Abstract
The development of chemotherapeutic resistance resulting in tumor relapse is thought largely to be a consequence of the mechanism of competitive release of pre-existing resistant cells in the tumor that are selected for growth after chemotherapeutic agents attack the population of chemo-sensitive cells which had previously dominated the collection of competing subclones. To study this process, we use an evolutionary game theory model, with a prisoner’s dilemma payoff matrix, based on a system of coupled replicator equations quantifying the clonal competition among three groups of cells: healthy cells (H), sensitive cells (S), and resistant cells (R). Maximum tolerated dose (MTD) schedules are effective at reducing the sensitive cell population which initially shrinks the tumor volume, but releases the resistant cells to re-populate and eventually re-grow the tumor in a more dangerous resistant form. By monitoring the state space associated with the three populations of cells as a coupled nonlinear dynamical system and using the nullcline structure of the system, we show how one can steer the tumor away from the resistant state with an adaptive chemotherapeutic schedule. The control parameters in our model adjust the selection pressure on the various subclones, which effectively allows us to tailor the fitness landscape to suppress the growth of the resistant population while keeping the sensitive population at low enough levels so the tumor volume remains small.