A Mathematical Model of Average Dynamics in a Stem Cell Hierarchy Suggests the Combinatorial Targeting of Cancer Stem Cells and Progenitor Cells as a Potential Strategy against Tumor Growth

Abstract

The cancer stem cell hypothesis states that tumors are maintained by a small subpopulation of stem-like cells, often called cancer stem cells (CSCs) or tumor initiating cells. CSCs can self-renew and give rise to more differentiated cells, which comprise the bulk of the tumor. In addition, CSCs are resistant to conventional therapy, which suggests that they are responsible for tumor relapse. This has led researchers to increase efforts to develop directed therapies against CSCs. However, some experiments in mice have shown that the elimination of CSCs might not ensure tumor eradication. This may be due to different events, such as residual CSCs after treatment, the plasticity of cells within the tumor, the presence of different CSCs having their own hierarchy within the same tumor, and the ability of more differentiated cells to maintain the disease, among others. Trying to decipher this complexity may benefit from dissecting the whole in its parts. Here, we hypothesize that tumor relapse after the selective targeting of CSCs may be due to intermediate progenitor (P) cells that can maintain the tumor volume. In order to support the hypothesis, we implemented a mathematical model derived using pseudo-reactions representing the events of each cell subpopulation within the tumor. We aimed to test if a minimal unidirectional hierarchical model consisting of CSCs, P, and terminally differentiated (D) cells could be adjusted to experimental data for selective CSC targeting. We further evaluated therapies ranging from nonselective to specifically directed and combination therapy. We found that selective killing of the CSC compartment has a delaying effect on the overall exponential tumor growth, but was not able to eliminate the disease. We show that therapy that targets both CSCs and intermediate progenitor (P) cells with a sufficient capacity to proliferate and differentiate could represent a more efficient treatment option for tumor depletion. Testing this hypothesis in vivo may allow us to discriminate within the array of possibilities of tumor relapse, and further open the idea of combination therapy against different subpopulations of tumor cells instead of segregating CSCs and bulk tumor cells.