Emergence of the Drug-Resistant Phenotype in Tumor Subpopulations: A Hybrid Model

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Abstract
A mathematical model is proposed that describes the emergence of drug resistance in a tumor cell population. The model is termed a hybrid in the sense that the population-wide dynamics are described by a stochastic birth-death-migration model with transition probabilities dependent on the deterministic distribution of drug within the average cell. In the model, the probability that a cell dies is proportional to the concentration of drug within the target site in the cell. The microphannacology describing the distribution of drug within the average cell is described by a standard well-mixed compartment model. Possible mechanisms that can confer drug resistance on a cell are described: decreased drug uptake, increased drug efflux, Intracellular metabolism or Inactivation, or both, of a drug, and a change in the level or sensitivity of a target. The biologic mechanisms underlying resistance and potential strategies for overcoming it are discussed within the context of our model. Results from a numerical simulation are presented as verification of the initial theory. [J Natl Cancer Inst 81:1392–1401, 1989]