A simple model of two interacting signaling pathways in embryonic Xenopus laevis
Edwin Tecarro - Department of Computer and Mathematical Sciences, University of Houston-Downtown, Houston, Tx 77002-1001, United States (email)
Abstract: 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, signaling pathway, transcritical bifurcation, MAPK, BMP
Received: August 2008; Revised: August 2009; Published: September 2009.