Math. Model. Nat. Phenom.
Volume 1, Number 2, 2006Hematopoiesis and blood diseases
|23 - 44
|15 May 2008
Optimal Proliferation Rate in a Cell Division Model
Department of Mathematics and Informatics, Institut Camille Jordan,
Ecole centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully, France
Corresponding author: firstname.lastname@example.org
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.
Mathematics Subject Classification: 35P05 / 92B05 / 93B60
Key words: cell division / long time asymptotic / eigenvalue / min-max / variation / asymmetry
© EDP Sciences, 2006
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