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Comptes Rendus Mathématique
Volume 341, n° 12
pages 731-736 (décembre 2005)
Doi : 10.1016/j.crma.2005.10.012
Received : 19 September 2005 ;  accepted : 11 October 2005
Fitness optimization in a cell division model
Optimisation du taux de croissance dans un modèle de division cellulaire
 

Philippe Michel a, b
a Département de mathématiques et applications, UMR 8553, École normale supérieure, 45, rue dʼUlm, 75230 Paris cedex 05, France 
b CEREMADE, Paris Dauphine, place de Lattre de Tassigny, 75775 Paris cedex 16, France 

Abstract

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. To cite this article: P. Michel, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Résumé

Nous considérons un modèle dʼévolution dʼune densité de cellules structurée en taille. Nous savons que la densité de cellules se comporte en temps long comme le produit dʼune fonction indépendante du temps et dʼune exponentielle dépendant du temps. Le taux de croissance exponentiel étant donné par un paramètre Maltusien dont nous allons montrer quʼil depend de la manière dont la cellule se divise, symétriquement ou non symétriquement. On donnera des exemples pour lesquels la division symétrique nʼest pas la mieux adaptée, cʼest-à-dire pour lesquels le taux de croissance exponentiel nʼest pas maximal. Pour citer cet article : P. Michel, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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