A computational cell cycle model that can describe three state properties, cell maturation age, specific mRNA and protein content, has been developed. Cell cycle progression is monitored by maturation age, and population heterogeneity is generated by the introduction of a probable random event embedded in the G1 phase. Specific mRNA is generated with a constant transcription rate at the single-cell level, and its turnover is governed by a first-order decay. Translation is modelled as a first-order dependence on the transcripts, and the protein product is subsequently exported. Dynamic chemostat simulations are used to demonstrate the ability of the model to track evolving parent and daughter subpopulations in maturation and cellular contents. The cell subpopulations eventually converge to an equilibrium distribution corresponding to the steady state of a chemostat, and halving of cellular content at cell division is the dominant driving force leading towards the population equilibrium state.