Mathematical models for multidrug resistance and its reversal.

Mathematical models describing drug resistance are briefly reviewed. One model which describes the molecular function of the P-glycoprotein pump in multidrug resistant (MDR) cell lines has been developed and is presented in detail. The pump is modeled as an energy dependent facilitated diffusion process. A partial differential equation linked to a pair of ordinary differential equations forms the core of the model. To describe MDR reversal, the model is extended to add an inhibitor. Equations for competitive, one-site noncompetitive, and two-site noncompetitive inhibition are derived. Numerical simulations have been run to describe P-glycoprotein dynamics both in the presence and absence of these kinds of inhibition. These results are briefly reviewed. The character of the pump and its response to inhibition are discussed within the context of the models. All discussions, descriptions, and conclusions are presented in nonmathematical terms. The paper is aimed at a scientifically sophisticated but mathematically innocent audience.