MATHEMATICAL-MODELS FOR MULTIDRUG-RESISTANCE AND ITS REVERSAL

Mathematical models describing drug resistance are briefly reviewed. O ne 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 facil itated diffusion process. A partial differential equation linked to a pair of ordinary differential equations forms the core of the model. T o describe MDR reversal, the model is extended to add an inhibitor. Eq uations for competitive, one-site noncompetitive, and two-site noncomp etitive inhibition are derived. Numerical simulations have been nm to describe P-glycoprotein dynamics both in the presence and absence of t hese kinds of inhibition. These results are briefly reviewed. The char acter of the pump and its response to inhibition are discussed within the context of the models. All discussions, descriptions, and conclusi ons are presented in nonmathematical terms. The paper is aimed at a sc ientifically sophisticated but mathematically innocent audience.