A mathematical model of cancer cells with phenotypic plasticity

Da Zhou, Xiufang Chen, Xingan Zhang


Purpose: The phenotypic plasticity of cancer cells is recently becoming a cutting-edge research area in cancer, which challenges the cellular hierarchy proposed by the conventional cancer stem cell theory. In this study, we establish a mathematical model for describing the phenotypic plasticity of cancer cells, based on which we try to find some salient features that can characterize the dynamic behavior of the phenotypic plasticity especially in comparison to the hierarchical model of cancer cells.

Methods: We model cancer as population dynamics composed of different phenotypes of cancer cells. In this model, not only can cancer cells divide (symmetrically and asymmetrically) and die, but they can also convert into other cellular phenotypes. According to the Law of Mass Action, the cellular processes can be captured by a system of ordinary differential equations (ODEs). On one hand, we can analyze the long-term stability of the model by applying qualitative method of ODEs. On the other hand, we are also concerned about the short-term behavior of the model by studying its transient dynamics. Meanwhile, we validate our model to the cell-state dynamics in published experimental data.

Results: Our results show that the phenotypic plasticity plays important roles in both stabilizing the distribution of different phenotypic mixture and maintaining the cancer stem cells proportion. In particular, the phenotypic plasticity model shows decided advantages over the hierarchical model in predicting the phenotypic equilibrium and cancer stem cells’ overshoot reported in previous biological experiments in cancer cell lines.

Conclusion: Since the validity of the phenotypic plasticity paradigm and the conventional cancer stem cell theory is still debated in experimental biology, it is worthy of theoretically searching for good indicators to distinguish the two models through quantitative methods. According to our study, the phenotypic equilibrium and overshoot behavior can be good candidates to validate the phenotypic plasticity in comparison to the cellular hierarchy of cancer cells.


Cite this article as:  Zhou D, Chen X, Zhang X. A mathematical model of cancer cells with phenotypic plasticity. Int J Cancer Ther Oncol 2015; 3(4):3402.

[This abstract was presented at the BIT’s 8th Annual World Cancer Congress, which was held from May 15-17, 2015 in Beijing, China.]

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