Mathematical Modeling of Drug-Induced Persistence in Cancer

Drug-tolerant persistence in tumor cells remains a significant challenge in oncology. Unlike resistance driven by genetic mutations, persistence is a reversible state arising from phenotypic shifts in response to external stress, such as cytotoxic agents. This state is often characterized by quiescence and low proliferation, although some cells may resume cycling. Here, we develop a mathematical model to describe the emergence of drug-induced persistence and its implications. We assume an initial steady-state population distribution of tumor cells across two continuous variables: x and s before drug treatment. The variable x reflects empirically derived epigenetic states conferring specific persistence potentials to a subpopulation, and s represents the degree to which different phenotypic states enable survival under drug exposure. The population probability density of a clone with a given x is then subjected to dynamics governed by our modified Fokker-Planck equation with an advection term dependent on s and drug concentration. The model captures adaptations through advection and diffusion, along with selection pressure from drug-induced death. Simulations provide quantitative insights into the emergence of (cycling) persistence and potential benefits of different treatment strategies. Our framework can also be generalized to study phenotypic plasticity and adaptation mechanisms under different external stresses and stimuli for both cancer cells and unicellular organisms.