Optimal Proliferation Rate in a Cell Division Model

Abstract

We consider a size structured cell population model where a mother cell gives birth totwo daughter cells. We know that the asymptotic behavior of the density of cells is given by thesolution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue givesthe exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends onthe division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) orasymmetric. We use a min-max principle and a differentiation principle to find the variation of thefirst eigenvalue with respect to a parameter of asymmetry of the cell division. We prove that thesymmetrical division is not always the best fitted division, i.e., the Maltusian parameter may be notoptimal.