# Modeling tumorspheres reveals cancer stem cell niche building and plasticity

## TL;DR

This paper presents a mathematical model of tumorsphere growth that captures the interactions between cancer stem cells and differentiated cells, revealing a bifurcation point and the roles of interspecific and intraspecific interactions in tumor dynamics.

## Contribution

The study introduces a novel two-population mathematical model that describes cancer stem cell and differentiated cell interactions, highlighting the role of phenotypic plasticity and microenvironmental factors.

## Key findings

- Identification of a bifurcation point where tumor cell composition shifts.
- Interspecific interactions stimulate tumor growth, while intraspecific interactions inhibit it.
- Model application to experimental data supports the role of plasticity and deregulated quorum sensing.

## Abstract

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.

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Source: https://tomesphere.com/paper/1904.06326