Mathematical analysis and numerical simulation of a model of morphogenesis
Ana I. Muñoz - Departamento de Matemática Aplicada, ESCET, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain (email)
Abstract: We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters.
Keywords: Reaction diffusion equations, Morphogenesis, Existence of solutions, Steady states, Numerical simulations.
Received: November 2009; Accepted: January 2011; Published: August 2011.
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