A mathematical model of the P-glycoprotein pump as a mediator of multidrug resistance.

Cells displaying the classic multidrug resistant (MDR) phenotype possess a transmembrane protein (p170 or P-glycoprotein) which can actively extrude cytotoxic agents from the cytoplasm. A mathematical model of this drug efflux pump has been developed. Outward transport is modeled as a facilitated diffusion process. Since energy-dependent efflux of cytotoxic agents requires that ATP also bind to p170, the model includes a dynamic calculation for efflux rate which considers Michaelis-Menten kinetics for both the substrate agent and ATP. The final system consists of one partial differential equation (PDE) for the facilitated diffusion of substrate agents out of the cell, a 2 x 2 ordinary differential equation (ODE) system for the dynamic calculation of the ATP-ADP pool, and a dynamic algebraic calculation of the efflux rate given substrate levels at the interior cell membrane interface and ATP levels in the cell. A stability analysis of the ATP-ADP pool distribution and a simplistic closed form solution of the linearized PDE are included. Numerical simulations are also provided.