Constrained optimisation of divisional load in hierarchically-organised tissues during homeostasis

It has been hypothesised that the structure of tissues and the hierarchy of differentiation from stem cell to terminally-differentiated cell play a significant role in reducing the incidence of cancer in that tissue. One specific mechanism by which this risk can be reduced is by minimising the number of divisions -- and hence the mutational risk -- that cells accumulate as they divide to maintain tissue homeostasis. Here we investigate a mathematical model of cell division in a hierarchical tissue, calculating and minimising the divisional load while constraining parameters such that homeostasis is maintained. We show that the minimal divisional load is achieved by binary division tress with progenitor cells incapable of self-renewal. Contrary to the protection hypothesis, we find that an increased stem cell turnover can lead to lower divisional load. Furthermore, we find that the optimal tissue structure depends on the time horizon of the duration of homeostasis, with faster stem cell division favoured in short-lived organisms and more progenitor compartments favoured in longer-lived organisms.