Journal of Theoretical Medicine
Volume 1 (1997), Issue 2, Pages 103-115

Multidrug Resistance and Its Reversal: Mathenatical Models

Research Support & Information Services, Roche Biosciences, MS S1-137, 3401 Hillview Avenue, Palo Alto, CA 94303, USA

Received 1 October 1996

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Classic multidrug resistance (MDR) is a phenomenon by which cells nonspecifically extrude noxious agents from the cutoplasm before lethal concentrations buils up. Some chemotherapeutically treated tumors exhibit these same dynamics. In tumor systems, the most common mechanism of facilitating MDR is the upregulation of the P-glycoprotein pump. This protein forms a transmembrance channel, and agter binding the chemotherapeutic agent and 2ATP molecules, forces the noxius agent through the channel. Hydrolysis of ATP to ADP provides the energy component of this reaction. General mathematical models describing drug resistamce are reviewed in this article. One model describing the molecular function of the P-glycoprotein pump in MDR cell lines is developed and presented in detail. The pump is modeled as an energy-dependent facilitated diffusion process. A partial differential equation is linked to a pair of ordinary differential equations to form the core of the model. To describe MDR reversal, the model is extended by additing an inhibitor to the equation system. Equations for competitive, one-site non-competitive, and allosteric non-competitive inhibition are then derived. Numerical simulations have been run to describe P-glycoprotein dynamics both in the presence and absence of inhibition, and these results are briefly reviewed. The character of the pump and its response to inhibition are discussed within the comtext of the models.