Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks.
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.
Ma'ayan
Avi
A
Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, 1 Gustave Levy Place, New York, NY 10029, USA.
Cecchi
Guillermo A
GA
Wagner
John
J
Rao
A Ravi
AR
Iyengar
Ravi
R
Stolovitzky
Gustavo
G
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
D005290:Ferric Compounds; C001215:ferrite