Adaptive therapy is a dynamic cancer treatment protocol that updates (or ‘adapts’) treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

Mitochondrial dysfunction caused by aberrant Complex I assembly and reduced activity of the electron transport chain is pathogenic in many genetic and age-related diseases. Mice missing the Complex I subunit NADH dehydrogenase [ubiquinone] iron-sulfur protein 4 (NDUFS4) are a leading mammalian model of severe mitochondrial disease that exhibit many characteristic symptoms of Leigh Syndrome including oxidative stress, neuroinflammation, brain lesions, and premature death. NDUFS4 knockout mice have decreased expression of nearly every Complex I subunit. As Complex I normally contains at least 8 iron-sulfur clusters and more than 25 iron atoms, we asked whether a deficiency of Complex I may lead to iron perturbations, thereby accelerating disease progression. Consistent with this, iron supplementation accelerates symptoms of brain degeneration in these mice, while iron restriction delays the onset of these symptoms, reduces neuroinflammation, and increases survival. NDUFS4 knockout mice display signs of iron overload in the liver including increased expression of hepcidin and show changes in iron-responsive element-regulated proteins consistent with increased cellular iron that were prevented by iron restriction. These results suggest that perturbed iron homeostasis may contribute to pathology in Leigh Syndrome and possibly other mitochondrial disorders.