Robustness analysis of EGFR signaling network with a multi-objective evolutionary algorithm.

Robustness, the ability to maintain performance in the face of perturbations and uncertainty, is believed to be a necessary property of biological systems. In this paper, we address the issue of robustness in an important signal transduction network--epidermal growth factor receptor (EGFR) network. First, we analyze the robustness in the EGFR signaling network using all rate constants against the Gauss variation which was described as "the reference parameter set" in the previous study [Kholodenko, B.N., Demin, O.V., Moehren, G., Hoek, J.B., 1999. Quantification of short term signaling by the epidermal growth factor receptor. J. Biol. Chem. 274, 30169-30181]. The simulation results show that signal time, signal duration and signal amplitude of the EGRR signaling network are relatively not robust against the simultaneous variation of the reference parameter set. Second, robustness is quantified using some statistical quantities. Finally, a multi-objective evolutionary algorithm (MOEA) is presented to search reaction rate constants which optimize the robustness of network and compared with the NSGA-II, which is a representation of a class of modern multi-objective evolutionary algorithms. Our simulation results demonstrate that signal time, signal duration and signal amplitude of the four key components--the most downstream variable in each of the pathways: R-Sh-G-S, R-PLP, R-G-S and the phosphorylated receptor RP in EGRR signaling network for the optimized parameter sets have better robustness than those for the reference parameter set and the NSGA-II. These results can provide valuable insight into experimental designs and the dynamics of the signal-response relationship between the dimerized and activated EGFR and the activation of downstream proteins.