Game-Theory Paradox Inspires Cancer Therapy
Often, two losing strategies can be combined into a winning one. Described in game theory as Parrondo’s paradox, this counterintuitive phenomenon shows up in physics, finance, and biology, among other fields. For example, organisms like jellyfish switch between solitary and communal lifestyles. While solitary existence makes them more prone to environmental stresses, communal aggregations can cause resource depletion. Either lifestyle on its own would spell trouble for the animals, but alternating between the two maximizes their chances of survival. Now De-Ming Liu and his colleagues at Lanzhou University, China, have proposed a way to harness Parrondo’s paradox for cancer treatment, combining two therapeutic strategies into one that might be more powerful in specific situations [1]. Their results could inspire new ways to tackle some hard-to-treat cancers by dramatically slowing down their progression.
Two chemotherapy strategies are followed for most cancers. Patients are either given the maximum tolerable dose (MTD) of a drug at certain intervals or they are treated with low but sustained doses in low-dose metronomic (LDM) chemotherapy. The former approach quickly kills drug-sensitive cancer cells, but it offers drug-resistant cancer cells an opportunity to proliferate, making the tumor harder to treat. With the latter approach, both types of cancer cells might survive the therapy and allow the cancer to return. In recent years, clinicians have started exploring adaptive therapy, an experimental treatment protocol that switches between the two regimens.
Adaptive therapy is investigated for cancers that aren’t expected to be eradicable. Its objective, instead, is slowing down the cancer progression. “Adaptive therapy aims to maintain tumor size within a manageable range by leveraging competition between drug-sensitive and drug-resistant cells,” explains Liu. But it requires complex techniques such as single-cell sequencing to quantify the fractions of sensitive and resistant cells—information that is fed into cancer-progression models to estimate the best time for switching between regimens. The need for costly and invasive monitoring makes this approach impractical.
The new work hints that this level of monitoring may not be necessary. Instead, the switching between the two types of treatments could occur at fixed times that are picked on the basis of cancer-development models. “Our results reveal that new adaptive-therapy strategies can be generated by simply alternating typical chemotherapy regimens,” says Liu. “This can significantly reduce the development cost and time of adaptive-therapy schedules.”
The researchers simulated a spatial model of the cancer ecosystem, populated by some healthy cells along with drug-sensitive and drug-resistant cancer cells. Sensitive cells underwent drug-induced death at a rate proportional to the drug concentration. On the other hand, resistant cells were fully unaffected by the drug but multiplied more slowly than sensitive cells, trading growth rate for resistance. The researchers then simulated how this population evolved under different treatment protocols.
According to the simulations, under the LDM regimen sensitive cells prevailed when the drug dose was too low to suppress them, while resistant cells prevailed at a sufficiently high dose. In the MTD regimen, alternating between high dose and no treatment led resistant cells to eventually dominate regardless of the length of the on-off period. Longer cycles fared worse in terms of the buildup of drug resistance, as a far greater number of sensitive cells perished in each cycle, making way for the resistant ones.
The goal of adaptive therapy is to contain the tumor by maintaining a tolerable population of sensitive cells that suppresses the resistant cells through their quick reproduction. In practice, however, this is hard to achieve because the MTD and LDM components that are combined in an adaptive-therapy run often eliminate, respectively, too many and too few of the sensitive cells. The simulation showed that for specific lengths of treatment cycles, a simple switch between the two regimes—which would entail a significant clinical simplification—avoids both extremes.
This alternation between the two regimens represents a “weak” form of Parrondo’s paradox (involving a combination of two suboptimal, rather than losing, strategies). The simulations show that the tumor’s drug resistance still emerges but might take twice as long to do so than either MTD or LDM alone—a slowdown consistent with the scope of adaptive therapy. “If the cure is extremely unlikely, then the best we can do is to give the patients as long a life and as good a quality of life as we can,” says Robert Noble, a mathematical oncologist at City St George’s, University of London.
Noble, however, says that the method outlined in the new study may not be ripe for a real-world clinical setting. “The alternating strategy fails much faster, and the tumor bounces back, if you slightly change the initial conditions,” adds Noble. Liu and colleagues, however, plan to conduct in vitro experiments to test their mathematical model and to select regimen parameters that would make their strategy more robust in a realistic setting.
Nevertheless, the study illustrates a promising shift away from cancer-treatment strategies that do not take into account the evolutionary dynamics of the cancer, says Noble. “It is an example of this burgeoning field where we are saying, ‘What if we use what we know about those dynamics?’” Understanding these dynamics, he added, could be key to developing smarter therapies.
–Sachin Rawat
Sachin Rawat is a freelance science writer based in Bangalore, India.
References
- D.-M. Liu, “Parrondo’s paradox in tumor ecosystems: Adaptive therapy strategies to delay the development of drug resistance,” Phys. Rev. E 112, 024404 (2025).