Mathematical analysis and numerical simulation of a model of morphogenesis | Zendy

Ana I. Muñoz | Zendy; J. Ignacio Tello | Zendy

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Mathematical analysis and numerical simulation of a model of morphogenesis

Author(s) -

Ana I. Muñoz,

J. Ignacio Tello

Publication year - 2011

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2011.8.1035

Subject(s) - ode , simple (philosophy) , mathematical model , boundary value problem , morphogenesis , boundary (topology) , computer simulation , biological system , mathematics , pattern formation , distribution (mathematics) , diffusion , statistical physics , mathematical analysis , physics , mechanics , biology , philosophy , statistics , biochemistry , genetics , epistemology , gene , thermodynamics

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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