Extinction kinetics for metastatic cancer stem cells

Abstract

Purpose: Cancer Stem Cells (CSC) are hypothesised to influence tumour growth through their self-replication, cell loss, and differentiation into growth-limited cell types. A model for the random gain and loss of metastatic CSC is developed to investigate how the balance between these processes might affect metastatic efficiency, tumour involution and treatment response.

Materials and methods: A stochastic birth-death model for metastasis was constructed for the replication and loss of CSC. The model was extended to account for single and sequential cancer treatments, with CSC repopulation.

Results: If CSC losses exceed gains, the metastasis would become extinct. The resultant extinction probability was greatest during a period of stochastic susceptibility; treatment could extend, or reestablish, this period.

Conclusion: Random CSC losses, with ‘seed and soil’ selection, provided a mechanistic explanation for the involution of metastases, as well as for metastatic inefficiency. With such background losses, and the growth limitations of differentiated cells, a metastasis could take years to reach macroscopic size. The susceptibility period could be protracted, providing for a window for therapeutic opportunity. Metastases with a high background CSC loss would be more responsive to treatment than stabler metastases. Modulation of this loss could enhance the efficacy of conventional cancer treatment.

Keywords:

• metastatic efficiency
• tumour control probability
• repopulation
• adjuvant cancer therapy

Acknowledgements

The author acknowledges the financial support of Patricia Rinaldo for this research.

Declaration of interest: The author reports no conflicts of interest. The author alone is responsible for the content and writing of the paper.