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Funneled Landscape Leads to Robustness of Cellular Networks: MAPK Signal Transduction

Jin Wang ^* , Bo Huang , Xuefeng Xia  and Zhirong Sun 

^* Department of Chemistry and Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794; State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin, 130022, People's Republic of China; and Department of Biological Science and Biotechnology, Ministry of Education Key Laboratory of Bioinformatics, Tsinghua University, Beijing, 100084, People's Republic of China

Correspondence: Address reprint requests and inquiries to Jin Wang, E-mail: jin.wang.1{at}stonybrook.edu; or to Zhirong Sun, E-mail: sunzhr{at}mail.tsinghua.edu.

We uncover the underlying potential energy landscape for a cellular network. We find that the potential energy landscape of the mitogen-activated protein-kinase signal transduction network is funneled toward the global minimum. The funneled landscape is quite robust against random perturbations. This naturally explains robustness from a physical point of view. The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network. Funneled landscape is a realization of the Darwinian principle of natural selection at the cellular network level. It provides an optimal criterion for network connections and design. Our approach is general and can be applied to other cellular networks.

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