# Optimal Proliferation Rate in a Cell Division Model

• Volume: 1, Issue: 2, page 23-44
• ISSN: 0973-5348

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## Abstract

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We consider a size structured cell population model where a mother cell gives birth to two daughter 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 cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a min-max principle and a differentiation principle to find the variation of the first eigenvalue with respect to a parameter of asymmetry of the cell division. We prove that the symmetrical division is not always the best fitted division, i.e., the Maltusian parameter may be not optimal.

## How to cite

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Michel, P.. "Optimal Proliferation Rate in a Cell Division Model." Mathematical Modelling of Natural Phenomena 1.2 (2010): 23-44. <http://eudml.org/doc/222252>.

@article{Michel2010,
abstract = { We consider a size structured cell population model where a mother cell gives birth to two daughter 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 cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a min-max principle and a differentiation principle to find the variation of the first eigenvalue with respect to a parameter of asymmetry of the cell division. We prove that the symmetrical division is not always the best fitted division, i.e., the Maltusian parameter may be not optimal. },
author = {Michel, P.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {cell division; long time asymptotic; eigenvalue; min-max; variation; asymmetry},
language = {eng},
month = {3},
number = {2},
pages = {23-44},
publisher = {EDP Sciences},
title = {Optimal Proliferation Rate in a Cell Division Model},
url = {http://eudml.org/doc/222252},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Michel, P.
TI - Optimal Proliferation Rate in a Cell Division Model
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 1
IS - 2
SP - 23
EP - 44
AB - We consider a size structured cell population model where a mother cell gives birth to two daughter 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 cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a min-max principle and a differentiation principle to find the variation of the first eigenvalue with respect to a parameter of asymmetry of the cell division. We prove that the symmetrical division is not always the best fitted division, i.e., the Maltusian parameter may be not optimal.
LA - eng
KW - cell division; long time asymptotic; eigenvalue; min-max; variation; asymmetry
UR - http://eudml.org/doc/222252
ER -

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