Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 105; no. 49; pp. 19235 - 19240
• Main Authors: Ma'ayan, Avi, Cecchi, Guillermo A, Wagner, John, Rao, A. Ravi, Iyengar, Ravi, Stolovitzky, Gustavo
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 09-12-2008; National Acad Sciences
• Subjects: Animals; Aviation; Biological Sciences; Biophysics - methods; Brain; Brain Mapping; Caenorhabditis elegans - physiology; Computer Simulation; Connectivity; Control loops; Dynamic stability; Ecology; Engineering - methods; Escherichia coli - physiology; Feedback control systems; Feedback, Physiological; Ferric Compounds; Food Chain; Gene Regulatory Networks; Hyperlinks; Internet; Loops; Magnetization; Models, Biological; Network topologies; Physical Sciences; Random allocation; Saccharomyces cerevisiae - physiology; Signal Transduction; Studies; Supercomputers; Topological properties; Topology; Yeasts
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.0805344105

Representation and analysis of complex biological and engineered systems as directed networks is useful for understanding their global structure/function organization. Enrichment of network motifs, which are over-represented subgraphs in real networks, can be used for topological analysis. Because counting network motifs is computationally expensive, only characterization of 3- to 5-node motifs has been previously reported. In this study we used a supercomputer to analyze cyclic motifs made of 3-20 nodes for 6 biological and 3 technological networks. Using tools from statistical physics, we developed a theoretical framework for characterizing the ensemble of cyclic motifs in real networks. We have identified a generic property of real complex networks, antiferromagnetic organization, which is characterized by minimal directional coherence of edges along cyclic subgraphs, such that consecutive links tend to have opposing direction. As a consequence, we find that the lack of directional coherence in cyclic motifs leads to depletion in feedback loops, where the number of nodes affected by feedback loops appears to be at a local minimum compared with surrogate shuffled networks. This topology provides more dynamic stability in large networks.