The prisoner’s dilemma as a cancer model

Abstract

Tumor development is an evolutionary process in which a heterogeneous population of cells with different growth capabilities compete for resources in order to gain a proliferative advantage. What are the minimal ingredients needed to recreate some of the emergent features of such a developing complex ecosystem? What is a tumor doing before we can detect it? We outline a mathematical model, driven by a stochastic Moran process, in which cancer cells and healthy cells compete for dominance in the population. Each are assigned payoffs according to a Prisoner’s Dilemma evolutionary game where the healthy cells are the cooperators and the cancer cells are the defectors. With point mutational dynamics, heredity, and a fitness landscape controlling birth and death rates, natural selection acts on the cell population and simulated ‘cancer-like’ features emerge, such as Gompertzian tumor growth driven by heterogeneity, the log-kill law which (linearly) relates therapeutic dose density to the (log) probability of cancer cell survival, and the Norton-Simon hypothesis which (linearly) relates tumor regression rates to tumor growth rates. We highlight the utility, clarity, and power that such models provide, despite (and because of) their simplicity and built-in assumptions.

Chemotherapeutic Dose Scheduling Based on Tumor Growth Rates Provides a Case for Low-Dose Metronomic High-Entropy Therapies

“…Previously, we have reported the model’s success in capturing current unperturbed growth models (i.e. Gompertzian growth) as an emergent phenomenon of this evolutionary model (10). Outcomes of our model simulations are quite robust to small parametric changes in all cases.…”

“…The model presented in (9, 10) and used in this paper to carry out our computational trials is a framework of primary tumor growth used to test the effect of various chemotherapeutic regimens, including MTD and LDM. The model is a stochastic Moran (finite-population birth-death) process (33) that drives tumor growth, with heritable mutations (34) operating over a fitness landscape so that natural selection can play out over many cell division timescales (described in more detail in (9, 10)).…”

“…The model is a stochastic Moran (finite-population birth-death) process (33) that drives tumor growth, with heritable mutations (34) operating over a fitness landscape so that natural selection can play out over many cell division timescales (described in more detail in (9, 10)). The birth-death replacement process is based on a fitness landscape function defined in terms of stochastic interactions with payoffs determined by the prisoner’s dilemma game (1, 2).…”

“…In our model, we can think of a cancer cell as a formerly cooperating healthy cell that has defected and begins to compete against the surrounding population of healthy cells for resources and reproductive prowess. The model demonstrates several simulated emergent ‘cancer-like’ features: Gompertzian tumor growth driven by heterogeneity (37, 38, 39), the log-kill law which (linearly) relates therapeutic dose density to the (log) probability of cancer cell survival, and the Norton-Simon hypothesis which (linearly) relates tumor regression rates to tumor growth rates, and intratumor molecular heterogeneity as a driver of tumor growth (10). …”

“…We wish to quantify the relationship between dose and dose density delivered using the Shannon entropy index (8) as a quantitative scheduling and dosage tool. We will first briefly review the prisoner’s dilemma evolutionary game theory model of primary tumor growth that we use to carry out our computational trials (9, 10) as well as the notion of Shannon Entropy as an index to compare chemotherapeutic regimens in order to show that high entropy schedules (with an adequate dose intensity) outperform low entropy schedules.…”