Mathematical modelling of plasticity and phenotype switching in cancer cell populations.

The cancer stem cell (CSC) hypothesis suggests that cancer stem cells proliferate via a hierarchical model of unidirectional differentiation. However, growing experimental evidence has advanced this hypothesis by introducing a bidirectional hierarchy, in which non-CSCs may dedifferentiate into CSCs. Various models have been developed enabling the incorporation of this plasticity within cancer cell populations, focusing on behaviour in the limit of a large number of cells. However, stochastic effects predominate in the limit of small numbers of cells, which correlates with biologically relevant assays such as the mammosphere formation assay (MFA). Here, we consider two mathematical models incorporating cellular plasticity, namely a two-compartment model and a hierarchical model, and by parameterizing these models with experimental data, we show this behavioural difference in the limits of large and small numbers of cells. Additionally, we analyse the effects of varying cellular plasticity on the survival of the cancer cell population, and show that interestingly, increased plasticity, in certain cases, may be advantageous in reducing the survival probability. Thus, this analysis highlights the necessity of experimentally studying both small and large populations of cancer cells concurrently to obtain valid model predictions, potentially aiding the design of novel therapeutics.