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SubMAP Aligning metabolic pathways with subnetwork mappings. Ferhat Ay , Tamer Kahveci RECOMB 2010. Bioinformatics Lab. University of Florida. What is Pathway Alignment?. R4. R6. R1. R3. R8. Pathway1. R2. R5. R7. Alignment. R3. R5. R1. Pathway2. R2. R7. R4. R6.

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SubMAP Aligning metabolic pathways with subnetwork mappings

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Submap aligning metabolic pathways with subnetwork mappings

SubMAP

Aligning metabolic pathways

with subnetwork mappings

Ferhat Ay, Tamer Kahveci

RECOMB 2010

Bioinformatics Lab.

University of Florida


Submap aligning metabolic pathways with subnetwork mappings

What is Pathway Alignment?

R4

R6

R1

R3

R8

Pathway1

R2

R5

R7

Alignment

R3

R5

R1

Pathway2

R2

R7

R4

R6

  • Global Alignment is GI-Complete

  • Local Alignment is NP-Complete


Submap aligning metabolic pathways with subnetwork mappings

Existing Methods

  • Heymans et al. Bioinformatics (2003) – Undirected, Hierarchical Enzyme Similarity

  • Clemente et al.Genome Informatics(2005) – Gene Ontology Similarity of Enzymes

  • Pinter et al. Bioinformatics (2005) – Directed,Only Multi-Source Trees

  • Singh et al. RECOMB (2007) – PPI Networks, Sequence Similarity

  • Dost et al. RECOMB (2007) – QNET, Color Coding, Tree queries of size at most 9

  • Cheng et al. Bioinformatics (2009) – MetNetAligner, Allows insertions & deletions

  • PROBLEMS

    • Restriction of one-to-one Mappings

    • Similarity of Biological Functions

    • Topology Restrictions


Submap aligning metabolic pathways with subnetwork mappings

Different Paths, Same Function

E. Coli

A. thaliana


Submap aligning metabolic pathways with subnetwork mappings

One-to-many (Subnetwork) Mappings

  • Biologically Relevant

  • Frequently Observed in Nature

  • Characterize Similarity

  • CHALLENGES

  • Exponential Number of Subnetworks

  • Defining Similarity Between Subnetworks

  • Overlapping Mappings (Consistency)


Submap aligning metabolic pathways with subnetwork mappings

Outline

Enumerating Subnetworks

Homological Similarity

Topological Similarity

One-to-one

Mapping

Subnetwork

Mappings

One-to-one

Mapping

Subnetwork

Mappings

Combining

Homology & Topology

Extracting Mappings


Submap aligning metabolic pathways with subnetwork mappings

Enumeration of Subnetworks

1

5

6

3

2

4

R1

1

2

3

4

5

6

R2

1,3

2,3

3,4

3,5

5,6

R3

1,2,3

1,3,4

1,3,5

2,3,4

2,3,5

3,4,5

3,5,6


Submap aligning metabolic pathways with subnetwork mappings

  • Homological Similarities (1-to-1)

Enzyme Similarity (SimE)

  • Hierarchical Enzyme Similarity – Webb EC.(2002)

  • Information-Content Enzyme Similarity – Pinter et al.(2005)

  • Gene Ontology Similarity of Enzymes– Clemente et al.(2003)

    Compound Similarity (SimC)

  • Identity Score for compounds

  • SIMCOMP Compound Similarity –

  • Hattori et al.(2003)

  • Reaction Similarity (SimR)

    • Defined in terms of SimE and SimC

  • L-Aspartate

    L-Lysine


    Submap aligning metabolic pathways with subnetwork mappings

    Homological Similarities(Subnetworks)

    Input

    compounds

    enzymes

    Output

    compounds

    Subnetwork1

    • (s1)

    Input

    compounds

    enzymes

    Output

    compounds

    Subnetwork2

    • (s2)

    Sim(s1,s2) = w1MWBM(inputs) + w2MWBM(enzymes) + w3MWBM(outputs)


    Submap aligning metabolic pathways with subnetwork mappings

    • Topological Similarities (1-to-1)

    |R| = 4

    BN (R3)= {R1,R2}

    FN (R3)= {R4}

    BN (R3)= {R1}

    FN (R3)= {R4,R5}

    R1

    R3

    R4

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

    2*1 + 1*2 4

    R2

    R4

    R1

    R3

    R5

    |R| = 4

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


    Submap aligning metabolic pathways with subnetwork mappings

    Topological Similarities (Subnetworks)

    4

    7

    1

    5

    1

    5

    6

    3

    2,3

    5,7

    2

    4

    Si

    Si

    5,6

    Pathway 1

    5,6,7

    Backward & Forward neighbors

    Support matrix

    S'j

    {Si,S'j}

    Pathway 2

    1

    FN(Si)FN(S'j)+BN(Si)BN(S'j)


