Game Theory of Tumor–Stroma Interactions in Multiple Myeloma: Effect of Nonlinear Benefits

Abstract

Cancer cells and stromal cells often exchange growth factors with paracrine effects that promote cell growth: a form of cooperation that can be studied by evolutionary game theory. Previous models have assumed that interactions between cells are pairwise or that the benefit of a growth factor is a linear function of its concentration. Diffusible factors, however, affect multiple cells and generally have nonlinear effects, and these differences are known to have important consequences for evolutionary dynamics. Here, we study tumor-stroma paracrine signaling using a model with multiplayer collective interactions in which growth factors have nonlinear effects. We use multiple myeloma as an example, modelling interactions between malignant plasma cells, osteoblasts, and osteoclasts. Nonlinear benefits can lead to results not observed in linear models, including internal mixed stable equilibria and cyclical dynamics. Models with linear effects, therefore, do not lead to a meaningful characterization of the dynamics of tumor-stroma interactions. To understand the dynamics and the effect of therapies it is necessary to estimate the shape of the benefit functions experimentally and parametrize models based on these functions.

The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer

“…This case of nonlinear fitness functions has generated extensive theoretical work in a public goods game, where cells can be producers (cooperators) or free-riders on shared resources produced by the others (defectors) [16]. The most relevant cases for cancer are the production of growth factors like vascular endothelial growth factors (VEGF) [12,159], the production of hostile environments like acidity due to the Warburg effect [13,14,46], or the coupling of both [115]. Archetti et al empirically estimated parameters of this nonlinear public goods game for neuroendocrine pancreatic cancer cells that produce insulin-like growth factor II, which supports proliferation and evasion of apoptosis [16,17].…”

Cooperation among cancer cells: applying game theory to cancer

“…In all these cases, cancer cells cooperate with each other, by producing diffusible factors that induce the stroma to provide a benefit to the tumor. Game theory has been used to describe tumor-stroma interactions in the production of matrix metalloproteinases and tissue inhibitors of metalloproteinases 60 , in the dynamics of prostate cancer progression and treatments 41 and in the dynamics of multiple myeloma 46,61,62 .…”

“…While these approaches suggest exploiting the interactions between different clones within the tumor (and highlight the importance of finding the right balance of attack and the right sequence of treatments), they do not specifically target cooperation. An example of the use of game theory of cooperation in the analysis of the stability of therapies, is the case of tumor-stroma interactions in multiple myeloma, where osteoblasts, osteoclasts and malignant plasma cells are players in a public goods game 46,61,66 . It has been shown that reducing the amount of malignant plasma cells (the current approach to treating multiple myeloma) is not an evolutionarily stable strategy, whereas changing the parameters of the game, for instance by targeting the growth factors produced by the stroma and by the tumor, could lead to the extinction of the malignant cells and re-establish a healthy osteoblast-osteoclast balance.…”

The contribution of evolutionary game theory to understanding and treating cancer

“…This case of non-linear fitness functions has generated extensive theoretical work in the case of public goods where cells can be producers (cooperators) or free-ride on shared resources produced by the others (defectors) [16]. The most relevant cases for cancer are the production of growth factors like VEGF [12,154], the production of hostile environments like acidity due to the Warburg effect [43,13,14], or the coupling of both [111]. Archetti et al (2015) empirically estimated parameters of this nonlinear public good game for neuroendocrine pancreatic cancer cells that produce insulin-like growth factor II which supports proliferation and evasion of apoptosis, [17].…”