.50.5

Power MethodIterations

0.51.00.40.3

0.30.50.80.8

0.11.00.20.9

0.60.90.50.5

0.20.30.60.9

0.21.00.40.6

1 0(1 )k kR R R RH A H H

******************************************Problem Formulation

0.51.00.40.3

0.30.50.80.8

0.11.00.20.9

0.60.90.50.5

0.20.30.60.9

0.21.00.40.6

Max Weight Bipartite Matching

04/21/23 18Ferhat Ay

Six Possible OrderingsONLY 3 ARE UNIQUE

○ Reactions First○ Enzymes First ○ Compounds First

R First Pruning

R1

R2

R3

R1

R3

R2

C1 C1

C2

C3

C4

C2

C3

E1

E2

E3

E1

E2

Consistency Assured !

Weighted Edges

Aligned Entities

Inconsistent Edges

Alignment Score ( SimP )

04/21/23 19Ferhat Ay

C2

C3

C4

C5

R1 R2C1

C2 C4R1 R2C1

C5

0 =< SimP <= 1SimP =1 for identical pathways

SimP = Sim(C1) + Sim(C2) +Sim(C4) + (1 – Sim(E1) + Sim(E2) 3 2

E1E1

E2E2

Outline

04/21/23 20Ferhat Ay

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

Impact of Alpha

04/21/23 21Ferhat Ay

= 0Only pairwise similarities of entities - No iterations = 1 Only topology of the graphs

= 0.7 is good !

Alternative Entities & Paths

04/21/23 22Ferhat Ay

Kim J. et al. (2007)

Eukaryotes (e.g. H.Sapiens) Mevalonate PathBacterias (e.g. E.Coli) Non-Mevalonate Path

Kuzuyama T. et al. (2006)

Phylogeny Prediction

04/21/23 23Ferhat Ay

Thermoprotei

Eukaryota

Archaea

NCBI Taxonomy

Our Prediction

Deuterostomia

Effect Of Consistency Restriction

04/21/23 24Ferhat Ay

Running Time

04/21/23 25Ferhat Ay

04/21/23 Ferhat Ay 26

For source code and more information:

www.cise.ufl.edu/~fay

04/21/23 Ferhat Ay 27

Error Tolerance

04/21/23 28Ferhat Ay

Pylogenetic Reconstruction

04/21/23 29Ferhat Ay

Effect Of Consistency Restriction

04/21/23 30Ferhat Ay

Z-Score Calculation

04/21/23 31Ferhat Ay

E1 C1

C2

E2 C3

C4

E3

E4

Challanges

04/21/23 32Ferhat Ay

E1 E2 E3

E4

E1 C1 E2 C3 E3 E1 E2 E3

- Where are the compounds?

- E1 C1 E2 or E1 C2 E2 ?

Pathway 1

Pathway 2

Abstraction is a Problem!

Pathway 1 Abstracted

Pathway 2 Abstracted

NO Abstraction Abstraction

Alignment Problem is NP Complete !