    Submap aligning metabolic pathways with subnetwork mappings

    Outline

    Enumerating Subnetworks

    Homological Similarity

    Topological Similarity

    One-to-one

    Mapping

    Subnetwork

    Mappings

    One-to-one

    Mapping

    Subnetwork

    Mappings

    Combining

    Homology & Topology

    Extracting Mappings


    Submap aligning metabolic pathways with subnetwork mappings

    Combining Homology & topology

    Hk+1= αAHk+ (1-α)H0

    Iteration 1: Support of aligned first degree neighbors added

    Iteration 2: Support of aligned second degree neighbors added

    Iteration 0: Only pairwise similarity of R3 and R3

    Iteration 3: Support of aligned third degree neighbors added

    R1

    R4

    R6

    R1

    R3

    R3

    R2

    R8

    R2

    R5

    R7

    R8

    R5

    R7

    Focus on R3 – R3 matching


    Submap aligning metabolic pathways with subnetwork mappings

    Combining Homology & topology

    Hk+1= αAHk+ (1-α)H0

    InitialSimilarity

    Matrix

    H0Vector

    HkVector

    FinalSimilarity

    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

    0.3

    0.5

    0.8

    0.8

    0.1

    1.0

    0.2

    0.9

    0.5

    1.0

    0.4

    0.3

    0.3

    0.5

    0.8

    0.8

    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


    Submap aligning metabolic pathways with subnetwork mappings

    Extracting Mappings (1-to-1)

    R1 R2 R3

    R1

    R1

    R1

    R2

    R3

    R4

    0.8

    0

    0.4

    0

    0.3

    1.0

    0

    0.5

    0

    0

    0.6

    0.9

    R2

    R2

    R3

    R3

    R4

    Maximum Weight Bipartite Matching


    Submap aligning metabolic pathways with subnetwork mappings

    Extracting Mappings (Subnetworks)

    1,2

    1

    1,2

    1

    Conflicts With

    1

    2

    1

    2

    3

    1

    4

    3,4,5

    4

    3,4,5

    Conflicts With

    4,5

    5

    4,5

    5

    Maximum bipartite matching will fail!


    Submap aligning metabolic pathways with subnetwork mappings

    How to Handle Conflicts?

    Label

    Mapping

    Weight

    Conflict Graph

    a

    1,2

    1

    0.7

    b

    1

    2

    0.6

    c

    3

    1

    0.4

    d

    4

    3,4,5

    0.9

    Find the set of non-conflicting mappings that maximizes the sum of sum of similarity scores.

    e

    4,5

    5

    0.8

    Subnetwork from pathway 1

    Subnetwork from pathway 2


    Submap aligning metabolic pathways with subnetwork mappings

    Maximum Weight Independent Set Problem

    • Given an undirected vertex weighted

    • graph find a vertex induced subgraph

    • That maximizes the sum of the vertex

    • weights (maximum weight)

    • That has no edges (independent set)

    • NP-Hard – Karp, 1972

    • Hard to approximate – Hastad, 1996

    • (There is no PTAS unless P=NP)

    9+8+2+0 = 19


    Submap aligning metabolic pathways with subnetwork mappings

    Finding the Best Alignment is NP-Hard

    MWIS problem in bounded degree

    graphs with max degree k+1

    Metabolic pathway alignment with

    subnetworks of size at most k


    Submap aligning metabolic pathways with subnetwork mappings

    How do we find the mappings?

    Label

    Mapping

    Weight

    Conflict Graph

    a

    1,2

    1

    0.7

    b

    1

    2

    0.6

    c

    3

    1

    0.4

    f(a) = 0.7

    • f(b) = 0.6/0.7

    • f(c) = 0.4/0.7

    • f(d) = 0.9/0.8

    • f(e) = 0.8/0.9

    f(a) = 0.7

    • f(b) = 0.6/0.7

    • f(c) = 0.4/0.7

    Alignment

    d

    4

    3,4,5

    0.9

    Choose the vertex v that maximizes

    w(v)

    f(v) =

    e

    4,5

    5

    0.8

    ∑u in N(v)w(u)


    Submap aligning metabolic pathways with subnetwork mappings

    EXPERIMENTAL

    RESULTS


    Submap aligning metabolic pathways with subnetwork mappings

    Alternative paths -1


    Submap aligning metabolic pathways with subnetwork mappings

    Comparison

    MetNetAligner: Cheng & Zelikovsky, Bioinformatics 2009.

    SubMAP: Ay & Kahveci, RECOMB 2010.


    Submap aligning metabolic pathways with subnetwork mappings

    Alternative paths - 2


    Submap aligning metabolic pathways with subnetwork mappings

    Alternative paths - 3


    Submap aligning metabolic pathways with subnetwork mappings

    Alternative paths - 4


    Submap aligning metabolic pathways with subnetwork mappings

    Mappings among major clades


    Submap aligning metabolic pathways with subnetwork mappings

    Number of subnetworks


    Submap aligning metabolic pathways with subnetwork mappings

    Performance of our algorithm

    k : maximum size of subnetwork


    Submap aligning metabolic pathways with subnetwork mappings

    Conclusion

    • Considering subnetworks improves the accuracy of metabolic pathway alignment and allows revealing alternative paths that are biologically relevant

    • Alignments within and across the clades have different characteristics in terms of their mapping cardinalities.

    • SubMAP can be effectively used for applications where identifying different entity sets with same/similarfunctions is necessary. e.g.: filling pathway holes and metabolic/phylogenic reconstruction.


    Submap aligning metabolic pathways with subnetwork mappings

    Obrigado


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