Abstract
Tumor heterogeneity is well documented for many characters, including the production of growth factors, which improve tumor proliferation and promote resistance against apoptosis and against immune reaction. What maintains heterogeneity remains an open question that has implications for diagnosis and treatment. While it has been suggested that therapies targeting growth factors are robust against evolved resistance, current therapies against growth factors, like antiangiogenic drugs, are not effective in the long term, as resistant mutants can evolve and lead to relapse. We use evolutionary game theory to study the dynamics of the production of growth factors by monolayers of cancer cells and to understand the effect of therapies that target growth factors. The dynamics depend on the production cost of the growth factor, on its diffusion range and on the type of benefit it confers to the cells. Stable heterogeneity is a typical outcome of the dynamics, while a pure equilibrium of nonproducer cells is possible under certain conditions. Such pure equilibrium can be the goal of new anticancer therapies. We show that current therapies, instead, can be effective only if growth factors are almost completely eliminated and if the reduction is almost immediate.
Highlights
Tumor heterogeneity Heterogeneity of cells within a tumor is well documented for many types of cancers and many distinguishable phenotypes (Marusyk and Polyak 2010) and has important implications for disease progression (Maley et al 2006), diagnosis, and therapeutic responses (Dexter and Leith 1986)
A basic question about heterogeneity is still unsolved (Merlo et al 2006): how can more than one clone stably coexist in a neoplasm? Given that the development of cancer is a process of clonal selection (Cairns 1975; Nowell 1976; Crespi and Summers 2005; Merlo et al 2006; Greaves and Maley 2012) in which cells compete for resources, space, and nutrients, one would predict that a mutant clone with a fitness advantage should drive other clones extinct and go to fixation
We develop a model of public goods production in the framework of evolutionary game theory and extend it to take into account specific features of the production of growth factors by cancer cells growing on a monolayer
Summary
Tumor heterogeneity Heterogeneity of cells within a tumor is well documented for many types of cancers and many distinguishable phenotypes (Marusyk and Polyak 2010) and has important implications for disease progression (Maley et al 2006), diagnosis, and therapeutic responses (Dexter and Leith 1986). From the standard approach, [in which an individual’s group is limited to her one-step neighbors and an individual plays multiple games centered on each of her neighbors (Perc et al 2013)], the interaction neighborhood and the update neighborhood are decoupled: a cell’s group (of size n) is not limited to her one-step neighbors but is defined by the diffusion range (d) of the growth factor, that is, the number of edges between the focal cell and the most distant cell whose contribution affects the fitness of the focal cell. Sampling of individuals follows a hypergeometric distribution and the average fitness of +/+ and À/À can be written as, respectively
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