Structural properties of the MAPK pathway topologies in PC12 cells
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J. Math. Biol. DOI 10.1007/s00285-012-0606-x
Structural properties of the MAPK pathway topologies in PC12 cells Elisa Franco · Franco Blanchini
Received: 24 November 2011 / Revised: 12 September 2012 © Springer-Verlag Berlin Heidelberg 2012
Abstract In this paper we propose and analyze parameter-free models for the mitogen-activated protein kinase (MAPK) pathway in PC12 rat neural cells. Experiments show that the dynamic behavior of this pathway depends on the input growth factor. The response to epidermal growth factor (EGF) is a short peak followed by a relaxation, while the response to nerve growth factor (NGF) is sustained. In the latter case, the system can be driven to a new state, which persists after the stimulus has vanished. Ultimately, these dynamic behaviors correspond to different cell fates: EFG stimulation induces proliferation, while NGF stimulation induces differentiation. The biochemical mechanisms responsible for the different input-dependent dynamic response are still unclear. One hypothesis is that each input generates a specific interaction topology among the kinases. Starting from experimental results that support this hypothesis, we derive and analyze qualitative models for the two network topologies. Our approach is based on invariant set theory and non-smooth Lyapunov functions. We demonstrate analytically that the network behaviors and stability properties are structurally dependent on the topology, and do not depend on specific parameter values of the underlying biochemical interactions. Keywords
MAPK pathway · Robustness · Lyapunov methods · Invariant sets theory
Mathematics Subject Classification
93D05 · 93D09 · 34C45 · 34C12
E. Franco (B) Department of Mechanical Engineering, University of California at Riverside, 900 University Avenue, Riverside, CA 92521, USA e-mail: [email protected] F. Blanchini Dipartimento di Matematica ed Informatica, Università degli Studi di Udine, Via delle Scienze 206, 33100 Udine, Italy e-mail: [email protected]
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E. Franco, F. Blanchini
1 Introduction Mitogen-activated protein kinases (MAPK) are proteins that respond to the binding of growth factors to cell surface receptors, propagating the signal to the nucleus. The pathway consists of three enzymes, MAP kinase (MAP1K, also known as extracellular signal regulated kinase, or ERK), MAP kinase kinase (MAP2K) and MAP kinase kinase kinase (MAP3K). These proteins are activated in series: mitogens binding to the cell surface activate, through double phosphorylation, MAP3K; in turn MAP3K activates MAP2K (again through two phosphorylation steps); finally, MAP2K activates MAP1K, which triggers gene expression events in the cell nucleus. MAP1K can be considered the cascade output. This pathway is conserved across a large number of living organisms, and regulates in particular cell growth, differentiation and survival/death (Robinson and Cobb 1997; Johnson and Lapadat 2002; Kholodenko and Birtwistle 2009). Mutations in the MAPK cascade have been linked to several types of genetic syndromes and canc
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