Mathematical Biosciences and Engineering, 2011, 8(4): 1035-1059. doi: 10.3934/mbe.2011.8.1035.

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

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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

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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords Steady states; Existence of solutions; Reaction diffusion equations; Morphogenesis; Numerical simulations.

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

 

Reader Comments

your name: *   your email: *  

Copyright Info: 2011, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved