A Numerical Method for Analysis of In Vitro Time-Dependent Inhibition Data. Part 1. Theoretical Considerations

Abstract

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 K I can be obtained with the numerical method, and even IC 50 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).

A Numerical Method for Analysis of In Vitro Time-Dependent Inhibition Data. Part 2. Application to Experimental Data

“…The plots in Fig. 2 are very similar, even though the plateau regions will converge to different values for quasi-irreversible and to the same value for partial inactivation (Nagar et al, 2014). Statistically, the fits to the two models were indistinguishable, with both AIC values of 2302.…”

“…For example, for the second repeat the AIC values were 2452, 2464, 2466, and 2477 for MMquasi-irreversible, EII-quasi-irreversible, MM-partial inactivation, and EII-partial inactivation, respectively. The improved fit for the EII model suggests that the discrepancy between the K I and the competitive K i is not due to inactivation during the substrate incubation (Nagar et al, 2014). As seen in Table 4, the kinetic parameters were almost identical for the two repeats, with K I1 = 4 mΜ and K I2 = 20 mΜ, k inact1 = 0.07 min…”

“…Further, quasi-irreversible (Ortiz de Montellano and Correia, 1995;Murray, 1997;Lin and Lu, 1998) and partialinactivation kinetics (Crowley and Hollenberg, 1995;Hollenberg et al, 2008) have been reported. Although a modification of the replot method can incorporate EII kinetics, the errors in the in vitro data tend to be magnified by the replot method and prevent parameter estimation (Nagar et al, 2014). Additionally, to our knowledge, reversible and partial inactivation cannot be evaluated with the replot method.…”

“…In our companion manuscript (Part 1; Nagar et al, 2014) in this issue of Drug Metabolism and Disposition, we describe a new numerical method to analyze in vitro TDI data. This method incorporates complex kinetic schemes, including EII, quasi-irreversible, and partial-inactivation kinetics.…”

“…Because K I1 ,, K I2 and k inact2 .. k inact1 for this dataset, the method described in Part 1 (Nagar et al, 2014) was used to obtain initial estimates, followed by automatic optimization with finite difference derivatives. The results for this fit are given in Table 6.…”