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Young-Rae Cho, Woochang Hwang, Murali Ramanathan and Aidong Zhang

Assessing Hierarchical Modularity in Protein Interaction Networks. Young-Rae Cho, Woochang Hwang, Murali Ramanathan and Aidong Zhang State University of New York at Buffalo. Scale-free & Modular Networks. Scale-free Networks

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Young-Rae Cho, Woochang Hwang, Murali Ramanathan and Aidong Zhang

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  1. Assessing Hierarchical Modularityin Protein Interaction Networks Young-Rae Cho, Woochang Hwang, Murali Ramanathan and Aidong Zhang State University of New York at Buffalo

  2. Scale-free & Modular Networks • Scale-free Networks • Power Law degree distribution4,1: P(k) ~ k –γ with 2 < γ < 3 • Disassortativity4,1,5 • Frequent connections between a hub and a peripheral node • Infrequent connections between two hubs • Small-world property11,1: Average geodesic path length l ~ loglogN • Modular Networks3,8,1 Bridges Bridging Nodes

  3. Bridge Measurement • Global Measurement • Betweenness Centrality7: • Local Measurement • Clustering Coefficient11: • Neighbor Significance: , • Similarity of Nodes: • Combined Bridge Measurement • Bridging Nodes: • Bridges:

  4. Hierarchical Modularization • Constraint • ∆C = C(G) – C(G’) ≥ 0 if v is a bridging node where V’ = V – {v} C(G): Average clustering coefficient of the nodes in graph G. C(G’): Average clustering coefficient of the nodes in the reduced graph G’, in which v with the highest BR(v) is removed. • Algorithm Successive Removal of Bridging Nodes Successive Removal of Bridges if ∆C< 0 No if G is split into Gi’ G Gi’ > θsize Gi’ Yes if G is split into Gi’ Replace each Gi’ to G

  5. Topological Analysis • Data: Core protein interaction data of Saccharomyces cerevisiae from DIP10,2 • Method: Remove v with the highest BR(v) and compute C(G), iteratively. • Results: • I & II (~ 30%): Bridging and interconnecting node removal zone. • III (~ 30%): Core node removal zone. • IV (~ 40%): Peripheral node removal zone.

  6. Biological Analysis • Data: Core protein interaction data of Saccharomyces cerevisiae from DIP10,2 • Method: Remove a set S of nodes v with the highest BR(v) and compute the proportion of lethal proteins in S, iteratively. • Results: • Bridging and interconnecting nodes are less lethal than core nodes. • Bridging and interconnecting nodes are more lethal than peripheral nodes.

  7. Modularization Results 6,9

  8. References Barabasi, A.-L. and Oltvai, Z. N., Nature Reviews: Genetics (2004) Dean, C. M., Salwinski, L., Xenarios, I. and Eisenberg, D., Molecular and Cellular Proteomics (2002) Hartwell, L. H., Hopfield, J. J., Leibler, S. and Murray, A. W., Nature (1999) Jeong, H., Mason, S. P., Barabasi, A.-L. and Oltvai, Z. N., Nature (2001) Maslov, S. and Sneppen, K., Science (2002) Mewes, H. W., at al., Nucleic Acid Research (2006) Newman, M. E. J., Physical Review E (2001) Ravasz, E., Somera, A. L., Mongru, D. A., Oltvai, Z. N. and Barabasi, A.-L., Science (2002) Ruepp, A., at al., Nucleic Acid Research (2004) Salwinski, L., at al., Nucleic Acid Research (2004) Watts, D. J. and Strogatz, S. H., Nature (1998)

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