Asymmetric cell division in a size-structured growth model

Abstract

A model for the simultaneous growth and division of a cell population structured by size is examined. The case considered here is that of asymmetrical cell division when cells are dividing into $\beta_1$ and $\beta_2$ daughter cells at a constant rate and the parameters for growth and mortality are constants. The model has a steady-size distribution solution which satisfies a nonlocal differential equation. The solution is in the form of a Dirichlet series which is shown to be the unique probability density function for the steady-size distribution.