Modeling of Interactions between Cancer Stem Cells and their Microenvironment: Predicting Clinical Response

Abstract

Mathematical models of cancer stem cells are useful in translational cancer research for facilitating the understanding of tumor growth dynamics and for predicting treatment response and resistance to combined targeted therapies. In this chapter, we describe appealing aspects of different methods used in mathematical oncology and discuss compelling questions in oncology that can be addressed with these modeling techniques. We describe a simplified version of a model of the breast cancer stem cell niche, illustrate the visualization of the model, and apply stochastic simulation to generate full distributions and average trajectories of cell type populations over time. We further discuss the advent of single-cell data in studying cancer stem cell heterogeneity and how these data can be integrated with modeling to advance understanding of the dynamics of invasive and proliferative populations during cancer progression and response to therapy.

Keywords: Breast cancer; Cancer stem cell; Mathematical model; Optimal therapy design.

Fig. 1

Types of stem cell division. A stem cell or stem-like cell can undergo symmetric self-renewal, giving rise two identical copies of themselves, or asymmetric self-renewal, giving rise to one identical copy of itself and one partially differentiated progenitor cell. It can also undergo symmetric differentiation, in which it gives rise to two partially differentiated daughter cells

Fig. 2

Schematic of microenvironmental signals governing BCSC state transitions. In this simplified model of the BCSC niche, we identify the species involved, including cell types (the proliferative epithelial BCSCs and the quiescent mesenchymal BCSC populations) and cytokines and intracellular signals that regulate transition between these two states. The reactions included in our model directly or indirectly play a role in regulating the BCSC state transitions

Fig. 3

Petri net generated by the simplified model of factors regulating transitions between proliferative and quiescent BCSC states. The Petri net demonstrates the interconnectivity of the model, defining its reactant species (ovals) and the transitions and events (boxes) that relate them to each other

Fig. 4

Sample output from stochastic simulation of stem cell state transitions. The first panel shows the full distribution of epithelial BCSC cell counts over 1000 simulations for a fixed period of time. For slower birth rates, BCSC cell populations reach smaller final counts. In the second panel, the average trajectories of epithelial-like BCSC populations are shown. When the birth rate is faster, BCSC cell counts initially diminish in response to therapy but later increase over time