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

V. Calvez (), N. Meunier (), N. Muller () and R. Voituriez ()
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V. Calvez: École Normale Supérieure de Lyon
N. Meunier: Université Paris Descartes
N. Muller: Université Paris Descartes
R. Voituriez: Université Pierre et Marie Curie

Chapter Chapter 6 in Integral Methods in Science and Engineering, 2013, pp 75-89 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7828-7_6

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DOI: 10.1007/978-1-4614-7828-7_6

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