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2009, 2009(Special): 753-760. doi: 10.3934/proc.2009.2009.753

A simple model of two interacting signaling pathways in embryonic Xenopus laevis

Edwin Tecarro 1, , Tung Bui 2, , Marsida Lisi 1, , Amy Sater 3, and  Akif Uzman 2,

1. 

Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Tx 77002-1001, United States, United States
2. 

Department of Natural Sciences, University of Houston-Downtown, Houston, Tx 77002-1001, United States, United States
3. 

Department of Biology and Biochemistry, University of Houston, Houston, TX 77204-5001, United States

Received  August 2008 Revised  August 2009 Published  September 2009

A mathematical model of MAPK and BMP-Smad1 signaling pathways in the embryonic development of Xenopus laevis is constructed. The model consists of a system of 4 coupled, nonlinear ordinary differential equations. Numerical computations characterize the biological result that a 4 to 6-fold increase in MAPK activity inhibits Smad1 activity and triggers the neural fate of the embryo's ectodermal cells. Bifurcation analysis of the model shows that this biological result can be explained via transcritical bifurcations involving steady-state MAPK and Smad1 activity levels.
Keywords: mathematical model, transcritical bifurcation, BMP, MAPK, signaling pathway.
Mathematics Subject Classification: Primary: 92B99; Secondary: 37N25.
Citation: Edwin Tecarro, Tung Bui, Marsida Lisi, Amy Sater, Akif Uzman. A simple model of two interacting signaling pathways in embryonic Xenopus laevis. Conference Publications, 2009, 2009 (Special) : 753-760. doi: 10.3934/proc.2009.2009.753
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