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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 4: 1035-1059. doi: 10.3934/mbe.2011.8.1035
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Mathematical analysis and numerical simulation of a model of morphogenesis

  • 1.
    Departamento de Matemática Aplicada, ESCET, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid
  • 2.
    Departamento de Matemática Aplicada, E.U. Informática. Universidad Politécnica de Madrid, Ctra. de Valencia, Km. 7. 28031 - Madrid
  • Received: 01 November 2009 Accepted: 29 June 2018 Published: 01 August 2011

  • MSC : Primary: 22E46, 53C35; Secondary: 57S20.

  • 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.

    Citation: Ana I. Muñoz, José Ignacio Tello. Mathematical analysis and numerical simulation of a model of morphogenesis[J]. Mathematical Biosciences and Engineering, 2011, 8(4): 1035-1059. doi: 10.3934/mbe.2011.8.1035

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  • 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.


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  • © 2011 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

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