Two models for yeast cell communication

Vincent Calvez (1) , Thomas Lepoutre (2, 3, 4) , Nicolas Meunier (5) , Nicolas Muller (5)

1 ENS de Lyon - École normale supérieure de Lyon
2 ICJ - Institut Camille Jordan
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
4 MMCS - Modélisation mathématique, calcul scientifique
5 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

We study two separate models for yeast cell-cell communication. Each model consists of a coupled system of two non-linear, non-local equations in one dimension of space. The first model describes the two cells in the transversal direction, orthogonal to the membrane, whereas the second model describes the two cells in the tangential direction, along the membrane. We study long time dynamics for each model, ranging from convergence to stable steady states (bistability in model 1), to possible finite time blow-up (formation of singularity in model 2). The biological interpretation of the mathematical results is discussed.

Mots clés: Blow-up; non-linear stability; asymptotic convergence; logarithmic Sobolev inequality; HWI inequality

Domaines: Equations aux dérivées partielles [math.AP]

Vincent Calvez, Thomas Lepoutre, Nicolas Meunier, Nicolas Muller. Two models for yeast cell communication. 2017. ⟨hal-01498673v1⟩