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. In this study, we develop a mathematical model to describe the emergence of drug-induced persistence and its implications. We assume an initial steady-state distribution of tumor cells across two variables: x (chance-to-persist) and s (phenotypic state related to drug survivability) before drug treatment. The variable x reflects epigenetic states conferring specific persistence potentials to subpopulations, while s represents the degree to which different phenotypic states enable survival under drug exposure. The population probability density 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 in s and selection pressure from drug-induced death. Simulations of various treatment schemes provide quantitative insights into the emergence of persistence, and our theory can be generalized to study phenotypic plasticity and investigate cellular adaptation mechanisms under different external stresses and stimuli.