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Non-linear analysis of a model for yeast cell communication

Vincent Calvez 1, 2 Thomas Lepoutre 3, 1, 2 Nicolas Meunier 4 Nicolas Muller 5 
2 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We study the non-linear stability of a coupled system of two non-linear transport-diffusion equations set in two opposite half-lines. This system describes some aspects of yeast pairwise cellular communication, through the concentration of some protein in the cell bulk and at the cell boundary. We show that it is of bistable type, provided that the intensity of active molecular transport is large enough. We prove the non-linear stability of the most concentrated steady state, for large initial data, by entropy and comparison techniques. For small initial data we prove the self-similar decay of the molecular concentration towards zero. Informally speaking, the rise of a dialog between yeast cells requires enough active molecular transport in this model. Besides, if the cells do not invest enough in the communication with their partner, they do not respond to each other; but a sufficient initial input from each cell in the dialog leads to the establishment of a stable activated state in both cells.
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Submitted on : Wednesday, November 20, 2019 - 2:33:35 PM
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Vincent Calvez, Thomas Lepoutre, Nicolas Meunier, Nicolas Muller. Non-linear analysis of a model for yeast cell communication. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2020, 54 (2), pp.619 - 648. ⟨10.1051/m2an/2019065⟩. ⟨hal-02372511⟩



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