Modelling the balance between quiescence and cell death in normal and tumour cell populations

When considering either human adult tissues (in vivo) or cell cultures (in vitro), cell number is regulated by the relationship between quiescent cells, proliferating cells, cell death and other controls of cell cycle duration. By formulating a mathematical description we see that even small alterations of this relationship may cause a non-growing population to start growing with doubling times characteristic of human tumours. Our model consists of two age structured partial differential equations for the proliferating and quiescent cell compartments. Model parameters are death rates from and transition rates between these compartments. The partial differential equations can be solved for the steady-age distributions, giving the distribution of the cells through the cell cycle, dependent on specific model parameter values. Appropriate formulas can then be derived for various population characteristic quantities such as labelling index, proliferation fraction, doubling time and potential doubling time of the cell population. Such characteristic quantities can be estimated experimentally, although with decreasing precision from in vitro, to in vivo experimental systems and to the clinic. The model can be used to investigate the effects of a single alteration of either quiescence or cell death control on the growth of the whole population and the non-trivial dependence of the doubling time and other observable quantities on particular underlying cell cycle scenarios of death and quiescence. The model indicates that tumour evolution in vivo is a sequence of steady-states, each characterised by particular death and quiescence rate functions. We suggest that a key passage of carcinogenesis is a loss of the communication between quiescence, death and cell cycle machineries, causing a defect in their precise, cell cycle dependent relationship.