Numerical Simulation of the Dynamics of Molecular Markers Involved in Cell Polarization

Chapter

Abstract

In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarization. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We characterize the following behaviors in the one-dimensional case: solutions are global if the mass is below the critical mass and they blow up in finite time above the critical mass. The higher-dimensional case is also discussed. The results are reminiscent of the classical Keller–Segel system in double the dimension. In addition, in the one-dimensional case we prove quantitative convergence results using relative entropy techniques. This work is complemented with a more realistic model that takes into account dynamical exchange of molecular content at the boundary. In the one-dimensional case we prove that blow-up is prevented. Furthermore, density converges towards a non trivial stationary configuration.

Keywords

Cell dynamics Cell polarization Entropy technique Exchange of molecular content 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • V. Calvez
    • 1
  • N. Meunier
    • 2
  • N. Muller
    • 2
  • R. Voituriez
    • 3
  1. 1.École Normale Supérieure de LyonLyon CedexFrance
  2. 2.Université Paris DescartesParisFrance
  3. 3.Université Pierre et Marie CurieParis CedexFrance

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