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Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior

Chaos 19, 033109 (2009); doi:10.1063/1.3187790

Published 24 July 2009

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Qingdao Huang and Hong Qian
Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA and College of Mathematics, Jilin University, Changchun 130012, People's Republic of China
We establish a mathematical model for a cellular biochemical signaling module in terms of a planar differential equation system. The signaling process is carried out by two phosphorylation-dephosphorylation reaction steps that share common kinase and phosphatase with saturated enzyme kinetics. The pair of equations is particularly simple in the present mathematical formulation, but they are singular. A complete mathematical analysis is developed based on an elementary perturbation theory. The dynamics exhibits the canonical competition behavior in addition to bistability. Although widely understood in ecological context, we are not aware of a full range of biochemical competition in a simple signaling network. The competition dynamics has broad implications to cellular processes such as cell differentiation and cancer immunoediting. The concepts of homogeneous and heterogeneous multisite phosphorylation are introduced and their corresponding dynamics are compared: there is no bistability in a heterogeneous dual phosphorylation system. A stochastic interpretation is also provided that further gives intuitive understanding of the bistable behavior inside the cells. ©2009 American Institute of Physics
History: Received 20 April 2009; accepted 6 July 2009; published 24 July 2009
Permalink: http://link.aip.org/link/?CHAOEH/19/033109/1
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1054-1500 (print)   1089-7682 (online)
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