Intrinsic noise, dissipation cost, and robustness of cellular networks: The underlying energy landscape of MAPK signal transduction

doi:10.1073/pnas.0708708105

Intrinsic noise, dissipation cost, and robustness of cellular networks: The underlying energy landscape of MAPK signal transduction

*Department of Chemistry, Physics, and Applied Mathematics, State University of New York, Stony Brook, NY 11794; and
^†State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China

Edited by José N. Onuchic, University of California at San Diego, La Jolla, CA, and approved January 31, 2008 (received for review September 13, 2007)

Abstract

We develop a probabilistic method for analyzing global features of a cellular network under intrinsic statistical fluctuations, which is important when there are finite numbers of molecules. By making a self-consistent mean field approximation of splitting the variables in order to reduce the large number of degrees of freedom, which is reasonable for a not very strongly interacting network, we discovered that the underlying energy landscape of the mitogen-activated protein kinases (MAPKs) signal transduction network (with experimentally measured or inferred parameters such as chemical reaction rate coefficients in the network) is funneled toward a global minimum characterized by the nonequilibrium steady-state fixed point of the system at the end of the signal transduction process. For this system, we also show that the energy landscape is robust against intrinsic fluctuations and random perturbation to the inherent chemical reaction rates. The ratio of the slope versus the roughness of the energy landscape becomes a quantitative measure of robustness and stability of the network. Furthermore, we quantify the dissipation cost of this nonequilibrium system through entropy production, caused by the nonequilibrium flux in the system. We found that a lower dissipation cost corresponds to a more robust network. This least dissipation property might provide a design principle for robust and functional networks. Finally, we find the possibility of bistable and oscillatory-like solutions, which are important for cell fate decisions, upon perturbations. The method described here can be used in a variety of biological networks.

Footnotes

^‡To whom correspondence should be addressed. E-mail: jin.wang.1{at}stonybrook.edu
Author contributions: J.W. designed research; S.L., B.H., and J.W. performed research; J.W. contributed new reagents/analytic tools; S.L., B.H., and J.W. analyzed data; and S.L. and J.W. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0708708105/DC1.