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Various mathematical approaches have been devised to relate the cytotoxic effect of drugs in cell culture to the drug concentration added to the cell culture medium. Such approaches can satisfactorily account for drug response when the drugs are free in solution, but the approach becomes problematic when the drug is delivered in a drug delivery system, such as a liposome. To address this problem, we have developed a simple model that assumes that the cytotoxic potency of a drug is a function of the intracellular drug level in a critical compartment. Upon exposure to drug, cell death commences after a lag time, and the cell kill rate is dependent on the amount of drug in the critical intracellular compartment. The computed number of cells in culture, at any time after exposure to the drug, takes into account the cell proliferation rate, the cell kill rate, the average intracellular drug concentration, and a lag time for cell killing. We have applied this model to compare the cytotoxic effect of doxorubicin (DOX), or DOX encapsulated in a liposome that is targeted to CD44 on B16F10 melanoma cells in culture. CD44 is the surface receptor that binds to hyaluronan and is overexpressed on various cancer cells, including B16F10. We have shown previously that the drug encapsulated in hyaluronan-targeted liposomes was more potent than was the free drug. The model required the determination of the cell-associated DOX after the cells were incubated with various concentrations of the free or the encapsulated drug for 3 h, and the quantification of cell number at various times after exposure to the drug. The uptake of encapsulated drug was greater than that of the free drug, and the ratio of cell association of encapsulated:free drug was 1.3 at 0.5 micro g/ml and increased to 3.3 at 20 micro g/ml DOX. The results demonstrate that the enhanced potency of the encapsulated drug could stem from its enhanced uptake. However, in certain cases, where larger amounts of the free drug were added, such that the intracellular amounts of drug exceeded those obtained from the encapsulated drug, the numbers of viable cells were still significantly smaller for the encapsulated drug. This finding demonstrates that for given amounts of intracellular DOX, the encapsulated form was more efficient in killing B16F10 cells than the free drug. The outcome was expressed in the kinetic model as a 5-6-fold larger rate constant of cell killing potency for the encapsulated drug versus the free drug. The model provides a quantitative framework for comparing the cytotoxic effect in cultured cells when applying the drug in the free form or in a delivery system.
Eliaz et al. (Thu,) studied this question.