  Cancer stem cells have been shown to be critical to the development of a
variety of solid cancers. The precise interplay mechanisms between cancer stem
cells and the rest of a tissue are still not elucidated. To shed light on the
interactions between stem and non-stem cancer cell populations we develop a
two-population mathematical model, which is suitable to describe tumorsphere
growth. Both interspecific and intraspecific interactions, mediated by the
microenvironment, are included. We show that there is a tipping point,
characterized by a transcritical bifurcation, where a purely non-stem cell
attractor is replaced by a new attractor that contains both stem and
differentiated cancer cells. The model is then applied to describe the outcome
of a recent experiment. This description reveals that, while the intraspecific
interactions are inhibitory, the interspecific interactions stimulate growth.
This can be understood in terms of stem cells needing differentiated cells to
reinforce their niches, and phenotypic plasticity favoring the
de-differentiation of differentiated cells into cancer stem cells. We posit
that this is a consequence of the deregulation of the quorum sensing that
maintains homeostasis in healthy tissues.

Cell Behavior;Other Condensed Matter