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

In: Integral Methods in Science and Engineering

Author

Listed:
  • V. Calvez

    (École Normale Supérieure de Lyon)

  • N. Meunier

    (Université Paris Descartes)

  • N. Muller

    (Université Paris Descartes)

  • R. Voituriez

    (Université Pierre et Marie Curie)

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.

Suggested Citation

  • V. Calvez & N. Meunier & N. Muller & R. Voituriez, 2013. "Numerical Simulation of the Dynamics of Molecular Markers Involved in Cell Polarization," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Haroldo F. de Campos Velho (ed.), Integral Methods in Science and Engineering, edition 127, chapter 0, pages 75-89, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7828-7_6
    DOI: 10.1007/978-1-4614-7828-7_6
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