The ability of cells and tissues to alter their response to chemical and radiological agents is a major impediment to the success of therapy. Such altered response to treatment occurs in infections by bacteria, viruses, fungi, and other pathogens, as well as in cancer. Despite advances in recent decades, this reduction in the effectiveness of treatments, broadly termed drug resistance, remains poorly understood, and in some circumstances is thought to be inevitable. One of the most clinically important examples of drug resistance is that involving the treatment of cancer via chemotherapies. A vast amount of experimental and mathematical research continues to shed light on our understanding of resistance to chemotherapy. Aside from understanding the mechanisms by which resistance to therapies may manifest, a fundamental question is when resistance arises. Pre-existing (also known as intrinsic) drug resistance often refers to the case when the organism contains a subpopulation (or a tumor contains a sub-clone) which resists treatment prior to the application of the external agent. Acquired resistance describes the phenomenon in which resistance first arises during the course of therapy from an initially drug-sensitive population. The study of acquired resistance is complicated by the question of how resistance emerges. Resistance can be spontaneously ("randomly") acquired during treatment as a result of random genetic mutations or stochastic non-genetic phenotype switching, and cells can be selected for in a classic Darwinian fashion. Alternatively, resistance could be induced ("caused") by the presence of the drug. That is, the drug itself may promote, in a "Lamarckian" sense the (sometimes reversible) formation of resistant cancer cells so that treatment has contradictory effects: it eliminates cells while simultaneously upregulating the resistant phenotype, often from the same initially-sensitive wild-type cells. Although there is experimental evidence for these three forms of drug resistance, differentiating them experimentally is non-trivial. For example, what appears to be drug-induced acquired resistance may simply be the rapid selection of a very small number of pre-existing resistant cells, or the selection of cells that spontaneously acquired resistance. Formulating and analyzing precise mathematical models describing the previously mentioned origins of drug resistance can lead to novel conclusions that may be difficult, or even impossible given current sequencing technology, to determine utilizing experimental methods alone. Our current work aims to validate our previously published mathematical model that distinguished between resistance modalities (JCO Clinical Cancer Informatics, 2019). In this lecture, I will describe a variant of that model and show it gives excellent fits across a range of drug doses, when fit to a set of experimental data that exhibits strong evidence of resistance induction. In addition, an optimal control problem is studied numerically, and our results suggest the importance of developing continuous-infusion devices.

(Joint work with Jana L. Gevertz, Samantha Prosperi, and James M. Greene)