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)

Improved Predictions of Drug–Drug Interactions Mediated by Time-Dependent Inhibition of CYP3A

Time-dependent inactivation (TDI) of cytochrome P450s (CYPs) is a leading cause of clinical drug–drug interactions (DDIs). Current methods tend to overpredict DDIs. In this study, a numerical approach was used to model complex CYP3A TDI in human-liver microsomes. The inhibitors evaluated included troleandomycin (TAO), erythromycin (ERY), verapamil (VER), and diltiazem (DTZ) along with the primary metabolites <i>N</i>-demethyl erythromycin (NDE), norverapamil (NV), and <i>N</i>-desmethyl diltiazem (NDD). The complexities incorporated into the models included multiple-binding kinetics, quasi-irreversible inactivation, sequential metabolism, inhibitor depletion, and membrane partitioning. The resulting inactivation parameters were incorporated into static in vitro–in vivo correlation (IVIVC) models to predict clinical DDIs. For 77 clinically observed DDIs, with a hepatic-CYP3A-synthesis-rate constant of 0.000 146 min^–1, the average fold difference between the observed and predicted DDIs was 3.17 for the standard replot method and 1.45 for the numerical method. Similar results were obtained using a synthesis-rate constant of 0.000 32 min^–1. These results suggest that numerical methods can successfully model complex in vitro TDI kinetics and that the resulting DDI predictions are more accurate than those obtained with the standard replot approach

Mechanism-Based Inhibition of CYP3A4 by Podophyllotoxin: Aging of an Intermediate Is Important for in Vitro/in Vivo Correlations

An in vitro observation of time-dependent inhibition (TDI) of metabolic enzymes often results in removing a potential drug from the drug pipeline. However, the accepted method for predicting TDIs of the important drug metabolizing cytochrome P450 enzymes often overestimates the drug interaction potential. Better models that take into account the complexities of the cytochrome P450 enzyme system will lead to better predictions. Herein we report the use of our previously described models for complex kinetics of podophyllotoxin. Spectral characterization of the kinetics indicates that an intermediate MI complex is formed, which slowly progresses to an essentially irreversible MI complex. The intermediate MI complex can release free enzyme during the time course of a typical 30 min TDI experiment. This slow rate of MI complex conversion results in an overprediction of the kinact value if this process is not included in the analysis of the activity versus time profile. In vitro kinetic experiments in rat liver microsomes predicted a lack of drug interaction between podophyllotoxin and midazolam. In vivo rat pharmacokinetic studies confirmed this lack of drug interaction

A numerical method for analysis of in vitro time-dependent inhibition data. Part 2. Application to experimental data

Time dependent inactivation (TDI) of cytochromes P450 (CYPs) is an important cause of drug-drug interactions (DDIs). The standard approach to characterize the kinetics of TDI is to determine the rate of enzyme loss, kobs, at various inhibitor concentrations, [I], and replot the kobs versus [I] to obtain KI and kinact. In Part 1, we used simulated datasets to develop and test a new numerical method to analyze in vitro TDI data. Here, we have applied this numerical method to 5 TDI datasets. Experimental datasets include the inactivation of CYP2B6, CYP2C8, and CYP3A4. None of the datasets exhibited MM-only kinetics, and the numerical method allowed use of more complex models to fit each dataset. Quasi-irreversible as well as partial inhibition kinetics were observed and parameterized. Three datasets required the use of an EII (multi-inhibitor binding) model. The mechanistic and clinical implications provided by these analyses are discussed. Together with the results in Part 1, we have developed and applied a new numerical method for analysis of in vitro TDI data. This method needs to be further validated with in vivo data