Nonlinear dynamical shaping of the fitness landscape of an evolving tumor to combat competitive release

Abstract

The development of chemotherapeutic resistance resulting in tumor relapse is largely the consequence of the mechanism of competitive release of pre-existing resistant tumor cells selected for regrowth after chemotherapeutic agents attack the previously dominant chemo-sensitive population. We introduce a prisoners dilemma mathematical model based on the replicator of three competing cell populations: healthy (cooperators), sensitive (defectors), and resistant (defectors) cells. The model is shown to recapitulate prostate-specific antigen measurement data from three clinical trials for metastatic castration-resistant prostate cancer patients treated with 1) prednisone, 2) mitoxantrone and prednisone and 3) docetaxel and prednisone. Continuous maximum tolerated dose schedules reduce the sensitive cell population, initially shrinking tumor volume, but subsequently \"release\" the resistant cells to re-populate and re-grow the tumor in a resistant form. Importantly, a model fit of prostate data shows the emergence of a positive fitness cost associated with a majority of patients for each drug, without predetermining a cost in the model a priori. While the specific mechanism associated with this cost may be very different for each of the drugs, a measurable fitness cost emerges in each. The evolutionary model allows us to quantify responses to conventional therapeutic strategies as well as to design adaptive strategies.