Geodesic
Phase transitions in a two-species model for cell segregation and logistic growth
Luis Almeida1 ; Kevin Atsou2 ; Marta Marulli3 ; Diane Peurichard4 ; Rémi Tesson5
1Sorbonne Université, CNRS, Laboratoire Jacques-Louis-Lions, 4 place Jussieu, 75005, Paris, France
2INRIA, Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis
3LAGA, UMR 7539, CNRS, Université Paris 13, France, University of Bologna, Italy
4Sorbonne Université, Inria, Mamba project-team, Laboratoire Jacques-Louis Lions, 4 place Jussieu, 75005, Paris, France
5Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
ESAIM. Proceedings, Tome 67 (2020), pp. 1-15
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We study a model of cell segregation in a population composed of two cell types. Starting from a model initially proposed in [3], we aim to understand the impact of a cell division process on the system’s segregation abilities. The original model describes a population of spherical cells interacting with their close neighbors by means of a repulsion potential and which centers are subject to Brownian motion. Here, we add a stochastic birth-death process in the agent-based model, that approaches a logistic growth term in the continuum limit. We address the linear stability of the spatially homogeneous steady states of the macroscopic model and obtain a precise criterion for the phase transition, which links the system segregation ability to the model parameters. By comparing the criterion with the one obtained without logistic growth, we show that the system’s segregation ability is the result of a complex interplay between logistic growth, diffusion and mechanical repulsive interactions. Numerical simulations are presented to illustrate the results obtained at the microscopic scale.
DOI : 10.1051/proc/202067001

Luis Almeida  1   ; Kevin Atsou  2   ; Marta Marulli  3   ; Diane Peurichard  4   ; Rémi Tesson  5

1 Sorbonne Université, CNRS, Laboratoire Jacques-Louis-Lions, 4 place Jussieu, 75005, Paris, France
2 INRIA, Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis
3 LAGA, UMR 7539, CNRS, Université Paris 13, France, University of Bologna, Italy
4 Sorbonne Université, Inria, Mamba project-team, Laboratoire Jacques-Louis Lions, 4 place Jussieu, 75005, Paris, France
5 Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France 
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     author = {Luis Almeida and Kevin Atsou and Marta Marulli and Diane Peurichard and R\'emi Tesson},
     title = {Phase transitions in a two-species model for cell segregation and logistic growth},
     journal = {ESAIM. Proceedings},
     pages = {1--15},
     year = {2020},
     volume = {67},
     doi = {10.1051/proc/202067001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202067001/}
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Luis Almeida; Kevin Atsou; Marta Marulli; Diane Peurichard; Rémi Tesson. Phase transitions in a two-species model for cell segregation and logistic growth. ESAIM. Proceedings, Tome 67 (2020), pp. 1-15. doi: 10.1051/proc/202067001

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