MBE
Mathematical analysis and numerical simulation of a model of morphogenesis
Ana I. Muñoz José Ignacio Tello
Mathematical Biosciences & Engineering 2011, 8(4): 1035-1059 doi: 10.3934/mbe.2011.8.1035
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: Steady states Existence of solutions Reaction diffusion equations Morphogenesis Numerical simulations.
DCDS
Mathematical analysis of a model of morphogenesis
José Ignacio Tello
Discrete & Continuous Dynamical Systems - A 2009, 25(1): 343-361 doi: 10.3934/dcds.2009.25.343
We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns) proposed by Lander, Nie and Wan in 2002. The model consists of a system of two equations: a PDE of parabolic type modeling the distribution of free morphogens with a dynamic boundary condition and an ODE describing the evolution of bound receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We prove existence and uniqueness of solutions and its asymptotic behavior.
keywords: reaction diffusion equations Morphogens stability of solutions.

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