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Bioinformatics 2008 24(13):i241-i249; doi:10.1093/bioinformatics/btn163
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© 2008 The Author(s)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Biomolecular network motif counting and discovery by color coding

Noga Alon 1, Phuong Dao 2, Iman Hajirasouliha 2, Fereydoun Hormozdiari 2 and S. Cenk Sahinalp 2,*

1Schools of Mathematical Sciences and Computer Science, Tel Aviv University, Ramat Aviv, Israel and 2School of Computing Science, Simon Fraser University, Burnaby, BC, Canada

*To whom correspondence should be addressed.


  Abstract

Protein–protein interaction (PPI) networks of many organisms share global topological features such as degree distribution, k-hop reachability, betweenness and closeness. Yet, some of these networks can differ significantly from the others in terms of local structures: e.g. the number of specific network motifs can vary significantly among PPI networks.

Counting the number of network motifs provides a major challenge to compare biomolecular networks. Recently developed algorithms have been able to count the number of induced occurrences of subgraphs with k≤ 7 vertices. Yet no practical algorithm exists for counting non-induced occurrences, or counting subgraphs with k≥ 8 vertices. Counting non-induced occurrences of network motifs is not only challenging but also quite desirable as available PPI networks include several false interactions and miss many others.

In this article, we show how to apply the ‘color coding’ technique for counting non-induced occurrences of subgraph topologies in the form of trees and bounded treewidth subgraphs. Our algorithm can count all occurrences of motif G' with k vertices in a network G with n vertices in time polynomial with n, provided k=O(log n). We use our algorithm to obtain ‘treelet’ distributions for k≤ 10 of available PPI networks of unicellular organisms (Saccharomyces cerevisiae Escherichia coli and Helicobacter Pyloris), which are all quite similar, and a multicellular organism (Caenorhabditis elegans) which is significantly different. Furthermore, the treelet distribution of the unicellular organisms are similar to that obtained by the ‘duplication model’ but are quite different from that of the ‘preferential attachment model’. The treelet distribution is robust w.r.t. sparsification with bait/edge coverage of 70% but differences can be observed when bait/edge coverage drops to 50%.

Contact:cenk{at}cs.sfu.ca


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