Heterogeneity for IGF-II production maintained by public goods dynamics in neuroendocrine pancreatic cancer

Abstract

The extensive intratumor heterogeneity revealed by sequencing cancer genomes is an essential determinant of tumor progression, diagnosis, and treatment. What maintains heterogeneity remains an open question because competition within a tumor leads to a strong selection for the fittest subclone. Cancer cells also cooperate by sharing molecules with paracrine effects, such as growth factors, and heterogeneity can be maintained if subclones depend on each other for survival. Without strict interdependence between subclones, however, nonproducer cells can free-ride on the growth factors produced by neighboring producer cells, a collective action problem known in game theory as the "tragedy of the commons," which has been observed in microbial cell populations. Here, we report that similar dynamics occur in cancer cell populations. Neuroendocrine pancreatic cancer (insulinoma) cells that do not produce insulin-like growth factor II (IGF-II) grow slowly in pure cultures but have a proliferation advantage in mixed cultures, where they can use the IGF-II provided by producer cells. We show that, as predicted by evolutionary game theory, producer cells do not go extinct because IGF-II acts as a nonlinear public good, creating negative frequency-dependent selection that leads to a stable coexistence of the two cell types. Intratumor cell heterogeneity can therefore be maintained even without strict interdependence between cell subclones. Reducing the amount of growth factors available within a tumor may lead to a reduction in growth followed by a new equilibrium, which may explain relapse in therapies that target growth factors.

Keywords: evolution; game theory; tumor.

Fig. 1.

IGF-II is a nonlinear public good. (A) Growth rates of producer (+/+) and nonproducer (−/−) cells in vitro (relative to day 1) at different concentrations of exogenous IGF-II in the growth medium. (B) Growth rates of +/+ and −/− cells in vitro (relative to the day with the minimum number of cells) with medium containing FBS (7% or 10%) or in conditioned (cond.) medium from −/− or +/+ cultures. Box plots show the median and the 25% and 75% quartiles (upper and lower fences, respectively). Asterisks show significant P values in a t test: *P < 0.05; **P < 0.005; ***P < 0.0005; ****P < 0.00005.

Fig. 2.

Long-term dynamics of IGF-II production in vitro. Observed changes in the frequency of IGF-II–producing cells (+/+) in mixed populations of +/+ cells and −/− cells seeded at varying ratios and under different concentration of FBS in the culture medium; the cost/benefit ratio of IGF-II increases with the amount of FBS.

Fig. 3.

Varying the cost/benefit ratio of IGF-II production changes the outcome of competition between producer and nonproducer cells. (A) Fitness is a nonlinear function of the fraction of +/+ cells; the fitness of +/+ cells depends also on the cost c of producing IGF-II. The dynamics depend on the relative fitness of the two types. Circles denote equilibria (●, stable; ○, unstable), and arrows show the direction of the dynamics (h = 0.2, s = 10, n = 30). (B) Alternative view of the dynamics of mixed populations. Equilibria occur where the difference in benefit between +/+ and −/− (i.e., the additional benefit for a +/+ cell due to its own production of IGF-II) equals c. (C) Experimentally observed changes in the frequency of +/+ cells in vitro after 5 d of coculture for different initial frequencies and different amounts of serum (a measure of the cost/benefit ratio of producing IGF-II), and with additional exogenous IGF-II (100 ng/mL). Error bars indicate the 25% and 75% quartiles.

Fig. 4.

Growth rates peak at intermediate frequencies of producers. (A) Predicted fitness of the two cell types (dotted blue curve, +/+; dotted yellow curve, −/−) and the average fitness of the population (solid black line) as a function of the frequency of +/+ cells. Circles show the equilibria (●, stable; ○, unstable), and arrows show the direction of the dynamics (h = 0.2, s = 30, c = 0.2, n = 10). (B) Benefit of growth factors and the corresponding predicted average tumor fitness (payoff) as a function of the frequency of +/+ cells in the population for given values of h (the position of the threshold: light to dark curves; h = 0.1 to 0.5, s = 20, c = 0.4, n = 10). (C) Observed growth rates of mixed cultures in vitro as a function of the fraction of +/+ cells. Boxes show the mean and the 25% and 75% quartiles (upper and lower fences, respectively).

Fig. 5.

Growth factor production as a public goods game on a network. (A) Cells in a monolayer occupy the nodes of a planar heterogeneous graph. The number of edges within the diffusion range d of the growth factor defines the interaction group [here, d = 2 (blue cells)]. (B) Snapshots of simulations in which −/− cells invade a population of +/+ cells (d = 3, c = 0.02, h = 0.5, s = 20). (C) Changes in the fraction of producer cells (+/+) and in tumor fitness over time in simulations (thick lines are the average of 10 simulations). (D) Fraction of +/+ cells and fitness at equilibrium as a function of the inflection point h and of the cost of production c for different values of the diffusion range d.