title: Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks.
abstract: 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.
authors.affiliation: Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, 1 Gustave Levy Place, New York, NY 10029, USA.
authors.forename: Avi
authors.initials: A
authors.lastname: Ma'ayan
authors.forename: Guillermo A
authors.initials: GA
authors.lastname: Cecchi
authors.forename: John
authors.initials: J
authors.lastname: Wagner
authors.forename: A Ravi
authors.initials: AR
authors.lastname: Rao
authors.forename: Ravi
authors.initials: R
authors.lastname: Iyengar
authors.forename: Gustavo
authors.initials: G
authors.lastname: Stolovitzky
mesh_terms: D000818:Animals; D001359:Aviation; D001703:Biophysics / Q000379:methods*; D001931:Brain Mapping; D017173:Caenorhabditis elegans / Q000502:physiology; D003198:Computer Simulation; D004463:Ecology; D004738:Engineering / Q000379:methods; D004926:Escherichia coli / Q000502:physiology; D025461:Feedback, Physiological; D005290:Ferric Compounds; D020387:Food Chain; D053263:Gene Regulatory Networks; D020407:Internet; D008954:Models, Biological; D012441:Saccharomyces cerevisiae / Q000502:physiology; D015398:Signal Transduction
chemical_list: D005290:Ferric Compounds; C001215:ferrite