Application of Modelling Techniques to the Planning of In Vitro Arsenic Kinetic Studies
Elaina M. Kenyon, Michael Fea, Mirek Styblo and Marina V. Evans
A kinetic model describing the hepatic methylation of arsenite ([As[III]) was developed on the basis of limited data from in vitro mechanistic studies. The model structure is as follows: sequential enzymic methylation of arsenite to its monomethylated (MMA) and dimethylated (DMA) products by first-order and Michaelis-Menten kinetics, respectively; uncompetitive inhibition of the formation of DMA by As(III); and first-order reversible binding of As(III), MMA and DMA to cytosolic proteins. Numerical sensitivity analysis was used to evaluate systematically the impact of changes in input parameters on model responses. Sensitivity analysis was used to investigate the possibility of designing experiments for robust testing of the uncompetitive inhibition hypothesis, and for further refining the model. Based on the sensitivity analysis, the MMA concentration is the most important response on which to focus. The parameters Vmax and ki can be reliably estimated by using the same concentration time-course data at intermediate initial arsenite concentrations of 1–5µM at 30 ± 5 minutes. Km must be estimated independently of Vmax, since the two parameters are highly correlated at all times, and the optimal experimental conditions would include lower initial concentrations of arsenite (0.1–0.5µM) and earlier time-points (about 8–18 minutes). The use of initial arsenite concentrations much above 5µM would not yield additional useful information, because the sensitivity coefficients for MMA, protein-bound MMA, DMA and protein-bound DMA tend to become extremely small or exhibit erratic trends. Overall trends in the sensitivity analysis indicated the desirability of performing measurements at times shorter than 60 minutes. This work demonstrates that physiological modelling and sensitivity analysis can be efficient tools for experimental planning and hypothesis testing when applied in the earliest phases of kinetic model development, thus allowing more-efficient and more-directed experimentation, and minimising the use of laboratory animals.