[Optimisation du taux de croissance dans un modèle de division cellulaire]
Nous considérons un modèle d'évolution d'une densité de cellules structurée en taille. Nous savons que la densité de cellules se comporte en temps long comme le produit d'une fonction indépendante du temps et d'une exponentielle dépendant du temps. Le taux de croissance exponentiel étant donné par un paramètre Maltusien dont nous allons montrer qu'il depend de la manière dont la cellule se divise, symétriquement ou non symétriquement. On donnera des exemples pour lesquels la division symétrique n'est pas la mieux adaptée, c'est-à-dire pour lesquels le taux de croissance exponentiel n'est pas maximal.
We consider a size structured cell population model where a mother cell gives birth to two cells. We know that the asymptotic behavior of the density of cells is given by the solution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue gives the exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends on the division rule for the mother, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We give some example where the symmetrical division is not the best fitted division, i.e., the Maltusian parameter is not optimal.
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@article{CRMATH_2005__341_12_731_0,
author = {Michel, Philippe},
title = {Fitness optimization in a cell division model},
journal = {Comptes Rendus. Math\'ematique},
pages = {731--736},
publisher = {Elsevier},
volume = {341},
number = {12},
year = {2005},
doi = {10.1016/j.crma.2005.10.012},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.10.012/}
}
TY - JOUR AU - Michel, Philippe TI - Fitness optimization in a cell division model JO - Comptes Rendus. Mathématique PY - 2005 SP - 731 EP - 736 VL - 341 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.10.012/ DO - 10.1016/j.crma.2005.10.012 LA - en ID - CRMATH_2005__341_12_731_0 ER -
Michel, Philippe. Fitness optimization in a cell division model. Comptes Rendus. Mathématique, Tome 341 (2005) no. 12, pp. 731-736. doi : 10.1016/j.crma.2005.10.012. http://archive.numdam.org/articles/10.1016/j.crma.2005.10.012/
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