# Optimal Proliferation Rate in a Cell Division Model

Mathematical Modelling of Natural Phenomena (2010)

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

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topMichel, 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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