Large Scale Metabolic NetworkAlignments by Compression

Michael Dang, Ferhat Ay, Tamer Kahveci

ACM-BCB 2011

Bioinformatics Lab.

University of Florida

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Network Alignment

Bayati et al. ICDM 2009

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Metabolic Network Alignment

Network Alignment

Alignment with

Heterogeneous Entities

Subnetwork

Mappings

Functional Similarity

of Reactions

Querying Network

databases

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Existing Work Heymans et al. (2003) – Undirected, Hierarchical Enzyme

Similarity

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

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

Dost et al. (2007) – QNET, Color Coding, Tree queries of size

at most 9

Kuchaiev et al. (2010) – GRAAL, Solely Based on

Network Topology

Ay et al. (2011) – SubMAP, Considers Subnetwork

Mappings

Shih et al. – Next Talk!

Clustering of input networks is necessary for aligning

large networks

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Alignment Phase - SubMAP

Ay et. al., RECOMB 2010, JCB

2011

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Performance Bottleneck

30 minutes2 Gigabytes

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Alignment with Compression

Compress Align

Refine

Ferhat Ay

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Alignment with/without compression

Without Compression

With Compression

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Outline of the method

• Compression Phase

• Minimum Degree Selection (MDS) method

• Optimality analysis

• Alignment Phase

• Refinement Phase

• Overall Complexity

• How Much Should We Compress?

• Experimental Results

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Compression PhaseOriginal Network

Encapsulated View

Compressed Network

What Alignment Algorithm Sees

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MDS – Minimum Degree Selection

Before AfterAfter

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Overall Compression

…………Level 1

Level 2

Step 1 Step 2 Step i

Level c

…………

……

……

…….…

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Optimality Condition for MDS

Optimal? Minimum Degree Node

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Optimality Condition for MDS

Minimum Degree Node

Optimal?

- Can be optimal- At most one node away

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How Far Away We Are from Optimal Compression?

“How far is our compressionmethod from the optimal compression?”

Number of compression steps for the optimal compression and MDS

Sizes of the compressed networks for the optimal compression and MDS

By the inequality

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Alignment PhaseNetwork 1

Network 2

Alignment

Compressed Network 1

Compressed Network 2

Network Alignment Algorithm

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Refinement Phase

Alignment Algorithm

Refine

Refined Alignment

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Complexity Analysis Compression Phase:

Alignment Phase:

Refinement Phase:

Overall Complexity (with compression):

Complexity of SubMAP (without compression):

k = largest subnetwork sizec = compression leveln, m = sizes of networks

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How much should we compress?

Examplesn=20, m=20, k=2 c ~ 1.37

n=20, m=80, k=1 c ~ 2.11

n=80, m=80, k=2 c ~ 2.15

n=200, m=400, k=1 c ~ 3.11

Experimental Results

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To compress or not to compress?

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Compression Rates in Practice

KEGG Metabolic Networks with sizes ranging from 10 to 279

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What Do We Gain by Compression?

Subnetwork size k=1Subnetwork size k=2

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What Do We Lose by Compression?

k/c 1 2 3

1 0.89 0.56 0.53

2 0.85 0.58 0.50

3 0.84 0.57 0.49

Correlation of mappings scores found by

compressed

alignment with the ones found by SubMAP

Conclusions

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We developed a scalable compression technique with optimality bounds.

Our method respects network topology while aligning the networks unlike clustering-based methods.

It provides significant improvement on resource utilization of existing network alignment algorithms.

Ferhat Ay

Future Directions

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Improving the scale of alignment to genome-wide metabolic networks (without initial clustering).

Evaluating the performance of our compression technique on PPI networks.

Improving the accuracy of compressed alignment w.r.t original alignment for larger levels of compression.

Integrating our compression framework with other existing network alignment methods.

Ferhat Ay

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Tamer Kahveci

Michael DangNSF IIS-0845439

NSF CCF-0829867

Acknowledements

Computing Innovation Fellow

University of Washington

Department of Genome Sciences

http://cifellows.org/http://www.gs.washington.edu/

http://noble.gs.washington.edu/~wnoble/

A bit of advertisement

THANK YOU.

QUESTIONS?

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APPENDIX

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