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

Purpose: Cell cycle non-specific anticancer agents such as cis-diamminedich loroplatinum(II) are believed to depend linearly on the value of the area u nder the drug concentration time curve, which is supported by a mathematica l model. However, the quantitative non-linear phenomena of both the cytocid al effect and DNA crosslink formation by cisdiammine(glycolato)platinum (ne daplatin) have been shown in vitro. Therefore, we developed a new mathemati cal model to explain these phenomena. Methods: We assumed that nedaplatin e nters 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 o riginal computer program. The calculated results were compared with the exp erimental data. Results: 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) (1 h(-1)), 1.6 x 10(8) (1 mol (-1/2) h(-1)), 5.45 x 10(1) (mol(-1)), respectively. The model fits the exp erimental results statistically. The model also demonstrated theoretical pr oof that continuous exposure at a low dose was superior to the short exposu re at a high dose seen in published experimental data. Conclusions: We deve loped a mathematical model to describe the non-linear pharmacodynamic effec t of nedaplatin in vitro. This model may provide a novel drug infusion proc edure for cancer patients.