The Mathematical Institute, University of Oxford, Eprints Archive

A mass action model of a fibroblast growth factor signaling pathway and its simplification

Gaffney, E. A. and Heath, J K and Kwiatkowska, M Z (2008) A mass action model of a fibroblast growth factor signaling pathway and its simplification. Bulletin of Mathematical Biology, 70 (8). pp. 2229-2263. ISSN n/a

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Abstract

We consider a kinetic law of mass action model for Fibroblast Growth Factor (FGF) signaling, focusing on the induction of the RAS-MAP kinase pathway via GRB2 binding. Our biologically simple model suffers a combinatorial explosion in the number of differential equations required to simulate the system. In addition to numerically solving the full model, we show that it can be accurately simplified. This requires combining matched asymptotics, the quasi-steady state hypothesis, and the fact subsets of the equations decouple asymptotically. Both the full and simplified models reproduce the qualitative dynamics observed experimentally and in previous stochastic models. The simplified model also elucidates both the qualitative features of GRB2 binding and the complex relationship between SHP2 levels, the rate SHP2 induces dephosphorylation and levels of bound GRB2. In addition to providing insight into the important and redundant features of FGF signaling, such work further highlights the usefulness of numerous simplification techniques in the study of mass action models of signal transduction, as also illustrated recently by Borisov and co-workers (Borisov et al. in Biophys. J. 89, 951–66, 2005, Biosystems 83, 152–66, 2006; Kiyatkin et al. in J. Biol. Chem. 281, 19925–9938, 2006). These developments will facilitate the construction of tractable models of FGF signaling, incorporating further biological realism, such as spatial effects or realistic binding stoichiometries, despite a more severe combinatorial explosion associated with the latter.

Item Type:Article
Uncontrolled Keywords:Signal transduction - FGF - Mathematical modeling - Law of mass action
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:875
Deposited By:Eamonn Gaffney
Deposited On:19 Dec 2009 08:33
Last Modified:19 Dec 2009 08:33

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