Reactive oxygen species (ROS) are primary effectors of cytotoxicity induced by many anti-cancer drugs. Rhythms in the pseudo-steady-state (PSS) levels of particular intracellular ROS in cancer cells and their relevance to drug effectiveness are unknown thus far. We report that the PSS levels of intracellular superoxide (SOX), an important ROS, exhibit an inherent rhythm in HCT116 colon cancer cells, which is entrained (reset) by the SOX inducer, menadione (MD). This reset was dependent on the expression of p53, and it doubled the sensitivity of the cells to MD. The period of oscillation was found to have a linear correlation with MD concentration, given by the equation, T, in h = 23.52 − 1.05 [MD concentration in µM]. Further, we developed a mathematical model to better understand the molecular mechanisms involved in rhythm reset. Biologically meaningful parameters were obtained through parameter estimation techniques; the model can predict experimental profiles of SOX, establish qualitative relations between interacting species in the system and serves as an important tool to understand the profiles of various species. The model was also able to successfully predict the rhythm reset in MD treated hepatoma cell line, HepG2. © 2019, The Author(s).