A mathematical model for the inhibition of the multidrug resistance-associated P-glycoprotein pump

An extension of an earlier model of the p170 glycoprotein pump is presented. In an earlier work (Michelson and Slate, Bull. math. Biol. 54, 1023-1038, 1992), the pump was modeled using an energy-dependent model of facilitated diffusion. In this paper we add an inhibitor to the model. New equations are derived which represent either competitive or non-competitive inhibition in the pumping action of the glycoprotein. Numerical simulations were run which provide a response surface (initial loading concentration of inhibitor and its ability to compete with an ideal anti-cancer drug vs a summary measure of cytoplasmic exposure) for each scenario. The importance of the exposure profile, how it is related to ultimate tumor cell survival, and the binding requirements for developing multidrug resistance inhibitors are discussed.