Cell cycle checkpoint models for cellular pharmacology of paclitaxel and platinum drugs

Abstract

A pharmacokinetic-pharmacodynamic mathematical model is developed for cellular pharmacology of chemotherapeutic drugs for which the decisive step towards cell death occurs at a point in the cell cycle, presumably corresponding to a cell cycle checkpoint. For each cell, the model assumes a threshold level of some intracellular species at that checkpoint, beyond which the cell dies. The threshold level is assumed to have a log-normal distribution in the cell population. The kinetics of formation of the lethal intracellular species depends on the drug, and on the cellular pharmacokinetics and binding kinetics of the cell. Specific models are developed for paclitaxel and for platinum drugs (cisplatin, oxaliplatin and carboplatin). In the case of paclitaxel, two separate mechanisms of cell death necessitate a model that accounts for two checkpoints, with different intracellular species. The model was tested on a number of in vitro cytotoxicity data sets for these drugs, and found overall to give significantly better fits than previously proposed cellular pharmacodynamic models. It provides an explanation for the asymptotic convergence of dose-response curves as exposure time becomes long.

Fig. 1

Schematic diagram illustrating definition of cell damage in the checkpoint model. The y-axis represents the concentration of the cellular bound species giving rise to the cytotoxic effect; because of the kinetics of uptake and binding this is not the same as extracellular concentration. A and B: times at which cells A and B pass through successive cell cycle checkpoints. Hatched region: interval of integration in Eq. 3. This interval includes all possible checkpoints at which the concentration c _k of the lethal species is maximal for a particular cell. The time t _m at which lethal species concentration peaks is equal to the exposure time T for the cases modeled in this study, because intracellular concentrations decay rapidly when extracellular exposure is stopped. For a general drug, however, t _m may be larger than T, depending on the cellular pharmacokinetics. Notation in Table II

Fig. 2

a Schematic depiction of cellular pharmacokinetics of cisplatin. Aquated form is active. Aquation is slow in the extracellular environment at physiological pH, but rapid intracellularly. Non-aquated cisplatin is exchanged more slowly than the aquated form. b Simplified kinetics assumed in present model. Total cisplatin is considered

Fig. 3

Comparison of model fits to experimental data of Au et al. (13) for paclitaxel acting on the DU145 human cell line. a Cell cycle checkpoint model. b C ⁿ T Hill model. c Single Hill model of Levasseur et al. (1998)

Fig. 4

Comparison of model fits to experimental data of Au et al. (13) for paclitaxel acting on the SKOV-3 human ovarian carcinomia cell line. a Cell cycle checkpoint model. b C ⁿ T Hill model. c Single Hill model of Levasseur et al. (10)

Fig. 5

Comparison of model fits to experimental data of Troger et al. (33) for cisplatin acting on a human cell line. a Cell cycle checkpoint model. b Peak bound intracellular model of El-Kareh and Secomb (3). c C ⁿ T Hill model. d Single Hill model of Levasseur et al. (10)

Fig. 6

Comparison of model fits to experimental data of Levasseur et al. (10) for cisplatin acting on the resistant A2780/CP3 human cell line. a Cell cycle checkpoint model. b C ⁿ T Hill model. c Single Hill model of Levasseur et al. (10)