Capitalizing on competition: An evolutionary model of competitive release in metastatic castration resistant prostate cancer treatment

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 selected for growth after chemotherapeutic agents attack the previously dom- inant population of chemo-sensitive cells. To study this process, we use a mathematical model based on the replicator equations with a prisoner's dilemma payoff matrix defining fitness levels of three competing cell populations: healthy cells (cooperators), sensitive cells (defectors), and resistant cells (defectors). The model is shown to recapitulate prostate- specific antigen (PSA) measurement data of patients (a surrogate for tumor growth) from three randomized clinical trials with metastatic castration-resistant prostate cancer for pa- tients treated with 1) prednisone only, 2) mitoxantrone and prednisone and 3) docetaxel and prednisone. In each trial, continuous maximum tolerated dose (MTD) schedules reduce the sensitive cell population, initially shrinking tumor volume, but subsequently release the resistant cells to re-populate and eventually re-grow the tumor in a resistant form. The evolutionary model allows us to quantify responses to conventional therapeutic strategies as well as to design novel adaptive strategies which are able to maintain the tumor volume at reduced levels by keeping a sufficient number of sensitive cells to prevent tumor re-growth from the resistant population.