Phase transitions in a two-species model for cell segregation and logistic growth
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.
Affiliations des auteurs :
Luis Almeida 1 ; Kevin Atsou 2 ; Marta Marulli 3 ; Diane Peurichard 4 ; Rémi Tesson 5
@article{EP_2020_67_a1,
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/}
}
TY - JOUR AU - Luis Almeida AU - Kevin Atsou AU - Marta Marulli AU - Diane Peurichard AU - Rémi Tesson TI - Phase transitions in a two-species model for cell segregation and logistic growth JO - ESAIM. Proceedings PY - 2020 SP - 1 EP - 15 VL - 67 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202067001/ DO - 10.1051/proc/202067001 LA - en ID - EP_2020_67_a1 ER -
%0 Journal Article %A Luis Almeida %A Kevin Atsou %A Marta Marulli %A Diane Peurichard %A Rémi Tesson %T Phase transitions in a two-species model for cell segregation and logistic growth %J ESAIM. Proceedings %D 2020 %P 1-15 %V 67 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202067001/ %R 10.1051/proc/202067001 %G en %F EP_2020_67_a1
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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