Cytocidal effect and DNA damage of nedaplatin: a mathematical model and analysis of experimental data

Cell cycle non-specific anticancer agents such as cis-diamminedichloroplatinum(II) are believed to depend linearly on the value of the area under the drug concentration time curve, which is supported by a mathematical model. However, the quantitative non-linear phenomena of both the cytocidal effect and DNA crosslink formation by cisdiammine(glycolato)platinum (nedaplatin) have been shown in vitro. Therefore, we developed a new mathematical model to explain these phenomena.

We assumed that nedaplatin enters intracellular fluid from medium through simple diffusion to form DNA crosslinks that kill cells. We developed a mathematical model to represent this assumption using differential equations that we then solved using an original computer program. The calculated results were compared with the experimental data.

The drug's simple diffusion rate constant, the DNA crosslink formation rate constant, and the crosslink-dependent cell death rate constant in the model were 1.8 x 10(-14) (l h-1), 1.6 x 10(8) (l mol-1/2 h-1), 5.45 x 10(1) (mol-1), respectively. The model fits the experimental results statistically. The model also demonstrated theoretical proof that continuous exposure at a low dose was superior to the short exposure at a high dose seen in published experimental data.

We developed a mathematical model to describe the non-linear pharmacodynamic effect of nedaplatin in vitro. This model may provide a novel drug infusion procedure for cancer patients.