The steady-states of a multi-compartment, age–size distribution model of cell-growth

Abstract

A model of cell-growth, describing the evolution of the age–size distribution of cells in different phases of cell-growth, is studied. The model is based on that used in several papers by Basse et al. and is composed of a system of partial differential equations, each describing the changes in the age–size distribution of cells in a specific phase of cell-growth. Here, the ‘age’ of a cell is considered to be the time spent in its current phase of cell-growth, while ‘size’ is considered to be the DNA content of the cell. The existence of steady age–size distributions (SASDs), where the age–size distributions retain the same shape but are scaled up or down as time increases, is investigated and it is shown that SASDs exist. A speculative discussion of the stability of these SASDs is also included, but their stability is not conclusively proved.