Transittability of complex networks and its applications to regulatory biomolecular networks.
We have often observed unexpected state transitions of complex systems. We are thus interested in how to steer a complex system from an unexpected state to a desired state. Here we introduce the concept of transittability of complex networks, and derive a new sufficient and necessary condition for state transittability which can be efficiently verified. We define the steering kernel as a minimal set of steering nodes to which control signals must directly be applied for transition between two specific states of a network, and propose a graph-theoretic algorithm to identify the steering kernel of a network for transition between two specific states. We applied our algorithm to 27 real complex networks, finding that sizes of steering kernels required for transittability are much less than those for complete controllability. Furthermore, applications to regulatory biomolecular networks not only validated our method but also identified the steering kernel for their phenotype transitions.
1] Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada [2] Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada.
Fang-Xiang
FX
Wu
Division of Biomedical Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada.
Lin
L
Wu
School of Information Science and Engineering, Central South University, Changsha, Hunan, China.
Jianxin
J
Wang
School of Computer, Wuhan University, Wuhan, Hubei, China.
Juan
J
Liu
1] Key Laboratory of Systems Biology, Shanghai Institutes for Biological Science, Chinese Academy Science, Shanghai 200031, China [2] Collaborative Research Center for Innovative Mathematical Modelling, Institute of Industrial Science, University of Tokyo, Tokyo153-8505, Japan.
Luonan
L
Chen
D000465:Algorithms; D002453:Cell Cycle; D002454:Cell Differentiation; D019295:Computational Biology / Q000379:methods*; D004249:DNA Damage; D058750:Epithelial-Mesenchymal Transition / Q000235:genetics; D005786:Gene Expression Regulation; D053263:Gene Regulatory Networks; D006801:Humans; D008954:Models, Biological; D015398:Signal Transduction; D006377:T-Lymphocytes, Helper-Inducer / Q000276:immunology / Q000378:metabolism; D016159:Tumor Suppressor Protein p53 / Q000378:metabolism; D015003:Yeasts / Q000235:genetics / Q000378:metabolism
D016159:Tumor Suppressor Protein p53