A numerical method for analysis of in vitro time-dependent inhibition data. Part 1. Theoretical considerations.

Inhibition of cytochromes P450 by time-dependent inhibitors (TDI) is a major cause of clinical drug-drug interactions. It is often difficult to predict in vivo drug interactions based on in vitro TDI data. In part 1 of these manuscripts, we describe a numerical method that can directly estimate TDI parameters for a number of kinetic schemes. Datasets were simulated for Michaelis-Menten (MM) and several atypical kinetic schemes. Ordinary differential equations were solved directly to parameterize kinetic constants. For MM kinetics, much better estimates of KI can be obtained with the numerical method, and even IC50 shift data can provide meaningful estimates of TDI kinetic parameters. The standard replot method can be modified to fit non-MM data, but normal experimental error precludes this approach. Non-MM kinetic schemes can be easily incorporated into the numerical method, and the numerical method consistently predicts the correct model at errors of 10% or less. Quasi-irreversible inactivation and partial inactivation can be modeled easily with the numerical method. The utility of the numerical method for the analyses of experimental TDI data is provided in our companion manuscript in this issue of Drug Metabolism and Disposition (Korzekwa et al., 2014b).