Parrondo's paradox in tumor ecosystems: Adaptive therapy strategies to delay the development of drug resistance.

Maximum tolerated dose (MTD) and low-dose metronomic (LDM) schedules are widely used clinical strategies in cancer chemotherapy despite the fact that both approaches have inherent limitations. MTD often leads to drug resistance in tumors, whereas LDM usually results in the predominance of drug-sensitive or drug-resistant cancer cells, depending on the specific dose applied. To circumvent these unfavorable outcomes, we propose in this work a promising adaptive therapy strategy that alternates MTD and LDM schemes across the treatment cycles. By studying a three-component tumor system with replicator equations, we find that alternate administration of MTD and LDM at different lengths of the treatment cycle can significantly delay the development of drug-resistant phenotypes compared to when the two schemes are operated separately. This outcome recapitulates the weak form of the Parrondo's paradox, where appropriate combinations of two individually suboptimal strategies can produce an even more superior outcome (a more favorable therapeutic effect in our case). We also validate the feasibility of the proposed adaptive therapy strategy in spatially distributed tumor ecosystems by implementing agent-based simulations. Our findings offer potential clues to the challenges in state-of-the-art adaptive therapy methods, which often require precise regulation of drug dose and timing based on the proportions of drug-sensitive and drug-resistant cancer cells within a tumor.