Mathematical models of the balance between apoptosis and proliferation

As our understanding of cellular behaviour grows, and we identify more and more genes involved in the control of such basic processes as cell division and programmed cell death, it becomes increasingly difficult to integrate such detailed knowledge into a meaningful whole. This is an area where mathematical modelling can complement experimental approaches, and even simple mathematical models can yield useful biological insights. This review presents examples of this in the context of understanding the combined effects of different levels of cell death and cell division in a number of biological systems including tumour growth, the homeostasis of immune memory and pre-implantation embryo development. The models we describe, although simplistic, yield insight into several phenomena that are difficult to understand using a purely experimental approach. This includes the different roles played by the apoptosis of stem cells and differentiated cells in determining whether or not a tumour can grow; the way in which a density dependent rate of apoptosis (for instance mediated by cell-cell contact or cytokine signalling) can lead to homeostasis; and the effect of stochastic fluctuations when the number of cells involved is small. We also highlight how models can maximize the amount of information that can be extracted from limited experimental data. The review concludes by summarizing the various mathematical frameworks that can be used to develop new models and the type of biological information that is required to do this.