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NJIT Mathematical Biology Seminar

Tuesday, November 13, 2007, 4:00pm
Cullimore Hall 611
New Jersey Institute of Technology

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Topology and dynamics of cyclic motifs in directed complex networks

Gustavo Stolovitzky

IBM Computational Biology Center and Biomed Informatics, Columbia University

Structure-function relationships of biological and engineered systems can be studied by representing them as directed graphs and identifying network motifs. Finding large-scale motifs may provide insight into how small motifs are assembled into larger units. A parallelized motif search program that ran on IBMb\200\231s BlueGene supercomputer to search for large-size cycles and characterize their topological and statistical properties was used to study six biological and three technological systems abstracted to directed graphs. The statistical properties of the ensemble of cycles are captured by a simple spin system model which favors a tendency of subsequent edges in a cycle to have opposite directions ("anti-ferromagnetic" order). This order can be explained only in part by the observation that most highly connected nodes are almost exclusively input or output hubs. We found, however, non-local contributions to this anti-ferromagnetism. A consequence of the anti-ferromagnetic order is a reduction of the number of feedback loops and long pathways. We show that networks abundant with source or sink nodes and reduced number of feedback loops may contribute to dynamic stability and modularity.