ABC efflux transporters are a key factor leading to multidrug resistance in cancer. Overexpression of these transporters significantly decreases the efficacy of anti-cancer drugs. Along with selection and induction, drug resistance may be transferred between cells, which is the focus of this paper. Specifically, we consider the intercellular transfer of P-glycoprotein (P-gp), a well-known ABC transporter that was shown to confer resistance to many common chemotherapeutic drugs. In a recent paper, Durán et al. (Bull Math Biol 78(6):1218-1237, 2016) studied the dynamics of mixed cultures of resistant and sensitive NCI-H460 (human non-small lung cancer) cell lines. As expected, the experimental data showed a gradual increase in the percentage of resistance cells and a decrease in the percentage of sensitive cells. The experimental work was accompanied with a mathematical model that assumed P-gp transfer from resistant cells to sensitive cells, rendering them temporarily resistant. The mathematical model provided a reasonable fit to the experimental data. In this paper, we develop a new mathematical model for the transfer of drug resistance between cancer cells. Our model is based on incorporating a resistance phenotype into a model of cancer growth (Greene et al. in J Theor Biol 367:262-277, 2015). The resulting model for P-gp transfer, written as a system of integro-differential equations, follows the dynamics of proliferating, quiescent, and apoptotic cells, with a varying resistance phenotype. We show that this model provides a good match to the dynamics of the experimental data of Durán et al. (2016). The mathematical model shows a better fit when resistant cancer cells have a slower division rate than the sensitive cells.
Keywords: Integro-differential equations; Multidrug resistance; P-glycoprotein.